A Comparison of the Cognitive and Personal Development of College-Level Mathematics Students and Developmental Mathematics Students at a Community College

ERIC Educational Resources Information Center

Smith, Bridgett Pressley

2010-01-01

Education is a major focal point of individual justice within a free society as well as a central point of human capital for the world. This study compared the cognitive and personal developmental levels of community college students enrolled in developmental-level mathematics courses to students enrolled in college-level mathematics courses. In…

Measuring Developmental Students' Mathematics Anxiety

ERIC Educational Resources Information Center

Ding, Yanqing

2016-01-01

This study conducted an item-level analysis of mathematics anxiety and examined the dimensionality of mathematics anxiety in a sample of developmental mathematics students (N = 162) by Multi-dimensional Random Coefficients Multinominal Logit Model (MRCMLM). The results indicate a moderately correlated factor structure of mathematics anxiety (r =…

Developmental Performance as a Predictor of Academic Success in Entry-Level College Mathematics.

ERIC Educational Resources Information Center

Johnson, Laurence F.

1996-01-01

Discusses a study examining the relationship between student academic performance in an exit-level, developmental mathematics course and subsequent academic performance in a college-level mathematics course. Finds that developmental course performance and student age were significantly and positively related to academic success, while length of…

Piloting a Web-Based Homework System in Developmental Mathematics Classrooms

ERIC Educational Resources Information Center

Dass, Wendi E.

2012-01-01

This Capstone project studied a pilot of the web-based homework system "Hawkes" in developmental mathematics classes at a mid-sized community college. The purpose of the study was to investigate how three instructors of developmental mathematics courses incorporated "Hawkes" in their classes, what obstacles they encountered,…

Placement and Success: Developmental Mathematics Instructors' Perceptions about Their Students

ERIC Educational Resources Information Center

Zientek, Linda Reichwein; Schneider, Cynthia L.; Onwuegbuzie, Anthony J.

2014-01-01

Decreasing the number of students placed in developmental mathematics and addressing barriers that hinder student success in such courses are concerns at both the state and national levels. The present study sought to capture 89 developmental mathematics faculty perceptions of factors that contribute to students' placement and hinder student…

Can Group Discussions and Individualized Assignments Help More Students Succeed in Developmental Mathematics?

ERIC Educational Resources Information Center

Jaafar, Reem

2015-01-01

Students taking developmental mathematics courses resist attempting word problems when they are presented to them. Although word problems can help students contextualize learning, develop better understanding of the concepts and apply world knowledge, they constitute an impediment to students' progress in developmental mathematics courses. A…

Technology Priorities and Preferences of Developmental Mathematics Instructors

ERIC Educational Resources Information Center

Zientek, Linda; Skidmore, Susan T.; Saxon, D. Patrick; Edmonson, Stacey

2015-01-01

With the omnipresence of technology in society came the inevitable integration into education. This manuscript provides results of a statewide survey of developmental mathematics instructors' technology preferences and priorities across all levels of developmental mathematics courses. The study was part of a larger project designed to explore the…

The Effect of Project-Based Learning on Student Self-Efficacy in a Developmental Mathematics Course

ERIC Educational Resources Information Center

Deutsch, Melissa

2017-01-01

Each year, post-secondary institutions across the nation enroll thousands of students into developmental mathematics courses. Success rates are low for students placed in developmental mathematics courses employing traditional teaching practices. Secondary institutions utilizing more engaging pedagogies and high impact practices, such as…

Delaying Developmental Mathematics: The Characteristics and Costs

ERIC Educational Resources Information Center

Johnson, Marianne; Kuennen, Eric

2004-01-01

This paper investigates which students delay taking a required developmental mathematics course and the impact of delay on student performance in introductory microeconomics. Analysis of a sample of 1462 students at a large Midwestern university revealed that, although developmental-level mathematics students did not reach the same level of…

Personal Traits and Experiential Characteristics of Developmental Mathematics Faculty: Impact on Student Success

ERIC Educational Resources Information Center

Preuss, Michael D.

2008-01-01

This ex post facto study of the relationship of selected personal traits and experiential characteristics of developmental mathematics faculty with student success rates was conducted at a rural, North Carolina community college. The data gathered was from all classroom based sections of three levels of developmental mathematics taught between…

Vicissitudes of Children's Mathematical Knowledge: Implications of Developmental Research for Early Childhood Mathematics Education

ERIC Educational Resources Information Center

Sophian, Catherine

2013-01-01

Hachey's (2013) article celebrates a revolution that is taking place in early childhood mathematics education, fueled in part by developmental research demonstrating the mathematical capabilities of young children. At the same time, Hachey notes that the mathematics revolution she describes is not yet complete. In this commentary, the author…

Analysis of the Effects of Online Homework on the Achievement, Persistence, and Attitude of Developmental Mathematics Students

ERIC Educational Resources Information Center

Barnsley, Amy Elizabeth

2014-01-01

This dissertation summarizes a study of the use of online homework with developmental mathematics students at the University of Alaska Fairbanks. To address the problem of high failure rates in developmental mathematics courses this study investigated the relationship between online homework and academic achievement, persistence, and attitude.…

Seeking mathematics success for college students: a randomized field trial of an adapted approach

NASA Astrophysics Data System (ADS)

Gula, Taras; Hoessler, Carolyn; Maciejewski, Wes

2015-11-01

Many students enter the Canadian college system with insufficient mathematical ability and leave the system with little improvement. Those students who enter with poor mathematics ability typically take a developmental mathematics course as their first and possibly only mathematics course. The educational experiences that comprise a developmental mathematics course vary widely and are, too often, ineffective at improving students' ability. This trend is concerning, since low mathematics ability is known to be related to lower rates of success in subsequent courses. To date, little attention has been paid to the selection of an instructional approach to consistently apply across developmental mathematics courses. Prior research suggests that an appropriate instructional method would involve explicit instruction and practising mathematical procedures linked to a mathematical concept. This study reports on a randomized field trial of a developmental mathematics approach at a college in Ontario, Canada. The new approach is an adaptation of the JUMP Math program, an explicit instruction method designed for primary and secondary school curriculae, to the college learning environment. In this study, a subset of courses was assigned to JUMP Math and the remainder was taught in the same style as in the previous years. We found consistent, modest improvement in the JUMP Math sections compared to the non-JUMP sections, after accounting for potential covariates. The findings from this randomized field trial, along with prior research on effective education for developmental mathematics students, suggest that JUMP Math is a promising way to improve college student outcomes.

The Effect of Math Anxiety on the Academic Success of Developmental Mathematics Students at a Texas Community College

ERIC Educational Resources Information Center

Fannin-Carroll, Kristen D.

2014-01-01

The purpose of this study was to examine the relationship between math anxiety and academic success of developmental mathematics students at a Texas community college based on age, gender, and level of developmental mathematics program. A quantitative, casual-comparative design was used to determine relationships. A total of 185 developmental…

A study of the continuum of integration of mathematics content with science concepts at the middle school level in West Virginia

NASA Astrophysics Data System (ADS)

Meisel, Edna Marie

The purpose of this study was to examine the practices and perceptions of regular education seventh grade middle school mathematics teachers in West Virginia concerning the integration of mathematics objectives with science concepts. In addition, this study also emphasized the use of integrated curriculum continuum models to study mathematics teachers' practices and perceptions for teaching mathematics objectives in connection with science concepts. It was argued that the integrated curriculum continuum model can be used to help educators begin to form a common definition of integrated curriculum. The population was described as the regular education seventh grade middle school mathematics teachers in West Virginia. The entire population (N = 173) was used as the participants in this study. Data was collected using an integrated curriculum practices and perceptions survey constructed by the researcher. This was a descriptive study that incorporated the Chi Square statistic to show trends in teacher practices and perceptions. Also, an ex post facto design, that incorporated the Mann-Whitney U statistic, was used to compare practices and perceptions between teachers grouped according to factors that influence teaching practices and perceptions. These factors included teaching certificate endorsement and teacher professional preparation. Results showed that the regular education seventh grade middle school mathematics teachers of West Virginia are teaching mathematics objectives mainly at a discipline-based level with no formal attempt for integration with science concepts. However, these teachers perceived that many of the mathematics objectives should be taught at varying levels of integration with science concepts. It was also shown that teachers who experienced professional preparation courses that emphasized integrated curriculum courses did teach many of the mathematics objectives at higher levels of integration with science than those teachers who did not experience integrated curriculum courses.

Mathematical toy model inspired by the problem of the adaptive origins of the sexual orientation continuum

NASA Astrophysics Data System (ADS)

Skinner, Brian

2016-09-01

Same-sex sexual behaviour is ubiquitous in the animal kingdom, but its adaptive origins remain a prominent puzzle. Here, I suggest the possibility that same-sex sexual behaviour arises as a consequence of the competition between an evolutionary drive for a wide diversity in traits, which improves the adaptability of a population, and a drive for sexual dichotomization of traits, which promotes opposite-sex attraction and increases the rate of reproduction. This trade-off is explored via a simple mathematical `toy model'. The model exhibits a number of interesting features and suggests a simple mathematical form for describing the sexual orientation continuum.

Mathematical toy model inspired by the problem of the adaptive origins of the sexual orientation continuum.

PubMed

Skinner, Brian

2016-09-01

Same-sex sexual behaviour is ubiquitous in the animal kingdom, but its adaptive origins remain a prominent puzzle. Here, I suggest the possibility that same-sex sexual behaviour arises as a consequence of the competition between an evolutionary drive for a wide diversity in traits, which improves the adaptability of a population, and a drive for sexual dichotomization of traits, which promotes opposite-sex attraction and increases the rate of reproduction. This trade-off is explored via a simple mathematical 'toy model'. The model exhibits a number of interesting features and suggests a simple mathematical form for describing the sexual orientation continuum.

On deformation of complex continuum immersed in a plane space

NASA Astrophysics Data System (ADS)

Kovalev, V. A.; Murashkin, E. V.; Radayev, Y. N.

2018-05-01

The present paper is devoted to mathematical modelling of complex continua deformations considered as immersed in an external plane space. The complex continuum is defined as a differential manifold supplied with metrics induced by the external space. A systematic derivation of strain tensors by notion of isometric immersion of the complex continuum into a plane space of a higher dimension is proposed. Problem of establishing complete systems of irreducible objective strain and extrastrain tensors for complex continuum immersed in an external plane space is resolved. The solution to the problem is obtained by methods of the field theory and the theory of rational algebraic invariants. Strain tensors of the complex continuum are derived as irreducible algebraic invariants of contravariant vectors of the external space emerging as functional arguments in the complex continuum action density. Present analysis is restricted to rational algebraic invariants. Completeness of the considered systems of rational algebraic invariants is established for micropolar elastic continua. Rational syzygies for non-quadratic invariants are discussed. Objective strain tensors (indifferent to frame rotations in the external plane space) for micropolar continuum are alternatively obtained by properly combining multipliers of polar decompositions of deformation and extra-deformation gradients. The latter is realized only for continua immersed in a plane space of the equal mathematical dimension.

The Effect of a Math Emporium Course Redesign in Developmental and Introductory Mathematics Courses on Student Achievement and Students' Attitudes toward Mathematics at a Two-Year College

ERIC Educational Resources Information Center

Bishop, Amy Renee

2010-01-01

The purpose of this research was to determine the effect of computer-based instruction on student mathematics achievement and students' attitudes toward mathematics in developmental and introductory mathematics courses, namely Elementary Algebra, Intermediate Algebra, and College Algebra, at a community college. The researcher also examined the…

The Impact of Chess Instruction on the Critical Thinking Ability and Mathematical Achievement of Developmental Mathematics Students

ERIC Educational Resources Information Center

Berkley, Darrin K.

2012-01-01

This sequential explanatory mixed-methods study determined whether the game of chess can be used as an educational tool to improve critical thinking skills of developmental mathematics students and improve mathematics achievement for these students. Five research questions were investigated. These questions were as follows: (a) Is there a…

The Behavioral Approach System (BAS) Model of Vulnerability to Bipolar Disorder: Evidence of a Continuum in BAS Sensitivity across Adolescence.

PubMed

Liu, Richard T; Burke, Taylor A; Abramson, Lyn Y; Alloy, Lauren B

2017-11-04

Behavioral Approach System (BAS) sensitivity has been implicated in the development of a variety of different psychiatric disorders. Prominent among these in the empirical literature are bipolar spectrum disorders (BSDs). Given that adolescence represents a critical developmental stage of risk for the onset of BSDs, it is important to clarify the latent structure of BAS sensitivity in this period of development. A statistical approach especially well-suited for delineating the latent structure of BAS sensitivity is taxometric analysis, which is designed to evaluate whether the latent structure of a construct is taxonic (i.e., categorical) or dimensional (i.e., continuous) in nature. The current study applied three mathematically non-redundant taxometric procedures (i.e., MAMBAC, MAXEIG, and L-Mode) to a large community sample of adolescents (n = 12,494) who completed two separate measures of BAS sensitivity: the BIS/BAS Scales Carver and White (Journal of Personality and Social Psychology, 67, 319-333. 1994) and the Sensitivity to Reward and Sensitivity to Punishment Questionnaire (Torrubia et al. Personality and Individual Differences, 31, 837-862. 2001). Given the significant developmental changes in reward sensitivity that occur across adolescence, the current investigation aimed to provide a fine-grained evaluation of the data by performing taxometric analyses at an age-by-age level (14-19 years; n for each age ≥ 883). Results derived from taxometric procedures, across all ages tested, were highly consistent, providing strong evidence that BAS sensitivity is best conceptualized as dimensional in nature. Thus, the findings suggest that BAS-related vulnerability to BSDs exists along a continuum of severity, with no natural cut-point qualitatively differentiating high- and low-risk adolescents. Clinical and research implications for the assessment of BSD-related vulnerability are discussed.

Mathematical problems in children with developmental coordination disorder.

PubMed

Pieters, Stefanie; Desoete, Annemie; Van Waelvelde, Hilde; Vanderswalmen, Ruth; Roeyers, Herbert

2012-01-01

Developmental coordination disorder (DCD) is a heterogeneous disorder, which is often co-morbid with learning disabilities. However, mathematical problems have rarely been studied in DCD. The aim of this study was to investigate the mathematical problems in children with various degrees of motor problems. Specifically, this study explored if the development of mathematical skills in children with DCD is delayed or deficient. Children with DCD performed significantly worse for number fact retrieval and procedural calculation in comparison with age-matched control children. Moreover, children with mild DCD differed significantly from children with severe DCD on both number fact retrieval and procedural calculation. In addition, we found a developmental delay of 1 year for number fact retrieval in children with mild DCD and a developmental delay of 2 years in children with severe DCD. No evidence for a mathematical deficit was found. Diagnostic implications are discussed. Copyright © 2012 Elsevier Ltd. All rights reserved.

Between and within Ethnic Differences in Strategic Learning: A Study of Developmental Mathematics Students

ERIC Educational Resources Information Center

Fong, Carlton J.; Zientek, Linda Reichwein; Yetkiner Ozel, Zeynep Ebrar; Phelps, Julie M.

2015-01-01

The present study investigated developmental mathematics students' efficacy beliefs for motivational, self-regulated learning, resource management, and cognitive strategies and which of these beliefs most differentiated European American, African American and Hispanic students in terms of their mathematics achievement. The diverse sample consisted…

Video Based Developmental Mathematics Learning System For Community College Students.

ERIC Educational Resources Information Center

Gormley, Tyrone D.

The University of Maine at Augusta uses an individualized video-taped mathematics instructional system to eliminate students' math weaknesses before they attempt college math. The course, "1 Mth Developmental Mathematics," is part of the Educational Assistance Program and teaches basic skills and concepts of arithmetic and algebra. The…

Closing the Gap: First Year Success in College Mathematics at an HBCU

ERIC Educational Resources Information Center

Harrington, Melissa A.; Lloyd, Andrew; Smolinski, Tomasz; Shahin, Mazen

2016-01-01

At our Historically-Black University, about 89% of first-year students place into developmental mathematics, negatively impacting retention and degree completion. In 2012, an NSF-funded learning enrichment project began offering the introductory and developmental mathematics courses on-line over the summer to incoming science, technology,…

Mutual relationship between mathematics and astronomy in the ancient Greece

NASA Astrophysics Data System (ADS)

Obradovic, S.

2006-05-01

In the paper we consider the foundations of mathematics in the ancient Greece as a deductive system, especially the Euclidean geometry. We investigate the concepts of continuum and discreteness in mathematics and nature. A special attention is given to the mathematics applied to the foundation of the Pythagorean concept of the universe and adoption of Aristotle's and Ptolemy's worldviews.

Bipotential continuum models for granular mechanics

NASA Astrophysics Data System (ADS)

Goddard, Joe

2014-03-01

Most currently popular continuum models for granular media are special cases of a generalized Maxwell fluid model, which describes the evolution of stress and internal variables such as granular particle fraction and fabric,in terms of imposed strain rate. It is shown how such models can be obtained from two scalar potentials, a standard elastic free energy and a ``dissipation potential'' given rigorously by the mathematical theory of Edelen. This allows for a relatively easy derivation of properly invariant continuum models for granular media and fluid-particle suspensions within a thermodynamically consistent framework. The resulting continuum models encompass all the prominent regimes of granular flow, ranging from the quasi-static to rapidly sheared, and are readily extended to include higher-gradient or Cosserat effects. Models involving stress diffusion, such as that proposed recently by Kamrin and Koval (PRL 108 178301), provide an alternative approach that is mentioned in passing. This paper provides a brief overview of a forthcoming review articles by the speaker (The Princeton Companion to Applied Mathematics, and Appl. Mech. Rev.,in the press, 2013).

A Quantitative Analysis of Methods Used for Avoidance and Acceleration of Developmental Mathematics Sequences in Community College

ERIC Educational Resources Information Center

Travers, Steven T.

2017-01-01

Many developmental mathematics programs at community colleges in recent years have undergone a process of redesign in an attempt increase the historical poor rate of student successful completion of required developmental coursework. Various curriculum and instructional design models that incorporate methods of avoiding and accelerating the…

The Myths of Redesign in Developmental Mathematics

ERIC Educational Resources Information Center

Cafarella, Brian V.

2016-01-01

Due to poor student success rates in developmental mathematics, many institutions have implemented various forms of redesign into their developmental math curricula. Since the goal of redesign is to increase student success, it is salient to explore all aspects of the redesign process. Many studies have focused on the positive outcomes of redesign…

Dermatoglyphic asymmetries and fronto-striatal dysfunction in young-adults reporting non-clinical psychosis

PubMed Central

Mittal, Vijay A.; Dean, Derek J.; Pelletier, Andrea

2012-01-01

Objective Growing evidence indicates that non-clinical psychotic-like experiences occur in otherwise healthy individuals, suggesting that psychosis may occur on a continuum. However, little is know about how the diathesis for formal psychosis maps on to individuals at the non-clinical side of this continuum. Our current understanding of the pathophysiology of schizophrenia implicates certain key factors such as early developmental abnormalities and fronto-striatal dysfunction. To date, no studies have examined these core factors in the context of non-clinical psychosis. Method A total of 221 young adults were assessed for distressing attenuated positive symptoms (DAPS), dermatoglyphic asymmetries (a marker of early developmental insult), and procedural memory (a proxy for fronto-striatal function). Results Participants reporting DAPS (n=16; 7.2%) and no-DAPS (n=205; 92.7%) were split into two groups. The DAPS group showed significantly elevated depression, elevated dermatoglyphic asymmetries, and a pattern of procedural learning consistent with other studies with formally psychotic patients. Conclusion The results indicate that the non-clinical side of the psychosis continuum also shares key vulnerability factors implicated in schizophrenia, suggesting that both early developmental disruption and abnormalities in fronto-striatal function are core aspects underlying the disorder. PMID:22519833

The Link between Logic, Mathematics and Imagination: Evidence from Children with Developmental Dyscalculia and Mathematically Gifted Children

ERIC Educational Resources Information Center

Morsanyi, Kinga; Devine, Amy; Nobes, Alison; Szucs, Denes

2013-01-01

This study examined performance on transitive inference problems in children with developmental dyscalculia (DD), typically developing controls matched on IQ, working memory and reading skills, and in children with outstanding mathematical abilities. Whereas mainstream approaches currently consider DD as a domain-specific deficit, we hypothesized…

Applying Piaget's Theory of Cognitive Development to Mathematics Instruction

ERIC Educational Resources Information Center

Ojose, Bobby

2008-01-01

This paper is based on a presentation given at National Council of Teachers of Mathematics (NCTM) in 2005 in Anaheim, California. It explicates the developmental stages of the child as posited by Piaget. The author then ties each of the stages to developmentally appropriate mathematics instruction. The implications in terms of not imposing…

Designing for Improvement in Professional Development for Community College Developmental Mathematics Faculty

ERIC Educational Resources Information Center

Edwards, Ann R.; Sandoval, Carlos; McNamara, Haley

2015-01-01

More than 60% of the nation's 14 million community college students are required to complete at least one developmental mathematics class before enrolling in college-credit courses; however, 80% of them do not successfully complete any college-level mathematics course within 3 years. To address this problem, the Community College Pathways…

The Efficacy of Instructional Strategy on Mathematics Achievement, Attitudes, and Anxiety Levels of Developmental Math Students

ERIC Educational Resources Information Center

Thomas-Browne, Carmen G.

2009-01-01

This dissertation investigated three instructional strategies in developmental math classes to determine if instructional strategy had a positive effect on student achievement, attitude towards mathematics, and anxiety level towards mathematics at a college in western Pennsylvania for students majoring in applied arts. The significance of this…

The Consequences of Delayed Enrollment in Developmental Mathematics

ERIC Educational Resources Information Center

Fike, David S.; Fike, Renea

2012-01-01

Though a large percentage of U.S. students enter higher education with mathematics deficiencies, many institutions allow these students to decide the timing of their enrollment in developmental mathematics courses. This study of 3476 first-time-in-college students entailed the review of student outcomes (Fall GPA, Fall-to-Spring retention,…

Evaluating the Effects of Mastery Learning in Postsecondary Developmental Mathematics

ERIC Educational Resources Information Center

Bradley, Kirk

2016-01-01

The purpose of this study was to determine which academic and affective student factors were significant to student success in a mastery learning program in developmental mathematics and to determine if the mastery learning program led to increased mathematical knowledge retention and success in the subsequent math course. The first phase of the…

Technology: The Key to the Reformation of Developmental Mathematics Pedagogy

ERIC Educational Resources Information Center

Ben-Jacob, Marion G.

2016-01-01

There is a movement nationwide to enhance the learning experience of college students who need to take courses in developmental mathematics. Technology is instrumental in eliminating the non-credit bearing courses from their programs of study. The restructuring of the mathematics programs allows for greater confidence on the parts of the students…

A Report on Student Achievement in a Pilot Program for Developmental Students.

ERIC Educational Resources Information Center

Best, Linda; Fung, Terry Y.

2001-01-01

Reports on the first phase of a two-year pilot study of a university-level mathematics requirement that accommodates the needs of developmental students. Finds that the 84% pass rate for this new class format is substantially higher than the 43% pass rate for traditional developmental mathematics courses offered during the same semester. (Contains…

The Differential Effects of Gender and Mathematics Anxiety-Apprehension on Developmental Students' Academic Performance and Persistence.

ERIC Educational Resources Information Center

Ikegulu, T. Nelson

The performance of 244 (111 male and 133 female) developmental college students was studied in relation to their perceived levels of mathematics anxiety (123 low and 121 high). The Mathematics Anxiety-Apprehension Survey (MAAS) (T. Ikegulu, 1998) was administered to students in four classes from two institutions. The product limit estimator…

Identifying Subtypes among Children with Developmental Coordination Disorder and Mathematical Learning Disabilities, Using Model-Based Clustering

ERIC Educational Resources Information Center

Pieters, Stefanie; Roeyers, Herbert; Rosseel, Yves; Van Waelvelde, Hilde; Desoete, Annemie

2015-01-01

A relationship between motor and mathematical skills has been shown by previous research. However, the question of whether subtypes can be differentiated within developmental coordination disorder (DCD) and/or mathematical learning disability (MLD) remains unresolved. In a sample of children with and without DCD and/or MLD, a data-driven…

Embedding Language Support in Developmental Mathematics Lessons: Exploring the Value of Design as Professional Development for Community College Mathematics Instructors

ERIC Educational Resources Information Center

Gomez, Kimberley; Gomez, Louis M.; Rodela, Katherine C.; Horton, Emily S.; Cunningham, Jahneille; Ambrocio, Rocio

2015-01-01

Three community college faculty members used improvement science techniques to design, develop, and refine contextualized developmental mathematics lessons, where language and literacy pedagogy and related supports figured prominently in these instructional materials. This article reports on the role that their design experiences played in…

Using Formative Assessment and Self-Regulated Learning to Help Developmental Mathematics Students Achieve: A Multi-Campus Program

ERIC Educational Resources Information Center

Hudesman, John; Crosby, Sara; Ziehmke, Niesha; Everson, Howard; Issac, Sharlene; Flugman, Bert; Zimmerman, Barry; Moylan, Adam

2014-01-01

The authors describe an Enhanced Formative Assessment and Self-Regulated Learning (EFA-SRL) program designed to improve the achievement of community college students enrolled in developmental mathematics courses. Their model includes the use of specially formatted quizzes designed to assess both the students' mathematics and metacognitive skill…

The Mathematics of Networks Science: Scale-Free, Power-Law Graphs and Continuum Theoretical Analysis

ERIC Educational Resources Information Center

Padula, Janice

2012-01-01

When hoping to initiate or sustain students' interest in mathematics teachers should always consider relevance, relevance to students' lives and in the middle and later years of instruction in high school and university, accessibility. A topic such as the mathematics behind networks science, more specifically scale-free graphs, is up-to-date,…

Microstructural comparison of the kinematics of discrete and continuum dislocations models

NASA Astrophysics Data System (ADS)

Sandfeld, Stefan; Po, Giacomo

2015-12-01

The Continuum Dislocation Dynamics (CDD) theory and the Discrete Dislocation Dynamics (DDD) method are compared based on concise mathematical formulations of the coarse graining of discrete data. A numerical tool for converting from a discrete to a continuum representation of a given dislocation configuration is developed, which allows to directly compare both simulation approaches based on continuum quantities (e.g. scalar density, geometrically necessary densities, mean curvature). Investigating the evolution of selected dislocation configurations within analytically given velocity fields for both DDD and CDD reveals that CDD contains a surprising number of important microstructural details.

A Multi-Metric Assessment on the Impact of I Can Learn[R] (ICL) Multimedia on Actual and Perceived Student Achievement in Developmental Mathematics

ERIC Educational Resources Information Center

Stokes, Sandra D.

2011-01-01

This quasi-experimental study focused on the initiatives undertaken by a community college's Academic Skills Enhancement Program (ASEP) commonly known as the Developmental Education Department to find an alternative delivery method to aid its students in learning developmental mathematics. Moreover, this study (1) conducted a comparative…

What Are We Developing? A Case Study of a College Mathematics Program

ERIC Educational Resources Information Center

Johnson, Pete

2007-01-01

Over one-third of all college mathematics enrollments are in courses considered to be developmental. While such courses have been the subject of a large body of research, one question that seems not to have been studied empirically is the alignment of the content of developmental and college level mathematics courses. This paper gives the results…

A Cognitive Analysis of Developmental Mathematics Students' Errors and Misconceptions in Real Number Computations and Evaluating Algebraic Expressions

ERIC Educational Resources Information Center

Titus, Freddie

2010-01-01

Fifty percent of college-bound students graduate from high school underprepared for mathematics at the post-secondary level. As a result, thirty-five percent of college students take developmental mathematics courses. What is even more shocking is the high failure rate (ranging from 35 to 42 percent) of students enrolled in developmental…

Drop-tower experiments for capillary surfaces in an exotic container

NASA Technical Reports Server (NTRS)

Concus, Paul; Finn, Robert; Weislogel, Mark

1991-01-01

Low-gravity drop-tower experiments are carried out for an 'exotic' rotationally-symmetric container, which admits an entire continuum of distinct equilibrium symmetric capillary free surfaces. It is found that an initial equilibrium planer interface, a member of the continuum, will reorient toward a non-symmetric interface, as predicted by recent mathematical theory.

American Mathematics from 1940 to the Day Before Yesterday

ERIC Educational Resources Information Center

Ewing, J. H.; And Others

1976-01-01

Ten recent results in pure mathematics are described, covering the continuum hypothesis, Diophantine equations, simple groups, resolution of singularities, Weil conjectures, Lie groups, Poincare conjecture, exotic spheres, differential equations, and the index theorem. Proofs are omitted, but references are provided. (DT)

First Steps for Early Success: State Strategies to Support Developmental Screening in Early Childhood Settings

ERIC Educational Resources Information Center

Johnson-Staub, Christine

2014-01-01

Young children's development occurs along a continuum, with milestones reached at ages that vary within an accepted timeframe. Milestones not met within the expected timeframe can raise concerns about developmental delays, health conditions, or other factors contributing negatively to the child's growth and learning. Monitoring children's…

Weaving Mathematical Instructional Strategies into Inclusive Settings.

ERIC Educational Resources Information Center

Karp, Karen S.; Voltz, Deborah L.

2000-01-01

This article describes a framework that allows teachers in inclusive elementary settings to interweave instructional strategies from a variety of paradigms to meet individual learning needs in inclusive mathematics classes. Factors to be considered are highlighted and an instructional continuum from more teacher-centered strategies to more…

An Out-of-Math Experience: Einstein, Relativity, and the Developmental Mathematics Student.

ERIC Educational Resources Information Center

Fiore, Greg

2000-01-01

Discusses Einstein's special relativity theory and some of the developmental mathematics involved. Presents motivational classroom materials used in discussing relative-motion problems, evaluating a radical expression, graphing with asymptotes, interpreting a graph, studying variation, and solving literal and radical equations. (KHR)

Las Matematicas: Lenguaje Universal. Grados Intermedios, Niveles 1-3. Teacher's Guide I (Mathematics: A Universal Language. Intermediate Grades, Level 1-3. Teacher's Guide I).

ERIC Educational Resources Information Center

Dissemination and Assessment Center for Bilingual Education, Austin, TX.

This guide covers the first part of a bilingual, sequential mathematics course. The course integrates culturally relevant situations and illustrations with mathematics to reinforce the student's self-concept and encourage cultural pride. This program may be used as a self-contained continuum, as a supplement to another course of study, for…

Las Matematicas: Lenguaje Universal. Grados Intermedios, Niveles 4-6. Teacher's Guide II (Mathematics: A Universal Language. Intermediate Grades, Levels 4-6. Teacher's Guide II).

ERIC Educational Resources Information Center

Dissemination and Assessment Center for Bilingual Education, Austin, TX.

This guide covers the second part of a bilingual, sequential mathematics course. The course integrates culturally relevant situations and illustrations with mathematics to reinforce the student's self-concept and encourage cultural pride. This program may be used as a self-contained continuum, as a supplement to another course of study, for…

Disabilities of Arithmetic and Mathematical Reasoning: Perspectives from Neurology and Neuropsychology.

ERIC Educational Resources Information Center

Rourke, Byron P.; Conway, James A.

1997-01-01

Reviews current research on brain-behavior relationships in disabilities of arithmetic and mathematical reasoning from both a neurological and a neuropsychological perspective. Defines developmental dyscalculia and the developmental importance of right versus left hemisphere integrity for the mediation of arithmetic learning and explores…

Developmental Dyscalculia and Low Numeracy in Chinese Children

ERIC Educational Resources Information Center

Chan, Winnie Wai Lan; Au, Terry K.; Tang, Joey

2013-01-01

Children struggle with mathematics for different reasons. Developmental dyscalculia and low numeracy--two kinds of mathematical difficulties--may have their roots, respectively, in poor understanding of exact non-symbolic numerosities and of symbolic numerals. This study was the first to explore whether Chinese children, despite cultural and…

Supplemental Instruction in Developmental Mathematics

ERIC Educational Resources Information Center

Phelps, Julie M.; Evans, Ruby

2006-01-01

Mirroring the changing demographics of the nation, the community college student population continues to grow in size and diversity. Almost half of all students who enter these institutions need at least one remedial course--which is often developmental mathematics. Developed in 1973, Supplemental Instruction (SI) has quickly gained recognition as…

Teaching Integer Operations Using Ring Theory

ERIC Educational Resources Information Center

Hirsch, Jenna

2012-01-01

A facility with signed numbers forms the basis for effective problem solving throughout developmental mathematics. Most developmental mathematics textbooks explain signed number operations using absolute value, a method that involves considering the problem in several cases (same sign, opposite sign), and in the case of subtraction, rewriting the…

Mathematics and Science Faculty Service Learning Handbook.

ERIC Educational Resources Information Center

Wozniak, Jacci

Resources developed by "Campus Compact," a coalition of over 550 colleges and universities established to create and enhance service learning opportunities for students, are presented in this handbook for mathematics and science faculty. A brief introduction defines service learning and provides a continuum of types of service learning, such as…

Working Memory and Mathematics: A Review of Developmental, Individual Difference, and Cognitive Approaches

ERIC Educational Resources Information Center

Raghubar, Kimberly P.; Barnes, Marcia A.; Hecht, Steven A.

2010-01-01

Working memory refers to a mental workspace, involved in controlling, regulating, and actively maintaining relevant information to accomplish complex cognitive tasks (e.g. mathematical processing). Despite the potential relevance of a relation between working memory and math for understanding developmental and individual differences in…

Teachers' Explanations of a Key Developmental Understanding of Multiplicative Reasoning

ERIC Educational Resources Information Center

Rhee, Katherine L.

2012-01-01

This qualitative research study explores teachers' understandings of multiplicative reasoning as a key developmental understanding (KDU). A KDU entails knowingly applying the same mathematical concepts within different contexts. A KDU supports an individual to build a connected understanding of mathematics as opposed to only understanding…

Promoting Student Learning and Productive Persistence in Developmental Mathematics: Research Frameworks Informing the Carnegie Pathways

ERIC Educational Resources Information Center

Edwards, Ann R.; Beattie, Rachel L.

2016-01-01

This paper focuses on two research-based frameworks that inform the design of instruction and promote student success in accelerated, developmental mathematics pathways. These are Learning Opportunities--productive struggle on challenging and relevant tasks, deliberate practice, and explicit connections, and Productive Persistence--promoting…

Developmental Mathematics and the Lansing Community College Math Lab.

ERIC Educational Resources Information Center

Rotman, Jack W.

Based on an extensive literature search, this paper reviews recent research and theoretical studies and discusses their applicability to Lansing Community College's (LCC's) Mathematics Laboratory. After noting the steps taken in data collection, part I describes LCC and its Math Lab, which offers developmental courses in a self-paced, mastery…

Connecting Expectations and Values: Students' Perceptions of Developmental Mathematics in a Computer-Based Learning Environment

ERIC Educational Resources Information Center

Jackson, Karen Latrice Terrell

2014-01-01

Students' perceptions influence their expectations and values. According to Expectations and Values Theory of Achievement Motivation (EVT-AM), students' expectations and values impact their behaviors (Eccles & Wigfield, 2002). This study seeks to find students' perceptions of developmental mathematics in a mastery learning computer-based…

Conformational Modeling of Continuum Structures in Robotics and Structural Biology: A Review

PubMed Central

Chirikjian, G. S.

2016-01-01

Hyper-redundant (or snakelike) manipulators have many more degrees of freedom than are required to position and orient an object in space. They have been employed in a variety of applications ranging from search-and-rescue to minimally invasive surgical procedures, and recently they even have been proposed as solutions to problems in maintaining civil infrastructure and the repair of satellites. The kinematic and dynamic properties of snakelike robots are captured naturally using a continuum backbone curve equipped with a naturally evolving set of reference frames, stiffness properties, and mass density. When the snakelike robot has a continuum architecture, the backbone curve corresponds with the physical device itself. Interestingly, these same modeling ideas can be used to describe conformational shapes of DNA molecules and filamentous protein structures in solution and in cells. This paper reviews several classes of snakelike robots: (1) hyper-redundant manipulators guided by backbone curves; (2) flexible steerable needles; and (3) concentric tube continuum robots. It is then shown how the same mathematical modeling methods used in these robotics contexts can be used to model molecules such as DNA. All of these problems are treated in the context of a common mathematical framework based on the differential geometry of curves, continuum mechanics, and variational calculus. Both coordinate-dependent Euler-Lagrange formulations and coordinate-free Euler-Poincaré approaches are reviewed. PMID:27030786

Conformational Modeling of Continuum Structures in Robotics and Structural Biology: A Review.

PubMed

Chirikjian, G S

Hyper-redundant (or snakelike) manipulators have many more degrees of freedom than are required to position and orient an object in space. They have been employed in a variety of applications ranging from search-and-rescue to minimally invasive surgical procedures, and recently they even have been proposed as solutions to problems in maintaining civil infrastructure and the repair of satellites. The kinematic and dynamic properties of snakelike robots are captured naturally using a continuum backbone curve equipped with a naturally evolving set of reference frames, stiffness properties, and mass density. When the snakelike robot has a continuum architecture, the backbone curve corresponds with the physical device itself. Interestingly, these same modeling ideas can be used to describe conformational shapes of DNA molecules and filamentous protein structures in solution and in cells. This paper reviews several classes of snakelike robots: (1) hyper-redundant manipulators guided by backbone curves; (2) flexible steerable needles; and (3) concentric tube continuum robots. It is then shown how the same mathematical modeling methods used in these robotics contexts can be used to model molecules such as DNA. All of these problems are treated in the context of a common mathematical framework based on the differential geometry of curves, continuum mechanics, and variational calculus. Both coordinate-dependent Euler-Lagrange formulations and coordinate-free Euler-Poincaré approaches are reviewed.

Continuum and discrete approach in modeling biofilm development and structure: a review.

PubMed

Mattei, M R; Frunzo, L; D'Acunto, B; Pechaud, Y; Pirozzi, F; Esposito, G

2018-03-01

The scientific community has recognized that almost 99% of the microbial life on earth is represented by biofilms. Considering the impacts of their sessile lifestyle on both natural and human activities, extensive experimental activity has been carried out to understand how biofilms grow and interact with the environment. Many mathematical models have also been developed to simulate and elucidate the main processes characterizing the biofilm growth. Two main mathematical approaches for biomass representation can be distinguished: continuum and discrete. This review is aimed at exploring the main characteristics of each approach. Continuum models can simulate the biofilm processes in a quantitative and deterministic way. However, they require a multidimensional formulation to take into account the biofilm spatial heterogeneity, which makes the models quite complicated, requiring significant computational effort. Discrete models are more recent and can represent the typical multidimensional structural heterogeneity of biofilm reflecting the experimental expectations, but they generate computational results including elements of randomness and introduce stochastic effects into the solutions.

Working Memory, Reading, and Mathematical Skills in Children with Developmental Coordination Disorder

ERIC Educational Resources Information Center

Alloway, Tracy Packiam

2007-01-01

The aim of the present study was investigate the relationship between working memory and reading and mathematical skills in 55 children diagnosed with developmental coordination disorder (DCD). The findings indicate a pervasive memory deficit in all memory measures. In particular, deficits observed in visuospatial short-term and working memory…

Using e-Learning Platforms for Mastery Learning in Developmental Mathematics Courses

ERIC Educational Resources Information Center

Boggs, Stacey; Shore, Mark; Shore, JoAnna

2004-01-01

Many colleges and universities have adopted e-learning platforms to utilize computers as an instructional tool in developmental (i.e., beginning and intermediate algebra) mathematics courses. An e-learning platform is a computer program used to enhance course instruction via computers and the Internet. Allegany College of Maryland is currently…

Community and Videos: An Action Plan to Increase Success Rates in California Community College Developmental Mathematics

ERIC Educational Resources Information Center

Long, Gary W.

2010-01-01

Success rates in California community college developmental mathematics courses have hovered around 50% for decades. These gatekeeper courses have prevented many students from earning college degrees. Since community college is the starting point for the majority of California's potential college graduates and the majority of these students…

Cooperative Learning in a Community College Setting: Developmental Coursework in Mathematics

ERIC Educational Resources Information Center

Rivera, Natalie

2013-01-01

This action research study, set in a community college in the southwestern United States, was designed to investigate the effects of implementing cooperative learning strategies in a developmental mathematics course. Introductory algebra was formerly taught in a lecture based format, and as such regularly had a low course completion rate. To…

A Review of the Literature on Online Developmental Mathematics: Research-Based Recommendations for Practice

ERIC Educational Resources Information Center

Coleman, Sandra Lee; Skidmore, Susan Troncoso; Martirosyan, Nara M.

2017-01-01

In this review of literature, the efficacy of online instruction for developmental mathematics students was explored. Current peer-reviewed articles, representing research from community college settings and written between 1996 and 2015, were reviewed. Based on those studies, several recommendations are offered regarding the online delivery of…

Are the K-2 Common Core State Standards for Mathematics Developmentally Appropriate?

ERIC Educational Resources Information Center

Otálora, Yenny

2016-01-01

In this article, I (a) illustrate how the K-2 CCSSM reflect the major findings from research studies carried out over the last 30 years on early mathematical abilities that indicate these standards are developmentally appropriate for young children, and (b) offer insights into some types of instructional strategies (e.g., student-centered…

Improving Mathematics Learning by Integrating Curricular Activities with Innovative and Developmentally Appropriate Digital Apps: Findings from the Next Generation Preschool Math Evaluation

ERIC Educational Resources Information Center

Presser, Ashley Lewis; Vahey, Philip; Dominguez, Ximena

2015-01-01

This paper describes findings from a blocked randomized design (BRD) field study conducted to examine the "Next Generation Preschool Math" (NGPM) program's implementation in preschool classrooms and promise in improving young children's mathematic learning. NGPM integrates traditional preschool activities with developmentally appropriate…

Improving on the American Dream: Mathematics Pathways to Student Success

ERIC Educational Resources Information Center

Clyburn, Gay M.

2013-01-01

Developmental mathematics is one of the most serious barriers to educational and economic achievement. Over 60 percent of all students entering community colleges in the United States are required to complete remedial/developmental courses as a first step towards earning associate's or bachelor's degrees. Then, to earn a degree,…

Teachers' Initial Orchestration of Students' Dynamic Geometry Software Use: Consequences for Students' Opportunities to Learn Mathematics

ERIC Educational Resources Information Center

Erfjord, Ingvald

2011-01-01

This paper reports from a case study with teachers at two schools in Norway participating in developmental projects aiming for inquiry communities in mathematics teaching and learning. In the reported case study, the teachers participated in one of the developmental projects focusing on implementation and use of computer software in mathematics…

Experiences of Adults with Developmental Disability and a Teacher of Mathematics in the Money Club

ERIC Educational Resources Information Center

Rodriguez, Anthony M.

2012-01-01

In my experiences, students with Developmental Disability (DD) are routinely excluded from Algebra and other high-level mathematics courses. People with DD do not have the opportunity to learn Algebra, which may support the understanding and provide purpose for learning money and budgeting skills that, perhaps, could help them avoid financial…

Scaffolding Mathematics Remediation for Academically At-Risk Students Following Developmental Education Reform in Florida

ERIC Educational Resources Information Center

Rebecca, Brower L.; Woods, Chenoa S.; Bertrand Jones, Tamara; Park, Toby J.; Hu, Shouping; Tandberg, David A.; Nix, Amanda; Rhaming, Sophia G.; Martindale, Sandra K.

2017-01-01

The purpose of this qualitative study is to understand how educational scaffolding may explain changing patterns of student success in mathematics in the era of developmental education (DE or remediation) reform in Florida College System (FCS) institutions. Specifically, we apply the concept of scaffolding to underprepared FCS students who are at…

Scaffolding Mathematics Remediation for Academically At-Risk Students Following Developmental Education Reform in Florida

ERIC Educational Resources Information Center

Brower, Rebecca L.; Woods, Chenoa S.; Jones, Tamara Bertrand; Park, Toby J.; Hu, Shouping; Tandberg, David A.; Nix, Amanda N.; Rahming, Sophia G.; Martindale, Sandra K.

2018-01-01

The purpose of this qualitative study is to understand how educational scaffolding may explain changing patterns of student success in mathematics in the era of developmental education (DE or remediation) reform in Florida College System (FCS) institutions. Specifically, we apply the concept of scaffolding to underprepared FCS students who are at…

Gender Differences in Solving Mathematics Problems among Two-Year College Students in a Developmental Algebra Class and Related Factors.

ERIC Educational Resources Information Center

Schonberger, Ann K.

A study was conducted at the University of Maine at Orono (UMO) to examine gender differences with respect to mathematical problem-solving ability, visual spatial ability, abstract reasoning ability, field independence/dependence, independent learning style, and developmental problem-solving ability (i.e., formal reasoning ability). Subjects…

Web-Delivered Supplemental Instruction: Dynamic Customizing of Search Algorithms to Enhance Independent Learning for Developmental Mathematics Students

ERIC Educational Resources Information Center

Taksa, Isak; Goldberg, Robert

2004-01-01

Traditional peer-to-peer Supplemental Instruction (SI) was introduced into higher education over a quarter of a century ago and promptly became an integral part of the developmental mathematics curricula in many senior and community colleges. Later, some colleges introduced Video-based Supplemental Instruction (VSI) and, in recent years,…

Developmental Mathematics in College: What the Research Is and Why There Isn't More.

ERIC Educational Resources Information Center

Schonberger, Ann K.

A review of the literature is presented on developmental mathematics courses in two- and four-year colleges and universities. The paper is organized within the categories of status studies, placement, program evaluation, class management, student characteristics, and thought processes. Highlights of the report include: (1) an average of 2.0…

Developmental and Interprofessional Care of the Preterm Infant: Neonatal Intensive Care Unit Through High-Risk Infant Follow-up.

PubMed

Lipner, Hildy S; Huron, Randye F

2018-02-01

Practices in the neonatal intensive care unit (NICU) that reduce infant stress and respond to behavioral cues positively influence developmental outcomes. Proactive developmental surveillance and timely introduction of early intervention services improve outcomes for premature infants. A model that emphasizes infant development and a continuum of care beginning in the NICU with transition to outpatient monitoring and provision of early intervention services is hypothesized to support the most optimal outcomes for premature infants. Copyright © 2017 Elsevier Inc. All rights reserved.

Linking Pupil and Teacher Competence in Reading and Mathematics in Vietnam

ERIC Educational Resources Information Center

Griffin, Patrick

2008-01-01

This article reports results derived from the national study of Grade 5 in Vietnamese primary schools in which teachers and pupils took tests in reading and mathematics. The test data were calibrated so that teacher and pupil results could be mapped onto the same continuum. Results showed that the overlapping tests for teachers and pupils were…

The EMERGE Summer Program: Supporting Incoming Freshmen's Success in Mathematics Developmental Coursework

ERIC Educational Resources Information Center

Bird, Katherine; Oppland-Cordell, Sarah; Hibdon, Joseph

2016-01-01

This paper describes the development, results, and future directions of the mathematics component of the EMERGE Summer Program at Northeastern Illinois University. Initiated summer 2014, EMERGE offered English and mathematics sessions for incoming freshmen. The mathematics session aimed to strengthen participants' mathematical foundations,…

AMATYC Members Offer Their Perceptions of Interactions that Occur in Developmental Mathematics Courses

ERIC Educational Resources Information Center

Sattler, Nancy J.

2005-01-01

This study investigated teacher perception of interactions used in on-line developmental mathematics courses at two-year colleges. A total of 98 AMATYC teachers were surveyed. The following conclusions were inferred from the study's findings: (a) The teacher responding to the survey was apt to be a female between the ages of 50 and 59, had taught…

Success and Persistence of Developmental Mathematics Students Based on Age and Ethnicity

ERIC Educational Resources Information Center

Wolfle, James D.

2012-01-01

This ex post facto study examined the fall-to-fall persistence and academic success of students in a medium-sized Virginia community college. The variables of age and ethnicity in combination with whether a student's first mathematics course was developmental were used to examine the effects of each. It was found that neither the interaction of…

Do Developmental Mathematics Programs Have a Causal Impact on Student Retention? An Application of Discrete-Time Survival and Regression-Discontinuity Analysis

ERIC Educational Resources Information Center

Lesik, Sally A.

2007-01-01

The impact of academic programs--such as developmental mathematics programs--on student retention, has been a controversial topic for administrators, policy makers, and faculty in higher education. Despite deep interest in the effectiveness of these programs in retaining students, scholars have been unable to determine whether such programs have a…

Students' Agency in an In-Class Computer-Centered Developmental Mathematics Classroom: The Best Laid Plans of Math and (Wo)men

ERIC Educational Resources Information Center

Aly, Geillan Dahab

2016-01-01

Community colleges are tasked with helping all students regardless of their academic background to receive a degree, certificate, or other form of education. Many of these students need support in learning the mathematical content necessary to take college-level courses. Since a large proportion of students in these developmental classes are…

Evaluating the Effectiveness of Developmental Mathematics by Embedding a Randomized Experiment within a Regression Discontinuity Design

ERIC Educational Resources Information Center

Moss, Brian G.; Yeaton, William H.; Lloyd, Jane E.

2014-01-01

Using a novel design approach, a randomized experiment (RE) was embedded within a regression discontinuity (RD) design (R-RE-D) to evaluate the impact of developmental mathematics at a large midwestern college ("n" = 2,122). Within a region of uncertainty near the cut-score, estimates of benefit from a prospective RE were closely…

Seeking Mathematics Success for College Students: A Randomized Field Trial of an Adapted Approach

ERIC Educational Resources Information Center

Gula, Taras; Hoessler, Carolyn; Maciejewski, Wes

2015-01-01

Many students enter the Canadian college system with insufficient mathematical ability and leave the system with little improvement. Those students who enter with poor mathematics ability typically take a developmental mathematics course as their first and possibly only mathematics course. The educational experiences that comprise a developmental…

A Cognitive Diagnostic Modeling of Attribute Mastery in Massachusetts, Minnesota, and the U.S. National Sample Using the TIMSS 2007

ERIC Educational Resources Information Center

Lee, Young-Sun; Park, Yoon Soo; Taylan, Didem

2011-01-01

Studies of international mathematics achievement such as the Trends in Mathematics and Science Study (TIMSS) have employed classical test theory and item response theory to rank individuals within a latent ability continuum. Although these approaches have provided insights into comparisons between countries, they have yet to examine how specific…

Interest and Identity Convergence for Equitable Mathematics' Teaching: Reflections on the Interplay of the Institutional and Individual on Teacher Development and Action

ERIC Educational Resources Information Center

Meister, Tara

2017-01-01

Propelled by Maxine Greene's (1988) continuum of freedom from normative structures to critical consciousness and action, I illuminate the institutional and individual influences on teacher development and action in mathematics teaching. I focus on the question: What barriers and openings, both individually and institutionally, spur teachers to…

An advanced kinetic theory for morphing continuum with inner structures

NASA Astrophysics Data System (ADS)

Chen, James

2017-12-01

Advanced kinetic theory with the Boltzmann-Curtiss equation provides a promising tool for polyatomic gas flows, especially for fluid flows containing inner structures, such as turbulence, polyatomic gas flows and others. Although a Hamiltonian-based distribution function was proposed for diatomic gas flow, a general distribution function for the generalized Boltzmann-Curtiss equations and polyatomic gas flow is still out of reach. With assistance from Boltzmann's entropy principle, a generalized Boltzmann-Curtiss distribution for polyatomic gas flow is introduced. The corresponding governing equations at equilibrium state are derived and compared with Eringen's morphing (micropolar) continuum theory derived under the framework of rational continuum thermomechanics. Although rational continuum thermomechanics has the advantages of mathematical rigor and simplicity, the presented statistical kinetic theory approach provides a clear physical picture for what the governing equations represent.

Continuum mechanics and thermodynamics in the Hamilton and the Godunov-type formulations

NASA Astrophysics Data System (ADS)

Peshkov, Ilya; Pavelka, Michal; Romenski, Evgeniy; Grmela, Miroslav

2018-01-01

Continuum mechanics with dislocations, with the Cattaneo-type heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunov-type system of the first-order, symmetric hyperbolic partial differential equations (SHTC equations). The compatibility with thermodynamics of the time reversible part of the governing equations is mathematically expressed in the former formulation as degeneracy of the Hamiltonian structure and in the latter formulation as the existence of a companion conservation law. In both formulations the time irreversible part represents gradient dynamics. The Godunov-type formulation brings the mathematical rigor (the local well posedness of the Cauchy initial value problem) and the possibility to discretize while keeping the physical content of the governing equations (the Godunov finite volume discretization).

Developmental Mathematics College Students' Experiences of Mathematical Practices in a 4-Week Summer Learning Community Using Local Communities of Mathematical Practice

ERIC Educational Resources Information Center

Naidu, Bhupinder

2013-01-01

The research literature concerning traditionally aged college mathematics students' who require remediation, in beginning Algebra topics, states that these students lack confidence in their mathematical skills, have experienced failure and frustration in the past, have low self confidence issues with respect to mathematics and often lack…

Flawed Mathematical Conceptualizations: Marlon's Dilemma

ERIC Educational Resources Information Center

Garrett, Lauretta

2013-01-01

Adult developmental mathematics students often work under great pressure to complete the mathematics sequences designed to help them achieve success (Bryk & Treisman, 2010). Results of a teaching experiment demonstrate how the ability to reason can be impeded by flaws in students' mental representations of mathematics. The earnestness of the…

What Role for Developmental Theories in Mathematics Study Programmes in French-Speaking Belgium? An Analysis of the Geometry Curriculum's Aspects, Framed by Van Hiele's Model

ERIC Educational Resources Information Center

Duroisin, Natacha; Demeuse, Marc

2015-01-01

One possible way of evaluating set curricula is to examine the consistency of study programmes with students' psycho-cognitive development. Three theories were used to evaluate matching between developmental theories and content proposed in the mathematics programmes (geometry section) for primary and the beginning of secondary education. These…

Random sex determination: When developmental noise tips the sex balance.

PubMed

Perrin, Nicolas

2016-12-01

Sex-determining factors are usually assumed to be either genetic or environmental. The present paper aims at drawing attention to the potential contribution of developmental noise, an important but often-neglected component of phenotypic variance. Mutual inhibitions between male and female pathways make sex a bistable equilibrium, such that random fluctuations in the expression of genes at the top of the cascade are sufficient to drive individual development toward one or the other stable state. Evolutionary modeling shows that stochastic sex determinants should resist elimination by genetic or environmental sex determinants under ecologically meaningful settings. On the empirical side, many sex-determination systems traditionally considered as environmental or polygenic actually provide evidence for large components of stochasticity. In reviewing the field, I argue that sex-determination systems should be considered within a three-ends continuum, rather than the classical two-ends continuum. © 2016 WILEY Periodicals, Inc.

Mathematics Ab Ovo: Hans Driesch and Entwicklungsmechanik.

PubMed

Priven, Silvia Waisse; Alfonso-Goldfarb, Ana M

2009-01-01

One of the factors leading to the creation of embryology as a modern discipline at the end of the 19th century was Wilhelm Roux's formulation of the program of Entwicklungsmechanik (developmental mechanics). A look into the work of Hans Driesch, an equal contributor to developmental mechanics, may shed further light on this process. For Roux, developmental mechanics was an anatomical science, but for Driesch it was associated with a mathematical and physical approach to the natural world. Likewise, Roux used the concept of mechanics as an analogy, but Driesch used it literally. Driesch's generation had been trained in a pedagogic context that emphasized mathematics and physics, which may explain why he went a step further than Roux to state that a true "mechanics" of development required the reduction of morphogenetic problems to the known laws of physics. It is argued here that this difference in background is behind the enthusiastic adoption and further development of Roux's program by Driesch's generation, a generation that conceived Entwicklungsmechanik to be the reduction of embryological processes to "the laws of matter in motion." This same mathematical and physical mindset would underscore Driesch's later construction of entelechy as a regulating factor in embryogenesis, through mathematical analysis grounded on the notion of mathematical functions.

The Effects of Motivation, Perceived Learning Strategy Use, and Mathematics Anxiety on the Mathematics Competency of Postsecondary Developmental Mathematics Students

ERIC Educational Resources Information Center

Grassl, Rebecca

2010-01-01

Mathematics competency continues to limit the success of many students and prevents their completion of a postsecondary degree, which ultimately prevents access to education, jobs, and upward social mobility. Furthermore, many postsecondary institutions admit students who do not meet the institution's mathematics proficiency requirements and then…

Bottle Caps as Prekindergarten Mathematical Tools

ERIC Educational Resources Information Center

Raisor, Jill M.; Hudson, Rick A.

2018-01-01

Early childhood provides a time of crucial growth in all developmental domains. Prekindergarten is an optimal time for young children to use objects of play as a medium to explore new cognitive concepts, including mathematical structure. Mathematical structure plays an important role in providing students a means to reason about mathematics,…

Using Analogies to Facilitate Conceptual Change in Mathematics Learning

ERIC Educational Resources Information Center

Vamvakoussi, Xenia

2017-01-01

The problem of adverse effects of prior knowledge in mathematics learning has been amply documented and theorized by mathematics educators as well as cognitive/developmental psychologists. This problem emerges when students' prior knowledge about a mathematical notion comes in contrast with new information coming from instruction, giving rise to…

Adolescent-Perceived Parent and Teacher Overestimation of Mathematics Ability: Developmental Implications for Students' Mathematics Task Values

ERIC Educational Resources Information Center

Gniewosz, Burkhard; Watt, Helen M. G.

2017-01-01

This study examines whether and how student-perceived parents' and teachers' overestimation of students' own perceived mathematical ability can explain trajectories for adolescents' mathematical task values (intrinsic and utility) controlling for measured achievement, following expectancy-value and self-determination theories. Longitudinal data…

Perceptions and Lived Experiences of Traditional Community College Developmental Mathematics Students

ERIC Educational Resources Information Center

Mathai, Mince John

2014-01-01

Many students graduate from high school without adequate proficiency in mathematics, which is necessary to successfully undertake the challenges of college-level mathematics courses. As the underprepared students pursue postsecondary education, these institutions are required to provide remediation in mathematics to equip them with basic…

Special relativity from observer's mathematics point of view

NASA Astrophysics Data System (ADS)

Khots, Boris; Khots, Dmitriy

2015-09-01

When we create mathematical models for quantum theory of light we assume that the mathematical apparatus used in modeling, at least the simplest mathematical apparatus, is infallible. In particular, this relates to the use of "infinitely small" and "infinitely large" quantities in arithmetic and the use of Newton - Cauchy definitions of a limit and derivative in analysis. We believe that is where the main problem lies in contemporary study of nature. We have introduced a new concept of Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. We use Einstein special relativity principles and get the analogue of classical Lorentz transformation. This work considers this transformation from Observer's Mathematics point of view.

Pleiotropic Effects of DCDC2 and DYX1C1 Genes on Language and Mathematics Traits in Nuclear Families of Developmental Dyslexia

PubMed Central

Mascheretti, Sara; Riva, Valentina; Cattaneo, Francesca; Rigoletto, Catia; Rusconi, Marianna; Gruen, Jeffrey R.; Giorda, Roberto; Lazazzera, Claudio; Molteni, Massimo

2014-01-01

Converging evidence indicates that developmental problems in oral language and mathematics can predate or co-occur with developmental dyslexia (DD). Substantial genetic correlations have been found between language, mathematics and reading traits, independent of the method of sampling. We tested for association of variants of two DD susceptibility genes, DCDC2 and DYX1C1, in nuclear families ascertained through a proband with DD using concurrent measurements of language and mathematics in both probands and siblings by the Quantitative Transmission Disequilibrium Test. Evidence for significant associations was found between DCDC2 and ‘Numerical Facts’ (p value = 0.02, with 85 informative families, genetic effect = 0.57) and between ‘Mental Calculation’ and DYX1C1 markers −3GA (p value = 0.05, with 40 informative families, genetic effect = −0.67) and 1249GT (p value = 0.02, with 49 informative families, genetic effect = −0.65). No statistically significant associations were found between DCDC2 or DYX1C1 and language phenotypes. Both DCDC2 and DYX1C1 DD susceptibility genes appear to have a pleiotropic role on mathematics but not language phenotypes. PMID:21046216

Pleiotropic effects of DCDC2 and DYX1C1 genes on language and mathematics traits in nuclear families of developmental dyslexia.

PubMed

Marino, Cecilia; Mascheretti, Sara; Riva, Valentina; Cattaneo, Francesca; Rigoletto, Catia; Rusconi, Marianna; Gruen, Jeffrey R; Giorda, Roberto; Lazazzera, Claudio; Molteni, Massimo

2011-01-01

Converging evidence indicates that developmental problems in oral language and mathematics can predate or co-occur with developmental dyslexia (DD). Substantial genetic correlations have been found between language, mathematics and reading traits, independent of the method of sampling. We tested for association of variants of two DD susceptibility genes, DCDC2 and DYX1C1, in nuclear families ascertained through a proband with DD using concurrent measurements of language and mathematics in both probands and siblings by the Quantitative Transmission Disequilibrium Test. Evidence for significant associations was found between DCDC2 and 'Numerical Facts' (p value = 0.02, with 85 informative families, genetic effect = 0.57) and between 'Mental Calculation' and DYX1C1 markers -3GA (p value = 0.05, with 40 informative families, genetic effect = -0.67) and 1249GT (p value = 0.02, with 49 informative families, genetic effect = -0.65). No statistically significant associations were found between DCDC2 or DYX1C1 and language phenotypes. Both DCDC2 and DYX1C1 DD susceptibility genes appear to have a pleiotropic role on mathematics but not language phenotypes.

The Impact of Instruction Incorporating Content Area Reading Strategies on Student Mathematical Achievement in a Community College Developmental Mathematics Course

ERIC Educational Resources Information Center

Rust, Amber Heller

2011-01-01

When a student is not successful in mathematics, teachers frequently assume the difficulty lies within the student's mathematical ability or negative disposition towards mathematics, but the difficulty may lie with the student's reading comprehension (Draper, Smith, Hall, & Siebert, 2005; Kane, Byrne, & Hater, 1974). Many…

The Relationship between Computational Fluency and Student Success in General Studies Mathematics

ERIC Educational Resources Information Center

Hegeman, Jennifer; Waters, Gavin

2012-01-01

Many developmental mathematics programs emphasize computational fluency with the assumption that this is a necessary contributor to student success in general studies mathematics. In an effort to determine which skills are most essential, scores on a computational fluency test were correlated with student success in general studies mathematics at…

An Analysis of Instruments that Measure the Quality of Mathematics Teaching in Early Childhood

ERIC Educational Resources Information Center

Kilday, Carolyn R.; Kinzie, Mable B.

2009-01-01

The evaluation of teaching quality in mathematics has become increasingly important following research reports indicating that preschoolers are developmentally able to engage in mathematic thought and that child performance in mathematics at this level is a strong predictor of later school achievement. As attention turns to early mathematics…

Nature and origins of mathematics difficulties in very preterm children: a different etiology than developmental dyscalculia.

PubMed

Simms, Victoria; Gilmore, Camilla; Cragg, Lucy; Clayton, Sarah; Marlow, Neil; Johnson, Samantha

2015-02-01

Children born very preterm (<32 wk) are at high risk for mathematics learning difficulties that are out of proportion to other academic and cognitive deficits. However, the etiology of mathematics difficulties in very preterm children is unknown. We sought to identify the nature and origins of preterm children's mathematics difficulties. One hundred and fifteen very preterm children aged 8-10 y were assessed in school with a control group of 77 term-born classmates. Achievement in mathematics, working memory, visuospatial processing, inhibition, and processing speed were assessed using standardized tests. Numerical representations and specific mathematics skills were assessed using experimental tests. Very preterm children had significantly poorer mathematics achievement, working memory, and visuospatial skills than term-born controls. Although preterm children had poorer performance in specific mathematics skills, there was no evidence of imprecise numerical representations. Difficulties in mathematics were associated with deficits in visuospatial processing and working memory. Mathematics difficulties in very preterm children are associated with deficits in working memory and visuospatial processing not numerical representations. Thus, very preterm children's mathematics difficulties are different in nature from those of children with developmental dyscalculia. Interventions targeting general cognitive problems, rather than numerical representations, may improve very preterm children's mathematics achievement.

Problems in Mathematics--Moving towards a Holistic Approach.

ERIC Educational Resources Information Center

Maree, J. G.

1992-01-01

Explanations for problems in mathematics are offered, and examples that may lead to a better understanding of problems in mathematics are discussed. Examples include the developmental, dyscalculia, dyspedagogia, behaviorist, medical, psychoanalytic, cultural, curricular, social, transactional, moral, and eclectic models. A case study exemplifies…

Dependent Handicapped: Curriculum Guide.

ERIC Educational Resources Information Center

Alberta Dept. of Education, Edmonton.

The curriculum guide takes a transdisciplinary approach to developing skills in severely and profoundly retarded students. The introductory section explains that the curriculum incorporates the principles of student dignity, a developmental focus, normalization and a continuum of services, and systematic teaching strategies. Offered are guidelines…

The mathematics behind chimera states

NASA Astrophysics Data System (ADS)

Omel’chenko, O. E.

2018-05-01

Chimera states are self-organized spatiotemporal patterns of coexisting coherence and incoherence. We give an overview of the main mathematical methods used in studies of chimera states, focusing on chimera states in spatially extended coupled oscillator systems. We discuss the continuum limit approach to these states, Ott-Antonsen manifold reduction, finite size chimera states, control of chimera states and the influence of system design on the type of chimera state that is observed.

Recent literature on structural modeling, identification, and analysis

NASA Technical Reports Server (NTRS)

Craig, Roy R., Jr.

1990-01-01

The literature on the mathematical modeling of large space structures is first reviewed, with attention given to continuum models, model order reduction, substructuring, and computational techniques. System identification and mode verification are then discussed with reference to the verification of mathematical models of large space structures. In connection with analysis, the paper surveys recent research on eigensolvers and dynamic response solvers for large-order finite-element-based models.

Industry-Education Partnerships: Bridging the Gap Between the Workplace and the Classroom

NASA Astrophysics Data System (ADS)

Harpole, S. H.

2004-12-01

Across the nation, business and industry are increasingly concerned about the quality of today's workforce and are issuing policy statements on both teacher preparation and teacher enhancement. Educational partnerships with industry are critical to the economic growth of the nation, particularly in rural areas where 31 percent of the nation's public schools are located. Through quality learning experiences that result from research/industry internships, teachers can better prepare for the 21st century workforce, become more aware of career opportunities, and emphasize the importance of preparation in science, technology, engineering and mathematics. To provide a model for successful industry-education partnerships, Mississippi State University is building on projects funded by the National Science Foundation, other funding agencies, and private foundations involving research/industry experiences for teachers. Industry-Education Partnerships: A Model for the Teacher Professional Continuum (NSF ESI-0353441) is developing a learning community model that spans the education continuum, connecting education and industry while focusing on preparing students to enter a workplace based on a global economy and researching the factors that contribute to successful partnerships. Research/work experiences will be provided to science, technology, engineering and mathematics (STEM) participants covering the teacher continuum.

Teaching Mathematics through Multicultural Literature

ERIC Educational Resources Information Center

Iliev, Nevin; D'Angelo, Frank

2014-01-01

Incorporating the use of children's literature when teaching mathematics to young children is a developmentally appropriate practice: "Literature … provides a means for children to encounter mathematical concepts and vocabulary in the context of something familiar, a story" (Fogelberg et al. 2008). Moreover, introducing culturally…

Gender identity disorder: a literature review from a developmental perspective.

PubMed

Shechner, Tomer

2010-01-01

The present paper reviews the theoretical and empirical literature on children and adolescents with gender variant behaviors. The organizational framework underlying this review is one that presents gender behavior in children and adolescents as a continuum rather than as a dichotomy of normal versus abnormal categories. Seven domains are reviewed in relation to gender variant behavior in general, and to Gender Identity Disorder (GID) in particular: theories of normative gender development, phenomenology, prevalence, assessment, developmental trajectories, comorbidity and treatment.

Co-Occurrence of Developmental Disorders: The Case of Developmental Dyscalculia

ERIC Educational Resources Information Center

Rubinsten, Orly

2009-01-01

Five to seven percent of children experience severe difficulties in learning mathematics and/or reading. Current trials that are focused on identifying biological markers suggest that these learning disabilities, known as Developmental Dyscalculia (DD) and Dyslexia (for reading), are due to underlying brain dysfunctions. One ongoing controversy…

Developmental Math: What's the Answer?

ERIC Educational Resources Information Center

Cafarella, Brian

2016-01-01

Developmental mathematics has been under the radar within higher education for some time. The reality is that there are many proven best practices in developmental math. Unfortunately, there are many obstacles that prevent student success. Moreover, the high rates of attrition and failure have led state legislators and college administrators to…

Modelling and Optimizing Mathematics Learning in Children

ERIC Educational Resources Information Center

Käser, Tanja; Busetto, Alberto Giovanni; Solenthaler, Barbara; Baschera, Gian-Marco; Kohn, Juliane; Kucian, Karin; von Aster, Michael; Gross, Markus

2013-01-01

This study introduces a student model and control algorithm, optimizing mathematics learning in children. The adaptive system is integrated into a computer-based training system for enhancing numerical cognition aimed at children with developmental dyscalculia or difficulties in learning mathematics. The student model consists of a dynamic…

Limb movements during embryonic development in the chick: evidence for a continuum in limb motor control antecedent to locomotion.

PubMed

Bradley, Nina S; Solanki, Dhara; Zhao, Dawn

2005-12-01

New imaging technologies are revealing ever-greater details of motor behavior in fetuses for clinical diagnosis and treatment. Understanding the form, mechanisms, and significance of fetal behavior will maximize imaging applications. The chick is readily available for experimentation throughout embryogenesis, making it an excellent model for this purpose. Yet in 40 yr since Hamburger and colleagues described chick embryonic behavior, we have not determined if motility belongs to a developmental continuum fundamental to posthatching behavior. This study examined kinematics and synchronized electromyography (EMG) during spontaneous limb movements in chicks at four time points between embryonic days (E) 9-18. We report that coordinated kinematic and/or EMG patterns were expressed at each time point. Variability observed in knee and ankle excursions at E15-E18 sorted into distinct in-phase and out-of-phase patterns. EMG patterns did not directly account for out-of-phase patterns, indicating study of movement biomechanics will be critical to fully understand motor control in the embryo. We also provide the first descriptions of 2- to 10-Hz limb movements emerging E15-E18 and a shift from in-phase to out-of-phase interlimb coordination E9-E18. Our findings revealed that coordinated limb movements persist across development and suggest they belong to a developmental continuum for locomotion. Limb patterns were consistent with the half center model for a locomotor pattern generator. Achievement of these patterns by E9 may thus indicate the embryo has completed a critical phase beyond which developmental progression may be less vulnerable to experimental perturbations or prenatal events.

A mathematical applications into the cells.

PubMed

Tiwari, Manjul

2012-01-01

Biology has become the new "physics" of mathematics, one of the areas of greatest mathematical applications. In turn, mathematics has provided powerful tools and metaphors to approach the astonishing complexity of biological systems. This has allowed the development of sound theoretical frameworks. Here, in this review article, some of the most significant contributions of mathematics to biology, ranging from population genetics, to developmental biology, and to networks of species interactions are summarized.

The Relationship of High School Preparation in Mathematics to the Enrollment of College Freshman in Postsecondary Developmental Mathematics Courses

ERIC Educational Resources Information Center

Lang, Erick

2012-01-01

A student's mathematical preparation is important in readiness for postsecondary study and ultimately success in a global job market. Nationally, a significant number of students are leaving high school unprepared for college-level course work in mathematics. A 2008 National Center for Educational Statistics report on Community Colleges indicates…

Characteristics and Impact of the Further Mathematics Knowledge Networks: Analysis of an English Professional Development Initiative on the Teaching of Advanced Mathematics

ERIC Educational Resources Information Center

Ruthven, Kenneth

2014-01-01

Reports from 13 Further Mathematics Knowledge Networks supported by the National Centre for Excellence in the Teaching of Mathematics [NCETM] are analysed. After summarizing basic characteristics of the networks regarding leadership, composition and pattern of activity, each of the following aspects is examined in greater depth: Developmental aims…

Developing Teaching of Mathematics to First Year Engineering Students

ERIC Educational Resources Information Center

Jaworski, Barbara; Matthews, Janette

2011-01-01

Engineering Students Understanding Mathematics (ESUM) is a developmental research project at a UK university. The motivating aim is that engineering students should develop a more conceptual understanding of mathematics through their participation in an innovation in teaching. A small research team has both studied and contributed to innovation,…

Discussion from a Mathematics Education Perspective

ERIC Educational Resources Information Center

Clements, Douglas; Sarama, Julie

2015-01-01

In a review of the special issue, we conclude that the articles are research gems in the domain of preschool mathematics education. Most share several features, such as their perspective on research methodology and their view of mathematics thinking and learning. They address the cognitive architecture and processes and the developmental levels…

Using Technology to Meet the Developmental Needs of Deaf Students To Improve Their Mathematical Word Problem Solving Skills.

ERIC Educational Resources Information Center

Kelly, Ronald R.

2003-01-01

Presents "Project Solve," a web-based problem-solving instruction and guided practice for mathematical word problems. Discusses implications for college students for whom reading and comprehension of mathematical word problem solving are difficult, especially learning disabled students. (Author/KHR)

Mathematical Meaning-Making and Its Relation to Design of Teaching

ERIC Educational Resources Information Center

Jaworski, Barbara

2015-01-01

This paper addresses the design of teaching to promote engineering students' conceptual understanding of mathematics, and its outcomes for mathematical meaning-making. Within a developmental research approach, inquiry-based tasks have been designed and evaluated, through the use of competencies proposed for their potential to promote conceptual…

[A magnetoencephalographic study of generalised developmental disorders. A new proposal for their classification].

PubMed

Muñoz Yunta, J A; Palau Baduell, M; Salvado Salvado, B; Amo, C; Fernandez Lucas, A; Maestu, F; Ortiz, T

2004-02-01

Autistic spectrum disorders (ASD) is a term that is not included in DSM IV or in ICD 10, which are the diagnostic tools most commonly used by clinical professionals but can offer problems in research when it comes to finding homogenous groups. From a neuropaediatric point of view, there is a need for a classification of the generalised disorders affecting development and for this purpose we used Wing's triad, which defines the continuum of the autistic spectrum, and the information provided by magnetoencephalography (MEG) as grouping elements. Specific generalised developmental disorders were taken as being those syndromes that partially expressed some autistic trait, but with their own personality so that they could be considered to be a specific disorder. ASD were classified as being primary, cryptogenic or secondary. The primary disorders, in turn, express a continuum that ranges from Savant syndrome to Asperger's syndrome and the different degrees of early infantile autism. MEG is a functional neuroimaging technique that has enabled us to back up this classification.

Classification of self-injurious behaviour across the continuum of relative environmental-biological influence.

PubMed

Hagopian, L P; Frank-Crawford, M A

2017-10-13

Self-injurious behaviour (SIB) is generally considered to be the product of interactions between dysfunction stemming from the primary developmental disability and experiences that occasion and reinforce SIB. As a result of these complex interactions, SIB presents as a heterogeneous problem. Recent research delineating subtypes of SIB that are nonsocially mediated, including one that is amenable to change and one that is highly invariant, enables classification of SIB across a broader continuum of relative environmental-biological influence. Directly examining how the functional classes of SIB differ has the potential to structure research, will improve our understanding this problem, and lead to more targeted behavioural and pharmacological interventions. Recognising that SIB is not a single entity but is composed of distinct functional classes would better align research with conceptual models that view SIB as the product of interactions between environmental and biological variables. © 2017 MENCAP and International Association of the Scientific Study of Intellectual and Developmental Disabilities and John Wiley & Sons Ltd.

Measuring Student Success from a Developmental Mathematics Course at an Elite Public Institution

ERIC Educational Resources Information Center

Hsu, Julian; Gehring, William J.

2016-01-01

This paper asks whether placement recommendations for a developmental math course at an elite public institution impact students' future academic performance, course-taking, and college outcomes. Researchers use these specific outcomes to measure whether developmental courses help students develop the skills necessary to succeed in college,…

Learning to Apply Algebra in the Community for Adults With Intellectual Developmental Disabilities.

PubMed

Rodriguez, Anthony M

2016-02-01

Students with intellectual and developmental disabilities (IDD) are routinely excluded from algebra and other high-level mathematics courses. High school students with IDD take courses in arithmetic and life skills rather than having an opportunity to learn algebra. Yet algebra skills can support the learning of money and budgeting skills. This study explores the feasibility of algebra instruction for adults with IDD through an experimental curriculum. Ten individuals with IDD participated in a 6-week course framing mathematics concepts within the context of everyday challenges in handling money. The article explores classroom techniques, discusses student strategies, and proposes possible avenues for future research analyzing mathematics instructional design strategies for individuals with IDD.

Gender differences in developmental dyscalculia depend on diagnostic criteria.

PubMed

Devine, Amy; Soltész, Fruzsina; Nobes, Alison; Goswami, Usha; Szűcs, Dénes

2013-10-01

Developmental dyscalculia (DD) is a learning difficulty specific to mathematics learning. The prevalence of DD may be equivalent to that of dyslexia, posing an important challenge for effective educational provision. Nevertheless, there is no agreed definition of DD and there are controversies surrounding cutoff decisions, specificity and gender differences. In the current study, 1004 British primary school children completed mathematics and reading assessments. The prevalence of DD and gender ratio were estimated in this sample using different criteria. When using absolute thresholds, the prevalence of DD was the same for both genders regardless of the cutoff criteria applied, however gender differences emerged when using a mathematics-reading discrepancy definition. Correlations between mathematics performance and the control measures selected to identify a specific learning difficulty affect both prevalence estimates and whether a gender difference is in fact identified. Educational implications are discussed.

Observing Change in the Family Therapy Supervisory Relationship.

ERIC Educational Resources Information Center

Moy, Caryl T.; Goodman, Earl O.

A common assumption in family therapy supervision is that the relationship between supervisor and supervisee changes over time, following a developmental continuum from the tentative competency of the supervisee as a therapist to relative competency. In particular, Ard (1973) theorizes that supervisees and supervisors move steadily together…

A Comparison between a Traditional and an Accelerated, Online, Adaptive Approach to Developmental Mathematics

ERIC Educational Resources Information Center

McGee, Daniel; Vasquez, Pedro; Cajigas, Jesus

2014-01-01

The University of Puerto Rico in Mayaguez (UPRM) has found that there are disadvantages to a semester long remedial mathematics course that is administered during the freshmen year to students with mathematics deficiencies in STEM (Science, Technology, Engineering and Math) programs. Correspondingly, the UPRM designed and implemented an…

Community College Pathways: A Descriptive Report of Summative Assessments and Student Learning

ERIC Educational Resources Information Center

Strother, Scott; Sowers, Nicole

2014-01-01

Carnegie's Community College Pathways (CCP) offers two pathways, Statway® and Quantway®, that reduce the amount of time required to complete developmental mathematics and earn college-level mathematics credit. The Pathways aim to improve student success in mathematics while maintaining rigorous content, pedagogy, and learning outcomes. It is…

Adult Student Learning Behaviors in a Roadblock Mathematics Course

ERIC Educational Resources Information Center

Tennant, Aimee

2012-01-01

Adult students are a growing population on college campuses. Adult students have lower graduation rates and longer times to graduation than traditional-age students. The ability to pass a college level mathematics course is a key factor in the graduation rates of all students. Past research has identified developmental mathematics, college…

Student Accountability and Formative Assessment and Its Effects on Motivation and Academic Achievement in Developmental Mathematics

ERIC Educational Resources Information Center

Koukounas, Susan M.

2016-01-01

The purpose of this study was to investigate whether high student accountability and formative assessment affected student motivation, learning and resource management strategies, and achievement in developmental algebra I. The setting was a fifteen-week semester at a community college in suburban New York. Two sections of developmental algebra I…

Gender differences in developmental dyscalculia depend on diagnostic criteria

PubMed Central

Devine, Amy; Soltész, Fruzsina; Nobes, Alison; Goswami, Usha; Szűcs, Dénes

2013-01-01

Developmental dyscalculia (DD) is a learning difficulty specific to mathematics learning. The prevalence of DD may be equivalent to that of dyslexia, posing an important challenge for effective educational provision. Nevertheless, there is no agreed definition of DD and there are controversies surrounding cutoff decisions, specificity and gender differences. In the current study, 1004 British primary school children completed mathematics and reading assessments. The prevalence of DD and gender ratio were estimated in this sample using different criteria. When using absolute thresholds, the prevalence of DD was the same for both genders regardless of the cutoff criteria applied, however gender differences emerged when using a mathematics-reading discrepancy definition. Correlations between mathematics performance and the control measures selected to identify a specific learning difficulty affect both prevalence estimates and whether a gender difference is in fact identified. Educational implications are discussed. PMID:27667904

Towards a physics on fractals: Differential vector calculus in three-dimensional continuum with fractal metric

NASA Astrophysics Data System (ADS)

Balankin, Alexander S.; Bory-Reyes, Juan; Shapiro, Michael

2016-02-01

One way to deal with physical problems on nowhere differentiable fractals is the mapping of these problems into the corresponding problems for continuum with a proper fractal metric. On this way different definitions of the fractal metric were suggested to account for the essential fractal features. In this work we develop the metric differential vector calculus in a three-dimensional continuum with a non-Euclidean metric. The metric differential forms and Laplacian are introduced, fundamental identities for metric differential operators are established and integral theorems are proved by employing the metric version of the quaternionic analysis for the Moisil-Teodoresco operator, which has been introduced and partially developed in this paper. The relations between the metric and conventional operators are revealed. It should be emphasized that the metric vector calculus developed in this work provides a comprehensive mathematical formalism for the continuum with any suitable definition of fractal metric. This offers a novel tool to study physics on fractals.

Developmental dynamics between mathematical performance, task motivation, and teachers' goals during the transition to primary school.

PubMed

Aunola, Kaisa; Leskinen, Esko; Nurmi, Jari-Erik

2006-03-01

It has been suggested that children's learning motivation and interest in a particular subject play an important role in their school performance, particularly in mathematics. However, few cross-lagged longitudinal studies have been carried out to investigate the prospective relationships between academic achievement and task motivation. Moreover, the role that the classroom context plays in this development is largely unknown. The aim of the study was to investigate the developmental dynamics of maths-related motivation and mathematical performance during children's transition to primary school. The role of teachers' pedagogical goals and classroom characteristics on this development was also investigated. A total of 196 Finnish children were examined four times: (0) in October during their preschool year; (1) in October and (2) April during their first grade of primary school; and (3) in October during their second grade. Children's mathematical performance was tested at each measurement point. Task motivation was examined at measurement points 2, 3, and 4 using the Task-value scale for children. First-grade teachers were interviewed in November about their pedagogical goals and classroom characteristics. The results showed that children's mathematical performance and related task motivation formed a cumulative developmental cycle: a high level of maths performance at the beginning of the first grade increased subsequent task motivation towards mathematics, which further predicted a high level of maths performance at the beginning of the second grade. The level of maths-related task motivation increased in those classrooms where the teachers emphasized motivation or self-concept development as their most important pedagogical goal.

What Community College Developmental Mathematics Students Understand about Mathematics

ERIC Educational Resources Information Center

Stigler, James W.; Givvin, Karen B.; Thompson, Belinda J.

2010-01-01

The nation is facing a crisis in its community colleges: more and more students are attending community colleges, but most of them are not prepared for college-level work. The problem may be most dire in mathematics. By most accounts, the majority of students entering community colleges are placed (based on placement test performance) into…

The Development of Logico-Mathematical Knowledge in a Block-Building Activity at Ages 1-4

ERIC Educational Resources Information Center

Kamii, Constance; Miyakawa, Yoko; Kato, Yasuhiko

2004-01-01

To study the developmental interrelationships among various aspects of logico-mathematical knowledge, 80 one- to 4-year-olds were individually asked to build "something tall" with 20 blocks. Percentages of new and significant behaviors increased with age and were analyzed in terms of the development of logico-mathematical relationships. It was…

A Comparison Study of Student Performance and Study Habits in College Algebra at a Hispanic Serving College

ERIC Educational Resources Information Center

Salinas, Lelia

2011-01-01

Large numbers of students arrive at colleges and universities unprepared, specifically in the area of mathematics. In Texas, approximately 47% of entering freshman students enroll in developmental mathematics. Mathematics is cited in the literature as cornerstone for success in science, and advanced technology. In this study, the extent to which…

The Rational Number Sub-Constructs as a Foundation for Problem Solving

ERIC Educational Resources Information Center

Doyle, Kathleen M.; Dias, Olen; Kennis, James R.; Czarnocha, Bronislaw; Baker, William

2016-01-01

One of the many roles of two year community colleges in the United States is to bridge the gap between secondary school and college for students who graduate from high school with weak mathematics skills that prevent them from enrolling in college level mathematics courses. At community colleges remedial or developmental mathematics courses review…

Differences in Developmental Education Enrollment and Performance at Texas 4-Year Universities: A Multiyear, Statewide Study

ERIC Educational Resources Information Center

Priesmeyer, Kimberly

2017-01-01

Purpose: The purpose of this journal-ready dissertation was to analyze the numbers and percentages of students enrolled in developmental education in reading, mathematics, and writing at 4-year universities in Texas from the 2002-2003 through the 2009-2010 academic years. In addition, students who were enrolled in developmental education in…

Computer Simulations: Inelegant Mathematics and Worse Social Science?

ERIC Educational Resources Information Center

Alker, Hayward R., Jr.

1974-01-01

Achievements, limitations, and difficulties of social science simulation efforts are discussed with particular reference to three examples. The pedagogical use of complementary developmental, philosophical, mathematical, and scientific approaches is advocated to minimize potential abuses of social simulation research. (LS)

Mathematical and Computational Aspects Related to Soil Modeling and Simulation

DTIC Science & Technology

2017-09-26

and simulation challenges at the interface of applied math (homogenization, handling of discontinuous behavior, discrete vs. continuum representations...applied math tools need to be established and used to figure out how to impose compatible boundary conditions, how to better approximate the gradient

An asymptotic Reissner-Mindlin plate model

NASA Astrophysics Data System (ADS)

Licht, Christian; Weller, Thibaut

2018-06-01

A mathematical study via variational convergence of a periodic distribution of classical linearly elastic thin plates softly abutted together shows that it is not necessary to use a different continuum model nor to make constitutive symmetry hypothesis as starting points to deduce the Reissner-Mindlin plate model.

What Mathematical Competencies Are Needed for Success in College.

ERIC Educational Resources Information Center

Garofalo, Joe

1990-01-01

Identifies requisite math skills for a microeconomics course, offering samples of supply curves, demand curves, equilibrium prices, elasticity, and complex graph problems. Recommends developmental mathematics competencies, including problem solving, reasoning, connections, communication, number and operation sense, algebra, relationships,…

The Impact of Developmental Education at Triton College.

ERIC Educational Resources Information Center

Chand, Sunil

1985-01-01

Describes the following aspects of the Developmental Education Program at Triton College: student placement, courses, faculty selection, reading and writing instruction, mathematics instruction, the Learning Assistance Center (LAC), LAC tutoring, LAC special projects, LAC management, special needs assistance program for disabled students, and…

Creating a Context in the Early Childhood Classroom. Spotlight: Cosmic Education.

ERIC Educational Resources Information Center

Engel, Janet Wolfe

2002-01-01

Describes how to create a context for Cosmic Education, which develops an awareness of the interrelationships between the elements of the cosmos and the individual's place in that continuum, in the early childhood Montessori classroom. Discusses the importance of meeting the child's developmental needs, and preparing the adult teacher spiritually,…

Selected Issues on Aging.

ERIC Educational Resources Information Center

Gordon, Ruby D.

Aging is a continuum which begins at birth and ends at death. A multidisciplinary approach is necessary to the study of aging as a part of developmental psychology. The individual is a biological organism as well as a member of society. Biological adjustments to life are affected by physical changes which influence motives and emotions. Some of…

ArtBreak: A Creative Group Counseling Program for Children

ERIC Educational Resources Information Center

Ziff, Katherine; Pierce, Lori; Johanson, Susan; King, Margaret

2012-01-01

This article describes the pilot of a school-based creative group-counseling program for children called ArtBreak, a choice-based studio art experience based on the restorative possibilities of art making delineated in the expressive therapies continuum (ETC; Kagin & Lusebrink, 1978). The ETC features a developmental hierarchy in relation to how…

Does Speech Emerge from Earlier Appearing Oral Motor Behaviors?.

ERIC Educational Resources Information Center

Moore, Christopher A.; Ruark, Jacki L.

1996-01-01

This study of the oral motor behaviors of seven toddlers (age 15 months) may be interpreted to indicate that: (1) mandibular coordination follows a developmental continuum from earlier emerging behaviors, such as chewing and sucking, through babbling, to speech, or (2) unique task demands give rise to distinct mandibular coordinative constraints…

Investigating Reading Metacognitive Strategy Awareness of Elementary Children: A Developmental Continuum Emerges

ERIC Educational Resources Information Center

Cobb, Jeanne B.

2017-01-01

This article describes a descriptive study utilizing a picture protocol technique that integrated the use of photographs of good readers and children's representational drawings with informal conversations about their habits and behaviors before, during, and after reading. The research participants included 228 children in kindergarten through 5th…

Mathematical skill in individuals with Williams Syndrome: Evidence from a standardized mathematics battery

PubMed Central

O’Hearn, Kirsten; Landau, Barbara

2007-01-01

Williams syndrome (WS) is a developmental disorder associated with relatively spared verbal skills and severe visuospatial deficits. It has also been reported that individuals with WS are impaired at mathematics. We examined mathematical skills in persons with WS using the second edition of the Test of Early Mathematical Ability (TEMA-2), which measures a wide range of skills. We administered the TEMA-2 to 14 individuals with WS and 14 children matched individually for mental age on the matrices subtest of the Kaufman Brief Intelligence Test. There were no differences between groups on the overall scores on the TEMA-2. However, an item-by-item analysis revealed group differences. Participants with WS performed more poorly than controls when reporting which of two numbers was closest to a target number, a task thought to utilize a mental number line subserved by the parietal lobe, consistent with previous evidence showing parietal abnormalities in people with WS. In contrast, people with WS performed better than the control group at reading numbers, suggesting that verbal math skills may be comparatively strong in WS. These findings add to evidence that components of mathematical knowledge may be differentially damaged in developmental disorders. PMID:17482333

Mathematical skill in individuals with Williams syndrome: evidence from a standardized mathematics battery.

PubMed

O'Hearn, Kirsten; Landau, Barbara

2007-08-01

Williams syndrome (WS) is a developmental disorder associated with relatively spared verbal skills and severe visuospatial deficits. It has also been reported that individuals with WS are impaired at mathematics. We examined mathematical skills in persons with WS using the second edition of the Test of Early Mathematical Ability (TEMA-2), which measures a wide range of skills. We administered the TEMA-2 to 14 individuals with WS and 14 children matched individually for mental-age on the matrices subtest of the Kaufman Brief Intelligence Test. There were no differences between groups on the overall scores on the TEMA-2. However, an item-by-item analysis revealed group differences. Participants with WS performed more poorly than controls when reporting which of two numbers was closest to a target number, a task thought to utilize a mental number line subserved by the parietal lobe, consistent with previous evidence showing parietal abnormalities in people with WS. In contrast, people with WS performed better than the control group at reading numbers, suggesting that verbal math skills may be comparatively strong in WS. These findings add to evidence that components of mathematical knowledge may be differentially damaged in developmental disorders.

The influence of continuum radiation fields on hydrogen radio recombination lines

NASA Astrophysics Data System (ADS)

Prozesky, Andri; Smits, Derck P.

2018-05-01

Calculations of hydrogen departure coefficients using a model with the angular momentum quantum levels resolved that includes the effects of external radiation fields are presented. The stimulating processes are important at radio frequencies and can influence level populations. New numerical techniques with a solid mathematical basis have been incorporated into the model to ensure convergence of the solution. Our results differ from previous results by up to 20 per cent. A direct solver with a similar accuracy but more efficient than the iterative method is used to evaluate the influence of continuum radiation on the hydrogen population structure. The effects on departure coefficients of continuum radiation from dust, the cosmic microwave background, the stellar ionising radiation, and free-free radiation are quantified. Tables of emission and absorption coefficients for interpreting observed radio recombination lines are provided.

The Impact of Self-Selected Reading for Enjoyment (SSRE) in a Southeastern Postsecondary Developmental Reading Program: A Mixed Methods Study

ERIC Educational Resources Information Center

Rodgers, Jennifer E.

2017-01-01

Developmental courses are offered at most two year and four year colleges and universities in order to meet the instructional needs of students who have shown skill deficiencies based upon test scores in the areas of reading, English, or mathematics. The purpose of developmental reading courses at the postsecondary level is to increase students'…

Developmental gains in visuospatial memory predict gains in mathematics achievement.

PubMed

Li, Yaoran; Geary, David C

2013-01-01

Visuospatial competencies are related to performance in mathematical domains in adulthood, but are not consistently related to mathematics achievement in children. We confirmed the latter for first graders and demonstrated that children who show above average first-to-fifth grade gains in visuospatial memory have an advantage over other children in mathematics. The study involved the assessment of the mathematics and reading achievement of 177 children in kindergarten to fifth grade, inclusive, and their working memory capacity and processing speed in first and fifth grade. Intelligence was assessed in first grade and their second to fourth grade teachers reported on their in-class attentive behavior. Developmental gains in visuospatial memory span (d = 2.4) were larger than gains in the capacity of the central executive (d = 1.6) that in turn were larger than gains in phonological memory span (d = 1.1). First to fifth grade gains in visuospatial memory and in speed of numeral processing predicted end of fifth grade mathematics achievement, as did first grade central executive scores, intelligence, and in-class attentive behavior. The results suggest there are important individual differences in the rate of growth of visuospatial memory during childhood and that these differences become increasingly important for mathematics learning.

Developmental Gains in Visuospatial Memory Predict Gains in Mathematics Achievement

PubMed Central

Li, Yaoran; Geary, David C.

2013-01-01

Visuospatial competencies are related to performance in mathematical domains in adulthood, but are not consistently related to mathematics achievement in children. We confirmed the latter for first graders and demonstrated that children who show above average first-to-fifth grade gains in visuospatial memory have an advantage over other children in mathematics. The study involved the assessment of the mathematics and reading achievement of 177 children in kindergarten to fifth grade, inclusive, and their working memory capacity and processing speed in first and fifth grade. Intelligence was assessed in first grade and their second to fourth grade teachers reported on their in-class attentive behavior. Developmental gains in visuospatial memory span (d = 2.4) were larger than gains in the capacity of the central executive (d = 1.6) that in turn were larger than gains in phonological memory span (d = 1.1). First to fifth grade gains in visuospatial memory and in speed of numeral processing predicted end of fifth grade mathematics achievement, as did first grade central executive scores, intelligence, and in-class attentive behavior. The results suggest there are important individual differences in the rate of growth of visuospatial memory during childhood and that these differences become increasingly important for mathematics learning. PMID:23936154

Effectiveness of working memory training among children with dyscalculia: evidence for transfer effects on mathematical achievement-a pilot study.

PubMed

Layes, Smail; Lalonde, Robert; Bouakkaz, Yamina; Rebai, Mohamed

2017-12-22

We examined whether the working memory (WM) capacity of developmentally dyscalculic children can be improved by a WM training program and whether outcomes relate to mathematical performance. The experimental design comprised two groups with developmental dyslexia with grade 4 schooling: an experimental group (n = 14; mean age = 129.74 months) and a control group (n = 14; mean age = 126.9 months). All participants were assessed on measures of WM, mathematic attainment, and nonverbal mental ability (Raven test) before and after training. The WM training program focused on manipulating and maintaining arithmetic information. The results show that both WM and mathematical performances improved significantly after intervention, indicating a strong relationship between these two constructs. The control group improved slightly in Raven's progressive matrices and a reading number task. These findings are discussed in terms of near and far transfer toward trained and untrained skills and stress the positive impact of WM training on learning mathematics in children with dyscalculia.

Parallel multiscale simulations of a brain aneurysm

PubMed Central

Grinberg, Leopold; Fedosov, Dmitry A.; Karniadakis, George Em

2012-01-01

Cardiovascular pathologies, such as a brain aneurysm, are affected by the global blood circulation as well as by the local microrheology. Hence, developing computational models for such cases requires the coupling of disparate spatial and temporal scales often governed by diverse mathematical descriptions, e.g., by partial differential equations (continuum) and ordinary differential equations for discrete particles (atomistic). However, interfacing atomistic-based with continuum-based domain discretizations is a challenging problem that requires both mathematical and computational advances. We present here a hybrid methodology that enabled us to perform the first multi-scale simulations of platelet depositions on the wall of a brain aneurysm. The large scale flow features in the intracranial network are accurately resolved by using the high-order spectral element Navier-Stokes solver εκ αr. The blood rheology inside the aneurysm is modeled using a coarse-grained stochastic molecular dynamics approach (the dissipative particle dynamics method) implemented in the parallel code LAMMPS. The continuum and atomistic domains overlap with interface conditions provided by effective forces computed adaptively to ensure continuity of states across the interface boundary. A two-way interaction is allowed with the time-evolving boundary of the (deposited) platelet clusters tracked by an immersed boundary method. The corresponding heterogeneous solvers ( εκ αr and LAMMPS) are linked together by a computational multilevel message passing interface that facilitates modularity and high parallel efficiency. Results of multiscale simulations of clot formation inside the aneurysm in a patient-specific arterial tree are presented. We also discuss the computational challenges involved and present scalability results of our coupled solver on up to 300K computer processors. Validation of such coupled atomistic-continuum models is a main open issue that has to be addressed in future work. PMID:23734066

The archetype-genome exemplar in molecular dynamics and continuum mechanics

NASA Astrophysics Data System (ADS)

Greene, M. Steven; Li, Ying; Chen, Wei; Liu, Wing Kam

2014-04-01

We argue that mechanics and physics of solids rely on a fundamental exemplar: the apparent properties of a system depend on the building blocks that comprise it. Building blocks are referred to as archetypes and apparent system properties as the system genome. Three entities are of importance: the archetype properties, the conformation of archetypes, and the properties of interactions activated by that conformation. The combination of these entities into the system genome is called assembly. To show the utility of the archetype-genome exemplar, this work presents the mathematical ingredients and computational implementation of theories in solid mechanics that are (1) molecular and (2) continuum manifestations of the assembly process. Both coarse-grained molecular dynamics (CGMD) and the archetype-blending continuum (ABC) theories are formulated then applied to polymer nanocomposites (PNCs) to demonstrate the impact the components of the assembly triplet have on a material genome. CGMD simulations demonstrate the sensitivity of nanocomposite viscosities and diffusion coefficients to polymer chain types (archetype), polymer-nanoparticle interaction potentials (interaction), and the structural configuration (conformation) of dispersed nanoparticles. ABC simulations show the contributions of bulk polymer (archetype) properties, occluded region of bound rubber (interaction) properties, and microstructural binary images (conformation) to predictions of linear damping properties, the Payne effect, and localization/size effects in the same class of PNC material. The paper is light on mathematics. Instead, the focus is on the usefulness of the archetype-genome exemplar to predict system behavior inaccessible to classical theories by transitioning mechanics away from heuristic laws to mechanism-based ones. There are two core contributions of this research: (1) presentation of a fundamental axiom—the archetype-genome exemplar—to guide theory development in computational mechanics, and (2) demonstrations of its utility in modern theoretical realms: CGMD, and generalized continuum mechanics.

Parallel multiscale simulations of a brain aneurysm.

PubMed

Grinberg, Leopold; Fedosov, Dmitry A; Karniadakis, George Em

2013-07-01

Cardiovascular pathologies, such as a brain aneurysm, are affected by the global blood circulation as well as by the local microrheology. Hence, developing computational models for such cases requires the coupling of disparate spatial and temporal scales often governed by diverse mathematical descriptions, e.g., by partial differential equations (continuum) and ordinary differential equations for discrete particles (atomistic). However, interfacing atomistic-based with continuum-based domain discretizations is a challenging problem that requires both mathematical and computational advances. We present here a hybrid methodology that enabled us to perform the first multi-scale simulations of platelet depositions on the wall of a brain aneurysm. The large scale flow features in the intracranial network are accurately resolved by using the high-order spectral element Navier-Stokes solver εκ αr . The blood rheology inside the aneurysm is modeled using a coarse-grained stochastic molecular dynamics approach (the dissipative particle dynamics method) implemented in the parallel code LAMMPS. The continuum and atomistic domains overlap with interface conditions provided by effective forces computed adaptively to ensure continuity of states across the interface boundary. A two-way interaction is allowed with the time-evolving boundary of the (deposited) platelet clusters tracked by an immersed boundary method. The corresponding heterogeneous solvers ( εκ αr and LAMMPS) are linked together by a computational multilevel message passing interface that facilitates modularity and high parallel efficiency. Results of multiscale simulations of clot formation inside the aneurysm in a patient-specific arterial tree are presented. We also discuss the computational challenges involved and present scalability results of our coupled solver on up to 300K computer processors. Validation of such coupled atomistic-continuum models is a main open issue that has to be addressed in future work.

Parallel multiscale simulations of a brain aneurysm

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grinberg, Leopold; Fedosov, Dmitry A.; Karniadakis, George Em, E-mail: george_karniadakis@brown.edu

2013-07-01

Cardiovascular pathologies, such as a brain aneurysm, are affected by the global blood circulation as well as by the local microrheology. Hence, developing computational models for such cases requires the coupling of disparate spatial and temporal scales often governed by diverse mathematical descriptions, e.g., by partial differential equations (continuum) and ordinary differential equations for discrete particles (atomistic). However, interfacing atomistic-based with continuum-based domain discretizations is a challenging problem that requires both mathematical and computational advances. We present here a hybrid methodology that enabled us to perform the first multiscale simulations of platelet depositions on the wall of a brain aneurysm.more » The large scale flow features in the intracranial network are accurately resolved by using the high-order spectral element Navier–Stokes solver NεκTαr. The blood rheology inside the aneurysm is modeled using a coarse-grained stochastic molecular dynamics approach (the dissipative particle dynamics method) implemented in the parallel code LAMMPS. The continuum and atomistic domains overlap with interface conditions provided by effective forces computed adaptively to ensure continuity of states across the interface boundary. A two-way interaction is allowed with the time-evolving boundary of the (deposited) platelet clusters tracked by an immersed boundary method. The corresponding heterogeneous solvers (NεκTαr and LAMMPS) are linked together by a computational multilevel message passing interface that facilitates modularity and high parallel efficiency. Results of multiscale simulations of clot formation inside the aneurysm in a patient-specific arterial tree are presented. We also discuss the computational challenges involved and present scalability results of our coupled solver on up to 300 K computer processors. Validation of such coupled atomistic-continuum models is a main open issue that has to be addressed in future work.« less

Developmental dyscalculia and low numeracy in Chinese children.

PubMed

Chan, Winnie Wai Lan; Au, Terry K; Tang, Joey

2013-05-01

Children struggle with mathematics for different reasons. Developmental dyscalculia and low numeracy - two kinds of mathematical difficulties - may have their roots, respectively, in poor understanding of exact non-symbolic numerosities and of symbolic numerals. This study was the first to explore whether Chinese children, despite cultural and linguistic factors supporting their mathematical learning, also showed such mathematical difficulties and whether such difficulties have measurable impact on children's early school mathematical performance. First-graders, classified as dyscalculia, low numeracy, or normal achievement, were compared for their performance in various school mathematical tasks requiring a grasp of non-symbolic numerosities (i.e., non-symbolic tasks) or an understanding of symbolic numerals (i.e., symbolic tasks). Children with dyscalculia showed poorer performance than their peers in non-symbolic tasks but not symbolic ones, whereas those with low numeracy showed poorer performance in symbolic tasks but not non-symbolic ones. As hypothesized, these findings suggested that dyscalculia and low numeracy were distinct deficits and caused by deficits in non-symbolic and symbolic processing, respectively. These findings went beyond prior research that only documented generally low mathematical achievements for these two groups of children. Moreover, these deficits appeared to be persistent and could not be remedied simply through day-to-day school mathematical learning. The present findings highlighted the importance of tailoring early learning support for children with these distinct deficits, and pointed to future directions for the screening of such mathematical difficulties among Chinese children. Copyright © 2013 Elsevier Ltd. All rights reserved.

Students' Reflections on Mathematics Homework Feedback

ERIC Educational Resources Information Center

Landers, Mara; Reinholz, Daniel

2015-01-01

Homework is considered an important aspect of learning mathematics, but little research has considered how students utilize feedback as part of the homework process. This mixed methods, quasi-experimental study examines how community college students in a developmental intermediate algebra course participated in a feedback reflection activity…

Selected Studies on Math Placement.

ERIC Educational Resources Information Center

Akst, Geoffrey; Hirsch, Lewis

1991-01-01

Drawing from a review of the literature and direct experience, this paper discusses key issues in developmental mathematics placement. First, the controversial practice of mandatory placement is examined, citing research results that support the practice and those that do not. Next, the diversity of developmental math placement standards is…

Developmental and Individual Differences in Understanding of Fractions

ERIC Educational Resources Information Center

Siegler, Robert S.; Pyke, Aryn A.

2013-01-01

We examined developmental and individual differences in 6th and 8th graders' fraction arithmetic and overall mathematics achievement and related them to differences in understanding of fraction magnitudes, whole number division, executive functioning, and metacognitive judgments within a crosssectional design. Results indicated that the difference…

Faculty Provisions of Accommodations for Students with Disabilities in Higher Education: An Analysis of Community College Faculty in the Traditional, Hybrid, and Online Mathematics Course Teaching Environments

ERIC Educational Resources Information Center

Mongiovi, Kelly Anne

2012-01-01

The purpose of this exploratory descriptive study was to examine the mathematics faculty provisions of accommodations for students with disabilities within a Florida Community College. Both developmental and college level mathematics courses were included in this study. This study examined courses taught in the traditional, hybrid, and online…

The Comet Cometh: Evolving Developmental Systems.

PubMed

Jaeger, Johannes; Laubichler, Manfred; Callebaut, Werner

In a recent opinion piece, Denis Duboule has claimed that the increasing shift towards systems biology is driving evolutionary and developmental biology apart, and that a true reunification of these two disciplines within the framework of evolutionary developmental biology (EvoDevo) may easily take another 100 years. He identifies methodological, epistemological, and social differences as causes for this supposed separation. Our article provides a contrasting view. We argue that Duboule's prediction is based on a one-sided understanding of systems biology as a science that is only interested in functional, not evolutionary, aspects of biological processes. Instead, we propose a research program for an evolutionary systems biology, which is based on local exploration of the configuration space in evolving developmental systems. We call this approach-which is based on reverse engineering, simulation, and mathematical analysis-the natural history of configuration space. We discuss a number of illustrative examples that demonstrate the past success of local exploration, as opposed to global mapping, in different biological contexts. We argue that this pragmatic mode of inquiry can be extended and applied to the mathematical analysis of the developmental repertoire and evolutionary potential of evolving developmental mechanisms and that evolutionary systems biology so conceived provides a pragmatic epistemological framework for the EvoDevo synthesis.

The role of mathematical models in understanding pattern formation in developmental biology.

PubMed

Umulis, David M; Othmer, Hans G

2015-05-01

In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics-whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: "It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations." This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, "The laws of Nature are written in the language of mathematics[Formula: see text] the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word." Mathematics has moved beyond the geometry-based model of Galileo's time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837-838, 2013). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades-that of how organisms can scale in size. Mathematical analysis alone cannot "solve" these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology.

Mathematical and computational modelling of skin biophysics: a review

PubMed Central

2017-01-01

The objective of this paper is to provide a review on some aspects of the mathematical and computational modelling of skin biophysics, with special focus on constitutive theories based on nonlinear continuum mechanics from elasticity, through anelasticity, including growth, to thermoelasticity. Microstructural and phenomenological approaches combining imaging techniques are also discussed. Finally, recent research applications on skin wrinkles will be presented to highlight the potential of physics-based modelling of skin in tackling global challenges such as ageing of the population and the associated skin degradation, diseases and traumas. PMID:28804267

Mathematical and computational modelling of skin biophysics: a review

NASA Astrophysics Data System (ADS)

Limbert, Georges

2017-07-01

The objective of this paper is to provide a review on some aspects of the mathematical and computational modelling of skin biophysics, with special focus on constitutive theories based on nonlinear continuum mechanics from elasticity, through anelasticity, including growth, to thermoelasticity. Microstructural and phenomenological approaches combining imaging techniques are also discussed. Finally, recent research applications on skin wrinkles will be presented to highlight the potential of physics-based modelling of skin in tackling global challenges such as ageing of the population and the associated skin degradation, diseases and traumas.

The mathematical modeling of rapid solidification processing. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Gutierrez-Miravete, E.

1986-01-01

The detailed formulation of and the results obtained from a continuum mechanics-based mathematical model of the planar flow melt spinning (PFMS) rapid solidification system are presented and discussed. The numerical algorithm proposed is capable of computing the cooling and freezing rates as well as the fluid flow and capillary phenomena which take place inside the molten puddle formed in the PFMS process. The FORTRAN listings of some of the most useful computer programs and a collection of appendices describing the basic equations used for the modeling are included.

Long-Term Care for People with Development Disabilities: A Critical Analysis.

ERIC Educational Resources Information Center

Palley, Howard A.; Van Hollen, Valerie

2000-01-01

Explores how the trends toward long-term community care affecting people with developmental disabilities developed. Appropriateness of care and quality of life issues are discussed. Reviews the development of long-term care for frail and disabled elderly people and explores the arguments for a continuum of care that have developed in this area.…

Detrimental Psychological Outcomes Associated with Pubertal Timing in Adolescent Boys

ERIC Educational Resources Information Center

Mendle, Jane; Ferrero, Joseph

2012-01-01

Though often discussed as a discrete event, puberty comprises one segment of a larger developmental continuum and is notable for rapid transformation across a multitude of domains. While an earlier timing of puberty relative to peers stands as one of the most well-replicated antecedents of adolescent difficulties for girls, findings have been less…

The Effect of Feature Complexity in Spanish Spelling in Grades 1-3

ERIC Educational Resources Information Center

Ford, Karen L.; Invernizzi, Marcia; Huang, Francis L.

2014-01-01

The current study explored a possible continuum of spelling features that children receiving literacy instruction in Spanish might be expected to master in Grades 1-3. We administered a developmental spelling inventory representing nine distinct Spanish spelling features to 864 students in bilingual and dual language schools across the U.S.…

Enhancing Emergent Literacy Skills in Inclusive Preschools for Young Children with Visual Impairments

ERIC Educational Resources Information Center

Day, Janice Neibaur; McDonnell, Andrea P.; Heathfield, Lora Tuesday

2005-01-01

Emergent literacy can be viewed as skills that are precursors to later reading and writing (Sulzby & Teale, 1991) or can be more broadly conceptualized as literacy acquisition that occurs along a developmental continuum. Because children with disabilities, such as visual impairments, can be at risk for later reading difficulties, it is critical…

From Crib to Kindergarten: A Continuum of Needs of the Visually Impaired Preschooler.

ERIC Educational Resources Information Center

Harrell, Lois

The paper focuses on the needs of visually impaired preschoolers in various developmental areas. The importance of attachment to a significant other for establishing trust is outlined and the fact that body awareness, object permanence, range of motion, spatial awareness and orientation must be logically and actively introduced is cited. Aspects…

More than Math: On the Affective Domain in Developmental Mathematics

ERIC Educational Resources Information Center

Guy, G. Michael; Cornick, Jonathan; Beckford, Ian

2015-01-01

Students at a large urban community college enrolled in fourteen sections of a developmental algebra class. While cognitive variables are often used to place students, affective characteristics may also influence their success. To explore the impact of affective variables, students took ACT's Engage survey measuring motivation, academic-related…

E-Sponsor Mentoring: Support for Students in Developmental Education

ERIC Educational Resources Information Center

Hodges, Russ; Payne, Emily Miller; Dietz, Albert; Hajovsky, Michelle

2014-01-01

Researchers investigated the use of two mentoring programs for students who were part of a support component of Fundamentals of Conceptual Understanding and Success (FOCUS), a comprehensive intervention grant for students enrolled in developmental mathematics coursework at a large public Texas university. The technology-based mentoring program,…

Exploring Attitudes and Achievement of Web-Based Homework in Developmental Algebra

ERIC Educational Resources Information Center

Leong, Kwan Eu; Alexander, Nathan

2013-01-01

The purpose of this study was to understand how students' attitudes were connected to their mathematics learning. This investigation was specific to web-based homework in developmental courses in the community college environment. The mixed-methods approach was used to analyze the relationship between students' attitudes and mathematical…

Gender Differences in Developmental Dyscalculia Depend on Diagnostic Criteria

ERIC Educational Resources Information Center

Devine, Amy; Soltesz, Fruzsina; Nobes, Alison; Goswami, Usha; Szucs, Denes

2013-01-01

Developmental dyscalculia (DD) is a learning difficulty specific to mathematics learning. The prevalence of DD may be equivalent to that of dyslexia, posing an important challenge for effective educational provision. Nevertheless, there is no agreed definition of DD and there are controversies surrounding cutoff decisions, specificity and gender…

CAI and Developmental Education.

ERIC Educational Resources Information Center

Anderson, Rick

This paper discusses the problems and achievements of computer assisted instruction (CAI) projects at University College, University of Cincinnati. The most intensive use of CAI on campus, the CAI Lab, is part of the Developmental Education Center's effort to serve students who lack mastery of basic college-level skills in mathematics and English.…

Improving Math Success in Higher Education Institutions

ERIC Educational Resources Information Center

Bisk, Richard

2013-01-01

Many students begin higher education unprepared for college-level work in mathematics and must take non-credit developmental courses. Furthermore, many are "math-phobic" and avoid courses, majors and careers that involve quantitative work. Yet science, technology, engineering and mathematics (STEM) fields are among the few job-growth…

Differentiated Instruction in Developmental Mathematics Classes and Achievement of Ethnic Minority Students

ERIC Educational Resources Information Center

Hood, Otis D., Jr.

2012-01-01

National educational assessment organizations present statistical information that an achievement gap exists between White students and students of color. This achievement gap closely relates to students representing lower SES conditions. This study examined the lack of achievement for ethnic minorities in the field of mathematics using an…

Exploring Students' Technology Acceptance in College Developmental Mathematics

ERIC Educational Resources Information Center

Williams, Handan

2012-01-01

Technology has become a large component of teaching and learning in mathematics education. Gaining insight into students' technology acceptance factors is a crucial step in understanding instructional design and implementation of technology-based learning programs. Despite the widespread use of technology in education, few research efforts…

The Challenge of Formative Assessment in Mathematics Education: Children's Minds, Teachers' Minds

ERIC Educational Resources Information Center

Ginsburg, Herbert P.

2009-01-01

The developmental psychology of mathematical thinking and the clinical interview method can make major contributions to education by transforming the process of formative assessment--the attempt to use information concerning student performance, knowledge, learning potential, and motivation to inform instruction. The clinical interview is a…

Community College Developmental Education Students' Understanding of Foundational Fraction Concepts

ERIC Educational Resources Information Center

Alexander, Cathleen Marie

2013-01-01

Mathematics, in general, and algebra courses, in particular, have been categorized as "gatekeepers" for higher education, better jobs, and even citizenship. For many low-income and working adults, community college is the institution where they choose to develop their mathematics understanding so they can pursue their dreams.…

Fractions Learning in Children with Mathematics Difficulties

ERIC Educational Resources Information Center

Tian, Jing; Siegler, Robert S.

2017-01-01

Learning fractions is difficult for children in general and especially difficult for children with mathematics difficulties (MD). Recent research on developmental and individual differences in fraction knowledge of children with MD and typically achieving (TA) children has demonstrated that U.S. children with MD start middle school behind their TA…

Fractions Learning in Children with Mathematics Difficulties

ERIC Educational Resources Information Center

Tian, Jing; Siegler, Robert S.

2016-01-01

Learning of fractions is difficult for children in general and especially difficult for children with mathematics difficulties (MD). Recent research on developmental and individual differences in fraction knowledge of MD and typically achieving (TA) children has demonstrated that U.S. children with MD start middle school behind TA peers in…

Playing Mathematical Instruments: Emerging Perceptuomotor Integration with an Interactive Mathematics Exhibit

ERIC Educational Resources Information Center

Nemirovsky, Ricardo; Kelton, Molly L.; Rhodehamel, Bohdan

2013-01-01

Research in experimental and developmental psychology, cognitive science, and neuroscience suggests that tool fluency depends on the merging of perceptual and motor aspects of its use, an achievement the authors call "perceptuomotor integration." Just as expertise in playing a piano relies on the interanimation of finger movements and…

The Relationship of Drawing and Mathematical Problem Solving: "Draw for Math" Tasks

ERIC Educational Resources Information Center

Edens, Kellah; Potter, Ellen

2007-01-01

This study examines a series of children's drawings ("Draw for Math" tasks) to determine the relationship of students' spatial understanding and mathematical problem solving. Level of spatial understanding was assessed by applying the framework of central conceptual structures suggested by Case (1996), a cognitive developmental researcher.…

Fundamentals of continuum mechanics – classical approaches and new trends

NASA Astrophysics Data System (ADS)

Altenbach, H.

2018-04-01

Continuum mechanics is a branch of mechanics that deals with the analysis of the mechanical behavior of materials modeled as a continuous manifold. Continuum mechanics models begin mostly by introducing of three-dimensional Euclidean space. The points within this region are defined as material points with prescribed properties. Each material point is characterized by a position vector which is continuous in time. Thus, the body changes in a way which is realistic, globally invertible at all times and orientation-preserving, so that the body cannot intersect itself and as transformations which produce mirror reflections are not possible in nature. For the mathematical formulation of the model it is also assumed to be twice continuously differentiable, so that differential equations describing the motion may be formulated. Finally, the kinematical relations, the balance equations, the constitutive and evolution equations and the boundary and/or initial conditions should be defined. If the physical fields are non-smooth jump conditions must be taken into account. The basic equations of continuum mechanics are presented following a short introduction. Additionally, some examples of solid deformable continua will be discussed within the presentation. Finally, advanced models of continuum mechanics will be introduced. The paper is dedicated to Alexander Manzhirov’s 60th birthday.

Modal kinematics for multisection continuum arms.

PubMed

Godage, Isuru S; Medrano-Cerda, Gustavo A; Branson, David T; Guglielmino, Emanuele; Caldwell, Darwin G

2015-05-13

This paper presents a novel spatial kinematic model for multisection continuum arms based on mode shape functions (MSF). Modal methods have been used in many disciplines from finite element methods to structural analysis to approximate complex and nonlinear parametric variations with simple mathematical functions. Given certain constraints and required accuracy, this helps to simplify complex phenomena with numerically efficient implementations leading to fast computations. A successful application of the modal approximation techniques to develop a new modal kinematic model for general variable length multisection continuum arms is discussed. The proposed method solves the limitations associated with previous models and introduces a new approach for readily deriving exact, singularity-free and unique MSF's that simplifies the approach and avoids mode switching. The model is able to simulate spatial bending as well as straight arm motions (i.e., pure elongation/contraction), and introduces inverse position and orientation kinematics for multisection continuum arms. A kinematic decoupling feature, splitting position and orientation inverse kinematics is introduced. This type of decoupling has not been presented for these types of robotic arms before. The model also carefully accounts for physical constraints in the joint space to provide enhanced insight into practical mechanics and impose actuator mechanical limitations onto the kinematics thus generating fully realizable results. The proposed method is easily applicable to a broad spectrum of continuum arm designs.

The link between logic, mathematics and imagination: evidence from children with developmental dyscalculia and mathematically gifted children.

PubMed

Morsanyi, Kinga; Devine, Amy; Nobes, Alison; Szűcs, Dénes

2013-07-01

This study examined performance on transitive inference problems in children with developmental dyscalculia (DD), typically developing controls matched on IQ, working memory and reading skills, and in children with outstanding mathematical abilities. Whereas mainstream approaches currently consider DD as a domain-specific deficit, we hypothesized that the development of mathematical skills is closely related to the development of logical abilities, a domain-general skill. In particular, we expected a close link between mathematical skills and the ability to reason independently of one's beliefs. Our results showed that this was indeed the case, with children with DD performing more poorly than controls, and high maths ability children showing outstanding skills in logical reasoning about belief-laden problems. Nevertheless, all groups performed poorly on structurally equivalent problems with belief-neutral content. This is in line with suggestions that abstract reasoning skills (i.e. the ability to reason about content without real-life referents) develops later than the ability to reason about belief-inconsistent fantasy content.A video abstract of this article can be viewed at http://www.youtube.com/watch?v=90DWY3O4xx8. © 2013 Blackwell Publishing Ltd.

Multicultural and multilingual approach: Mathematics, science, and engineering education for junior high school minority students and high school administrators. Final report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Crumbly, I.J.; Hodges, J.

1994-09-01

During the 1993 school year, LLNL and the US Department of Energy`s San Francisco Field Office provided funds through grant {number_sign}DE-FG03-93SF20045/A000 to assist Cooperative Developmental Energy Program (CDEP) with its network coalition of high school counselors from 19 states and with its outreach and early intervention program in mathematics, science and engineering for minority junior high school students. The program for high school counselors is called the National Educators Orientation Program (NEOP) and the outreach program for minority junior high school students is called the Mathematics, Science and Engineering Academy (MSEA). A total of 35 minority and female rising eighthmore » grade students participated in the Second Annual Mathematics, Science, and Engineering Academy sponsored by the Cooperative Developmental Energy Program of Fort Valley State College (FVSC). There were 24 students from the middle Georgia area, 4 students from Oakland, California, and 7 students from Portland, Oregon. Each student was selected by counselor in his or her respective school. The selection criteria were based on the students` academic performance in science and mathematics courses.« less

Determining Dynamical Path Distributions usingMaximum Relative Entropy

DTIC Science & Technology

2015-05-31

entropy to a one-dimensional continuum labeled by a parameter η. The resulting η-entropies are equivalent to those proposed by Renyi [12] or by Tsallis [13...1995). [12] A. Renyi , “On measures of entropy and information,”Proc. 4th Berkeley Simposium on Mathematical Statistics and Probability, Vol 1, p. 547-461

Fostering Culturally and Developmentally Responsive Teaching through Improvisational Practice

ERIC Educational Resources Information Center

Graue, Elizabeth; Whyte, Kristin; Delaney, Kate Kresin

2014-01-01

In this article we explore an effort to rethink curricular decision-making with a group of public pre-K teachers working in a context of curriculum escalation and commitment to play-based pedagogy. Through a professional development program designed to support developmentally and culturally responsive early mathematics, we examine how teachers…

Mapping Success: Performance-Based Scholarships, Student Services, and Developmental Math at Hillsborough Community College

ERIC Educational Resources Information Center

Sommo, Colleen; Boynton, Melissa; Collado, Herbert; Diamond, John; Gardenhire, Alissa; Ratledge, Alyssa; Rudd, Timothy; Weiss, Michael J.

2014-01-01

In 2010, Hillsborough Community College (HCC), a large multicampus institution in Tampa, Florida, worked with MDRC to create the Mathematics Access Performance Scholarship (MAPS) program to help academically underprepared community college students succeed in developmental math. MAPS provides an incentive for low-income students referred to…

Arithmetic Abilities in Children with Developmental Dyslexia: Performance on French ZAREKI-R Test

ERIC Educational Resources Information Center

De Clercq-Quaegebeur, Maryse; Casalis, Séverine; Vilette, Bruno; Lemaitre, Marie-Pierre; Vallée, Louis

2018-01-01

A high comorbidity between reading and arithmetic disabilities has already been reported. The present study aims at identifying more precisely patterns of arithmetic performance in children with developmental dyslexia, defined with severe and specific criteria. By means of a standardized test of achievement in mathematics ("Calculation and…

Specifying Theories of Developmental Dyslexia: A Diffusion Model Analysis of Word Recognition

ERIC Educational Resources Information Center

Zeguers, Maaike H. T.; Snellings, Patrick; Tijms, Jurgen; Weeda, Wouter D.; Tamboer, Peter; Bexkens, Anika; Huizenga, Hilde M.

2011-01-01

The nature of word recognition difficulties in developmental dyslexia is still a topic of controversy. We investigated the contribution of phonological processing deficits and uncertainty to the word recognition difficulties of dyslexic children by mathematical diffusion modeling of visual and auditory lexical decision data. The first study showed…

Effectiveness of a Corequisite Delivery Model for Developmental Mathematics

ERIC Educational Resources Information Center

Fair, Katherine Eileen

2017-01-01

The purpose of this quantitative quasi-experimental study is to determine the effectiveness of a corequisite delivery model for developmental math students at a 4-year public institution. Nationally, close to fifty percent of incoming college students are placed in non-credit bearing remedial courses (Complete College America, 2012). Students must…

The Creative Curriculum[R] for Preschool: Developmental Continuum Assessment Toolkit for Ages 3-5.

ERIC Educational Resources Information Center

Dodge, Diane Trister; Colker, Laura J.; Heroman, Cate

Intended for use with the Creative Curriculum for Early Childhood, this integrated ongoing student assessment toolkit is designed for preschool teachers to help them focus on all aspects of a child's development, thereby giving them a way to ensure that all children in their classes are making progress. The assessment kit uses a strength-based…

Using Case Study Multi-Methods to Investigate Close(r) Collaboration: Course-Based Tutoring and the Directive/Nondirective Instructional Continuum

ERIC Educational Resources Information Center

Corbett, Steven J.

2011-01-01

This essay presents case studies of "course-based tutoring" (CBT) and one-to-one tutorials in two sections of developmental first-year composition (FYC) at a large West Coast research university. The author's study uses a combination of rhetorical and discourse analyses and ethnographic and case study multi-methods to investigate both…

Embracing the Big Picture: The State of New Jersey's Road toward a PK3 Continuum. ACNJ Policy Brief

ERIC Educational Resources Information Center

Rice, Cynthia

2007-01-01

There is evidence demonstrating that when young children are part of a learning environment that is based on high standards/expectations, administrative and teacher leadership and continuity in learning opportunities across these grades, the better their developmental outcomes will be through grade three and in future years. By experiencing an…

The Empathizing-Systemizing Theory, Social Abilities, and Mathematical Achievement in Children

PubMed Central

Escovar, Emily; Rosenberg-Lee, Miriam; Uddin, Lucina Q.; Menon, Vinod

2016-01-01

The Empathizing-Systemizing (E-S) theory describes a profile of traits that have been linked to autism spectrum disorders, and are thought to encompass a continuum that includes typically developing (TD) individuals. Although systemizing is hypothesized to be related to mathematical abilities, empirical support for this relationship is lacking. We examine the link between empathizing and systemizing tendencies and mathematical achievement in 112 TD children (57 girls) to elucidate how socio-cognitive constructs influence early development of mathematical skills. Assessment of mathematical achievement included standardized tests designed to examine calculation skills and conceptual mathematical reasoning. Empathizing and systemizing were assessed using the Combined Empathy Quotient-Child (EQ-C) and Systemizing Quotient-Child (SQ-C). Contrary to our hypothesis, we found that mathematical achievement was not related to systemizing or the discrepancy between systemizing and empathizing. Surprisingly, children with higher empathy demonstrated lower calculation skills. Further analysis using the Social Responsiveness Scale (SRS) revealed that the relationship between EQ-C and mathematical achievement was mediated by social ability rather than autistic behaviors. Finally, social awareness was found to play a differential role in mediating the relationship between EQ-C and mathematical achievement in girls. These results identify empathy, and social skills more generally, as previously unknown predictors of mathematical achievement. PMID:26972835

The Empathizing-Systemizing Theory, Social Abilities, and Mathematical Achievement in Children.

PubMed

Escovar, Emily; Rosenberg-Lee, Miriam; Uddin, Lucina Q; Menon, Vinod

2016-03-14

The Empathizing-Systemizing (E-S) theory describes a profile of traits that have been linked to autism spectrum disorders, and are thought to encompass a continuum that includes typically developing (TD) individuals. Although systemizing is hypothesized to be related to mathematical abilities, empirical support for this relationship is lacking. We examine the link between empathizing and systemizing tendencies and mathematical achievement in 112 TD children (57 girls) to elucidate how socio-cognitive constructs influence early development of mathematical skills. Assessment of mathematical achievement included standardized tests designed to examine calculation skills and conceptual mathematical reasoning. Empathizing and systemizing were assessed using the Combined Empathy Quotient-Child (EQ-C) and Systemizing Quotient-Child (SQ-C). Contrary to our hypothesis, we found that mathematical achievement was not related to systemizing or the discrepancy between systemizing and empathizing. Surprisingly, children with higher empathy demonstrated lower calculation skills. Further analysis using the Social Responsiveness Scale (SRS) revealed that the relationship between EQ-C and mathematical achievement was mediated by social ability rather than autistic behaviors. Finally, social awareness was found to play a differential role in mediating the relationship between EQ-C and mathematical achievement in girls. These results identify empathy, and social skills more generally, as previously unknown predictors of mathematical achievement.

The Effects of a Model Developmental Mathematics Program on Elementary and Middle School Preservice Teachers

ERIC Educational Resources Information Center

Gerber, Lindsey N.

2012-01-01

Teacher quality is instrumental in improving student performance. Unfortunately, discrepancies between teacher preparation programs and national and state K-12 student standards have contributed to the difficult task of producing quality teachers. The contemporary mathematics education paradigm used at most colleges and universities relies on…

Developmental Dynamics between Mathematical Performance, Task Motivation, and Teachers' Goals during the Transition to Primary School

ERIC Educational Resources Information Center

Aunola, Kaisa; Leskinen, Esko; Nurmi, Jari-Erik

2006-01-01

Background: It has been suggested that children's learning motivation and interest in a particular subject play an important role in their school performance, particularly in mathematics. However, few cross-lagged longitudinal studies have been carried out to investigate the prospective relationships between academic achievement and task…

Biological Gender Differences in Students' Errors on Mathematics Achievement Tests

ERIC Educational Resources Information Center

Stewart, Christie; Root, Melissa M.; Koriakin, Taylor; Choi, Dowon; Luria, Sarah R.; Bray, Melissa A.; Sassu, Kari; Maykel, Cheryl; O'Rourke, Patricia; Courville, Troy

2017-01-01

This study investigated developmental gender differences in mathematics achievement, using the child and adolescent portion (ages 6-19 years) of the Kaufman Test of Educational Achievement-Third Edition (KTEA-3). Participants were divided into two age categories: 6 to 11 and 12 to 19. Error categories within the Math Concepts & Applications…

Mathematically Gifted Children: Developmental Brain Characteristics and Their Prognosis for Well-Being

ERIC Educational Resources Information Center

O'Boyle, Michael W.

2008-01-01

Research in cognitive neuroscience suggests that the brains of mathematically gifted children are quantitatively and qualitatively different from those of average math ability. Math-gifted children exhibit signs of enhanced right-hemisphere development, and when engaged in the thinking process, tend to rely on mental imagery. They further manifest…

Leveraging Technology to Improve Developmental Mathematics Course Completion: Evaluation of a Large-Scale Intervention

ERIC Educational Resources Information Center

Wladis, Claire; Offenholley, Kathleen; George, Michael

2014-01-01

This study hypothesizes that course passing rates in remedial mathematics classes can be improved through early identification of at-risk students using a department-wide midterm, followed by a mandated set of online intervention assignments incorporating immediate and elaborate feedback for all students identified as "at-risk" by their…

Developing Students' Relational Understanding: Innovations and Insights

ERIC Educational Resources Information Center

Stump, Sheryl

2009-01-01

I recently had the opportunity to teach a developmental mathematics class at a community college, something a little different from what I usually do as a mathematics teacher educator at a university. I welcomed the chance to examine the curriculum and try some new approaches. In particular, I wanted to explore the development of some fundamental…

On Meaning Making in Mathematics Education: Social, Emotional, Semiotic

ERIC Educational Resources Information Center

Seeger, Falk

2011-01-01

This paper is an attempt to add to the foundation of our understanding of meaning making in mathematics education. This attempt seems to be necessary as a growing body of research, primarily in developmental psychology, begins to change our view of early human development. Empathy, reciprocity, and implicit understanding seem to be more suitable…

Beyond Performance Results: Analyzing the Informational and Developmental Potentials of Standardized Mathematics Tests

ERIC Educational Resources Information Center

di Martino, Pietro; Baccaglini-Frank, Anna

2017-01-01

In this article, we discuss the potential of a critical approach to standardized tests and their results. In particular, we explore and discuss this potential not only for the assessment of students' mathematical competence, but also for teachers' professional development. We identify and describe two kinds of potential: the Informational…

Imagining a Future in PreK: How Professional Identity Shapes Notions of Early Mathematics

ERIC Educational Resources Information Center

Graue, Elizabeth; Karabon, Anne; Delaney, Katherine Kresin; Whyte, Kristin; Kim, Jiwon; Wager, Anita

2015-01-01

This article describes how early childhood teachers engaged in a public preK professional development program. We examine how developing teacher identities mediated engagement with the discourses of developmentally appropriate practice, early mathematics, and funds of knowledge and how they connected present practice to an imagined future. We…

An Examination of the Implementation of Mathematics Lessons in a Chinese Kindergarten Classroom in the Setting of Standards Reform

ERIC Educational Resources Information Center

Hu, Bi Ying; Quebec Fuentes, Sarah; Ma, Jingjing; Ye, Feiwei; Roberts, Sherron Killingsworth

2017-01-01

In China, the "2001 Kindergarten Education Guidelines (Trial)", or "New Outline", delineates what constitutes high-quality, developmentally appropriate practices in all early childhood education curriculum domains, including mathematics. The "New Outline" is known for advocating a child-centered, play-based approach…

Developmental Relations among Motor and Cognitive Processes and Mathematics Skills

ERIC Educational Resources Information Center

Kim, Helyn; Duran, Chelsea A. K.; Cameron, Claire E.; Grissmer, David

2018-01-01

This study explored transactional associations among visuomotor integration, attention, fine motor coordination, and mathematics skills in a diverse sample of one hundred thirty-five 5-year-olds (kindergarteners) and one hundred nineteen 6-year-olds (first graders) in the United States who were followed over the course of 2 school years.…

Mathematics for Young Learners: 60 Games & Activities for Ages 3 through 7.

ERIC Educational Resources Information Center

Ellerby, Richard S.

By studying and practicing metacognition, teachers and parents are instilling positive attitudes toward learning by teaching how-to-learn skills that prepare children for assessing their own thinking about learning as they become more and more developmentally prepared. This book stresses the strategies for thinking in mathematical terms without…

Recent Research on Number Learning.

ERIC Educational Resources Information Center

Kieren, Thomas E., Ed.

Presented are materials related to the work of the Number and Measure and Rational Numbers working group of the Georgia Center for the Study of the Learning and Teaching of Mathematics. Much of the content reports on attempts to bring constructs from developmental psychology and mathematics to bear in understanding children's ideas of number and…

A Developmental Mapping Program Integrating Geography and Mathematics.

ERIC Educational Resources Information Center

Muir, Sharon Pray; Cheek, Helen Neely

Presented and discussed is a model which can be used by educators who want to develop an interdisciplinary map skills program in geography and mathematics. The model assumes that most children in elementary schools perform cognitively at Piaget's concrete operational stage, that readiness for map skills can be assessed with Piagetian or…

Continuum mathematical modelling of pathological growth of blood vessels

NASA Astrophysics Data System (ADS)

Stadnik, N. E.; Dats, E. P.

2018-04-01

The present study is devoted to the mathematical modelling of a human blood vessel pathological growth. The vessels are simulated as the thin-walled circular tube. The boundary value problem of the surface growth of an elastic thin-walled cylinder is solved. The analytical solution is obtained in terms of velocities of stress strain state parameters. The condition of thinness allows us to study finite displacements of cylinder surfaces by means of infinitesimal deformations. The stress-strain state characteristics, which depend on the mechanical parameters of the biological processes, are numerically computed and graphically analysed.

Choice of mathematical models for technological process of glass rod drawing

NASA Astrophysics Data System (ADS)

Alekseeva, L. B.

2017-10-01

The technological process of drawing glass rods (light guides) is considered. Automated control of the drawing process is reduced to the process of making decisions to ensure a given quality. The drawing process is considered as a control object, including the drawing device (control device) and the optical fiber forming zone (control object). To study the processes occurring in the formation zone, mathematical models are proposed, based on the continuum mechanics basics. To assess the influence of disturbances, a transfer function is obtained from the basis of the wave equation. Obtaining the regression equation also adequately describes the drawing process.

Mathematical difficulties as decoupling of expectation and developmental trajectories

PubMed Central

McLean, Janet F.; Rusconi, Elena

2014-01-01

Recent years have seen an increase in research articles and reviews exploring mathematical difficulties (MD). Many of these articles have set out to explain the etiology of the problems, the possibility of different subtypes, and potential brain regions that underlie many of the observable behaviors. These articles are very valuable in a research field, which many have noted, falls behind that of reading and language disabilities. Here will provide a perspective on the current understanding of MD from a different angle, by outlining the school curriculum of England and the US and connecting these to the skills needed at different stages of mathematical understanding. We will extend this to explore the cognitive skills which most likely underpin these different stages and whose impairment may thus lead to mathematics difficulties at all stages of mathematics development. To conclude we will briefly explore interventions that are currently available, indicating whether these can be used to aid the different children at different stages of their mathematical development and what their current limitations may be. The principal aim of this review is to establish an explicit connection between the academic discourse, with its research base and concepts, and the developmental trajectory of abstract mathematical skills that is expected (and somewhat dictated) in formal education. This will possibly help to highlight and make sense of the gap between the complexity of the MD range in real life and the state of its academic science. PMID:24567712

Investigating Meaning in Learning: A Case Study of Adult Developmental Mathematics

ERIC Educational Resources Information Center

Glasser, Tim

2011-01-01

The objective of this article is to investigate meaning and relevance in the context of adult developmental math learning and instruction. In this case study, at the Art Institute of San Francisco, 12 vocational instructors and four math learners are interviewed on their early and current math experiences. During the semi-structured interviews,…

Brain Hyper-Connectivity and Operation-Specific Deficits during Arithmetic Problem Solving in Children with Developmental Dyscalculia

ERIC Educational Resources Information Center

Rosenberg-Lee, Miriam; Ashkenazi, Sarit; Chen, Tianwen; Young, Christina B.; Geary, David C.; Menon, Vinod

2015-01-01

Developmental dyscalculia (DD) is marked by specific deficits in processing numerical and mathematical information despite normal intelligence (IQ) and reading ability. We examined how brain circuits used by young children with DD to solve simple addition and subtraction problems differ from those used by typically developing (TD) children who…

Learning to Apply Algebra in the Community for Adults with Intellectual Developmental Disabilities

ERIC Educational Resources Information Center

Rodriguez, Anthony M.

2016-01-01

Students with intellectual and developmental disabilities (IDD) are routinely excluded from algebra and other high-level mathematics courses. High school students with IDD take courses in arithmetic and life skills rather than having an opportunity to learn algebra. Yet algebra skills can support the learning of money and budgeting skills. This…

Number Processing and Heterogeneity of Developmental Dyscalculia: Subtypes with Different Cognitive Profiles and Deficits

ERIC Educational Resources Information Center

Skagerlund, Kenny; Träff, Ulf

2016-01-01

This study investigated if developmental dyscalculia (DD) in children with different profiles of mathematical deficits has the same or different cognitive origins. The defective approximate number system hypothesis and the access deficit hypothesis were tested using two different groups of children with DD (11-13 years old): a group with…

Neurocognitive Approaches to Developmental Disorders of Numerical and Mathematical Cognition: The Perils of Neglecting the Role of Development

ERIC Educational Resources Information Center

Ansari, Daniel

2010-01-01

The present paper provides a critical overview of how adult neuropsychological models have been applied to the study of the atypical development of numerical cognition. Specifically, the following three assumptions are challenged: 1. Profiles of strength and weaknesses do not change over developmental time. 2. Similar neuronal structures are…

Working Memory and Learning in Children with Developmental Coordination Disorder and Specific Language Impairment

ERIC Educational Resources Information Center

Alloway, Tracy Packiam; Archibald, Lisa

2008-01-01

The authors compared 6- to 11-year-olds with developmental coordination disorder (DCD) and those with specific language impairment (SLI) on measures of memory (verbal and visuospatial short-term and working memory) and learning (reading and mathematics). Children with DCD with typical language skills were impaired in all four areas of memory…

Creating an Alternative Developmental Math Pathway at Delaware Technical Community College

ERIC Educational Resources Information Center

Bradley, John Patrick, Jr.

2017-01-01

Developmental mathematics pass rates at Delaware Technical Community College (DTCC) have remained the same or decreased for a number of years despite two different math curriculum redesigns. They hover around 50 percent or below at each campus, even after the implementation of a second redesign this past Fall 2016 semester. The first redesign…

College Completion and Participation in a Developmental Math Course for Hispanic and White Non-Hispanic Students

ERIC Educational Resources Information Center

Glazier, Stephen Gene

2011-01-01

Purpose, Scope, and Method of Study. The population of interest in the study consisted of white and Hispanic high school graduates in the United States who attended college and completed a college developmental mathematics course. Data from the National Educational Longitudinal Study of 1988 were employed, and a longitudinal, quasi-experimental…

Getting Developmental Education Up to Speed: A Look at MDRC's Research. Issue Focus

ERIC Educational Resources Information Center

Malbin, Joshua

2016-01-01

When they arrive at community colleges or open-enrollment universities, most students take placement exams in English and mathematics to determine whether they are ready for college-level courses. Students with low scores are referred to developmental--remedial--courses. Forty percent of all entering college students and over half of entering…

An Initial Survey of Fractional Graph and Table Area in Behavioral Journals

ERIC Educational Resources Information Center

Kubina, Richard M., Jr.; Kostewicz, Douglas E.; Datchuck, Shawn M.

2008-01-01

This study examined the fractional graph area (FGA), the proportion of page space used to display statistical graphics, in 11 behavioral journals and places behavior analysis on a continuum with other natural, mathematical, and social science disciplines. The composite FGA of all 11 journals puts behavior analysis within the range of the social…

Connecting the Dots: Postsecondary's Role in Preparing K-12 Students

ERIC Educational Resources Information Center

Partnership for Assessment of Readiness for College and Careers, 2012

2012-01-01

For the first time in the nation's history 46 States and the District of Columbia have agreed that all K-12 students will be educated along a common continuum of high academic expectations known as the Common Core State Standards (CCSS). Having clear, consistent standards in English language arts/literacy and mathematics will help ensure that all…

Relation Between Mathematical Performance, Math Anxiety, and Affective Priming in Children With and Without Developmental Dyscalculia.

PubMed

Kucian, Karin; Zuber, Isabelle; Kohn, Juliane; Poltz, Nadine; Wyschkon, Anne; Esser, Günter; von Aster, Michael

2018-01-01

Many children show negative emotions related to mathematics and some even develop mathematics anxiety. The present study focused on the relation between negative emotions and arithmetical performance in children with and without developmental dyscalculia (DD) using an affective priming task. Previous findings suggested that arithmetic performance is influenced if an affective prime precedes the presentation of an arithmetic problem. In children with DD specifically, responses to arithmetic operations are supposed to be facilitated by both negative and mathematics-related primes (= negative math priming effect ).We investigated mathematical performance, math anxiety, and the domain-general abilities of 172 primary school children (76 with DD and 96 controls). All participants also underwent an affective priming task which consisted of the decision whether a simple arithmetic operation (addition or subtraction) that was preceded by a prime (positive/negative/neutral or mathematics-related) was true or false. Our findings did not reveal a negative math priming effect in children with DD. Furthermore, when considering accuracy levels, gender, or math anxiety, the negative math priming effect could not be replicated. However, children with DD showed more math anxiety when explicitly assessed by a specific math anxiety interview and showed lower mathematical performance compared to controls. Moreover, math anxiety was equally present in boys and girls, even in the earliest stages of schooling, and interfered negatively with performance. In conclusion, mathematics is often associated with negative emotions that can be manifested in specific math anxiety, particularly in children with DD. Importantly, present findings suggest that in the assessed age group, it is more reliable to judge math anxiety and investigate its effects on mathematical performance explicitly by adequate questionnaires than by an affective math priming task.

Relation Between Mathematical Performance, Math Anxiety, and Affective Priming in Children With and Without Developmental Dyscalculia

PubMed Central

Kucian, Karin; Zuber, Isabelle; Kohn, Juliane; Poltz, Nadine; Wyschkon, Anne; Esser, Günter; von Aster, Michael

2018-01-01

Many children show negative emotions related to mathematics and some even develop mathematics anxiety. The present study focused on the relation between negative emotions and arithmetical performance in children with and without developmental dyscalculia (DD) using an affective priming task. Previous findings suggested that arithmetic performance is influenced if an affective prime precedes the presentation of an arithmetic problem. In children with DD specifically, responses to arithmetic operations are supposed to be facilitated by both negative and mathematics-related primes (=negative math priming effect).We investigated mathematical performance, math anxiety, and the domain-general abilities of 172 primary school children (76 with DD and 96 controls). All participants also underwent an affective priming task which consisted of the decision whether a simple arithmetic operation (addition or subtraction) that was preceded by a prime (positive/negative/neutral or mathematics-related) was true or false. Our findings did not reveal a negative math priming effect in children with DD. Furthermore, when considering accuracy levels, gender, or math anxiety, the negative math priming effect could not be replicated. However, children with DD showed more math anxiety when explicitly assessed by a specific math anxiety interview and showed lower mathematical performance compared to controls. Moreover, math anxiety was equally present in boys and girls, even in the earliest stages of schooling, and interfered negatively with performance. In conclusion, mathematics is often associated with negative emotions that can be manifested in specific math anxiety, particularly in children with DD. Importantly, present findings suggest that in the assessed age group, it is more reliable to judge math anxiety and investigate its effects on mathematical performance explicitly by adequate questionnaires than by an affective math priming task. PMID:29755376

On the Question of an Identity Status Category Order: Rasch Model Step and Scale Statistics Used to Identify Category Order

ERIC Educational Resources Information Center

Al-Owidha, Amjed; Green, Kathy E.; Kroger, Jane

2009-01-01

The question of whether or not a developmental continuum underlies James Marcia's identity statuses has been a topic of debate among identity researchers for nearly 20 years. This study addressed the prefatory question of whether the identity statuses can be empirically ordered in a theoretically optimal way. This question was addressed via use of…

The Effects of Parental Literacy Involvement and Child Reading Interest on the Development of Emergent Literacy Skills

ERIC Educational Resources Information Center

Carroll, Crystal

2013-01-01

Acquisition of literacy is best conceptualized as a developmental continuum, with its origins early in the life of a child, rather than an all-or-none phenomenon that begins when children start school. How parents expose their children to literacy even before they enter school is important for the later development of reading. The home environment…

Behavior Change in a Student with a Dual Diagnosis of Deafness and Pervasive Development Disorder: A Case Study

ERIC Educational Resources Information Center

Easterbrooks, S. R.; Handley, C. M.

2005-01-01

The broad term "pervasive developmental disorder" (PPD) describes a set of symptoms that occur along a continuum of severity; these symptoms are often referred to as "autism spectrum disorders" (ASDs). Little is known about the incidence and prevalence of ASDs among students who are deaf or hard of hearing (DHH). Teachers of DHH students, who must…

Update: Report on Innovations in Developmental Mathematics--Moving Mathematical Graveyards

ERIC Educational Resources Information Center

Merseth, Katherine K.

2011-01-01

Every year tens of thousands of students step foot on community college campuses, many for the first time. These students all have one thing in common: hope. They enter these institutions with lofty goals and a fervent expectation that the educative experience they are about to embark upon will fundamentally improve their lives. Yet, their hopes…

Head Start Program Quality: Examination of Classroom Quality and Parent Involvement in Predicting Children's Vocabulary, Literacy, and Mathematics Achievement Trajectories

ERIC Educational Resources Information Center

Wen, Xiaoli; Bulotsky-Shearer, Rebecca J.; Hahs-Vaughn, Debbie L.; Korfmacher, Jon

2012-01-01

Guided by a developmental-ecological framework and Head Start's two-generational approach, this study examined two dimensions of Head Start program quality, classroom quality and parent involvement and their unique and interactive contribution to children's vocabulary, literacy, and mathematics skills growth from the beginning of Head Start…

Emotions, Self-Regulated Learning, and Achievement in Mathematics: A Growth Curve Analysis

ERIC Educational Resources Information Center

Ahmed, Wondimu; van der Werf, Greetje; Kuyper, Hans; Minnaert, Alexander

2013-01-01

The purpose of the current study was twofold: (a) to investigate the developmental trends of 4 academic emotions (anxiety, boredom, enjoyment, and pride) and (b) to examine whether changes in emotions are linked to the changes in students' self-regulatory strategies (shallow, deep, and meta-cognitive) and achievement in mathematics. Four hundred…

A Review of Mathematical Learning Disabilities in Children with Fragile X Syndrome

ERIC Educational Resources Information Center

Murphy, Melissa M.

2009-01-01

The prevalence rate of mathematical learning disabilities (MLD) among children with fragile X syndrome who do not meet criteria for intellectual and developmental disabilities ([approximately equal to] 50% of female children) exceeds the rate reported in the general population. The purpose of this article is two-fold: (1) to review the findings on…

Number Sense Mediated by Mathematics Self-Concept in Impacting Middle School Mathematics Achievement

ERIC Educational Resources Information Center

Geronime, Lara K.

2012-01-01

The purpose of the current study was to extend the research on number sense to the middle school level and to simultaneously consider socioemotional elements related to the construct at this developmental stage. Its genesis was initially rooted in an ongoing and dramatic emphasis by U.S. policymakers, researchers, and educators on improving…

Mobile Technology and Mathematics Learning in the Early Grades. Interactive STEM Research + Practice Brief

ERIC Educational Resources Information Center

Presser, Ashley Lewis; Busey, Amy

2016-01-01

This research brief describes the value of using mobile technologies in and out of elementary mathematics classrooms, and investigates the view that teachers may not be getting the guidance they need to best leverage those technologies. The authors explore three areas of concern: How can teachers use technology in developmentally appropriate ways…

Early-Years Swimming: Creating Opportunities for Adding Mathematical Capital to Under 5s

ERIC Educational Resources Information Center

Jorgensen, Robyn

2013-01-01

Drawing on survey data from over 2000 parents, this paper explores the possibility of early-years swimming to add mathematical capital to young children. Using developmental milestones as the basis, it was found that parents reported significantly earlier achievement on many of these milestones. Such data suggest that the early years swim…

Cognitive Developmental Level Gender, and the Development of Learned Helplessness on Mathematical Calculation and Reasoning Tasks.

ERIC Educational Resources Information Center

Monaco, Nanci M.; Gentile, J. Ronald

1987-01-01

This study was designed to test whether a learned helplessness treatment would decrease performance on mathematical tasks and to extend learned helplessness findings to include the cognitive development dimension. Results showed no differential advantages to either sex in resisting effects of learned helplessness or in benefiting from strategy…

Defective Number Sense or Impaired Access? Differential Impairments in Different Subgroups of Children with Mathematics Difficulties

ERIC Educational Resources Information Center

Wong, Terry T.-Y.; Ho, Connie S.-H.; Tang, Joey

2017-01-01

Developmental dyscalculia (DD) is a specific learning disability in mathematics that affects around 6% of the population. Currently, the core deficit of DD remains unknown. While the number sense deficit hypothesis suggests that the core deficit of DD lies in the inability to represent nonsymbolic numerosity, the access deficit hypothesis suggests…

Quantum Dynamics in Continuum for Proton Transport I: Basic Formulation.

PubMed

Chen, Duan; Wei, Guo-Wei

2013-01-01

Proton transport is one of the most important and interesting phenomena in living cells. The present work proposes a multiscale/multiphysics model for the understanding of the molecular mechanism of proton transport in transmembrane proteins. We describe proton dynamics quantum mechanically via a density functional approach while implicitly model other solvent ions as a dielectric continuum to reduce the number of degrees of freedom. The densities of all other ions in the solvent are assumed to obey the Boltzmann distribution. The impact of protein molecular structure and its charge polarization on the proton transport is considered explicitly at the atomic level. We formulate a total free energy functional to put proton kinetic and potential energies as well as electrostatic energy of all ions on an equal footing. The variational principle is employed to derive nonlinear governing equations for the proton transport system. Generalized Poisson-Boltzmann equation and Kohn-Sham equation are obtained from the variational framework. Theoretical formulations for the proton density and proton conductance are constructed based on fundamental principles. The molecular surface of the channel protein is utilized to split the discrete protein domain and the continuum solvent domain, and facilitate the multiscale discrete/continuum/quantum descriptions. A number of mathematical algorithms, including the Dirichlet to Neumann mapping, matched interface and boundary method, Gummel iteration, and Krylov space techniques are utilized to implement the proposed model in a computationally efficient manner. The Gramicidin A (GA) channel is used to demonstrate the performance of the proposed proton transport model and validate the efficiency of proposed mathematical algorithms. The electrostatic characteristics of the GA channel is analyzed with a wide range of model parameters. The proton conductances are studied over a number of applied voltages and reference concentrations. A comparison with experimental data verifies the present model predictions and validates the proposed model.

Fractal continuum model for tracer transport in a porous medium.

PubMed

Herrera-Hernández, E C; Coronado, M; Hernández-Coronado, H

2013-12-01

A model based on the fractal continuum approach is proposed to describe tracer transport in fractal porous media. The original approach has been extended to treat tracer transport and to include systems with radial and uniform flow, which are cases of interest in geoscience. The models involve advection due to the fluid motion in the fractal continuum and dispersion whose mathematical expression is taken from percolation theory. The resulting advective-dispersive equations are numerically solved for continuous and for pulse tracer injection. The tracer profile and the tracer breakthrough curve are evaluated and analyzed in terms of the fractal parameters. It has been found in this work that anomalous transport frequently appears, and a condition on the fractal parameter values to predict when sub- or superdiffusion might be expected has been obtained. The fingerprints of fractality on the tracer breakthrough curve in the explored parameter window consist of an early tracer breakthrough and long tail curves for the spherical and uniform flow cases, and symmetric short tailed curves for the radial flow case.

Enhancing Faculty Pedagogy and Student Outcomes in Developmental Math and English through an Online Community of Practice

ERIC Educational Resources Information Center

Khoule, Alioune; Pacht, Michelle; Schwartz, Jesse W.; van Slyck, Phyllis

2015-01-01

One of the most important topics for faculty in public higher education, especially at community colleges, is how to help developmental students succeed. Students requiring basic mathematics and English courses are the most at-risk college students in public education today. The authors received a grant from the Kresge Foundation that funded the…

Predictors of Persistence for Developmental Math Students in a Community and Technical College System

ERIC Educational Resources Information Center

Davidson, J. Cody; Petrosko, Joseph M.

2015-01-01

At two-year public community colleges, the 2011 three-year persistence rate was 23.9%. From 1988 to 2006, between 40% and 60% of all first-time community college students were referred to and enrolled in at least one developmental education course. More students begin college underprepared in mathematics than any other subject area, and only about…

The Use of Non-Cognitives and Learning Strategies as a Predictor for Completion of Developmental Mathematics at a Community College

ERIC Educational Resources Information Center

Healy, Megan

2012-01-01

With a large global, national, state, and local drive for post-secondary credentials, higher education institutes are exploring new retention and graduation strategies to meet the needs of the employers and employees. Many students who are unprepared for college level work will enter a community college to take developmental courses. Developmental…

Gradient Models in Molecular Biophysics: Progress, Challenges, Opportunities

PubMed Central

Bardhan, Jaydeep P.

2014-01-01

In the interest of developing a bridge between researchers modeling materials and those modeling biological molecules, we survey recent progress in developing nonlocal-dielectric continuum models for studying the behavior of proteins and nucleic acids. As in other areas of science, continuum models are essential tools when atomistic simulations (e.g. molecular dynamics) are too expensive. Because biological molecules are essentially all nanoscale systems, the standard continuum model, involving local dielectric response, has basically always been dubious at best. The advanced continuum theories discussed here aim to remedy these shortcomings by adding features such as nonlocal dielectric response, and nonlinearities resulting from dielectric saturation. We begin by describing the central role of electrostatic interactions in biology at the molecular scale, and motivate the development of computationally tractable continuum models using applications in science and engineering. For context, we highlight some of the most important challenges that remain and survey the diverse theoretical formalisms for their treatment, highlighting the rigorous statistical mechanics that support the use and improvement of continuum models. We then address the development and implementation of nonlocal dielectric models, an approach pioneered by Dogonadze, Kornyshev, and their collaborators almost forty years ago. The simplest of these models is just a scalar form of gradient elasticity, and here we use ideas from gradient-based modeling to extend the electrostatic model to include additional length scales. The paper concludes with a discussion of open questions for model development, highlighting the many opportunities for the materials community to leverage its physical, mathematical, and computational expertise to help solve one of the most challenging questions in molecular biology and biophysics. PMID:25505358

Gradient Models in Molecular Biophysics: Progress, Challenges, Opportunities.

PubMed

Bardhan, Jaydeep P

2013-12-01

In the interest of developing a bridge between researchers modeling materials and those modeling biological molecules, we survey recent progress in developing nonlocal-dielectric continuum models for studying the behavior of proteins and nucleic acids. As in other areas of science, continuum models are essential tools when atomistic simulations (e.g. molecular dynamics) are too expensive. Because biological molecules are essentially all nanoscale systems, the standard continuum model, involving local dielectric response, has basically always been dubious at best. The advanced continuum theories discussed here aim to remedy these shortcomings by adding features such as nonlocal dielectric response, and nonlinearities resulting from dielectric saturation. We begin by describing the central role of electrostatic interactions in biology at the molecular scale, and motivate the development of computationally tractable continuum models using applications in science and engineering. For context, we highlight some of the most important challenges that remain and survey the diverse theoretical formalisms for their treatment, highlighting the rigorous statistical mechanics that support the use and improvement of continuum models. We then address the development and implementation of nonlocal dielectric models, an approach pioneered by Dogonadze, Kornyshev, and their collaborators almost forty years ago. The simplest of these models is just a scalar form of gradient elasticity, and here we use ideas from gradient-based modeling to extend the electrostatic model to include additional length scales. The paper concludes with a discussion of open questions for model development, highlighting the many opportunities for the materials community to leverage its physical, mathematical, and computational expertise to help solve one of the most challenging questions in molecular biology and biophysics.

Gradient models in molecular biophysics: progress, challenges, opportunities

NASA Astrophysics Data System (ADS)

Bardhan, Jaydeep P.

2013-12-01

In the interest of developing a bridge between researchers modeling materials and those modeling biological molecules, we survey recent progress in developing nonlocal-dielectric continuum models for studying the behavior of proteins and nucleic acids. As in other areas of science, continuum models are essential tools when atomistic simulations (e.g., molecular dynamics) are too expensive. Because biological molecules are essentially all nanoscale systems, the standard continuum model, involving local dielectric response, has basically always been dubious at best. The advanced continuum theories discussed here aim to remedy these shortcomings by adding nonlocal dielectric response. We begin by describing the central role of electrostatic interactions in biology at the molecular scale, and motivate the development of computationally tractable continuum models using applications in science and engineering. For context, we highlight some of the most important challenges that remain, and survey the diverse theoretical formalisms for their treatment, highlighting the rigorous statistical mechanics that support the use and improvement of continuum models. We then address the development and implementation of nonlocal dielectric models, an approach pioneered by Dogonadze, Kornyshev, and their collaborators almost 40 years ago. The simplest of these models is just a scalar form of gradient elasticity, and here we use ideas from gradient-based modeling to extend the electrostatic model to include additional length scales. The review concludes with a discussion of open questions for model development, highlighting the many opportunities for the materials community to leverage its physical, mathematical, and computational expertise to help solve one of the most challenging questions in molecular biology and biophysics.

The Soccer Ball Model: A Useful Visualization Protocol for Scaling Concepts in Continua

ERIC Educational Resources Information Center

Arce, Pedro E.; Pascal, Jennifer; Torres, Cynthia

2010-01-01

When studying the physics of transport, it is necessary to develop conservation equations, and the concept of a continuum scale must be introduced. Most textbooks do not address this issue, assuming that the mathematical steps are familiar to the learner. In fact, students are introduced to physical concepts, such as mass, momentum, and energy for…

Distinguishing Models of Professional Development: The Case of an Adaptive Model's Impact on Teachers' Knowledge, Instruction, and Student Achievement

ERIC Educational Resources Information Center

Koellner, Karen; Jacobs, Jennifer

2015-01-01

We posit that professional development (PD) models fall on a continuum from highly adaptive to highly specified, and that these constructs provide a productive way to characterize and distinguish among models. The study reported here examines the impact of an adaptive mathematics PD model on teachers' knowledge and instructional practices as well…

Students' Mathematics Self-Efficacy, Anxiety, and Course Level at a Community College

ERIC Educational Resources Information Center

Spaniol, Scott R.

2017-01-01

Research suggests that student success in mathematics is positively correlated to math self-efficacy and negatively correlated to math anxiety. At a Hispanic serving community college in the Midwest, developmental math students had a lower pass rate than did college-level math students, but the role of math self-efficacy and math anxiety on these…

A Phenomenological Study of the Persistence of Unsuccessful Students in Developmental Mathematics at a Community College

ERIC Educational Resources Information Center

Canfield, Barbara

2013-01-01

There are a large number of students entering college underprepared for college-level mathematics (Carnegie Foundation for the Advancement of Teaching, 2011). While this problem is not new, it has become the focus of national attention because of the impact it has on college completion and workforce development. There is much written in the…

Developmental Change in the Influence of Domain-General Abilities and Domain-Specific Knowledge on Mathematics Achievement: An Eight-Year Longitudinal Study

ERIC Educational Resources Information Center

Geary, David C.; Nicholas, Alan; Li, Yaoran; Sun, Jianguo

2017-01-01

The contributions of domain-general abilities and domain-specific knowledge to subsequent mathematics achievement were longitudinally assessed (n = 167) through 8th grade. First grade intelligence and working memory and prior grade reading achievement indexed domain-general effects, and domain-specific effects were indexed by prior grade…

IEA's TIMSS 2003 International Report on Achievement in the Mathematics Cognitive Domains: Findings from a Developmental Project

ERIC Educational Resources Information Center

Mullis, Ina V. S.; Martin, Michael O.; Foy, Pierre

2005-01-01

This report documents the process undertaken to produce scales in three cognitive domains: knowing, applying, and reasoning. Included are the final scales showing differences among countries, as well as within countries. TIMSS 2003 is the third and most recently completed round of IEA's Trends in International Mathematics and Science Study, a…

Estuche de evaluacion del continuo del desarrollo de El Curriculo Creativo (The Creative Curriculum Developmental Continuum Assessment Toolkit for Ages 3-5).

ERIC Educational Resources Information Center

Dodge, Diane Trister; Colker, Laura J.; Heroman, Cate

Intended for use with the Creative Curriculum for Early Childhood, this integrated ongoing student assessment toolkit, in Spanish, is designed for preschool teachers to help them focus on all aspects of a child's development, thereby giving them a way to ensure that all children in their classes are making progress. The assessment kit uses a…

Examining the Effects of a State-Funded 4K Program on Reading Gains and Kindergarten Reading Readiness in a Wisconsin School District

ERIC Educational Resources Information Center

Mueller, Kristin A.

2013-01-01

The purpose of this quantitative study was to examine the effects of attending a state-funded 4K program located in a large southern Wisconsin suburban school district. Reading gains were measured as results of the Creative Curriculum Developmental Continuum assessment given in the fall and spring of 4K, and then sequentially, kindergarten-reading…

The Role of Mathematical Models in Understanding Pattern Formation in Developmental Biology

PubMed Central

Umulis, David M.

2016-01-01

In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics—whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: “It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations.” This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, “The laws of Nature are written in the language of mathematics…the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word.” Mathematics has moved beyond the geometry-based model of Galileo’s time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837–838, 2013). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades—that of how organisms can scale in size. Mathematical analysis alone cannot “solve” these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology. PMID:25280665

Integrating Technology into the Developmental Mathematics Classroom: A WebQuest

ERIC Educational Resources Information Center

Salsovic, Annette

2007-01-01

Although the WebQuest has been around for several years, it appears that not many educators are aware of it, or know how to use it. Thus, it is important to not only expose developmental educators to the use of this strategy, but also to help them realize how they can easily implement it into their curriculum. The use of a Webquest integrates…

Does Remediation Work for All Students? How the Effects of Postsecondary Remedial and Developmental Courses Vary by Level of Academic Preparation. NCPR Brief

ERIC Educational Resources Information Center

Boatman, Angela; Long, Bridget Terry

2011-01-01

This Brief summarizes a study that addresses the impact of remedial and developmental courses on students with a range of levels of preparedness. Using longitudinal data from Tennessee, the authors estimate the effects of placement into varying levels of mathematics, reading, and writing courses for students attending public two- and four-year…

Research Methods in Healthcare Epidemiology and Antimicrobial Stewardship-Mathematical Modeling.

PubMed

Barnes, Sean L; Kasaie, Parastu; Anderson, Deverick J; Rubin, Michael

2016-11-01

Mathematical modeling is a valuable methodology used to study healthcare epidemiology and antimicrobial stewardship, particularly when more traditional study approaches are infeasible, unethical, costly, or time consuming. We focus on 2 of the most common types of mathematical modeling, namely compartmental modeling and agent-based modeling, which provide important advantages-such as shorter developmental timelines and opportunities for extensive experimentation-over observational and experimental approaches. We summarize these advantages and disadvantages via specific examples and highlight recent advances in the methodology. A checklist is provided to serve as a guideline in the development of mathematical models in healthcare epidemiology and antimicrobial stewardship. Infect Control Hosp Epidemiol 2016;1-7.

Mathematics Education and the Objectivist Programme in HPS

NASA Astrophysics Data System (ADS)

Glas, Eduard

2013-06-01

Using history of mathematics for studying concepts, methods, problems and other internal features of the discipline may give rise to a certain tension between descriptive adequacy and educational demands. Other than historians, educators are concerned with mathematics as a normatively defined discipline. Teaching cannot but be based on a pre-understanding of what mathematics `is' or, in other words, on a normative (methodological, philosophical) view of the identity or nature of the discipline. Educators are primarily concerned with developments at the level of objective mathematical knowledge, that is: with the relations between successive theories, problems and proposed solutions—relations which are independent of whatever has been the role of personal or collective beliefs, convictions, traditions and other historical circumstances. Though not exactly `historical' in the usual sense, I contend that this `objectivist' approach does represent one among other entirely legitimate and valuable approaches to the historical development of mathematics. Its retrospective importance to current practitioners and students is illustrated by a reconstruction of the development of Eudoxus's theory of proportionality in response to the problem of irrationality, and the way in which Dedekind some two millennia later almost literally used this ancient theory for the rigorous introduction of irrational numbers and hence of the real number continuum.

Mathematical models in simulation process in rehabilitation of persons with disabilities

NASA Astrophysics Data System (ADS)

Gorie, Nina; Dolga, Valer; Mondoc, Alina

2012-11-01

The problems of people with disability are varied. A disability may be physical, cognitive, mental, sensory, emotional, developmental or some combination of these. The major disabilities which can appear in people's lives are: the blindness, the deafness, the limb-girdle muscular dystrophy, the orthopedic impairment, the visual impairment. A disability is an umbrella term, covering impairments, activity limitations and participation restrictions. A disability may occur during a person's lifetime or may be present from birth. The authors conclude that some of these disabilities like physical, cognitive, mental, sensory, emotional, developmental can be rehabilitated. Starting from this state of affairs the authors present briefly the possibility of using certain mechatronic systems for rehabilitation of persons with different disabilities. The authors focus their presentation on alternative calling the Stewart platform in order to achieve the proposed goal. The authors present a mathematical model of systems theory approach under the parallel system and described its contents can. The authors analyze in a meaningful mathematical model describing the procedure of rehabilitation process. From the affected function biomechanics and taking into account medical recommendations the authors illustrate the mathematical models of rehabilitation work. The authors assemble a whole mathematical model of parallel structure and the rehabilitation process and making simulation and highlighting the results estimated. The authors present in the end work the results envisaged in the end analysis work, conclusions and steps for future work program..

Mind the Gap: A Semicontinuum Model for Discrete Electrical Propagation in Cardiac Tissue.

PubMed

Costa, Caroline Mendonca; Silva, Pedro Andre Arroyo; dos Santos, Rodrigo Weber

2016-04-01

Electrical propagation in cardiac tissue is a discrete or discontinuous phenomenon that reflects the complexity of the anatomical structures and their organization in the heart, such as myocytes, gap junctions, microvessels, and extracellular matrix, just to name a few. Discrete models or microscopic and discontinuous models are, so far, the best options to accurately study how structural properties of cardiac tissue influence electrical propagation. These models are, however, inappropriate in the context of large scale simulations, which have been traditionally performed by the use of continuum and macroscopic models, such as the monodomain and the bidomain models. However, continuum models may fail to reproduce many important physiological and physiopathological aspects of cardiac electrophysiology, for instance, those related to slow conduction. In this study, we develop a new mathematical model that combines characteristics of both continuum and discrete models. The new model was evaluated in scenarios of low gap-junctional coupling, where slow conduction is observed, and was able to reproduce conduction block, increase of the maximum upstroke velocity and of the repolarization dispersion. None of these features can be captured by continuum models. In addition, the model overcomes a great disadvantage of discrete models, as it allows variation of the spatial resolution within a certain range.

Assessing the failure of continuum formula for solid-solid drag force using discrete element method in large size ratios

NASA Astrophysics Data System (ADS)

Jalali, Payman; Hyppänen, Timo

2017-06-01

In loose or moderately-dense particle mixtures, the contact forces between particles due to successive collisions create average volumetric solid-solid drag force between different granular phases (of different particle sizes). The derivation of the mathematical formula for this drag force is based on the homogeneity of mixture within the calculational control volume. This assumption especially fails when the size ratio of particles grows to a large value of 10 or greater. The size-driven inhomogeneity is responsible to the deviation of intergranular force from the continuum formula. In this paper, we have implemented discrete element method (DEM) simulations to obtain the volumetric mean force exchanged between the granular phases with the size ratios greater than 10. First, the force is calculated directly from DEM averaged over a proper time window. Second, the continuum formula is applied to calculate the drag forces using the DEM quantities. We have shown the two volumetric forces are in good agreement as long as the homogeneity condition is maintained. However, the relative motion of larger particles in a cloud of finer particles imposes the inhomogeneous distribution of finer particles around the larger ones. We have presented correction factors to the volumetric force from continuum formula.

Number Line Estimation: The Use of Number Line Magnitude Estimation to Detect the Presence of Math Disability in Postsecondary Students

ERIC Educational Resources Information Center

McDonald, Steven A.

2010-01-01

This study arose from an interest in the possible presence of mathematics disabilities among students enrolled in the developmental math program at a large university in the Mid-Atlantic region. Research in mathematics learning disabilities (MLD) has included a focus on the construct of working memory and number sense. A component of number sense…

Mathematics--An Approach for Slow Learners. Section 2--The Beginnings of Number. Notes for Teachers of Mathematics, Volume 6.

ERIC Educational Resources Information Center

Leeds Education Authority (England). Mathematics Curriculum Study Group.

This is one of a series of monographs developed by teachers in elementary schools near Leeds, England. This document focuses on early instruction of number concepts. It is considered essential that these ideas be presented first in concrete form. The working group attempted to provide a detailed progression in the developmental stages leading to…

Validation of the Spanish Version of the Woodcock-Johnson Mathematics Achievement Tests for Children Aged 6 to 13

ERIC Educational Resources Information Center

Diamantopoulou, Sofia; Pina, Violeta; Valero-Garcia, Ana V.; Gonzalez-Salinas, Carmen; Fuentes, Luis J.

2012-01-01

This study validated the four mathematics tests of the Spanish version of the Woodcock-Johnson III (WJ-III) Achievement (ACH) battery for use in the first six grades of school in Spain. Developmental effects and gender differences were also examined. Participants were a normal population sample of 424 (216 boys) children aged 6 to 13 years.…

Linking Measures of Adult Nicotine Dependence to a Common Latent Continuum and a Comparison with Adolescent Patterns

PubMed Central

Strong, David R.; Schonbrun, Yael Chatav; Schaffran, Christine; Griesler, Pamela C.; Kandel, Denise

2012-01-01

Background An ongoing debate regarding the nature of Nicotine Dependence (ND) is whether the same instrument can be applied to measure ND among adults and adolescents. Using a hierarchical item response model (IRM), we examined evidence for a common continuum underlying ND symptoms among adults and adolescents. Method The analyses are based on two waves of interviews with subsamples of parents and adolescents from a multi-ethnic longitudinal cohort of 1,039 6th–10th graders from the Chicago Public Schools (CPS). Adults and adolescents who reported smoking cigarettes the last 30 days prior to waves 3 and 5 completed three common instruments measuring ND symptoms and one item measuring loss of autonomy. Results A stable continuum of ND, first identified among adolescents, was replicated among adults. However, some symptoms, such as tolerance and withdrawal, differed markedly across adults and adolescents. The majority of mFTQ items were observed within the highest levels of ND, the NDSS items within the lowest levels, and the DSM-IV items were arrayed in the middle and upper third of the continuum of dependence severity. Loss of Autonomy was positioned at the lower end of the continuum. We propose a ten-symptom measure of ND for adolescents and adults. Conclusions Despite marked differences in the relative severity of specific ND symptoms in each group, common instrumentation of ND can apply to adults and adolescents. The results increase confidence in the ability to describe phenotypic heterogeneity in ND across important developmental periods. PMID:21855236

Development and Application of Methods for Estimating Operating Characteristics of Discrete Test Item Responses without Assuming any Mathematical Form.

ERIC Educational Resources Information Center

Samejima, Fumiko

In latent trait theory the latent space, or space of the hypothetical construct, is usually represented by some unidimensional or multi-dimensional continuum of real numbers. Like the latent space, the item response can either be treated as a discrete variable or as a continuous variable. Latent trait theory relates the item response to the latent…

The Principle of the Fermionic Projector: An Approach for Quantum Gravity?

NASA Astrophysics Data System (ADS)

Finster, Felix

In this short article we introduce the mathematical framework of the principle of the fermionic projector and set up a variational principle in discrete space-time. The underlying physical principles are discussed. We outline the connection to the continuum theory and state recent results. In the last two sections, we speculate on how it might be possible to describe quantum gravity within this framework.

Developmental Relations Among Motor and Cognitive Processes and Mathematics Skills.

PubMed

Kim, Helyn; Duran, Chelsea A K; Cameron, Claire E; Grissmer, David

2018-03-01

This study explored transactional associations among visuomotor integration, attention, fine motor coordination, and mathematics skills in a diverse sample of one hundred thirty-five 5-year-olds (kindergarteners) and one hundred nineteen 6-year-olds (first graders) in the United States who were followed over the course of 2 school years. Associations were dynamic, with more reciprocal transactions occurring in kindergarten than in the later grades. Specifically, visuomotor integration and mathematics exhibited ongoing reciprocity in kindergarten and first grade, attention contributed to mathematics in kindergarten and first grade, mathematics contributed to attention across the kindergarten year only, and fine motor coordination contributed to mathematics indirectly, through visuomotor integration, across kindergarten and first grade. Implications of examining the hierarchical interrelations among processes underlying the development of children's mathematics skills are discussed. © 2017 The Authors. Child Development © 2017 Society for Research in Child Development, Inc.

Labelling effects and adolescent responses to peers with depression: an experimental investigation.

PubMed

Dolphin, Louise; Hennessy, Eilis

2017-06-24

The impact of illness labels on the stigma experiences of individuals with mental health problems is a matter of ongoing debate. Some argue that labels have a negative influence on judgments and should be avoided in favour of information emphasising the existence of a continuum of mental health/illness. Others believe that behavioral symptoms are more powerful influencers of stigma than labels. The phenomenon has received little attention in adolescent research, despite the critical importance of the peer group at this developmental stage. This study employs a novel experimental design to examine the impact of the depression label and continuum information on adolescents' responses to peers with depression. Participants were 156 adolescents, 76 male, 80 female (M = 16.25 years; SD = .361), assigned to one of three conditions (Control, Label, Continuum). Participants respond to four audio-visual vignette characters (two clinically depressed) on three occasions. Outcome measures included judgment of the mental health of the vignette characters and emotional responses to them. Neither the provision of a depression label or continuum information influenced perceptions of the mental health of the characters in the audio-visual vignettes or participants' emotional responses to them. The findings have implications for the design of interventions to combat depression stigma with adolescents. Interventions should not necessarily target perceptions of psychiatric labels, but rather perceptions of symptomatic behaviour.

A continuum model for dynamic analysis of the Space Station

NASA Technical Reports Server (NTRS)

Thomas, Segun

1989-01-01

Dynamic analysis of the International Space Station using MSC/NASTRAN had 1312 rod elements, 62 beam elements, 489 nodes and 1473 dynamic degrees of freedom. A realtime, man-in-the-loop simulation of such a model is impractical. This paper discusses the mathematical model for realtime dynamic simulation of the Space Station. Several key questions in structures and structural dynamics are addressed. First, to achieve a significant reduction in the number of dynamic degrees of freedom, a continuum equivalent representation of the Space Station truss structure which accounted for the unsymmetry of the basic configuration and resulted in the coupling of extensional and transverse deformation, is developed. Next, dynamic equations for the continuum equivalent of the Space Station truss structure are formulated using a matrix version of Kane's dynamical equations. Flexibility is accounted for by using a theory that accommodates extension, bending in two principal planes and shear displacement. Finally, constraint equations suitable for dynamic analysis of flexible bodies with closed loop configuration are developed and solution of the resulting system of equations is based on the zero eigenvalue theorem.

A mathematical model of the maximum power density attainable in an alkaline hydrogen/oxygen fuel cell

NASA Technical Reports Server (NTRS)

Kimble, Michael C.; White, Ralph E.

1991-01-01

A mathematical model of a hydrogen/oxygen alkaline fuel cell is presented that can be used to predict the polarization behavior under various power loads. The major limitations to achieving high power densities are indicated and methods to increase the maximum attainable power density are suggested. The alkaline fuel cell model describes the phenomena occurring in the solid, liquid, and gaseous phases of the anode, separator, and cathode regions based on porous electrode theory applied to three phases. Fundamental equations of chemical engineering that describe conservation of mass and charge, species transport, and kinetic phenomena are used to develop the model by treating all phases as a homogeneous continuum.

Mathematical difficulties in developmental coordination disorder: Symbolic and nonsymbolic number processing.

PubMed

Gomez, Alice; Piazza, Manuela; Jobert, Antoinette; Dehaene-Lambertz, Ghislaine; Dehaene, Stanislas; Huron, Caroline

2015-01-01

At school, children with Developmental Coordination Disorder (DCD) struggle with mathematics. However, little attention has been paid to their numerical cognition abilities. The goal of this study was to better understand the cognitive basis for mathematical difficulties in children with DCD. Twenty 7-to-10 years-old children with DCD were compared to twenty age-matched typically developing children using dot and digit comparison tasks to assess symbolic and nonsymbolic number processing and in a task of single digits additions. Results showed that children with DCD had lower performance in nonsymbolic and symbolic number comparison tasks than typically developing children. They were also slower to solve simple addition problems. Moreover, correlational analyses showed that children with DCD who experienced greater impairments in the nonsymbolic task also performed more poorly in the symbolic tasks. These findings suggest that DCD impairs both nonsymbolic and symbolic number processing. A systematic assessment of numerical cognition in children with DCD could provide a more comprehensive picture of their deficits and help in proposing specific remediation. Copyright © 2015 Elsevier Ltd. All rights reserved.

Differential effects of the classroom on African American and non-African American's mathematics achievement.

PubMed

Schenke, Katerina; Nguyen, Tutrang; Watts, Tyler W; Sarama, Julie H; Clements, Douglas H

2017-08-01

We examined whether African American students differentially responded to dimensions of the observed classroom-learning environment compared with non-African American students. Further, we examined whether these dimensions of the classroom mediated treatment effects of a preschool mathematics intervention targeted at students from low-income families. Three observed dimensions of the classroom (teacher expectations and developmental appropriateness; teacher confidence and enthusiasm; and support for mathematical discourse) were evaluated in a sample of 1,238 preschool students in 101 classrooms. Using multigroup multilevel mediation where African American students were compared to non-African American students, we found that teachers in the intervention condition had higher ratings on the observed dimensions of the classroom compared with teachers in the control condition. Further, ratings on teacher expectations and developmental appropriateness had larger associations with the achievement of African American students than for non-African Americans. Findings suggest that students within the same classroom may react differently to that learning environment and that classroom learning environments could be structured in ways that are beneficial for students who need the most support.

Competence with Fractions Predicts Gains in Mathematics Achievement

PubMed Central

Bailey, Drew H.; Hoard, Mary K.; Nugent, Lara; Geary, David C.

2012-01-01

Competence with fractions predicts later mathematics achievement, but the co-developmental pattern between fractions knowledge and mathematics achievement is not well understood. We assessed this co-development through examination of the cross-lagged relation between a measure of conceptual knowledge of fractions and mathematics achievement in sixth and seventh grade (n = 212). The cross-lagged effects indicated that performance on the sixth grade fractions concepts measure predicted one year gains in mathematics achievement (β = .14, p<.01), controlling for the central executive component of working memory and intelligence, but sixth grade mathematics achievement did not predict gains on the fractions concepts measure (β = .03, p>.50). In a follow-up assessment, we demonstrated that measures of fluency with computational fractions significantly predicted seventh grade mathematics achievement above and beyond the influence of fluency in computational whole number arithmetic, performance on number fluency and number line tasks, and central executive span and intelligence. Results provide empirical support for the hypothesis that competence with fractions underlies, in part, subsequent gains in mathematics achievement. PMID:22832199

EPAs Virtual Embryo: Modeling Developmental Toxicity

EPA Science Inventory

Embryogenesis is regulated by concurrent activities of signaling pathways organized into networks that control spatial patterning, molecular clocks, morphogenetic rearrangements and cell differentiation. Quantitative mathematical and computational models are needed to better unde...

Quantum dynamics in continuum for proton transport II: Variational solvent-solute interface.

PubMed

Chen, Duan; Chen, Zhan; Wei, Guo-Wei

2012-01-01

Proton transport plays an important role in biological energy transduction and sensory systems. Therefore, it has attracted much attention in biological science and biomedical engineering in the past few decades. The present work proposes a multiscale/multiphysics model for the understanding of the molecular mechanism of proton transport in transmembrane proteins involving continuum, atomic, and quantum descriptions, assisted with the evolution, formation, and visualization of membrane channel surfaces. We describe proton dynamics quantum mechanically via a new density functional theory based on the Boltzmann statistics, while implicitly model numerous solvent molecules as a dielectric continuum to reduce the number of degrees of freedom. The density of all other ions in the solvent is assumed to obey the Boltzmann distribution in a dynamic manner. The impact of protein molecular structure and its charge polarization on the proton transport is considered explicitly at the atomic scale. A variational solute-solvent interface is designed to separate the explicit molecule and implicit solvent regions. We formulate a total free-energy functional to put proton kinetic and potential energies, the free energy of all other ions, and the polar and nonpolar energies of the whole system on an equal footing. The variational principle is employed to derive coupled governing equations for the proton transport system. Generalized Laplace-Beltrami equation, generalized Poisson-Boltzmann equation, and generalized Kohn-Sham equation are obtained from the present variational framework. The variational solvent-solute interface is generated and visualized to facilitate the multiscale discrete/continuum/quantum descriptions. Theoretical formulations for the proton density and conductance are constructed based on fundamental laws of physics. A number of mathematical algorithms, including the Dirichlet-to-Neumann mapping, matched interface and boundary method, Gummel iteration, and Krylov space techniques are utilized to implement the proposed model in a computationally efficient manner. The gramicidin A channel is used to validate the performance of the proposed proton transport model and demonstrate the efficiency of the proposed mathematical algorithms. The proton channel conductances are studied over a number of applied voltages and reference concentrations. A comparison with experimental data verifies the present model predictions and confirms the proposed model. Copyright © 2011 John Wiley & Sons, Ltd.

Low-pass filtered continuum streambed and bedload sediment mass balance laws for an alluvial, gravel-bed stream

NASA Astrophysics Data System (ADS)

DeTemple, B.; Wilcock, P.

2011-12-01

In an alluvial, gravel-bed stream governed by a plane-bed bedload transport regime, the physicochemical properties, size distribution, and granular architecture of the sediment grains that constitute the streambed surface influence many hydrodynamic, geomorphic, chemical, and ecological processes. Consequently, the abilities to accurately characterize the morphology and model the morphodynamics of the streambed surface and its interaction with the bedload above and subsurface below are necessary for a more complete understanding of how sediment, flow, organisms, and biogeochemistry interact. We report on our progress in the bottom-up development of low-pass filtered continuum streambed and bedload sediment mass balance laws for an alluvial, gravel-bed stream. These balance laws are assembled in a four stage process. First, the stream sediment-water system is conceptually abstracted as a nested, multi-phase, multi-species, structured continuum. Second, the granular surface of an aggregate of sediment grains is mathematically defined. Third, an integral approach to mass balance, founded in the continuum theory of multiphase flow, is used to formulate primordial, differential, instantaneous, local, continuum, mass balance laws applicable at any material point within a gravel-bed stream. Fourth, area averaging and time-after-area averaging, employing planform, low-pass filtering expressed as correlation or convolution integrals and based on the spatial and temporal filtering techniques found in the fields of multiphase flow, porous media flow, and large eddy simulation of turbulent fluid flow, are applied to smooth the primordial equations while maximizing stratigraphic resolution and preserving the definitions of relevant morphodynamic surfaces. Our approach unifies, corrects, contextualizes, and generalizes prior efforts at developing stream sediment continuity equations, including the top-down derivations of the surface layer (or "active layer") approach of Hirano [1971a,b] and probabilistic approach of Parker et al. [2000], as well as the bottom-up, low-pass filtered continuum approach of Coleman & Nikora [2009] which employed volume and volume-after-time averaging. It accommodates partial transport (e.g., Wilcock & McArdell [1997], Wilcock [1997a,b]). Additionally, it provides: (1) precise definitions of the geometry and kinematics of sediment in a gravel-bed stream required to collect and analyze the high resolution spatial and temporal datasets that are becoming ever more present in both laboratory and field investigations, (2) a mathematical framework for the use of tracer grains in gravel-bed streams, including the fate of streambed-emplaced tracers as well as the dispersion of tracers in the bedload, (3) spatial and temporal averaging uncompromised by the Reynolds rules necessary to assess the nature of scale separation, and (4) a kinematic foundation for hybrid Langrangian-Eulerian models of sediment morphodynamics.

Developmental Outcomes of Late Preterm Infants From Infancy to Kindergarten

PubMed Central

Kaciroti, Niko; Richards, Blair; Oh, Wonjung; Lumeng, Julie C.

2016-01-01

OBJECTIVE: To compare developmental outcomes of late preterm infants (34–36 weeks’ gestation) with infants born at early term (37–38 weeks’ gestation) and term (39–41 weeks’ gestation), from infancy through kindergarten. METHODS: Sample included 1000 late preterm, 1800 early term, and 3200 term infants ascertained from the Early Childhood Longitudinal Study, Birth Cohort. Direct assessments of development were performed at 9 and 24 months by using the Bayley Short Form–Research Edition T-scores and at preschool and kindergarten using the Early Childhood Longitudinal Study, Birth Cohort reading and mathematics θ scores. Maternal and infant characteristics were obtained from birth certificate data and parent questionnaires. After controlling for covariates, we compared mean developmental outcomes between late preterm and full-term groups in serial cross-sectional analyses at each timepoint using multilinear regression, with pairwise comparisons testing for group differences by gestational age categories. RESULTS: With covariates controlled at all timepoints, at 9 months late preterm infants demonstrated less optimal developmental outcomes (T = 47.31) compared with infants born early term (T = 49.12) and term (T = 50.09) (P < .0001). This association was not seen at 24 months, (P = .66) but reemerged at preschool. Late preterm infants demonstrated less optimal scores in preschool reading (P = .0006), preschool mathematics (P = .0014), and kindergarten reading (P = .0007) compared with infants born at term gestation. CONCLUSIONS: Although late preterm infants demonstrate comparable developmental outcomes to full-term infants (early term and full-term gestation) at 24 months, they demonstrate less optimal reading outcomes at preschool and kindergarten timepoints. Ongoing developmental surveillance for late preterm infants is warranted into preschool and kindergarten. PMID:27456513

Percolating Contact Subnetworks on the Edge of Isostaticity

DTIC Science & Technology

2011-01-01

pressure, and cyclic loading of photoelastic disks under constant vol- ume. D. M. Walker · A. Tordesillas (B) Department of Mathematics and Statistics ...Complex networks · Spanning trees · Force chains · Force cycles · Isostatic 1 Introduction Ioannis Vardoulakis and his collaborators brought soil ...57, 706–727 (2009) 2. Vardoulakis, I.: Shear-banding and liquefaction in granular mate- rials on the basis of a Cosserat continuum theory. Ingenieur

Frontiers in Applied and Computational Mathematics 05’

DTIC Science & Technology

2005-03-01

dynamics, forcing subsets to have the same oscillation numbers and interleaving spiking times . Our analysis follows the theory of coupled systems of...continuum is described by a continuous- time stochastic process, as are their internal dynamics. Soluble factors, such as cytokines, are represent- ed...scale of a partide pas- sage time through the reaction zone. Both are realistic for many systems of physical interest. A higher order theory includes

Semantic language as a mechanism explaining the association between ADHD symptoms and reading and mathematics underachievement.

PubMed

Gremillion, Monica L; Martel, Michelle M

2012-11-01

ADHD is associated with academic underachievement, but it remains unclear what mechanism accounts for this association. Semantic language is an underexplored mechanism that provides a developmental explanation for this association. The present study will examine whether semantic language deficits explain the association between ADHD and reading and mathematics underachievement, taking into account alternative explanations for associations, including verbal working memory (WM) impairments, as well as specificity of effects to inattentive and hyperactive-impulsive ADHD symptom domains. Participants in this cross-sectional study were 546 children (54 % male) ages six to twelve (M = 9.77, SD = 1.49). ADHD symptoms were measured via maternal and teacher report during structured interviews and on standardized rating forms. Children completed standardized semantic language, verbal WM, and academic testing. Semantic language fully mediated the ADHD-reading achievement association and partially mediated the ADHD-mathematics achievement association. Verbal WM also partially mediated the ADHD-mathematics association but did not mediate the ADHD-reading achievement association. Results generalized across inattentive and hyperactive-impulsive ADHD symptom domains. Semantic language explained the association between ADHD and reading underachievement and partially explained the association between ADHD and mathematics underachievement. Together, language impairment and WM fully explained the association between ADHD and reading underachievement, in line with developmental models suggesting that language and WM conjointly influence the development of attention and subsequent academic achievement. This work has implication for the development of tailored interventions for academic underachievement in children with ADHD.

Punishment insensitivity in early childhood: A developmental, dimensional approach

PubMed Central

Nichols, Sara R.; Briggs-Gowan, Margaret; Estabrook, Ryne; Burns, James; Kestler, Jacqueline; Berman, Grace; Henry, David; Wakschlag, Lauren

2014-01-01

Impairment in learning from punishment ("punishment insensitivity") is an established feature of severe antisocial behavior in adults and youth but it has not been well studied as a developmental phenomenon. In early childhood, differentiating a normal:abnormal spectrum of punishment insensitivity is key for distinguishing normative misbehavior from atypical manifestations. This study employed a novel measure, the Multidimensional Assessment Profile of Disruptive Behavior (MAPDB), to examine the distribution, dimensionality, and external validity of punishment insensitivity in a large, demographically diverse community sample of preschoolers (three-five years) recruited from pediatric clinics (N=1,855). Caregivers completed surveys from which a seven-item Punishment Insensitivity scale was derived. Findings indicated that Punishment Insensitivity behaviors are relatively common in young children, with at least 50% of preschoolers exhibiting them sometimes. Item response theory analyses revealed a Punishment Insensitivity spectrum. Items varied along a severity continuum: most items needed to occur "Often" in order to be severe and behaviors that were qualitatively atypical or intense were more severe. Although there were item-level differences across sociodemographic groups, these were small. Construct, convergent, and divergent validity were demonstrated via association to low concern for others and noncompliance, motivational regulation, and a disruptive family context. Incremental clinical utility was demonstrated in relation to impairment. Early childhood punishment insensitivity varies along a severity continuum and is atypical when it predominates. Implications for understanding the phenomenology of emergent disruptive behavior are discussed. PMID:25425187

Mathematical approach to nonlocal interactions using a reaction-diffusion system.

PubMed

Tanaka, Yoshitaro; Yamamoto, Hiroko; Ninomiya, Hirokazu

2017-06-01

In recent years, spatial long range interactions during developmental processes have been introduced as a result of the integration of microscopic information, such as molecular events and signaling networks. They are often called nonlocal interactions. If the profile of a nonlocal interaction is determined by experiments, we can easily investigate how patterns generate by numerical simulations without detailed microscopic events. Thus, nonlocal interactions are useful tools to understand complex biosystems. However, nonlocal interactions are often inconvenient for observing specific mechanisms because of the integration of information. Accordingly, we proposed a new method that could convert nonlocal interactions into a reaction-diffusion system with auxiliary unknown variables. In this review, by introducing biological and mathematical studies related to nonlocal interactions, we will present the heuristic understanding of nonlocal interactions using a reaction-diffusion system. © 2017 Japanese Society of Developmental Biologists.

Linking Biological and Cognitive Aging: Toward Improving Characterizations of Developmental Time

PubMed Central

DeCarlo, Correne A.; Dixon, Roger A.

2011-01-01

Objectives. Chronological age is the most frequently employed predictor in life-span developmental research, despite repeated assertions that it is best conceived as a proxy for true mechanistic changes that influence cognition across time. The present investigation explores the potential that selected functional biomarkers may contribute to the more effective conceptual and operational definitions of developmental time. Methods. We used data from the Victoria Longitudinal Study to explore both static and dynamic biological or physiological markers that arguably influence process-specific mechanisms underlying cognitive changes in late life. Multilevel models were fit to test the dynamic coupling between change in theoretically relevant biomarkers (e.g., grip strength, pulmonary function) and change in select cognitive measures (e.g., executive function, episodic and semantic memory). Results. Results showed that, independent of the passage of developmental time (indexed as years in study), significant time-varying covariation was observed linking corresponding declines for select cognitive outcomes and biological markers. Discussion. Our findings support the interpretation that cognitive decline is not due to chronological aging per se but rather reflects multiple causal factors from a broad range of biological and physical health domains that operate along the age continuum. PMID:21743053

Selection of trilateral continuums of life history strategies under food web interactions.

PubMed

Fujiwara, Masami

2018-03-14

The study of life history strategies has a long history in ecology and evolution, but determining the underlying mechanisms driving the evolution of life history variation and its consequences for population regulation remains a major challenge. In this study, a food web model with constant environmental conditions was used to demonstrate how multi-species consumer-resource interactions (food-web interactions) can create variation in the duration of the adult stage, age of maturation, and fecundity among species. The model included three key ecological processes: size-dependent species interactions, energetics, and transition among developmental stages. Resultant patterns of life history variation were consistent with previous empirical observations of the life history strategies of aquatic organisms referred to as periodic, equilibrium, and opportunistic strategies (trilateral continuums of life history strategies). Results from the simulation model suggest that these three life history strategies can emerge from food web interactions even when abiotic environmental conditions are held constant.

Patterns of gender development.

PubMed

Martin, Carol Lynn; Ruble, Diane N

2010-01-01

A comprehensive theory of gender development must describe and explain long-term developmental patterning and changes and how gender is experienced in the short term. This review considers multiple views on gender patterning, illustrated with contemporary research. First, because developmental research involves understanding normative patterns of change with age, several theoretically important topics illustrate gender development: how children come to recognize gender distinctions and understand stereotypes, and the emergence of prejudice and sexism. Second, developmental researchers study the stability of individual differences over time, which elucidates developmental processes. We review stability in two domains-sex segregation and activities/interests. Finally, a new approach advances understanding of developmental patterns, based on dynamic systems theory. Dynamic systems theory is a metatheoretical framework for studying stability and change, which developed from the study of complex and nonlinear systems in physics and mathematics. Some major features and examples show how dynamic approaches have been and could be applied in studying gender development.

Patterns of Gender Development

PubMed Central

Martin, Carol Lynn; Ruble, Diane N.

2013-01-01

A comprehensive theory of gender development must describe and explain long-term developmental patterning and changes and how gender is experienced in the short term. This review considers multiple views on gender patterning, illustrated with contemporary research. First, because developmental research involves understanding normative patterns of change with age, several theoretically important topics illustrate gender development: how children come to recognize gender distinctions and understand stereotypes, and the emergence of prejudice and sexism. Second, developmental researchers study the stability of individual differences over time, which elucidates developmental processes. We review stability in two domains—sex segregation and activities/interests. Finally, a new approach advances understanding of developmental patterns, based on dynamic systems theory. Dynamic systems theory is a metatheoretical framework for studying stability and change, which developed from the study of complex and nonlinear systems in physics and mathematics. Some major features and examples show how dynamic approaches have been and could be applied in studying gender development. PMID:19575615

What Is the Long-Run Impact of Learning Mathematics During Preschool?

PubMed

Watts, Tyler W; Duncan, Greg J; Clements, Douglas H; Sarama, Julie

2018-03-01

The current study estimated the causal links between preschool mathematics learning and late elementary school mathematics achievement using variation in treatment assignment to an early mathematics intervention as an instrument for preschool mathematics change. Estimates indicate (n = 410) that a standard deviation of intervention-produced change at age 4 is associated with a 0.24-SD gain in achievement in late elementary school. This impact is approximately half the size of the association produced by correlational models relating later achievement to preschool math change, and is approximately 35% smaller than the effect reported by highly controlled ordinary least squares (OLS) regression models (Claessens et al., 2009; Watts et al., ) using national data sets. Implications for developmental theory and practice are discussed. © 2017 The Authors. Child Development © 2017 Society for Research in Child Development, Inc.

Comparison of motor delays in young children with fetal alcohol syndrome to those with prenatal alcohol exposure and with no prenatal alcohol exposure.

PubMed

Kalberg, Wendy O; Provost, Beth; Tollison, Sean J; Tabachnick, Barbara G; Robinson, Luther K; Eugene Hoyme, H; Trujillo, Phyllis M; Buckley, David; Aragon, Alfredo S; May, Philip A

2006-12-01

Researchers are increasingly considering the importance of motor functioning of children with fetal alcohol spectrum disorder (FASD). The purpose of this study was to assess the motor development of young children with fetal alcohol syndrome (FAS) to determine the presence and degree of delay in their motor skills and to compare their motor development with that of matched children without FAS. The motor development of 14 children ages 20 to 68 months identified with FAS was assessed using the Vineland Adaptive Behavior Scales (VABS). In addition, 2 comparison groups were utilized. Eleven of the children with FAS were matched for chronological age, gender, ethnicity, and communication age to: (1) 11 children with prenatal alcohol exposure who did not have FAS and (2) 11 matched children without any reported prenatal alcohol exposure. The motor scores on the VABS were compared among the 3 groups. Most of the young children with FAS in this study showed clinically important delays in their motor development as measured on the VABS Motor Domain, and their fine motor skills were significantly more delayed than their gross motor skills. In the group comparisons, the young children with FAS had significantly lower Motor Domain standard (MotorSS) scores than the children not exposed to alcohol prenatally. They also had significantly lower Fine Motor Developmental Quotients than the children in both the other groups. No significant group differences were found in gross motor scores. For MotorSS scores and Fine Motor Developmental Quotients, the means and standard errors indicated a continuum in the scores from FAS to prenatal alcohol exposure to nonexposure. These findings strongly suggest that all young children with FAS should receive complete developmental evaluations that include assessment of their motor functioning, to identify problem areas and provide access to developmental intervention programs that target deficit areas such as fine motor skills. Fine motor delays in children with FAS may be related to specific neurobehavioral deficits that affect fine motor skills. The findings support the concept of an FASD continuum in some areas of motor development.

Parental effects in ecology and evolution: mechanisms, processes and implications

PubMed Central

Badyaev, Alexander V.; Uller, Tobias

2009-01-01

As is the case with any metaphor, parental effects mean different things to different biologists—from developmental induction of novel phenotypic variation to an evolved adaptation, and from epigenetic transference of essential developmental resources to a stage of inheritance and ecological succession. Such a diversity of perspectives illustrates the composite nature of parental effects that, depending on the stage of their expression and whether they are considered a pattern or a process, combine the elements of developmental induction, homeostasis, natural selection, epigenetic inheritance and historical persistence. Here, we suggest that by emphasizing the complexity of causes and influences in developmental systems and by making explicit the links between development, natural selection and inheritance, the study of parental effects enables deeper understanding of developmental dynamics of life cycles and provides a unique opportunity to explicitly integrate development and evolution. We highlight these perspectives by placing parental effects in a wider evolutionary framework and suggest that far from being only an evolved static outcome of natural selection, a distinct channel of transmission between parents and offspring, or a statistical abstraction, parental effects on development enable evolution by natural selection by reliably transferring developmental resources needed to reconstruct, maintain and modify genetically inherited components of the phenotype. The view of parental effects as an essential and dynamic part of an evolutionary continuum unifies mechanisms behind the origination, modification and historical persistence of organismal form and function, and thus brings us closer to a more realistic understanding of life's complexity and diversity. PMID:19324619

A proposal for a new multiaxial model of psychiatric diagnosis. A continuum-based patient model derived from evolutionary developmental gene-environment interaction.

PubMed

Leigh, Hoyle

2009-01-01

To review recent genetic and neuroscientific research on psychiatric syndromes based on the current diagnostic scheme, and develop a better-fitting multiaxial patient-oriented diagnostic model. DSM I, published in 1952, considered psychiatric illnesses as reactions or extremes of adaptations of the patient's personality to stressful environmental demands. Personality itself was determined by constitution and psychodynamic development. In 1980, this continuum model gave way to an atheoretical categorical diagnostic scheme (DSM III), based on research diagnostic criteria for obtaining 'pure cultures' of patients for biological research. Subsequent research using the 'pure cultures' suggests that psychiatric syndromes represent a phenotypic continuum determined by genes, childhood traumas, and recent stress, mitigated by childhood nurturance, education, and current social support. Specific gene x childhood abuse x recent stress interactions have been discovered, which may serve as a model of how interacting vulnerability genes may or may not result in a psychiatric syndrome, depending on the individual's developmental history and current stress. A continuum model is proposed, with genes interacting with early experiences of stress or nurturance resulting in brain states that may evince minor but persistent symptoms (neurosis) or maladaptive patterns of behavior (personality disorder). The addition of recent or current stress may precipitate a major psychiatric syndrome. While a severe genetic predisposition, such as a mutation, may be sufficient to cause a major syndrome, major psychiatric syndromes are best conceptualized as dysregulation of evolutionarily adaptive brain functions, such as anxiety and vigilance. A new multiaxial model of psychiatric diagnosis is proposed based on this model: axis I for phenomenological diagnoses that include major psychiatric syndromes (e.g. depressive syndrome, psychosis), neuroses, personality disorders, and isolated symptoms; axis II for geno-neuroscience diagnoses, some of which may represent biological conditions associated with axis I, i.e. genes, specific brain morphology, and the functional state of specific brain areas based on laboratory and imaging studies; axis III for medical diseases and conditions; axis IV for stress (childhood, recent, and current); axis V for psychosocial assets (intelligence, education, school/work, social support, and global assessment of functioning) over past 5 years and current. (c) 2008 S. Karger AG, Basel.

Report of the NASA Mammalian Developmental Biology Working Group

NASA Technical Reports Server (NTRS)

Keefe, J. R.

1985-01-01

Development is considered to encompass all aspects of the mammalian life span from initial initial germ cell production through the complete life cycle to death of the organism. Thus, gamete production, fertilization, embryogenesis, implantation, fetogenesis, birth, peri- and postnatal maturation, and aging were all considered as stages of a development continuum relevant to problems of Space Biology. Deliberations thus far have been limited to stages of the development cycle from fertilization to early postnatal life. The deliberations are detailed.

Tailoring the Psychotherapy to the Borderline Patient

PubMed Central

HORWITZ, LEONARD; GABBARD, GLEN O.; ALLEN, JON G.; COLSON, DONALD B.; FRIESWYK, SIEBOLT; NEWSOM, GAVIN E.; COYNE, LOLAFAYE

1996-01-01

Views still differ as to the optimal psychodynamic treatment of borderline patients. Recommendations range from psychoanalysis and exploratory psychotherapy to an explicitly supportive treatment aimed at strengthening adaptive defenses. The authors contend that no single approach is appropriate for all patients in this wide-ranging diagnostic category, which spans a continuum from close-to-neurotic to close-to-psychotic levels of functioning. Careful differentiations based on developmental considerations, ego structures, and relationship patterns provide the basis for the optimal treatment approach. PMID:22700301

Nonlinear modelling of cancer: bridging the gap between cells and tumours

PubMed Central

Lowengrub, J S; Frieboes, H B; Jin, F; Chuang, Y-L; Li, X; Macklin, P; Wise, S M; Cristini, V

2010-01-01

Despite major scientific, medical and technological advances over the last few decades, a cure for cancer remains elusive. The disease initiation is complex, and including initiation and avascular growth, onset of hypoxia and acidosis due to accumulation of cells beyond normal physiological conditions, inducement of angiogenesis from the surrounding vasculature, tumour vascularization and further growth, and invasion of surrounding tissue and metastasis. Although the focus historically has been to study these events through experimental and clinical observations, mathematical modelling and simulation that enable analysis at multiple time and spatial scales have also complemented these efforts. Here, we provide an overview of this multiscale modelling focusing on the growth phase of tumours and bypassing the initial stage of tumourigenesis. While we briefly review discrete modelling, our focus is on the continuum approach. We limit the scope further by considering models of tumour progression that do not distinguish tumour cells by their age. We also do not consider immune system interactions nor do we describe models of therapy. We do discuss hybrid-modelling frameworks, where the tumour tissue is modelled using both discrete (cell-scale) and continuum (tumour-scale) elements, thus connecting the micrometre to the centimetre tumour scale. We review recent examples that incorporate experimental data into model parameters. We show that recent mathematical modelling predicts that transport limitations of cell nutrients, oxygen and growth factors may result in cell death that leads to morphological instability, providing a mechanism for invasion via tumour fingering and fragmentation. These conditions induce selection pressure for cell survivability, and may lead to additional genetic mutations. Mathematical modelling further shows that parameters that control the tumour mass shape also control its ability to invade. Thus, tumour morphology may serve as a predictor of invasiveness and treatment prognosis. PMID:20808719

Nonlinear modelling of cancer: bridging the gap between cells and tumours

NASA Astrophysics Data System (ADS)

Lowengrub, J. S.; Frieboes, H. B.; Jin, F.; Chuang, Y.-L.; Li, X.; Macklin, P.; Wise, S. M.; Cristini, V.

2010-01-01

Despite major scientific, medical and technological advances over the last few decades, a cure for cancer remains elusive. The disease initiation is complex, and including initiation and avascular growth, onset of hypoxia and acidosis due to accumulation of cells beyond normal physiological conditions, inducement of angiogenesis from the surrounding vasculature, tumour vascularization and further growth, and invasion of surrounding tissue and metastasis. Although the focus historically has been to study these events through experimental and clinical observations, mathematical modelling and simulation that enable analysis at multiple time and spatial scales have also complemented these efforts. Here, we provide an overview of this multiscale modelling focusing on the growth phase of tumours and bypassing the initial stage of tumourigenesis. While we briefly review discrete modelling, our focus is on the continuum approach. We limit the scope further by considering models of tumour progression that do not distinguish tumour cells by their age. We also do not consider immune system interactions nor do we describe models of therapy. We do discuss hybrid-modelling frameworks, where the tumour tissue is modelled using both discrete (cell-scale) and continuum (tumour-scale) elements, thus connecting the micrometre to the centimetre tumour scale. We review recent examples that incorporate experimental data into model parameters. We show that recent mathematical modelling predicts that transport limitations of cell nutrients, oxygen and growth factors may result in cell death that leads to morphological instability, providing a mechanism for invasion via tumour fingering and fragmentation. These conditions induce selection pressure for cell survivability, and may lead to additional genetic mutations. Mathematical modelling further shows that parameters that control the tumour mass shape also control its ability to invade. Thus, tumour morphology may serve as a predictor of invasiveness and treatment prognosis.

The Theory of Multiple Intelligences.

ERIC Educational Resources Information Center

Gardner, Howard

1987-01-01

The multiple intelligence theory is based on cultural contexts, biological analysis, developmental theories, and a vertical theory of faculties. Seven intelligences are identified: linguistic, logical mathematical, musical, spatial, bodily kinesthetic, interpersonal, and intrapersonal. The theory's educational implications are described,…

Evaluating the Effectiveness of the 2001-2002 NASA CONNECT(tm) Program

NASA Technical Reports Server (NTRS)

Pinelli, Thomas E.; Frank, Kari Lou; Lambert, Matthew A.; Williams, Amy C.

2002-01-01

NASA CONNECT(tm) is a research and standards-based, integrated mathematics, science, and technology series of 30-minute instructional distance learning (television and web-based) programs for students in grades 6-8. Respondents who evaluated the programs in the 2001-2002 NASA CONNECT(tm) series reported that (1) they used the programs in the series; (2) the goals and objectives for the series were met; (3) the programs were aligned with the national mathematics, science, and technology standards; (4) the program content was developmentally appropriate for grade level; and (5) the programs in the series enhanced and enriched the teaching of mathematics, science, and technology.

Evaluating the Effectiveness of the 2002-2003 NASA CONNECT(TM) Program

NASA Technical Reports Server (NTRS)

Pinelli, Thomas E.; Lambert, Matthew A.; Williams, Amy C.

2004-01-01

NASA CONNECT is a research-, inquiry-, and standards-based, integrated mathematics, science, and technology series of 30-minute instructional distance learning (television and web-based) programs for students in grades 6 8. Respondents who evaluated the programs in the 2002 2003 NASA CONNECT series reported that (1) they used the programs in the series; (2) the goals and objectives for the series were met; (3) the programs were aligned with the national mathematics, science, and technology standards; (4) the program content was developmentally appropriate for grade level; and (5) the programs in the series enhanced and enriched the teaching of mathematics, science, and technology.

Reasoning algebraically with IT: A cognitive perspective

NASA Astrophysics Data System (ADS)

Mok, Ida; Johnson, David

2000-12-01

The focus of this paper is on the implications of key findings and theoretical positions from social psychology and cognitive developmental psychology (Piagetian/neo-Piagetian) for the use of IT tools to support learning in algebra. Particular reference is made to the research of the UK Cognitive Acceleration through Mathematics Education (CAME) project. The feasibility of the CAME model in the exploration of mathematical relationships supported by graphics calculators was addressed in a small-scale study in Hong Kong. The research provides evidence that, with appropriate mediation, cognitive conflict can be utilised to provide valuable appropriate for students to engage in increasingly higher levels of mathematical thinking.

Number sense in infancy predicts mathematical abilities in childhood.

PubMed

Starr, Ariel; Libertus, Melissa E; Brannon, Elizabeth M

2013-11-05

Human infants in the first year of life possess an intuitive sense of number. This preverbal number sense may serve as a developmental building block for the uniquely human capacity for mathematics. In support of this idea, several studies have demonstrated that nonverbal number sense is correlated with mathematical abilities in children and adults. However, there has been no direct evidence that infant numerical abilities are related to mathematical abilities later in childhood. Here, we provide evidence that preverbal number sense in infancy predicts mathematical abilities in preschool-aged children. Numerical preference scores at 6 months of age correlated with both standardized math test scores and nonsymbolic number comparison scores at 3.5 years of age, suggesting that preverbal number sense facilitates the acquisition of numerical symbols and mathematical abilities. This relationship held even after controlling for general intelligence, indicating that preverbal number sense imparts a unique contribution to mathematical ability. These results validate the many prior studies purporting to show number sense in infancy and support the hypothesis that mathematics is built upon an intuitive sense of number that predates language.

Number sense in infancy predicts mathematical abilities in childhood

PubMed Central

Starr, Ariel; Libertus, Melissa E.; Brannon, Elizabeth M.

2013-01-01

Human infants in the first year of life possess an intuitive sense of number. This preverbal number sense may serve as a developmental building block for the uniquely human capacity for mathematics. In support of this idea, several studies have demonstrated that nonverbal number sense is correlated with mathematical abilities in children and adults. However, there has been no direct evidence that infant numerical abilities are related to mathematical abilities later in childhood. Here, we provide evidence that preverbal number sense in infancy predicts mathematical abilities in preschool-aged children. Numerical preference scores at 6 months of age correlated with both standardized math test scores and nonsymbolic number comparison scores at 3.5 years of age, suggesting that preverbal number sense facilitates the acquisition of numerical symbols and mathematical abilities. This relationship held even after controlling for general intelligence, indicating that preverbal number sense imparts a unique contribution to mathematical ability. These results validate the many prior studies purporting to show number sense in infancy and support the hypothesis that mathematics is built upon an intuitive sense of number that predates language. PMID:24145427

Attentional networks in developmental dyscalculia

PubMed Central

2010-01-01

Background Very little is known about attention deficits in developmental dyscalculia, hence, this study was designed to provide the missing information. We examined attention abilities of participants suffering from developmental dyscalculia using the attention networks test - interactions. This test was designed to examine three different attention networks--executive function, orienting and alerting--and the interactions between them. Methods Fourteen university students that were diagnosed as suffering from developmental dyscalculia--intelligence and reading abilities in the normal range and no indication of attention-deficit hyperactivity disorder--and 14 matched controls were tested using the attention networks test - interactions. All participants were given preliminary tests to measure mathematical abilities, reading, attention and intelligence. Results The results revealed deficits in the alerting network--a larger alerting effect--and in the executive function networks--a larger congruity effect in developmental dyscalculia participants. The interaction between the alerting and executive function networks was also modulated by group. In addition, developmental dyscalculia participants were slower to respond in the non-cued conditions. Conclusions These results imply specific attentional deficits in pure developmental dyscalculia. Namely, those with developmental dyscalculia seem to be deficient in the executive function and alertness networks. They suffer from difficulty in recruiting attention, in addition to the deficits in numerical processing. PMID:20157427

Attentional networks in developmental dyscalculia.

PubMed

Askenazi, Sarit; Henik, Avishai

2010-01-07

Very little is known about attention deficits in developmental dyscalculia, hence, this study was designed to provide the missing information. We examined attention abilities of participants suffering from developmental dyscalculia using the attention networks test - interactions. This test was designed to examine three different attention networks--executive function, orienting and alerting--and the interactions between them. Fourteen university students that were diagnosed as suffering from developmental dyscalculia--intelligence and reading abilities in the normal range and no indication of attention-deficit hyperactivity disorder--and 14 matched controls were tested using the attention networks test-interactions. All participants were given preliminary tests to measure mathematical abilities, reading, attention and intelligence. The results revealed deficits in the alerting network--a larger alerting effect--and in the executive function networks--a larger congruity effect in developmental dyscalculia participants. The interaction between the alerting and executive function networks was also modulated by group. In addition, developmental dyscalculia participants were slower to respond in the non-cued conditions. These results imply specific attentional deficits in pure developmental dyscalculia. Namely, those with developmental dyscalculia seem to be deficient in the executive function and alertness networks. They suffer from difficulty in recruiting attention, in addition to the deficits in numerical processing.

Case Studies.

ERIC Educational Resources Information Center

Emerson, Allen; And Others

1994-01-01

Three cases of use of collaborative learning techniques in the college classroom are described: a developmental mathematics course, a graduate-level writing project, and college science instruction. Each case includes description of specific class activities and assignments, results, and teacher concerns and comments. (MSE)

Appendix F. Developmental enforcement algorithm definition document : predictive braking enforcement algorithm definition document.

DOT National Transportation Integrated Search

2012-05-01

The purpose of this document is to fully define and describe the logic flow and mathematical equations for a predictive braking enforcement algorithm intended for implementation in a Positive Train Control (PTC) system.

Assessing the Effectiveness of a Mathematics-Focused, Instructional Technology Program for Grades 6-8: A 5-Year Trend Analysis of NASA CONNECT(tm) Evaluation Data

NASA Technical Reports Server (NTRS)

Glassman, Nanci A.; Perry, Jeannine B.; Giersch, Christopher E.; Lambert, Matthew A.; Pinelli, Thomas E.

2004-01-01

NASA CONNECT is a research-, inquiry, and standards-based, integrated mathematics, science, and technology series of 30-minute instructional distance learning (television and web-based) programs for students in grades 6 8. Respondents who evaluated the programs in the series over the first five seasons (1998-99 through 2002-03) reported that (1) they used the programs in the series; (2) the goals and objectives for the series were met; (3) the programs were aligned with the national mathematics, science, and technology standards; (4) the program content was developmentally appropriate for the grade level; and (5) the programs in the series enhanced and enriched the teaching of mathematics, science, and technology.

Mathematics in the lower primary years: A research-based perspective on curricula and teaching practice

NASA Astrophysics Data System (ADS)

Wright, Bob

1994-07-01

Drawing on current research the author explicates twelve assertions relating to curricula, teaching, learners and learning environments in lower primary school mathematics. Topics discussed include: unchanging and under-challenging curricula; the need for greater emphasis on developing children's verbal number strategies and number sense, and on activities specifically suited to prenumerical children; curriculum constraints on teachers; the role of problem solving and differing interpretations of problem solving; the need for a better understanding of how children learn mathematics; differences in children's knowledge; "anti-interventionism," discovery learning, constructivism, children's autonomy and developmental learning; the need for compensatory programs; and learning in collaborative settings. The author concludes that learning and teaching lower primary mathematics continues to be an important area of focus and challenge for teachers and researchers.

Continuum-level modelling of cellular adhesion and matrix production in aggregates.

PubMed

Geris, Liesbet; Ashbourn, Joanna M A; Clarke, Tim

2011-05-01

Key regulators in tissue-engineering processes such as cell culture and cellular organisation are the cell-cell and cell-matrix interactions. As mathematical models are increasingly applied to investigate biological phenomena in the biomedical field, it is important, for some applications, that these models incorporate an adequate description of cell adhesion. This study describes the development of a continuum model that represents a cell-in-gel culture system used in bone-tissue engineering, namely that of a cell aggregate embedded in a hydrogel. Cell adhesion is modelled through the use of non-local (integral) terms in the partial differential equations. The simulation results demonstrate that the effects of cell-cell and cell-matrix adhesion are particularly important for the survival and growth of the cell population and the production of extracellular matrix by the cells, concurring with experimental observations in the literature.

Representation of the Numerosity ‘zero’ in the Parietal Cortex of the Monkey

PubMed Central

Okuyama, Sumito; Kuki, Toshinobu; Mushiake, Hajime

2015-01-01

Zero is a fundamental concept in mathematics and modern science. Empty sets are considered a precursor of the concept of numerosity zero and a part of numerical continuum. How is numerosity zero (the absence of visual items) represented in the primate cortex? To address this question, we trained monkeys to perform numerical operations including numerosity zero. Here we show a group of neurons in the posterior parietal cortex of the monkey activated in response to numerosity ‘zero’. ‘Zero’ neurons are classified into exclusive and continuous types; the exclusive type discretely encodes numerical absence and the continuous type encodes numerical absence as a part of a numerical continuum. “Numerosity-zero” neurons enhance behavioral discrimination of not only zero numerosity but also non-zero numerosities. Representation of numerosity zero in the parietal cortex may be a precursor of non-verbal concept of zero in primates. PMID:25989598

Representation of the Numerosity 'zero' in the Parietal Cortex of the Monkey.

PubMed

Okuyama, Sumito; Kuki, Toshinobu; Mushiake, Hajime

2015-05-22

Zero is a fundamental concept in mathematics and modern science. Empty sets are considered a precursor of the concept of numerosity zero and a part of numerical continuum. How is numerosity zero (the absence of visual items) represented in the primate cortex? To address this question, we trained monkeys to perform numerical operations including numerosity zero. Here we show a group of neurons in the posterior parietal cortex of the monkey activated in response to numerosity 'zero'. 'Zero' neurons are classified into exclusive and continuous types; the exclusive type discretely encodes numerical absence and the continuous type encodes numerical absence as a part of a numerical continuum. "Numerosity-zero" neurons enhance behavioral discrimination of not only zero numerosity but also non-zero numerosities. Representation of numerosity zero in the parietal cortex may be a precursor of non-verbal concept of zero in primates.

Evaluating the Effectiveness of the 2001-2002 NASA "Why?" Files Program

NASA Technical Reports Server (NTRS)

Pinelli, Thomas E.; Frank, Kari Lou; Lambert, Matthew A.

2002-01-01

This report contains the results of the evaluation conducted for the 2001-2002 NASA 'Why?' Files program that was conducted in March 2002. The analysis is based on the results of 139 surveys collected from educators registered for the program. Respondents indicated that (1) the programs in the series are aligned with the national mathematics, science, and technology standards; (2) the programs are developmentally (grade level) appropriate; and (3) the programs enhance and enrich the teaching and learning of mathematics, science, and technology.

Analysis of airborne radiometric data. Volume 3. Topical reports

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reed, J.H.; Shreve, D.C.; Sperling, M.

1978-05-01

This volume consists of four topical reports: a general discussion of the philosophy of unfolding spectra with continuum and discrete components, a mathematical treatment of the effects of various physical parameters on the uncollided gamma-ray spectrum at aircraft elevations, a discussion of the application of the unfolding code MAZNAI to airborne data, and a discussion of the effects of the nonlinear relationship between energy deposited and pulse height in NaI(T1) detectors.

Developmental Origins of Low Mathematics Performance and Normal Variation in Twins from 7 to 9 Years

PubMed Central

Haworth, Claire M. A.; Kovas, Yulia; Petrill, Stephen A.; Plomin, Robert

2009-01-01

A previous publication reported the etiology of mathematics performance in 7-year-old twins (Oliver et al., 2004). As part of the same longitudinal study we investigated low mathematics performance and normal variation in a representative United Kingdom sample of 1713 same-sex 9-year-old twins based on teacher-assessed National Curriculum standards. Univariate individual differences and DeFries-Fulker extremes analyses were performed. Similar to our results at 7 years, all mathematics scores at 9 years showed high heritability (.62–.75) and low shared environmental estimates (.00–.11) for both the low performance group and the full sample. Longitudinal analyses were performed from 7 to 9 years. These longitudinal analyses indicated strong genetic continuity from 7 to 9 years for both low performance and mathematics in the normal range. We conclude that, despite the considerable differences in mathematics curricula from 7 to 9 years, the same genetic effects largely operate at the two ages. PMID:17539370

Developmental origins of low mathematics performance and normal variation in twins from 7 to 9 years.

PubMed

Haworth, Claire M A; Kovas, Yulia; Petrill, Stephen A; Plomin, Robert

2007-02-01

A previous publication reported the etiology of mathematics performance in 7-year-old twins (Oliver et al., 2004). As part of the same longitudinal study we investigated low mathematics performance and normal variation in a representative United Kingdom sample of 1713 same-sex 9-year-old twins based on teacher-assessed National Curriculum standards. Univariate individual differences and DeFries-Fulker extremes analyses were performed. Similar to our results at 7 years, all mathematics scores at 9 years showed high heritability (.62-.75) and low shared environmental estimates (.00-.11) for both the low performance group and the full sample. Longitudinal analyses were performed from 7 to 9 years. These longitudinal analyses indicated strong genetic continuity from 7 to 9 years for both low performance and mathematics in the normal range. We conclude that, despite the considerable differences in mathematics curricula from 7 to 9 years, the same genetic effects largely operate at the two ages.

Punishment Insensitivity in Early Childhood: A Developmental, Dimensional Approach.

PubMed

Nichols, Sara R; Briggs-Gowan, Margaret J; Estabrook, Ryne; Burns, James L; Kestler, Jacqueline; Berman, Grace; Henry, David B; Wakschlag, Lauren S

2015-08-01

Impairment in learning from punishment ("punishment insensitivity") is an established feature of severe antisocial behavior in adults and youth but it has not been well studied as a developmental phenomenon. In early childhood, differentiating a normal: abnormal spectrum of punishment insensitivity is key for distinguishing normative misbehavior from atypical manifestations. This study employed a novel measure, the Multidimensional Assessment Profile of Disruptive Behavior (MAP-DB), to examine the distribution, dimensionality, and external validity of punishment insensitivity in a large, demographically diverse community sample of preschoolers (3-5 years) recruited from pediatric clinics (N = 1,855). Caregivers completed surveys from which a seven-item Punishment Insensitivity scale was derived. Findings indicated that Punishment Insensitivity behaviors are relatively common in young children, with at least 50 % of preschoolers exhibiting them sometimes. Item response theory analyses revealed a Punishment Insensitivity spectrum. Items varied along a severity continuum: most items needed to occur "Often" in order to be severe and behaviors that were qualitatively atypical or intense were more severe. Although there were item-level differences across sociodemographic groups, these were small. Construct, convergent, and divergent validity were demonstrated via association to low concern for others and noncompliance, motivational regulation, and a disruptive family context. Incremental clinical utility was demonstrated in relation to impairment. Early childhood punishment insensitivity varies along a severity continuum and is atypical when it predominates. Implications for understanding the phenomenology of emergent disruptive behavior are discussed.

Cortical circuits for mathematical knowledge: evidence for a major subdivision within the brain's semantic networks.

PubMed

Amalric, Marie; Dehaene, Stanislas

2017-02-19

Is mathematical language similar to natural language? Are language areas used by mathematicians when they do mathematics? And does the brain comprise a generic semantic system that stores mathematical knowledge alongside knowledge of history, geography or famous people? Here, we refute those views by reviewing three functional MRI studies of the representation and manipulation of high-level mathematical knowledge in professional mathematicians. The results reveal that brain activity during professional mathematical reflection spares perisylvian language-related brain regions as well as temporal lobe areas classically involved in general semantic knowledge. Instead, mathematical reflection recycles bilateral intraparietal and ventral temporal regions involved in elementary number sense. Even simple fact retrieval, such as remembering that 'the sine function is periodical' or that 'London buses are red', activates dissociated areas for math versus non-math knowledge. Together with other fMRI and recent intracranial studies, our results indicated a major separation between two brain networks for mathematical and non-mathematical semantics, which goes a long way to explain a variety of facts in neuroimaging, neuropsychology and developmental disorders.This article is part of a discussion meeting issue 'The origins of numerical abilities'. © 2017 The Author(s).

Developmental tumors and adjacent cortical dysplasia: single or dual pathology?

PubMed

Palmini, André; Paglioli, Eliseu; Silva, Vinicius Duval

2013-12-01

Developmental tumors often lead to refractory partial seizures and constitute a well-defined, surgically remediable epilepsy syndrome. Dysplastic features are often associated with these tumors, and their significance carries both practical and conceptual relevance. If associated focal cortical dysplasia (FCD) relates to the extent of the epileptogenic tissue, then presurgical evaluation and surgical strategies should target both the tumor and the surrounding dyslaminated cortex. Furthermore, the association has been included in the recently revised classification of FCD and the epileptogenicity of this associated dysplastic tissue is crucial to validate such revision. In addition to the possibility of representing dual pathology, the association of developmental tumors and adjacent dysplasia may instead represent a single developmental lesion with distinct parts distributed along a histopathologic continuum. Moreover, the possibility that this adjacent dyslamination is of minor epileptogenic relevance should also be entertained. Surgical data show that complete resection of the solid tumors and immediately adjacent tissue harboring satellites may disrupt epileptogenic networks and lead to high rates of seizure freedom, challenging the epileptogenic relevance of more extensive adjacent dyslaminated cortex. Whether the latter is a primary or secondary abnormality and whether dyslaminated cortex in the context of a second lesion may produce seizures after complete resection of the main lesion is still to be proven. Wiley Periodicals, Inc. © 2013 International League Against Epilepsy.

Classifying acoustic signals into phoneme categories: average and dyslexic readers make use of complex dynamical patterns and multifractal scaling properties of the speech signal

PubMed Central

2015-01-01

Several competing aetiologies of developmental dyslexia suggest that the problems with acquiring literacy skills are causally entailed by low-level auditory and/or speech perception processes. The purpose of this study is to evaluate the diverging claims about the specific deficient peceptual processes under conditions of strong inference. Theoretically relevant acoustic features were extracted from a set of artificial speech stimuli that lie on a /bAk/-/dAk/ continuum. The features were tested on their ability to enable a simple classifier (Quadratic Discriminant Analysis) to reproduce the observed classification performance of average and dyslexic readers in a speech perception experiment. The ‘classical’ features examined were based on component process accounts of developmental dyslexia such as the supposed deficit in Envelope Rise Time detection and the deficit in the detection of rapid changes in the distribution of energy in the frequency spectrum (formant transitions). Studies examining these temporal processing deficit hypotheses do not employ measures that quantify the temporal dynamics of stimuli. It is shown that measures based on quantification of the dynamics of complex, interaction-dominant systems (Recurrence Quantification Analysis and the multifractal spectrum) enable QDA to classify the stimuli almost identically as observed in dyslexic and average reading participants. It seems unlikely that participants used any of the features that are traditionally associated with accounts of (impaired) speech perception. The nature of the variables quantifying the temporal dynamics of the speech stimuli imply that the classification of speech stimuli cannot be regarded as a linear aggregate of component processes that each parse the acoustic signal independent of one another, as is assumed by the ‘classical’ aetiologies of developmental dyslexia. It is suggested that the results imply that the differences in speech perception performance between average and dyslexic readers represent a scaled continuum rather than being caused by a specific deficient component. PMID:25834769

DOE Office of Scientific and Technical Information (OSTI.GOV)

Du, Qiang

The rational design of materials, the development of accurate and efficient material simulation algorithms, and the determination of the response of materials to environments and loads occurring in practice all require an understanding of mechanics at disparate spatial and temporal scales. The project addresses mathematical and numerical analyses for material problems for which relevant scales range from those usually treated by molecular dynamics all the way up to those most often treated by classical elasticity. The prevalent approach towards developing a multiscale material model couples two or more well known models, e.g., molecular dynamics and classical elasticity, each of whichmore » is useful at a different scale, creating a multiscale multi-model. However, the challenges behind such a coupling are formidable and largely arise because the atomistic and continuum models employ nonlocal and local models of force, respectively. The project focuses on a multiscale analysis of the peridynamics materials model. Peridynamics can be used as a transition between molecular dynamics and classical elasticity so that the difficulties encountered when directly coupling those two models are mitigated. In addition, in some situations, peridynamics can be used all by itself as a material model that accurately and efficiently captures the behavior of materials over a wide range of spatial and temporal scales. Peridynamics is well suited to these purposes because it employs a nonlocal model of force, analogous to that of molecular dynamics; furthermore, at sufficiently large length scales and assuming smooth deformation, peridynamics can be approximated by classical elasticity. The project will extend the emerging mathematical and numerical analysis of peridynamics. One goal is to develop a peridynamics-enabled multiscale multi-model that potentially provides a new and more extensive mathematical basis for coupling classical elasticity and molecular dynamics, thus enabling next generation atomistic-to-continuum multiscale simulations. In addition, a rigorous studyof nite element discretizations of peridynamics will be considered. Using the fact that peridynamics is spatially derivative free, we will also characterize the space of admissible peridynamic solutions and carry out systematic analyses of the models, in particular rigorously showing how peridynamics encompasses fracture and other failure phenomena. Additional aspects of the project include the mathematical and numerical analysis of peridynamics applied to stochastic peridynamics models. In summary, the project will make feasible mathematically consistent multiscale models for the analysis and design of advanced materials.« less

Cross-sectional comparisons of the mathematical performance of children with learning disabilities: are we on the right track toward comprehensive programming?

PubMed

Cawley, J F; Miller, J H

1989-04-01

This study examines the mathematical performance of 220 children from 8 years through 17 years of age diagnosed as having learning disabilities. Student records were searched for data indicating performance on standardized test instruments relating to mathematics. Data for the Woodcock-Johnson Psycho-Educational Achievement Battery math subtests and for the IQ scores from the Wechsler Intelligence Scale for Children-Revised were obtained. Comparisons were made among children at different ages and among specific age clusters. Primary attention was directed toward calculations and applications of math concepts and principles. Developmental patterns across the ages studied were discovered. Implications for long-term comprehensive programming are presented.

Evaluating the Effectiveness of the 2002-2003 NASA SCIence Files(TM) Program

NASA Technical Reports Server (NTRS)

Pinelli, Thomas E.; Lambert, Matthew A.; Williams, Amy C.

2004-01-01

NASA SCIence Files (tm) is a research-, inquiry-, and standards-based, integrated mathematics, science, and technology series of 60-minute instructional distance learning (television and web-based) programs for students in grades 3-5. Respondents who evaluated the programs in the 2002-2003 NASA SCIence Files (tm) series reported that (1) they used the programs in the series; (2) the goals and objectives for the series were met; (3) the programs were aligned with the national mathematics, science, and technology standards; (4) the program content was developmentally appropriate for grade level; and (5) the programs in the series enhanced and enriched the teaching of mathematics, science, and technology.

Longitudinal development of number line estimation and mathematics performance in primary school children.

PubMed

Friso-van den Bos, Ilona; Kroesbergen, Evelyn H; Van Luit, Johannes E H; Xenidou-Dervou, Iro; Jonkman, Lisa M; Van der Schoot, Menno; Van Lieshout, Ernest C D M

2015-06-01

Children's ability to relate number to a continuous quantity abstraction visualized as a number line is widely accepted to be predictive of mathematics achievement. However, a debate has emerged with respect to how children's placements are distributed on this number line across development. In the current study, different models were applied to children's longitudinal number placement data to get more insight into the development of number line representations in kindergarten and early primary school years. In addition, longitudinal developmental relations between number line placements and mathematical achievement, measured with a national test of mathematics, were investigated using cross-lagged panel modeling. A group of 442 children participated in a 3-year longitudinal study (ages 5-8 years) in which they completed a number-to-position task every 6 months. Individual number line placements were fitted to various models, of which a one-anchor power model provided the best fit for many of the placements at a younger age (5 or 6 years) and a two-anchor power model provided better fit for many of the children at an older age (7 or 8 years). The number of children who made linear placements also grew with age. Cross-lagged panel analyses indicated that the best fit was provided with a model in which number line acuity and mathematics performance were mutually predictive of each other rather than models in which one ability predicted the other in a non-reciprocal way. This indicates that number line acuity should not be seen as a predictor of math but that both skills influence each other during the developmental process. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

Single-Cell RNA-Sequencing Reveals a Continuous Spectrum of Differentiation in Hematopoietic Cells.

PubMed

Macaulay, Iain C; Svensson, Valentine; Labalette, Charlotte; Ferreira, Lauren; Hamey, Fiona; Voet, Thierry; Teichmann, Sarah A; Cvejic, Ana

2016-02-02

The transcriptional programs that govern hematopoiesis have been investigated primarily by population-level analysis of hematopoietic stem and progenitor cells, which cannot reveal the continuous nature of the differentiation process. Here we applied single-cell RNA-sequencing to a population of hematopoietic cells in zebrafish as they undergo thrombocyte lineage commitment. By reconstructing their developmental chronology computationally, we were able to place each cell along a continuum from stem cell to mature cell, refining the traditional lineage tree. The progression of cells along this continuum is characterized by a highly coordinated transcriptional program, displaying simultaneous suppression of genes involved in cell proliferation and ribosomal biogenesis as the expression of lineage specific genes increases. Within this program, there is substantial heterogeneity in the expression of the key lineage regulators. Overall, the total number of genes expressed, as well as the total mRNA content of the cell, decreases as the cells undergo lineage commitment. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

To Infinity. . .and beyond!

ERIC Educational Resources Information Center

Larson, Jeffrey M.; Jacobson, Michael S.; Den Ouden, Katherine M.; Basile, Carole G.

2012-01-01

Developmentally, middle school students progress from being concrete thinkers and learners to abstract thinkers. Traditional middle school mathematics instruction introduces a curriculum that is intuitive and taught within a natural trajectory of the content. However, with this traditional approach, students may miss out on being exposed to…

Behavior change in a student with a dual diagnosis of deafness and pervasive developmental disorder: a case study.

PubMed

Easterbrooks, Susan R; Handley, C Michele

The broad term pervasive developmental disorder (PPD) describes a set of symptoms that occur along a continuum of severity; these symptoms are often referred to as autism spectrum disorders (ASDs). Little is known about the incidence and prevalence of ASDs among students who are deaf or hard of hearing (DHH). Teachers of DHH students, who must work with individuals with dual diagnoses, are at a loss for guidance from the literature. The authors review the literature on ASDs (also referred to as PDD) within the DHH population, provide results of a single-subject study to reduce PDD-type behaviors in a child with hearing loss, and argue that teachers of students who are DHH must learn about practices associated with applied behavior analysis as an tool for intervening therapeutically with children with dual diagnoses of hearing loss plus an ASD.

Using Community-based Participatory Research to Adapt keepin’ it REAL: Creating a Socially, Developmentally, and Academically Appropriate Prevention Curriculum for 5th Graders

PubMed Central

Harthun, Mary L.; Dustman, Patricia A.; Reeves, Leslie J.; Marsiglia, Flavio F.; Hecht, Michael L.

2010-01-01

This paper reports on a process in which program designers, classroom teachers, and students worked together to adapt the 7th grade “keepin’ it REAL” prevention curriculum to a developmentally, socially, and academically appropriate curriculum for 5th graders. A Community-Based Participatory Research methodology (CBPR), combined with a 9-step adaptation model, emphasized a collaborative approach, both transformative and empowering. Essential adaptation elements were the Risk-to-Resiliency Continuum; the teaching of a wide range of skills including risk assessment, decision making, and resistance strategies; and, maintaining the theoretical grounding of Narrative Theory, Communication Competence, and Focus Theory of Norms. This paper describes how CBPR methodology can be conducted successfully while focusing on sustained theoretical grounding and effective research practices in a school-based setting. PMID:21057596

Developmental engineering: a new paradigm for the design and manufacturing of cell-based products. Part II: from genes to networks: tissue engineering from the viewpoint of systems biology and network science.

PubMed

Lenas, Petros; Moos, Malcolm; Luyten, Frank P

2009-12-01

The field of tissue engineering is moving toward a new concept of "in vitro biomimetics of in vivo tissue development." In Part I of this series, we proposed a theoretical framework integrating the concepts of developmental biology with those of process design to provide the rules for the design of biomimetic processes. We named this methodology "developmental engineering" to emphasize that it is not the tissue but the process of in vitro tissue development that has to be engineered. To formulate the process design rules in a rigorous way that will allow a computational design, we should refer to mathematical methods to model the biological process taking place in vitro. Tissue functions cannot be attributed to individual molecules but rather to complex interactions between the numerous components of a cell and interactions between cells in a tissue that form a network. For tissue engineering to advance to the level of a technologically driven discipline amenable to well-established principles of process engineering, a scientifically rigorous formulation is needed of the general design rules so that the behavior of networks of genes, proteins, or cells that govern the unfolding of developmental processes could be related to the design parameters. Now that sufficient experimental data exist to construct plausible mathematical models of many biological control circuits, explicit hypotheses can be evaluated using computational approaches to facilitate process design. Recent progress in systems biology has shown that the empirical concepts of developmental biology that we used in Part I to extract the rules of biomimetic process design can be expressed in rigorous mathematical terms. This allows the accurate characterization of manufacturing processes in tissue engineering as well as the properties of the artificial tissues themselves. In addition, network science has recently shown that the behavior of biological networks strongly depends on their topology and has developed the necessary concepts and methods to describe it, allowing therefore a deeper understanding of the behavior of networks during biomimetic processes. These advances thus open the door to a transition for tissue engineering from a substantially empirical endeavor to a technology-based discipline comparable to other branches of engineering.

Strategic development in exact calculation: group and individual differences in four achievement subtypes.

PubMed

Wylie, Judith; Jordan, Julie-Ann; Mulhern, Gerry

2012-09-01

This longitudinal study sought to identify developmental changes in strategy use between 5 and 7 years of age when solving exact calculation problems. Four mathematics and reading achievement subtypes were examined at four time points. Five strategies were considered: finger counting, verbal counting, delayed retrieval, automatic retrieval, and derived fact retrieval. Results provided unique insights into children's strategic development in exact calculation at this early stage. Group analysis revealed relationships between mathematical and/or reading difficulties and strategy choice, shift, and adaptiveness. Use of derived fact retrieval by 7 years of age distinguished children with mathematical difficulties from other achievement subtypes. Analysis of individual differences revealed marked heterogeneity within all subtypes, suggesting (inter alia) no marked qualitative distinction between our two mathematical difficulty subtypes. Copyright © 2012 Elsevier Inc. All rights reserved.

Intracellular Fluid Mechanics: Coupling Cytoplasmic Flow with Active Cytoskeletal Gel

NASA Astrophysics Data System (ADS)

Mogilner, Alex; Manhart, Angelika

2018-01-01

The cell is a mechanical machine, and continuum mechanics of the fluid cytoplasm and the viscoelastic deforming cytoskeleton play key roles in cell physiology. We review mathematical models of intracellular fluid mechanics, from cytoplasmic fluid flows, to the flow of a viscous active cytoskeletal gel, to models of two-phase poroviscous flows, to poroelastic models. We discuss application of these models to cell biological phenomena, such as organelle positioning, blebbing, and cell motility. We also discuss challenges of understanding fluid mechanics on the cellular scale.

The complexities in conceptualizing neurodiversity. Comment on ;Implications of the idea of neurodiversity for understanding the origins of developmental disorders; by Nobuo Masataka

NASA Astrophysics Data System (ADS)

Harris, Yvette R.

2017-03-01

The Masataka review article [1] provides an in-depth analysis of neurodiversity with specific attention given to children and adults on the Autism Spectrum Disorder continuum (ASD). In this review, Masataka chronicles the history of the neurodiversity movement, with a specific focus on the rationale for the movement, discusses the relevant research examining the perceptual, social and cognitive differences between neurotypical and neuroatypical children and adults and concludes the review with implications and suggestions for interventions and social policy.

Remodeling a tissue: subtraction adds insight.

PubMed

Axelrod, Jeffrey D

2012-11-27

Sculpting a body plan requires both patterning of gene expression and translating that pattern into morphogenesis. Developmental biologists have made remarkable strides in understanding gene expression patterning, but despite a long history of fascination with the mechanics of morphogenesis, knowledge of how patterned gene expression drives the emergence of even simple shapes and forms has grown at a slower pace. The successful merging of approaches from cell biology, developmental biology, imaging, engineering, and mathematical and computational sciences is now accelerating progress toward a fuller and better integrated understanding of the forces shaping morphogenesis.

Evaluation of the Triple Code Model of numerical processing-Reviewing past neuroimaging and clinical findings.

PubMed

Siemann, Julia; Petermann, Franz

2018-01-01

This review reconciles past findings on numerical processing with key assumptions of the most predominant model of arithmetic in the literature, the Triple Code Model (TCM). This is implemented by reporting diverse findings in the literature ranging from behavioral studies on basic arithmetic operations over neuroimaging studies on numerical processing to developmental studies concerned with arithmetic acquisition, with a special focus on developmental dyscalculia (DD). We evaluate whether these studies corroborate the model and discuss possible reasons for contradictory findings. A separate section is dedicated to the transfer of TCM to arithmetic development and to alternative accounts focusing on developmental questions of numerical processing. We conclude with recommendations for future directions of arithmetic research, raising questions that require answers in models of healthy as well as abnormal mathematical development. This review assesses the leading model in the field of arithmetic processing (Triple Code Model) by presenting knowledge from interdisciplinary research. It assesses the observed contradictory findings and integrates the resulting opposing viewpoints. The focus is on the development of arithmetic expertise as well as abnormal mathematical development. The original aspect of this article is that it points to a gap in research on these topics and provides possible solutions for future models. Copyright © 2017 Elsevier Ltd. All rights reserved.

Mathematics anxiety in children with developmental dyscalculia.

PubMed

Rubinsten, Orly; Tannock, Rosemary

2010-07-15

Math anxiety, defined as a negative affective response to mathematics, is known to have deleterious effects on math performance in the general population. However, the assumption that math anxiety is directly related to math performance, has not yet been validated. Thus, our primary objective was to investigate the effects of math anxiety on numerical processing in children with specific deficits in the acquisition of math skills (Developmental Dyscalculia; DD) by using a novel affective priming task as an indirect measure. Participants (12 children with DD and 11 typically-developing peers) completed a novel priming task in which an arithmetic equation was preceded by one of four types of priming words (positive, neutral, negative or related to mathematics). Children were required to indicate whether the equation (simple math facts based on addition, subtraction, multiplication or division) was true or false. Typically, people respond to target stimuli more quickly after presentation of an affectively-related prime than after one that is unrelated affectively. Participants with DD responded faster to targets that were preceded by both negative primes and math-related primes. A reversed pattern was present in the control group. These results reveal a direct link between emotions, arithmetic and low achievement in math. It is also suggested that arithmetic-affective priming might be used as an indirect measure of math anxiety.

Developmental dyscalculia is related to visuo-spatial memory and inhibition impairment☆

PubMed Central

Szucs, Denes; Devine, Amy; Soltesz, Fruzsina; Nobes, Alison; Gabriel, Florence

2013-01-01

Developmental dyscalculia is thought to be a specific impairment of mathematics ability. Currently dominant cognitive neuroscience theories of developmental dyscalculia suggest that it originates from the impairment of the magnitude representation of the human brain, residing in the intraparietal sulcus, or from impaired connections between number symbols and the magnitude representation. However, behavioral research offers several alternative theories for developmental dyscalculia and neuro-imaging also suggests that impairments in developmental dyscalculia may be linked to disruptions of other functions of the intraparietal sulcus than the magnitude representation. Strikingly, the magnitude representation theory has never been explicitly contrasted with a range of alternatives in a systematic fashion. Here we have filled this gap by directly contrasting five alternative theories (magnitude representation, working memory, inhibition, attention and spatial processing) of developmental dyscalculia in 9–10-year-old primary school children. Participants were selected from a pool of 1004 children and took part in 16 tests and nine experiments. The dominant features of developmental dyscalculia are visuo-spatial working memory, visuo-spatial short-term memory and inhibitory function (interference suppression) impairment. We hypothesize that inhibition impairment is related to the disruption of central executive memory function. Potential problems of visuo-spatial processing and attentional function in developmental dyscalculia probably depend on short-term memory/working memory and inhibition impairments. The magnitude representation theory of developmental dyscalculia was not supported. PMID:23890692

Inhibition, Conflict Detection, and Number Conservation

ERIC Educational Resources Information Center

Lubin, Amélie; Simon, Grégory; Houdé, Olivier; De Neys, Wim

2015-01-01

The acquisition of number conservation is a critical step in children's numerical and mathematical development. Classic developmental studies have established that children's number conservation is often biased by misleading intuitions. However, the precise nature of these conservation errors is not clear. A key question is whether conservation…

77 FR 13297 - Applications for New Awards; Education Research and Special Education Research Grant Programs

Federal Register 2010, 2011, 2012, 2013, 2014

2012-03-06

... national leadership in expanding fundamental knowledge and understanding of developmental and school..., Management, and Leadership Mathematics and Science Education Postsecondary and Adult Education Reading and...: Policies, Organization, Management, and Leadership. [ssquf] Early Learning Programs and Policies. [ssquf...

Computer Based Screening Dyscalculia: Cognitive and Neuropsychological Correlates

ERIC Educational Resources Information Center

Cangoz, Banu; Altun, Arif; Olkun, Sinan; Kacar, Funda

2013-01-01

Mathematical skills are becoming increasingly critical for achieving academic and professional success. Developmental dyscalculia (DD) is a childhood-onset disorder characterized by the presence of abnormalities in the acquisition of arithmetic skills affecting approximately 5% of school age children. Diagnosing students with possible dyscalculia…

[Assessment.

ERIC Educational Resources Information Center

Boylan, Hunter R., Ed.; Kerstiens, Gene, Ed.

1989-01-01

These four serial issues examine the effectiveness and appropriateness of a variety of assessment tests as well as their relationship to developmental education. Included are reviews of the following tests: (1) the Comparative Guidance and Placement Program, a self-scoring test of English and mathematics; (2) the Stanford Achievement Test, an…

Affect: How Important Is It?

ERIC Educational Resources Information Center

Higbee, Jeanne L.; Dwinell, Patricia L.

1995-01-01

Reviews the current literature to determine the extent to which affect influences the achievement levels of students. Highlights research findings in mathematics, reading, writing, and instructional strategies. Suggests that although affect may be a significant factor in determining the academic success of developmental freshmen, more research is…

Number Processing and Heterogeneity of Developmental Dyscalculia: Subtypes With Different Cognitive Profiles and Deficits.

PubMed

Skagerlund, Kenny; Träff, Ulf

2016-01-01

This study investigated if developmental dyscalculia (DD) in children with different profiles of mathematical deficits has the same or different cognitive origins. The defective approximate number system hypothesis and the access deficit hypothesis were tested using two different groups of children with DD (11-13 years old): a group with arithmetic fact dyscalculia (AFD) and a group with general dyscalculia (GD). Several different aspects of number magnitude processing were assessed in these two groups and compared with age-matched typically achieving children. The GD group displayed weaknesses with both symbolic and nonsymbolic number processing, whereas the AFD group displayed problems only with symbolic number processing. These findings provide evidence that the origins of DD in children with different profiles of mathematical problems diverge. Children with GD have impairment in the innate approximate number system, whereas children with AFD suffer from an access deficit. These findings have implications for researchers' selection procedures when studying dyscalculia, and also for practitioners in the educational setting. © Hammill Institute on Disabilities 2014.

Developmental and Individual Differences in Understanding of Fractions

PubMed Central

Siegler, Robert S.; Pyke, Aryn A.

2014-01-01

We examined developmental and individual differences in 6th and 8th graders’ fraction arithmetic and overall mathematics achievement and related them to differences in understanding of fraction magnitudes, whole number division, executive functioning, and metacognitive judgments within a cross sectional design. Results indicated that the difference between low achieving and higher achieving children’s fraction arithmetic knowledge, already substantial in 6th grade, was much greater in 8th grade. The fraction arithmetic knowledge of low achieving children was similar in the two grades, whereas higher achieving children showed much greater knowledge in 8th than 6th grade, despite both groups having been in the same classrooms, using the same textbooks, and having the same teachers and classmates. Individual differences in both fraction arithmetic and mathematics achievement test scores were predicted by differences in fraction magnitude knowledge and whole number division, even after the contributions of reading achievement and executive functioning were statistically controlled. Instructional implications of the findings are discussed. PMID:23244401

Sex Differences in Mathematics and Reading Achievement Are Inversely Related: Within- and Across-Nation Assessment of 10 Years of PISA Data

PubMed Central

Stoet, Gijsbert; Geary, David C.

2013-01-01

We analyzed one decade of data collected by the Programme for International Student Assessment (PISA), including the mathematics and reading performance of nearly 1.5 million 15 year olds in 75 countries. Across nations, boys scored higher than girls in mathematics, but lower than girls in reading. The sex difference in reading was three times as large as in mathematics. There was considerable variation in the extent of the sex differences between nations. There are countries without a sex difference in mathematics performance, and in some countries girls scored higher than boys. Boys scored lower in reading in all nations in all four PISA assessments (2000, 2003, 2006, 2009). Contrary to several previous studies, we found no evidence that the sex differences were related to nations’ gender equality indicators. Further, paradoxically, sex differences in mathematics were consistently and strongly inversely correlated with sex differences in reading: Countries with a smaller sex difference in mathematics had a larger sex difference in reading and vice versa. We demonstrate that this was not merely a between-nation, but also a within-nation effect. This effect is related to relative changes in these sex differences across the performance continuum: We did not find a sex difference in mathematics among the lowest performing students, but this is where the sex difference in reading was largest. In contrast, the sex difference in mathematics was largest among the higher performing students, and this is where the sex difference in reading was smallest. The implication is that if policy makers decide that changes in these sex differences are desired, different approaches will be needed to achieve this for reading and mathematics. Interventions that focus on high-achieving girls in mathematics and on low achieving boys in reading are likely to yield the strongest educational benefits. PMID:23516422

Sex differences in mathematics and reading achievement are inversely related: within- and across-nation assessment of 10 years of PISA data.

PubMed

Stoet, Gijsbert; Geary, David C

2013-01-01

We analyzed one decade of data collected by the Programme for International Student Assessment (PISA), including the mathematics and reading performance of nearly 1.5 million 15 year olds in 75 countries. Across nations, boys scored higher than girls in mathematics, but lower than girls in reading. The sex difference in reading was three times as large as in mathematics. There was considerable variation in the extent of the sex differences between nations. There are countries without a sex difference in mathematics performance, and in some countries girls scored higher than boys. Boys scored lower in reading in all nations in all four PISA assessments (2000, 2003, 2006, 2009). Contrary to several previous studies, we found no evidence that the sex differences were related to nations' gender equality indicators. Further, paradoxically, sex differences in mathematics were consistently and strongly inversely correlated with sex differences in reading: Countries with a smaller sex difference in mathematics had a larger sex difference in reading and vice versa. We demonstrate that this was not merely a between-nation, but also a within-nation effect. This effect is related to relative changes in these sex differences across the performance continuum: We did not find a sex difference in mathematics among the lowest performing students, but this is where the sex difference in reading was largest. In contrast, the sex difference in mathematics was largest among the higher performing students, and this is where the sex difference in reading was smallest. The implication is that if policy makers decide that changes in these sex differences are desired, different approaches will be needed to achieve this for reading and mathematics. Interventions that focus on high-achieving girls in mathematics and on low achieving boys in reading are likely to yield the strongest educational benefits.

Morphing Continuum Theory: A First Order Approximation to the Balance Laws

NASA Astrophysics Data System (ADS)

Wonnell, Louis; Cheikh, Mohamad Ibrahim; Chen, James

2017-11-01

Morphing Continuum Theory is constructed under the framework of Rational Continuum Mechanics (RCM) for fluid flows with inner structure. This multiscale theory has been successfully emplyed to model turbulent flows. The framework of RCM ensures the mathematical rigor of MCT, but contains new material constants related to the inner structure. The physical meanings of these material constants have yet to be determined. Here, a linear deviation from the zeroth-order Boltzmann-Curtiss distribution function is derived. When applied to the Boltzmann-Curtiss equation, a first-order approximation of the MCT governing equations is obtained. The integral equations are then related to the appropriate material constants found in the heat flux, Cauchy stress, and moment stress terms in the governing equations. These new material properties associated with the inner structure of the fluid are compared with the corresponding integrals, and a clearer physical interpretation of these coefficients emerges. The physical meanings of these material properties is determined by analyzing previous results obtained from numerical simulations of MCT for compressible and incompressible flows. The implications for the physics underlying the MCT governing equations will also be discussed. This material is based upon work supported by the Air Force Office of Scientific Research under Award Number FA9550-17-1-0154.

Evaluating the Effectiveness of the 2000-2001 NASA CONNECT(TM) Program

NASA Technical Reports Server (NTRS)

Pinelli, Thomas E.; Frank, Kari Lou; Lambert, Matthew A.

2002-01-01

This report contains the results of the evaluation conducted for the 2000-2001 NASA CONNECT(TM) program conducted in March 2001. The analysis is based on the results collected from 154 surveys collected from educators registered for the program. Respondents indicated that the objectives for each program were met; the programs were aligned with the national (mathematics, science, and technology) standards; the programs were developmentally (grade level) appropriate; and the programs in the 2000-2001 NASA CONNECT(TM) series enhanced/enriched the teaching of mathematics, science, and technology.

On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process.

PubMed

Flegg, Jennifer A; Menon, Shakti N; Maini, Philip K; McElwain, D L Sean

2015-01-01

Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e., capillary sprout growth, has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made toward the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration.

On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process

PubMed Central

Flegg, Jennifer A.; Menon, Shakti N.; Maini, Philip K.; McElwain, D. L. Sean

2015-01-01

Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e., capillary sprout growth, has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made toward the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration. PMID:26483695

Predicting reading and mathematics from neural activity for feedback learning.

PubMed

Peters, Sabine; Van der Meulen, Mara; Zanolie, Kiki; Crone, Eveline A

2017-01-01

Although many studies use feedback learning paradigms to study the process of learning in laboratory settings, little is known about their relevance for real-world learning settings such as school. In a large developmental sample (N = 228, 8-25 years), we investigated whether performance and neural activity during a feedback learning task predicted reading and mathematics performance 2 years later. The results indicated that feedback learning performance predicted both reading and mathematics performance. Activity during feedback learning in left superior dorsolateral prefrontal cortex (DLPFC) predicted reading performance, whereas activity in presupplementary motor area/anterior cingulate cortex (pre-SMA/ACC) predicted mathematical performance. Moreover, left superior DLPFC and pre-SMA/ACC activity predicted unique variance in reading and mathematics ability over behavioral testing of feedback learning performance alone. These results provide valuable insights into the relationship between laboratory-based learning tasks and learning in school settings, and the value of neural assessments for prediction of school performance over behavioral testing alone. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Executive functioning as a predictor of children's mathematics ability: inhibition, switching, and working memory.

PubMed

Bull, R; Scerif, G

2001-01-01

Children's mathematical skills were considered in relation to executive functions. Using multiple measures--including the Wisconsin Card Sorting Task (WCST), dual-task performance, Stroop task, and counting span-it was found that mathematical ability was significantly correlated with all measures of executive functioning, with the exception of dual-task performance. Furthermore, regression analyses revealed that each executive function measure predicted unique variance in mathematics ability. These results are discussed in terms of a central executive with diverse functions (Shallice & Burgess, 1996) and with recent evidence from Miyake, et al. (2000) showing the unity and diversity among executive functions. It is proposed that the particular difficulties for children of lower mathematical ability are lack of inhibition and poor working memory, which result in problems with switching and evaluation of new strategies for dealing with a particular task. The practical and theoretical implications of these results are discussed, along with suggestions for task changes and longitudinal studies that would clarify theoretical and developmental issues related to executive functioning.

A developmental basis for stochasticity in floral organ numbers

PubMed Central

Kitazawa, Miho S.; Fujimoto, Koichi

2014-01-01

Stochasticity ubiquitously inevitably appears at all levels from molecular traits to multicellular, morphological traits. Intrinsic stochasticity in biochemical reactions underlies the typical intercellular distributions of chemical concentrations, e.g., morphogen gradients, which can give rise to stochastic morphogenesis. While the universal statistics and mechanisms underlying the stochasticity at the biochemical level have been widely analyzed, those at the morphological level have not. Such morphological stochasticity is found in foral organ numbers. Although the floral organ number is a hallmark of floral species, it can distribute stochastically even within an individual plant. The probability distribution of the floral organ number within a population is usually asymmetric, i.e., it is more likely to increase rather than decrease from the modal value, or vice versa. We combined field observations, statistical analysis, and mathematical modeling to study the developmental basis of the variation in floral organ numbers among 50 species mainly from Ranunculaceae and several other families from core eudicots. We compared six hypothetical mechanisms and found that a modified error function reproduced much of the asymmetric variation found in eudicot floral organ numbers. The error function is derived from mathematical modeling of floral organ positioning, and its parameters represent measurable distances in the floral bud morphologies. The model predicts two developmental sources of the organ-number distributions: stochastic shifts in the expression boundaries of homeotic genes and a semi-concentric (whorled-type) organ arrangement. Other models species- or organ-specifically reproduced different types of distributions that reflect different developmental processes. The organ-number variation could be an indicator of stochasticity in organ fate determination and organ positioning. PMID:25404932

Mathematical Physics in Italy in the XIX Century: The Theory of Elasticity

NASA Astrophysics Data System (ADS)

Capecchi, Danilo

In the second half of the nineteenth century there was in Italy an important group of mathematicians who focused their attention on mathematical physics. The most prominent of them were Enrico Betti, Eugenio Beltrami, Gregorio Ricci-Curbastro and some others (Vito Volterra, Carlo Somigliana and Tullio Levi Civita) whose activity persevered for many years in the twentieth century. In this article, I will write about the contribution of this group to the theory of elasticity. The best representative writing on continuum mechanics and elasticity as theories of mathematical physics is presented in the book Teoria della elasticità by Enrico Betti. The book is interesting not only for the particular results found but also for its structure which became paradigmatic for the development of subsequent texts on elasticity, not only those in Italian. Betti's interest was concentrated on the mathematical aspects of a physical theory. Physical principles are not discussed; they are only exposed in the most formal way possible. The objective is to arrive, without discussing epistemological or empirical problems, at the formulation and solution of differential equations that rule elasticity, as had become classic in the emerging mathematical physics. Beltrami wrote no complete books on elasticity; however, his contribution to this field was perhaps more original than that of Betti. A similar consideration holds true for Volterra and Somigliana.

What Is Developmentally Appropriate Teaching?

ERIC Educational Resources Information Center

Clements, Douglas H.; Fuson, Karen C.; Sarama, Julie

2017-01-01

Teachers are on the front line in any educational controversy. Increasingly, some bloggers, newspaper articles, and other media have criticized the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) as being inappropriate for children in kindergarten and first grade. However, both research and expert practice reveal that children are…

Young Scientists Discuss Recent Advances, Future Challenges.

ERIC Educational Resources Information Center

Baum, Rudy M.

1989-01-01

Discusses a National Academy of Science forum at which a group of outstanding young researchers in astronomy, molecular and developmental biology, physics, chemistry, mathematics, atmospheric science, and materials science met for three days of formal presentations and informal conversations. Provides a short synopsis of major speakers. (MVL)

Undergraduate Student Motivation in Modularized Developmental Mathematics Courses

ERIC Educational Resources Information Center

Pachlhofer, Keith A.

2017-01-01

This study used the Motivated Strategies for Learning Questionnaire in modularized courses at three institutions across the nation (N = 189), and multiple regression was completed to investigate five categories of student motivation that predicted academic success and course completion. The overall multiple regression analysis was significant and…

Community College Pathways: 2013-2014 Descriptive Report

ERIC Educational Resources Information Center

Sowers, Nicole; Yamada, Hiroyuki

2015-01-01

The Community College Pathways initiative consists of two pathways, Statway® and Quantway®, that accelerate post-secondary students' progress through their developmental mathematics sequence and a college-level course for credit. Launched in 2011, the Pathways have been remarkably successful, helping thousands of students achieve success in…

A Concurrent Support Course for Intermediate Algebra

ERIC Educational Resources Information Center

Cooper, Cameron I.

2011-01-01

This article summarizes the creation and implementation of a concurrent support class for TRS 92--Intermediate Algebra, a developmental mathematics course at Fort Lewis College in Durango, Colorado. The concurrent course outlined in this article demonstrates a statistically significant increase in student success rates since its inception.…

Effectiveness of a developmental curricular design to graduate culturally competent health practitioners.

PubMed

Boggis, Debra

2012-01-01

With the goal to facilitate cultural competency development of students enrolled in graduate-level health professional education, this study examined the effectiveness of a curricular program guided by the Intercultural Developmental Continuum (IDC) as measured by the Intercultural Developmental Inventory (IDI). The IDI was administered to 17 occupational therapy (OT) students and a control group of 25 non-OT health professional students upon matriculation into their respective programs of graduate study and again upon completion of 3 years of study. OT students participated in a cultural curricular design guided by the IDC, while the control group participated in cultural study not guided by the IDC. Though OT students did not show a significant change in overall developmental orientation mean scores from pre-test to post-test (t = 0.847, p = 0.41), the results indicate that the designed intercultural curriculum increased intercultural competence among those OT students who began their program with the monocultural mindset of polarization (an "us vs. them" evaluative viewpoint) and moved to the interculturally transitional mindset of minimization (recognizing cultural commonalities and elimination of the "us vs. them" mindset). The control group showed a significant decrease in developmental orientation mean scores at post-test (t = 6.1, p < 0.001). No significant group or group by baseline interaction effects were found when comparing overall post-developmental scores adjusting for baseline (F = 2.4, p = 0.131). The curriculum design as guided by the IDC, though it did not significantly increase overall cultural competency of OT students, appears to have mitigated a decrease in competence. Results suggest that the cultural challenges that students face appear to be considerable and, without targeted, integrated intercultural preparation, can overwhelm new health professionals' intercultural capability.

Design and evaluation of the computer-based training program Calcularis for enhancing numerical cognition

PubMed Central

Käser, Tanja; Baschera, Gian-Marco; Kohn, Juliane; Kucian, Karin; Richtmann, Verena; Grond, Ursina; Gross, Markus; von Aster, Michael

2013-01-01

This article presents the design and a first pilot evaluation of the computer-based training program Calcularis for children with developmental dyscalculia (DD) or difficulties in learning mathematics. The program has been designed according to insights on the typical and atypical development of mathematical abilities. The learning process is supported through multimodal cues, which encode different properties of numbers. To offer optimal learning conditions, a user model completes the program and allows flexible adaptation to a child's individual learning and knowledge profile. Thirty-two children with difficulties in learning mathematics completed the 6–12-weeks computer training. The children played the game for 20 min per day for 5 days a week. The training effects were evaluated using neuropsychological tests. Generally, children benefited significantly from the training regarding number representation and arithmetic operations. Furthermore, children liked to play with the program and reported that the training improved their mathematical abilities. PMID:23935586

Intrinsic Motivation and Achievement in Mathematics in Elementary School: A Longitudinal Investigation of Their Association.

PubMed

Garon-Carrier, Gabrielle; Boivin, Michel; Guay, Frédéric; Kovas, Yulia; Dionne, Ginette; Lemelin, Jean-Pascal; Séguin, Jean R; Vitaro, Frank; Tremblay, Richard E

2016-01-01

This study examined the associations between intrinsic motivation and achievement in mathematics in a sample of 1,478 Canadian school-age children followed from Grades 1 to 4 (ages 7-10). Children self-reported their intrinsic motivation toward mathematics, whereas achievement was measured through direct assessment of mathematics abilities. Cross-lagged models showed that achievement predicted intrinsic motivation from Grades 1 to 2, and from Grades 2 to 4. However, intrinsic motivation did not predict achievement at any time. This developmental pattern of association was gender invariant. Contrary to the hypothesis that motivation and achievement are reciprocally associated over time, our results point to a directional association from prior achievement to subsequent intrinsic motivation. Results are discussed in light of their theoretical and practical implications. © 2015 The Authors. Child Development © 2015 Society for Research in Child Development, Inc.

Developing workshop module of realistic mathematics education: Follow-up workshop

NASA Astrophysics Data System (ADS)

Palupi, E. L. W.; Khabibah, S.

2018-01-01

Realistic Mathematics Education (RME) is a learning approach which fits the aim of the curriculum. The success of RME in teaching mathematics concepts, triggering students’ interest in mathematics and teaching high order thinking skills to the students will make teachers start to learn RME. Hence, RME workshop is often offered and done. This study applied development model proposed by Plomp. Based on the study by RME team, there are three kinds of RME workshop: start-up workshop, follow-up workshop, and quality boost. However, there is no standardized or validated module which is used in that workshops. This study aims to develop a module of RME follow-up workshop which is valid and can be used. Plopm’s developmental model includes materials analysis, design, realization, implementation, and evaluation. Based on the validation, the developed module is valid. While field test shows that the module can be used effectively.

Cognitive and Neural Correlates of Mathematical Giftedness in Adults and Children: A Review

PubMed Central

Myers, Timothy; Carey, Emma; Szűcs, Dénes

2017-01-01

Most mathematical cognition research has focused on understanding normal adult function and child development as well as mildly and moderately impaired mathematical skill, often labeled developmental dyscalculia and/or mathematical learning disability. In contrast, much less research is available on cognitive and neural correlates of gifted/excellent mathematical knowledge in adults and children. In order to facilitate further inquiry into this area, here we review 40 available studies, which examine the cognitive and neural basis of gifted mathematics. Studies associated a large number of cognitive factors with gifted mathematics, with spatial processing and working memory being the most frequently identified contributors. However, the current literature suffers from low statistical power, which most probably contributes to variability across findings. Other major shortcomings include failing to establish domain and stimulus specificity of findings, suggesting causation without sufficient evidence and the frequent use of invalid backward inference in neuro-imaging studies. Future studies must increase statistical power and neuro-imaging studies must rely on supporting behavioral data when interpreting findings. Studies should investigate the factors shown to correlate with math giftedness in a more specific manner and determine exactly how individual factors may contribute to gifted math ability. PMID:29118725

Mathematics interventions for children and adolescents with Down syndrome: a research synthesis.

PubMed

Lemons, C J; Powell, S R; King, S A; Davidson, K A

2015-08-01

Many children and adolescents with Down syndrome fail to achieve proficiency in mathematics. Researchers have suggested that tailoring interventions based on the behavioural phenotype may enhance efficacy. The research questions that guided this review were (1) what types of mathematics interventions have been empirically evaluated with children and adolescents with Down syndrome?; (2) do the studies demonstrate sufficient methodological rigor?; (3) is there evidence of efficacy for the evaluated mathematics interventions?; and (4) to what extent have researchers considered aspects of the behavioural phenotype in selecting, designing and/or implementing mathematics interventions for children and adolescents with Down syndrome? Nine studies published between 1989 and 2012 were identified for inclusion. Interventions predominantly focused on early mathematics skills and reported positive outcomes. However, no study met criteria for methodological rigor. Further, no authors explicitly considered the behavioural phenotype. Additional research using rigorous experimental designs is needed to evaluate the efficacy of mathematics interventions for children and adolescents with Down syndrome. Suggestions for considering the behavioural phenotype in future research are provided. © 2015 MENCAP and International Association of the Scientific Study of Intellectual and Developmental Disabilities and John Wiley & Sons Ltd.

Duplication of the pituitary gland associated with multiple blastogenesis defects: Duplication of the pituitary gland (DPG)-plus syndrome. Case report and review of literature.

PubMed

Manjila, Sunil; Miller, Erin A; Vadera, Sumeet; Goel, Rishi K; Khan, Fahd R; Crowe, Carol; Geertman, Robert T

2012-01-01

Duplication of the pituitary gland (DPG) is a rare craniofacial developmental anomaly occurring during blastogenesis with postulated etiology such as incomplete twinning, teratogens, median cleft face syndrome or splitting of the notochord. The complex craniocaudal spectrum of blastogenesis defects associated with DPG is examined with an illustrative case. We report for the first time in the medical literature some unique associations with DPG, such as a clival encephalocele, third cerebral peduncle, duplicate odontoid process and a double tongue with independent volitional control. This patient also has the previously reported common associations such as duplicated sella, cleft palate, hypertelorism, callosal agenesis, hypothalamic enlargement, nasopharyngeal teratoma, fenestrated basilar artery and supernumerary teeth. This study also reviews 37 cases of DPG identified through MEDLINE literature search from 1880 to 2011. It provides a detailed analysis of the current case through physical examination and imaging. The authors propose that the developmental deformities associated with duplication of pituitary gland (DPG) occur as part of a developmental continuum, not as chance associations. Considering the fact that DPG is uniquely and certainly present throughout the spectrum of these blastogenesis defects, we suggest the term DPG-plus syndrome.

Computer modeling in developmental biology: growing today, essential tomorrow.

PubMed

Sharpe, James

2017-12-01

D'Arcy Thompson was a true pioneer, applying mathematical concepts and analyses to the question of morphogenesis over 100 years ago. The centenary of his famous book, On Growth and Form , is therefore a great occasion on which to review the types of computer modeling now being pursued to understand the development of organs and organisms. Here, I present some of the latest modeling projects in the field, covering a wide range of developmental biology concepts, from molecular patterning to tissue morphogenesis. Rather than classifying them according to scientific question, or scale of problem, I focus instead on the different ways that modeling contributes to the scientific process and discuss the likely future of modeling in developmental biology. © 2017. Published by The Company of Biologists Ltd.

Quantum mechanics problems in observer's mathematics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khots, Boris; Khots, Dmitriy; iMath Consulting LLC, Omaha, Nebraska

2012-11-06

This work considers the ontology, guiding equation, Schrodinger's equation, relation to the Born Rule, the conditional wave function of a subsystem in a setting of arithmetic, algebra and topology provided by Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. Certain results and communications pertaining to solutions of these problems are provided. In particular, we prove the following theorems: Theorem I (Two-slit interference). Let {Psi}{sub 1} be a wave from slit 1, {Psi}{sub 2} - from slit 2, andmore » {Psi} = {Psi}{sub 1}+{Psi}{sub 2}. Then the probability of {Psi} being a wave equals to 0.5. Theorem II (k-bodies solution). For W{sub n} from m-observer point of view with m>log{sub 10}((2 Multiplication-Sign 10{sup 2n}-1){sup 2k}+1), the probability of standard expression of Hamiltonian variation is less than 1 and depends on n,m,k.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zimmerman, Jonathan A.; Jones, Reese E.; Templeton, Jeremy Alan

Materials with characteristic structures at nanoscale sizes exhibit significantly different mechani-cal responses from those predicted by conventional, macroscopic continuum theory. For example,nanocrystalline metals display an inverse Hall-Petch effect whereby the strength of the materialdecreases with decreasing grain size. The origin of this effect is believed to be a change in defor-mation mechanisms from dislocation motion across grains and pileup at grain boundaries at mi-croscopic grain sizes to rotation of grains and deformation within grain boundary interface regionsfor nanostructured materials. These rotational defects are represented by the mathematical conceptof disclinations. The ability to capture these effects within continuum theory, thereby connectingnanoscalemore » materials phenomena and macroscale behavior, has eluded the research community.The goal of our project was to develop a consistent theory to model both the evolution ofdisclinations and their kinetics. Additionally, we sought to develop approaches to extract contin-uum mechanical information from nanoscale structure to verify any developed continuum theorythat includes dislocation and disclination behavior. These approaches yield engineering-scale ex-pressions to quantify elastic and inelastic deformation in all varieties of materials, even those thatpossess highly directional bonding within their molecular structures such as liquid crystals, cova-lent ceramics, polymers and biological materials. This level of accuracy is critical for engineeringdesign and thermo-mechanical analysis is performed in micro- and nanosystems. The researchproposed here innovates on how these nanoscale deformation mechanisms should be incorporatedinto a continuum mechanical formulation, and provides the foundation upon which to develop ameans for predicting the performance of advanced engineering materials.4 AcknowledgmentThe authors acknowledge helpful discussions with Farid F. Abraham, Youping Chen, Terry J.Delph, Remi Dingreville, James W. Foulk III, Robert J. Hardy, Richard Lehoucq, Alejandro Mota,Gregory J. Wagner, Edmund B. Webb III and Xiaowang Zhou. Support for this project was pro-vided by the Enabling Predictive Simulation Investment Area of Sandia's Laboratory DirectedResearch and Development (LDRD) program.5« less

Developmental Change in the Influence of Domain-General Abilities and Domain-Specific Knowledge on Mathematics Achievement: An Eight-Year Longitudinal Study

PubMed Central

Geary, David C.; Nicholas, Alan; Li, Yaoran; Sun, Jianguo

2016-01-01

The contributions of domain-general abilities and domain-specific knowledge to subsequent mathematics achievement were longitudinally assessed (n = 167) through 8th grade. First grade intelligence and working memory and prior grade reading achievement indexed domain-general effects and domain-specific effects were indexed by prior grade mathematics achievement and mathematical cognition measures of prior grade number knowledge, addition skills, and fraction knowledge. Use of functional data analysis enabled grade-by-grade estimation of overall domain-general and domain-specific effects on subsequent mathematics achievement, the relative importance of individual domain-general and domain-specific variables on this achievement, and linear and non-linear across-grade estimates of these effects. The overall importance of domain-general abilities for subsequent achievement was stable across grades, with working memory emerging as the most important domain-general ability in later grades. The importance of prior mathematical competencies on subsequent mathematics achievement increased across grades, with number knowledge and arithmetic skills critical in all grades and fraction knowledge in later grades. Overall, domain-general abilities were more important than domain-specific knowledge for mathematics learning in early grades but general abilities and domain-specific knowledge were equally important in later grades. PMID:28781382

Waves and patterning in developmental biology: vertebrate segmentation and feather bud formation as case studies

PubMed Central

Baker, Ruth E.; Schnell, Santiago; Maini, Philip K.

2014-01-01

In this article we will discuss the integration of developmental patterning mechanisms with waves of competency that control the ability of a homogeneous field of cells to react to pattern forming cues and generate spatially heterogeneous patterns. We base our discussion around two well known patterning events that take place in the early embryo: somitogenesis and feather bud formation. We outline mathematical models to describe each patterning mechanism, present the results of numerical simulations and discuss the validity of each model in relation to our example patterning processes. PMID:19557684

A new way of describing meiosis that uses fractal dimension to predict metaphase I

PubMed Central

2005-01-01

Meiosis, the reductive nuclear division, is a continuum, but for purposes of communication, is described in stages. In sexually-reproducing organisms, including the dwarf mistletoe Arceuthobium americanum, prophase I of meiosis is prolonged (8 months for female A. americanum). Conversely, metaphase I, where chromosome pairs line up along a dividing cell's "equator", is relatively brief, difficult to predict, but critical regarding the random distribution of the paternal and maternal chromosomes in sexual organisms. However, descriptions of meiosis as either a continuum or stages are limited to qualitative observations. A quantification of meiosis can provide mathematical descriptors and allow for the prediction of when chromosomes reach the equator; this will not only be useful to researchers of cell division, but also to those requiring a large sample of metaphase I materials. Here, the probability-density function was used to calculate the fractal dimension of A. americanum nuclei undergoing early meiosis, and it predicted the onset of metaphase I by 2 days. PMID:16094465

Homogenized boundary conditions and resonance effects in Faraday cages

PubMed Central

Hewitt, I. J.

2016-01-01

We present a mathematical study of two-dimensional electrostatic and electromagnetic shielding by a cage of conducting wires (the so-called ‘Faraday cage effect’). Taking the limit as the number of wires in the cage tends to infinity, we use the asymptotic method of multiple scales to derive continuum models for the shielding, involving homogenized boundary conditions on an effective cage boundary. We show how the resulting models depend on key cage parameters such as the size and shape of the wires, and, in the electromagnetic case, on the frequency and polarization of the incident field. In the electromagnetic case, there are resonance effects, whereby at frequencies close to the natural frequencies of the equivalent solid shell, the presence of the cage actually amplifies the incident field, rather than shielding it. By appropriately modifying the continuum model, we calculate the modified resonant frequencies, and their associated peak amplitudes. We discuss applications to radiation containment in microwave ovens and acoustic scattering by perforated shells. PMID:27279775

Numerical simulation of a flow-like landslide using the particle finite element method

NASA Astrophysics Data System (ADS)

Zhang, Xue; Krabbenhoft, Kristian; Sheng, Daichao; Li, Weichao

2015-01-01

In this paper, an actual landslide process that occurred in Southern China is simulated by a continuum approach, the particle finite element method (PFEM). The PFEM attempts to solve the boundary-value problems in the framework of solid mechanics, satisfying the governing equations including momentum conservation, displacement-strain relation, constitutive relation as well as the frictional contact between the sliding mass and the slip surface. To warrant the convergence behaviour of solutions, the problem is formulated as a mathematical programming problem, while the particle finite element procedure is employed to tackle the issues of mesh distortion and free-surface evolution. The whole procedure of the landslide, from initiation, sliding to deposition, is successfully reproduced by the continuum approach. It is shown that the density of the mass has little influence on the sliding process in the current landslide, whereas both the geometry and the roughness of the slip surface play important roles. Comparative studies are also conducted where a satisfactory agreement is obtained.

Continuum Limit of Total Variation on Point Clouds

NASA Astrophysics Data System (ADS)

García Trillos, Nicolás; Slepčev, Dejan

2016-04-01

We consider point clouds obtained as random samples of a measure on a Euclidean domain. A graph representing the point cloud is obtained by assigning weights to edges based on the distance between the points they connect. Our goal is to develop mathematical tools needed to study the consistency, as the number of available data points increases, of graph-based machine learning algorithms for tasks such as clustering. In particular, we study when the cut capacity, and more generally total variation, on these graphs is a good approximation of the perimeter (total variation) in the continuum setting. We address this question in the setting of Γ-convergence. We obtain almost optimal conditions on the scaling, as the number of points increases, of the size of the neighborhood over which the points are connected by an edge for the Γ-convergence to hold. Taking of the limit is enabled by a transportation based metric which allows us to suitably compare functionals defined on different point clouds.

Homogenized boundary conditions and resonance effects in Faraday cages

NASA Astrophysics Data System (ADS)

Hewett, D. P.; Hewitt, I. J.

2016-05-01

We present a mathematical study of two-dimensional electrostatic and electromagnetic shielding by a cage of conducting wires (the so-called `Faraday cage effect'). Taking the limit as the number of wires in the cage tends to infinity, we use the asymptotic method of multiple scales to derive continuum models for the shielding, involving homogenized boundary conditions on an effective cage boundary. We show how the resulting models depend on key cage parameters such as the size and shape of the wires, and, in the electromagnetic case, on the frequency and polarization of the incident field. In the electromagnetic case, there are resonance effects, whereby at frequencies close to the natural frequencies of the equivalent solid shell, the presence of the cage actually amplifies the incident field, rather than shielding it. By appropriately modifying the continuum model, we calculate the modified resonant frequencies, and their associated peak amplitudes. We discuss applications to radiation containment in microwave ovens and acoustic scattering by perforated shells.

Homogenized boundary conditions and resonance effects in Faraday cages.

PubMed

Hewett, D P; Hewitt, I J

2016-05-01

We present a mathematical study of two-dimensional electrostatic and electromagnetic shielding by a cage of conducting wires (the so-called 'Faraday cage effect'). Taking the limit as the number of wires in the cage tends to infinity, we use the asymptotic method of multiple scales to derive continuum models for the shielding, involving homogenized boundary conditions on an effective cage boundary. We show how the resulting models depend on key cage parameters such as the size and shape of the wires, and, in the electromagnetic case, on the frequency and polarization of the incident field. In the electromagnetic case, there are resonance effects, whereby at frequencies close to the natural frequencies of the equivalent solid shell, the presence of the cage actually amplifies the incident field, rather than shielding it. By appropriately modifying the continuum model, we calculate the modified resonant frequencies, and their associated peak amplitudes. We discuss applications to radiation containment in microwave ovens and acoustic scattering by perforated shells.

Characteristics of Korean International Mathematical Olympiad (IMO) Winners and Various Developmental Influences

ERIC Educational Resources Information Center

Choi, Kyong Mi

2009-01-01

This study investigated characteristics of five IMO winners and influences from their formal and informal educational experiences. In particular, this study provides in-depth understanding of former Korean IMO winners' characteristics and environmental influences. Also, implications including education for parents of the gifted, professional…

Improving Success in Developmental Mathematics: An Interview with Paul Nolting

ERIC Educational Resources Information Center

Boylan, Hunter R.

2011-01-01

This article presents an interview with Dr. Paul Nolting, a national expert in assessing individual math learning problems, developing effective student learning strategies, and assessing institutional variables that affect math success. Since his dissertation in 1986 on improving math success with study skills Dr. Nolting has consulted with over…

Grades 4-6: Arkansas Public School Course Content Guide.

ERIC Educational Resources Information Center

Arkansas State Dept. of Education, Little Rock.

Provided as a framework for use in curriculum development are Arkansas' course content guides for the intermediate elementary grades four, five, and six. At each grade level, language arts, mathematics, reading, social studies, and science skills have been identified at three instructional levels: basic, developmental, and extensional. Basic…

From Cognitive Science to School Practice: Building the Bridge

ERIC Educational Resources Information Center

Singer, Mihaela

2003-01-01

The paper is focused on recent researches in neuroscience and developmental psychology regarding mathematical abilities of infants. A model that tries to explain these findings is developed. The model underlies the mental operations that could be systematically trained to generate efficient school learning. The model is built from a cognitive…

Evolving Agents as a Metaphor for the Developing Child

ERIC Educational Resources Information Center

Schlesinger, Matthew

2004-01-01

The emerging field of Evolutionary Computation (EC), inspired by neo-Darwinian principles (e.g. natural selection, mutation, etc.), offers developmental psychologists a wide array of mathematical tools for simulating ontogenetic processes. In this brief review, I begin by highlighting three of the approaches that EC researchers employ (Artificial…

Developing Compressed Beginning and Intermediate Algebra Courses

ERIC Educational Resources Information Center

Walker, Sylvia E.

2017-01-01

The purpose of this project was two-fold. First, it would provide an opportunity for students to complete the developmental math course sequence more quickly, thereby enabling students to proceed to a college-level mathematics course sooner. To accomplish this, the classroom was designed with computer-assisted homework courses that blended…

Math 3008--Developmental Mathematics II. Course Outline.

ERIC Educational Resources Information Center

New York Inst. of Tech., Old Westbury.

This document contains the course syllabus and 12 independent practice modules for an introductory college algebra course designed to develop student proficiency in the basic algebraic skills. This is designed as the second of a two-semester sequence. Topics include performing operations with radicals and exponents; learning to solve equations;…

Math 3007--Developmental Mathematics I. Course Outline.

ERIC Educational Resources Information Center

New York Inst. of Tech., Old Westbury.

This document contains the course syllabus and 12 independent practice modules for an introductory college algebra course designed to develop student proficiency in the basic algebraic skills. This course is designed as the first of a two-semester sequence. Topics include operations with signed numbers; simple operations on monomials and…

Math 3013--Developmental Mathematics I and II. Course Outline.

ERIC Educational Resources Information Center

New York Inst. of Tech., Old Westbury.

This document contains the course syllabus and 12 independent practice modules for an introductory college algebra course that requires some previous knowledge of algebra and the ability to work at a rapid pace. Topics include the basic operations with signed integers; fractions; decimals; literal expressions; algebraic fractions; radicals;…

Regression Analyses of Self-Regulatory Concepts to Predict Community College Math Achievement and Persistence

ERIC Educational Resources Information Center

Gramlich, Stephen Peter

2010-01-01

Open door admissions at community colleges bring returning adults, first timers, low achievers, disabled persons, and immigrants. Passing and retention rates for remedial and non-developmental math courses can be comparatively inadequate (LAVC, 2005; CCPRDC, 2000; SBCC, 2004; Seybert & Soltz, 1992; Waycaster, 2002). Mathematics achievement…

The Influence of Relational Knowledge and Executive Function on Preschoolers' Repeating Pattern Knowledge

ERIC Educational Resources Information Center

Miller, Michael R.; Rittle-Johnson, Bethany; Loehr, Abbey M.; Fyfe, Emily R.

2016-01-01

Children's knowledge of repeating patterns (e.g., ABBABB) is a central component of early mathematics, but the developmental mechanisms underlying this knowledge are currently unknown. We sought clarity on the importance of relational knowledge and executive function (EF) to preschoolers' understanding of repeating patterns. One hundred…

A Review of Human Spatial Representations Computational, Neuroscience, Mathematical, Developmental, and Cognitive Psychology Considerations

DTIC Science & Technology

2000-12-18

Gallistel , 1988). Hermer and Spelke (1996) found that the young children were able to detect, remember, and use the same nongeometric information...America, 50, 637-642. Margules, J., & Gallistel , C. R. (1988). Heading in the rat: Determination by environmental shape. Animal Learning & Behavior, 16(4

The Journal of the Society for Accelerative Learning and Teaching. Volume 15, 1990.

ERIC Educational Resources Information Center

Journal of the Society for Accelerative Learning and Teaching, 1990

1990-01-01

Articles in this volume of the Journal of the Society for Accelerative Learning and Teaching (SALT) include the following: "Accelerated Learning Components in Elementary Classrooms"; "Ball-Stick Bird: Teaching with the Story Engram"; "A SALT Pilot Study in College Developmental Mathematics"; "Black Education in…

Simplicial lattices in classical and quantum gravity: Mathematical structure and application

NASA Astrophysics Data System (ADS)

Lafave, Norman Joseph

1989-03-01

Geometrodynamics can be understood more clearly in the language of geometry than in the language of differential equations. This is the primary motivation for the development of calculational schemes based on Regge Calculus as an alternative to those schemes based on Ricci Calculus. The mathematics of simplicial lattices were developed to the same level of sophistication as the mathematics of pseudo--Riemannian geometry for continuum manifolds. This involves the definition of the simplicial analogues of several concepts from differential topology and differential geometry-the concept of a point, tangent spaces, forms, tensors, parallel transport, covariant derivatives, connections, and curvature. These simplicial analogues are used to define the Einstein tensor and the extrinsic curvature on a simplicial geometry. This mathematical formalism was applied to the solution of several outstanding problems in the development of a Regge Calculus based computational scheme for general geometrodynamic problems. This scheme is based on a 3 + 1 splitting of spacetime within the Regge Calculus prescription known as Null-Strut Calculus (NSC). NSC describes the foliation of spacetime into spacelike hypersurfaces built of tetrahedra. These hypersurfaces are coupled by light rays (null struts) to past and future momentum-like structures, geometrically dual to the tetrahedral lattice of the hypersurface. Avenues of investigation for NSC in quantum gravity are described.

Developmental dyscalculia is related to visuo-spatial memory and inhibition impairment.

PubMed

Szucs, Denes; Devine, Amy; Soltesz, Fruzsina; Nobes, Alison; Gabriel, Florence

2013-01-01

Developmental dyscalculia is thought to be a specific impairment of mathematics ability. Currently dominant cognitive neuroscience theories of developmental dyscalculia suggest that it originates from the impairment of the magnitude representation of the human brain, residing in the intraparietal sulcus, or from impaired connections between number symbols and the magnitude representation. However, behavioral research offers several alternative theories for developmental dyscalculia and neuro-imaging also suggests that impairments in developmental dyscalculia may be linked to disruptions of other functions of the intraparietal sulcus than the magnitude representation. Strikingly, the magnitude representation theory has never been explicitly contrasted with a range of alternatives in a systematic fashion. Here we have filled this gap by directly contrasting five alternative theories (magnitude representation, working memory, inhibition, attention and spatial processing) of developmental dyscalculia in 9-10-year-old primary school children. Participants were selected from a pool of 1004 children and took part in 16 tests and nine experiments. The dominant features of developmental dyscalculia are visuo-spatial working memory, visuo-spatial short-term memory and inhibitory function (interference suppression) impairment. We hypothesize that inhibition impairment is related to the disruption of central executive memory function. Potential problems of visuo-spatial processing and attentional function in developmental dyscalculia probably depend on short-term memory/working memory and inhibition impairments. The magnitude representation theory of developmental dyscalculia was not supported. Copyright © 2013 The Authors. Published by Elsevier Ltd.. All rights reserved.

Detrimental Psychological Outcomes Associated with Early Pubertal Timing in Adolescent Girls

PubMed Central

Mendle, Jane; Turkheimer, Eric; Emery, Robert E.

2010-01-01

Though often discussed as though it were a discrete event, puberty comprises one segment of a larger developmental continuum and is notable for rapid transformation across a multitude of domains. Research suggests that an earlier rate of pubertal maturation in girls correlates with a number of detrimental outcomes compared with on-time or later maturation. The present review synthesizes the research on negative psychological sequelae of early pubertal timing in adolescent girls. Emphasis is on three theoretical perspectives by which precocious development is believed to affect the emergence of adverse outcomes: biological, psychosocial, and selection effects. PMID:20740062

On the implications of the classical ergodic theorems: analysis of developmental processes has to focus on intra-individual variation.

PubMed

Molenaar, Peter C M

2008-01-01

It is argued that general mathematical-statistical theorems imply that standard statistical analysis techniques of inter-individual variation are invalid to investigate developmental processes. Developmental processes have to be analyzed at the level of individual subjects, using time series data characterizing the patterns of intra-individual variation. It is shown that standard statistical techniques based on the analysis of inter-individual variation appear to be insensitive to the presence of arbitrary large degrees of inter-individual heterogeneity in the population. An important class of nonlinear epigenetic models of neural growth is described which can explain the occurrence of such heterogeneity in brain structures and behavior. Links with models of developmental instability are discussed. A simulation study based on a chaotic growth model illustrates the invalidity of standard analysis of inter-individual variation, whereas time series analysis of intra-individual variation is able to recover the true state of affairs. (c) 2007 Wiley Periodicals, Inc.

Mathematics anxiety in children with developmental dyscalculia

PubMed Central

2010-01-01

Background Math anxiety, defined as a negative affective response to mathematics, is known to have deleterious effects on math performance in the general population. However, the assumption that math anxiety is directly related to math performance, has not yet been validated. Thus, our primary objective was to investigate the effects of math anxiety on numerical processing in children with specific deficits in the acquisition of math skills (Developmental Dyscalculia; DD) by using a novel affective priming task as an indirect measure. Methods Participants (12 children with DD and 11 typically-developing peers) completed a novel priming task in which an arithmetic equation was preceded by one of four types of priming words (positive, neutral, negative or related to mathematics). Children were required to indicate whether the equation (simple math facts based on addition, subtraction, multiplication or division) was true or false. Typically, people respond to target stimuli more quickly after presentation of an affectively-related prime than after one that is unrelated affectively. Result Participants with DD responded faster to targets that were preceded by both negative primes and math-related primes. A reversed pattern was present in the control group. Conclusion These results reveal a direct link between emotions, arithmetic and low achievement in math. It is also suggested that arithmetic-affective priming might be used as an indirect measure of math anxiety. PMID:20633269

Perceptions of Constructivist Pedagogy in Project Lead the Way

NASA Astrophysics Data System (ADS)

Capers, Gesa Maria

In 2016, six of six American Nobel Prize winners in science were immigrants. The numbers of U.S. educated graduates who enter the Science, Technology, Engineering, and Mathematics (STEM) fields have been on the decline, and policymakers and educators have continually sought new policies and programs to try resolve this problem with long-term solutions. In recent years, several Alabama schools have implemented Project Lead the Way (PLTW), a program that is aimed toward promoting students' interest in STEM. The purpose of this qualitative multiple case study was to explore how Alabama's educators perceived the use of constructivist pedagogy in PLTW on student learning behaviors and student interests in science and mathematics. Piaget's developmental theory and Vygotsky's social developmental theory provided the theoretical framework for this study. The data collection procedure for this multiple case study included one-on-one interviews with 23 educators in four Alabama PLTW schools. Themes that emerged from the study included motivation and enthusiasm, critical thinking and problem solving, career awareness, student interest in science and math, collaboration, hands-on learning, confidence and engagement, perceived problems, and satisfaction with PLTW. All interviewees perceived that with PLTW's emphasis on constructivist pedagogy, students were excited, engaged, practiced critical thinking and problem solving skills, and that participation in PLTW had a positive effect on the students' learning behaviors and interests in science and mathematics.

Imbedded-Fracture Formulation of THMC Processes in Fractured Media

NASA Astrophysics Data System (ADS)

Yeh, G. T.; Tsai, C. H.; Sung, R.

2016-12-01

Fractured media consist of porous materials and fracture networks. There exist four approaches to mathematically formulating THMC (Thermal-Hydrology-Mechanics-Chemistry) processes models in the system: (1) Equivalent Porous Media, (2) Dual Porosity or Dual Continuum, (3) Heterogeneous Media, and (4) Discrete Fracture Network. The first approach cannot explicitly explore the interactions between porous materials and fracture networks. The second approach introduces too many extra parameters (namely, exchange coefficients) between two media. The third approach may make the problems too stiff because the order of material heterogeneity may be too much. The fourth approach ignore the interaction between porous materials and fracture networks. This talk presents an alternative approach in which fracture networks are modeled with a lower dimension than the surrounding porous materials. Theoretical derivation of mathematical formulations will be given. An example will be illustrated to show the feasibility of this approach.

Mathematical modeling of spinning elastic bodies for modal analysis.

NASA Technical Reports Server (NTRS)

Likins, P. W.; Barbera, F. J.; Baddeley, V.

1973-01-01

The problem of modal analysis of an elastic appendage on a rotating base is examined to establish the relative advantages of various mathematical models of elastic structures and to extract general inferences concerning the magnitude and character of the influence of spin on the natural frequencies and mode shapes of rotating structures. In realization of the first objective, it is concluded that except for a small class of very special cases the elastic continuum model is devoid of useful results, while for constant nominal spin rate the distributed-mass finite-element model is quite generally tractable, since in the latter case the governing equations are always linear, constant-coefficient, ordinary differential equations. Although with both of these alternatives the details of the formulation generally obscure the essence of the problem and permit very little engineering insight to be gained without extensive computation, this difficulty is not encountered when dealing with simple concentrated mass models.

Geometrical and quantum mechanical aspects in observers' mathematics

NASA Astrophysics Data System (ADS)

Khots, Boris; Khots, Dmitriy

2013-10-01

When we create mathematical models for Quantum Mechanics we assume that the mathematical apparatus used in modeling, at least the simplest mathematical apparatus, is infallible. In particular, this relates to the use of "infinitely small" and "infinitely large" quantities in arithmetic and the use of Newton Cauchy definitions of a limit and derivative in analysis. We believe that is where the main problem lies in contemporary study of nature. We have introduced a new concept of Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. We prove that Euclidean Geometry works in sufficiently small neighborhood of the given line, but when we enlarge the neighborhood, non-euclidean Geometry takes over. We prove that the physical speed is a random variable, cannot exceed some constant, and this constant does not depend on an inertial coordinate system. We proved the following theorems: Theorem A (Lagrangian). Let L be a Lagrange function of free material point with mass m and speed v. Then the probability P of L = m 2 v2 is less than 1: P(L = m 2 v2) < 1. Theorem B (Nadezhda effect). On the plane (x, y) on every line y = kx there is a point (x0, y0) with no existing Euclidean distance between origin (0, 0) and this point. Conjecture (Black Hole). Our space-time nature is a black hole: light cannot go out infinitely far from origin.

Children's understanding of area concepts: development, curriculum and educational achievement.

PubMed

Bond, Trevor G; Parkinson, Kellie

2010-01-01

As one part of a series of studies undertaken to investigate the contribution of developmental attributes of learners to school learning, a representative sample of forty-two students (age from 5 years and 3 months to 13 years and 1 month) was randomly selected from a total student population of 142 students at a small private primary school in northern Australia. Those children's understandings of area concepts taught during the primary school years were assessed by their performance in two testing situations. The first consisted of a written classroom test of ability to solve area problems with items drawn directly from school texts, school examinations and other relevant curriculum documents. The second, which focused more directly on each child's cognitive development, was an individual interview for each child in which four "area" tasks such as the Meadows and Farmhouse Experiment taken from Chapter 11 of The Child's Conception of Geometry (Piaget, Inhelder and Szeminska, 1960, pp. 261-301) were administered. Analysis using the Rasch Partial Credit Model provided a finely detailed quantitative description of the developmental and learning progressions revealed in the data. It is evident that the school mathematics curriculum does not satisfactorily match the learner's developmental sequence at some key points. Moreover, the children's ability to conserve area on the Piagetian tasks, rather than other learner characteristics, such as age and school grade seems to be a precursor for complete success on the mathematical test of area. The discussion focuses on the assessment of developmental (and other) characteristics of school-aged learners and suggests how curriculum and school organization might better capitalize on such information in the design and sequencing of learning experiences for school children. Some features unique to the Rasch family of measurement models are held to have special significance in elucidating the development/attainment nexus.

Cognition, emotion, and arithmetic in primary school: A cross-cultural investigation.

PubMed

Rodic, Maja; Cui, Jiaxin; Malykh, Sergey; Zhou, Xinlin; Gynku, Elena I; Bogdanova, Elena L; Zueva, Dina Y; Y Bogdanova, Olga; Kovas, Yulia

2018-06-01

The study investigated cross-cultural differences in variability and average performance in arithmetic, mathematical reasoning, symbolic and non-symbolic magnitude processing, intelligence, spatial ability, and mathematical anxiety in 890 6- to 9-year-old children from the United Kingdom, Russia, and China. Cross-cultural differences explained 28% of the variance in arithmetic and 17.3% of the variance in mathematical reasoning, with Chinese children outperforming the other two groups. No cross-cultural differences were observed for spatial ability and mathematical anxiety. In all samples, symbolic magnitude processing and mathematical reasoning were independently related to early arithmetic. Other factors, such as non-symbolic magnitude processing, mental rotation, intelligence, and mathematical anxiety, produced differential patterns across the populations. The results are discussed in relation to potential influences of parental practice, school readiness, and linguistic factors on individual differences in early mathematics. Statement of contribution What is already known on this subject? Cross-cultural differences in mathematical ability are present in preschool children. Similar mechanisms of mathematical development operate in preschool children from the United Kingdom, Russia, and China. Tasks that require understanding of numbers are best predictors of arithmetic in preschool children. What does this study add? Cross-cultural differences in mathematical ability become greater with age/years of formal education. Similar mechanisms of mathematical development operate in early primary school children from the United Kingdom, Russia, and China. Symbolic number magnitude and mathematical reasoning are the main predictors of arithmetic in all three populations. © 2018 The Authors British Journal of Developmental Psychology published by John Wiley & Sons Ltd on behalf of British Psychological Society.

Familial aggregation patterns in mathematical ability.

PubMed

Wijsman, Ellen M; Robinson, Nancy M; Ainsworth, Kathryn H; Rosenthal, Elisabeth A; Holzman, Ted; Raskind, Wendy H

2004-01-01

Mathematical talent is an asset in modern society both at an individual and a societal level. Environmental factors such as quality of mathematics education undoubtedly affect an individual's performance, and there is some evidence that genetic factors also may play a role. The current study was performed to investigate the feasibility of undertaking genetics studies on mathematical ability. Because the etiology of low ability in mathematics is likely to be multifactorial and heterogeneous, we evaluated families ascertained through a proband with high mathematical performance in grade 7 on the SAT to eliminate, to some degree, adverse environmental factors. Families of sex-matched probands, selected for high verbal performance on the SAT, served as the comparison group. We evaluated a number of proxy measures for their usefulness in the study of clustering of mathematical talent. Given the difficulty of testing mathematics performance across developmental ages, especially with the added complexity of decreasing exposure to formal mathematics concepts post schooling, we also devised a semiquantitative scale that incorporated educational, occupational, and avocational information as a surrogate for an academic mathematics measure. Whereas several proxy measures showed no evidence of a genetic basis, we found that the semiquantitative scale of mathematical talent showed strong evidence of a genetic basis, with a differential response as a function of the performance measure used to select the proband. This observation suggests that there may be a genetic basis to specific mathematical talent, and that specific, as opposed to proxy, investigative measures that are designed to measure such talent in family members could be of benefit for this purpose.

Modeling the Impact of Interventions Along the HIV Continuum of Care in Newark, New Jersey

PubMed Central

Birger, Ruthie B.; Hallett, Timothy B.; Sinha, Anushua; Grenfell, Bryan T.; Hodder, Sally L.

2014-01-01

Background. The human immunodeficiency virus (HIV) epidemic in Newark, New Jersey, is among the most severe in the United States. Prevalence ranges up to 3.3% in some groups. The aim of this study is to use a mathematical model of the epidemic in Newark to assess the impact of interventions along the continuum of care, leading to virologic suppression. Methods. A model was constructed of HIV infection including specific care-continuum steps. The model was calibrated to HIV/AIDS cases in Newark among different populations over a 10-year period. Interventions applied to model fits were increasing proportions tested, linked and retained in care, linked and adherent to treatment, and increasing testing frequency, high-risk-group testing, and adherence. Impacts were assessed by measuring incidence and death reductions 10 years postintervention. Results. The most effective interventions for reducing incidence were improving treatment adherence and increasing testing frequency and coverage. No single intervention reduced incidence in 2023 by >5%, and the most effective combination of interventions reduced incidence by approximately 16% (2%–24%). The most efficacious interventions for reducing deaths were increasing retention, linkage to care, testing coverage, and adherence. Increasing retention reduced deaths by approximately 27% (24%–29%); the most efficacious combination of interventions reduced deaths in 2023 by approximately 52% (46%–57%). Conclusions. Reducing HIV deaths in Newark over a 10-year period may be a realizable goal, but reducing incidence is less likely. Our results highlight the importance of addressing leaks across the entire continuum of care and reinforcing efforts to prevention new HIV infections with additional interventions. PMID:24140971

A model for one-dimensional morphoelasticity and its application to fibroblast-populated collagen lattices.

PubMed

Menon, Shakti N; Hall, Cameron L; McCue, Scott W; McElwain, D L Sean

2017-10-01

The mechanical behaviour of solid biological tissues has long been described using models based on classical continuum mechanics. However, the classical continuum theories of elasticity and viscoelasticity cannot easily capture the continual remodelling and associated structural changes in biological tissues. Furthermore, models drawn from plasticity theory are difficult to apply and interpret in this context, where there is no equivalent of a yield stress or flow rule. In this work, we describe a novel one-dimensional mathematical model of tissue remodelling based on the multiplicative decomposition of the deformation gradient. We express the mechanical effects of remodelling as an evolution equation for the effective strain, a measure of the difference between the current state and a hypothetical mechanically relaxed state of the tissue. This morphoelastic model combines the simplicity and interpretability of classical viscoelastic models with the versatility of plasticity theory. A novel feature of our model is that while most models describe growth as a continuous quantity, here we begin with discrete cells and develop a continuum representation of lattice remodelling based on an appropriate limit of the behaviour of discrete cells. To demonstrate the utility of our approach, we use this framework to capture qualitative aspects of the continual remodelling observed in fibroblast-populated collagen lattices, in particular its contraction and its subsequent sudden re-expansion when remodelling is interrupted.

Is Learning in Developmental Math Associated with Community College Outcomes?

ERIC Educational Resources Information Center

Quarles, Christopher L.; Davis, Mickey

2017-01-01

Objective: Remedial mathematics courses are widely considered a barrier to student success in community college, and there has been a significant amount of work recently to reform them. Yet, there is little research that explicitly examines whether increasing learning in remedial classes improves grades or completion rates. This study examines the…

Examining the Impact of Redesigned Developmental Math Courses in Community Colleges

ERIC Educational Resources Information Center

Okimoto, Hae; Heck, Ronald

2015-01-01

At community colleges, student preparedness for college-level work is a significant initial barrier. Over 70% of community college students are reported to be inadequately prepared for college mathematics. Because students need to pass college-level math in order to enroll in subsequent courses required for their majors or to complete general…

An Epidemiological Study of Number Processing and Mental Calculation in Greek Schoolchildren

ERIC Educational Resources Information Center

Koumoula, Anastasia; Tsironi, Vanda; Stamouli, Victoria; Bardani, Irini; Stavroula, Siapati; Graham, Annik; Kafantaris, Ignatios; Charalambidou, Irini; Dellatolas, Georges; von Aster, Michael

2004-01-01

The aim of this study was to validate and standardize an instrument for the diagnosis of developmental dyscalculia (mathematics disorder) in a Greek population and to obtain relevant epidemiological data. We used the "Neuropsychological Test Battery for Number Processing and Calculation in Children" (NUCALC) in a community sample of 240 students…

Does the Approximate Number System Serve as a Foundation for Symbolic Mathematics?

ERIC Educational Resources Information Center

Szkudlarek, Emily; Brannon, Elizabeth M.

2017-01-01

In this article we first review evidence for the approximate number system (ANS), an evolutionarily ancient and developmentally conservative cognitive mechanism for representing number without language. We then critically review five different lines of support for the proposal that symbolic representations of number build upon the ANS, and discuss…

More than a Network: Building Professional Communities for Educational Improvement

ERIC Educational Resources Information Center

Dolle, Jonathan R.; Gomez, Louis M.; Russell, Jennifer Lin; Bryk, Anthony S.

2013-01-01

This chapter is a case study of the Carnegie Foundation for the Advancement of Teaching's Pathways [TM] program. The goal of the Statway [Registered Trademark] and Quantway [Registered Trademark] pathways is to improve the success rate of community college students who place into developmental mathematics. What makes these programs unique is…

Grades 1-3: Arkansas Public School Course Content Guide.

ERIC Educational Resources Information Center

Arkansas State Dept. of Education, Little Rock.

Provided as a framework for use in curriculum development are Arkansas' course content guides for the primary grades one, two, and three. At each grade level, language arts, mathematics, and reading skills have been identified at three instructional levels: basic, developmental, and extensional. Basic skills are those which all students must…

The Peak in the Middle: Developing Mathematically Gifted Students in the Middle Grades

ERIC Educational Resources Information Center

Saul, Mark; Assouline, Susan; Sheffield, Linda

2010-01-01

Good teaching is responsive to individual differences, tailoring instruction to meet the needs of individual learners. In gifted education, students need a curriculum that is differentiated (by level, complexity, breadth, and depth), developmentally appropriate, and conducted at a more rapid rate. This collection of essays from experts in the…

A Paradigmatic Example of an Artificially Intelligent Instructional System.

ERIC Educational Resources Information Center

Brown, John Seely; Burton, Richard R.

This paper describes the philosophy of intelligent instructional systems and presents an example of one such system in the domain of manipulative mathematics--BLOCKS. The notion of BLOCKS as a paradigmatic system is explicated from both the system development and educational viewpoints. From a developmental point of view, the modular design of…

Semantic Language as a Mechanism Explaining the Association between ADHD Symptoms and Reading and Mathematics Underachievement

ERIC Educational Resources Information Center

Gremillion, Monica L.; Martel, Michelle M.

2012-01-01

ADHD is associated with academic underachievement, but it remains unclear what mechanism accounts for this association. Semantic language is an underexplored mechanism that provides a developmental explanation for this association. The present study will examine whether semantic language deficits explain the association between ADHD and reading…

Predicting Reading and Mathematics from Neural Activity for Feedback Learning

ERIC Educational Resources Information Center

Peters, Sabine; Van der Meulen, Mara; Zanolie, Kiki; Crone, Eveline A.

2017-01-01

Although many studies use feedback learning paradigms to study the process of learning in laboratory settings, little is known about their relevance for real-world learning settings such as school. In a large developmental sample (N = 228, 8-25 years), we investigated whether performance and neural activity during a feedback learning task…

The Developmental Dynamics between Interest, Self-Concept of Ability, and Academic Performance

ERIC Educational Resources Information Center

Viljaranta, Jaana; Tolvanen, Asko; Aunola, Kaisa; Nurmi, Jari-Erik

2014-01-01

Only a few studies have examined the direction of associations between academic achievement, interest, and self-concept of ability simultaneously by using longitudinal data over several school years. To examine the cross-lagged relationships between students' interest, self-concept of ability, and performance in mathematics and reading,…

Placement Evaluations and Remedial Education: Are Students Shopping for Bargains?

ERIC Educational Resources Information Center

Fletcher, Stephen H.

2014-01-01

The purpose of this study is to provide evidence that students may be doing comparison shopping when it comes to community college placement in English and mathematics courses. Comparisons may occur because of the difference in the placement process across campuses and the variation in the levels of developmental education offered. The…

Public Elementary and Secondary Education in the '80s.

ERIC Educational Resources Information Center

Broudy, H. S.

Privatism, vouchers, too many pressure groups, and a deemphasis of citizenship present the worst stumbling blocks to education. A five-point curriculum model includes: (1) the symbolics of information--the skills of language and computation; (2) the key concepts of a selected set of the physical sciences and mathematics; (3) developmental studies…

High School Students' Knowledge of a Square as a Basis for Developing a Geometric Learning Progression

ERIC Educational Resources Information Center

Seah, Rebecca; Horne, Marj; Berenger, Adrian

2016-01-01

This study surveyed and analysed four secondary school students' writing about a square. Sfard's discursive approach to understanding mathematical discourse was used to analyse the responses collected from 214 Australian secondary school students. The results showed that geometric knowledge was developed experientially and not developmentally.…

Using Research-Based Instruction to Improve Math Outcomes with Underprepared Students

ERIC Educational Resources Information Center

Pearce, Lee R.; Pearce, Kristi L.; Siewert, Daluss J.

2017-01-01

The authors used a mixed-methods research design to evaluate a multi-tiered system of supports model to address the disturbing failure rates of underprepared college students placed in developmental mathematics at a small state university. While qualitative data gathered from using Participatory Action Research methods directed the two-year…

Adult Learners' Knowledge of Fraction Addition and Subtraction

ERIC Educational Resources Information Center

Muckridge, Nicole A.

2017-01-01

The purpose of this study was to examine adult developmental mathematics (ADM) students' knowledge of fraction addition and subtraction as it relates to their demonstrated fraction schemes and ability to disembed in multiplicative contexts with whole numbers. The study was conducted using a mixed methods sequential explanatory design. In the first…

Informal Numeracy Skills: The Structure and Relations among Numbering, Relations, and Arithmetic Operations in Preschool

ERIC Educational Resources Information Center

Purpura, David J.; Lonigan, Christopher J.

2013-01-01

Validating the structure of informal numeracy skills is critical to understanding the developmental trajectories of mathematics skills at early ages; however, little research has been devoted to construct evaluation of the Numbering, Relations, and Arithmetic Operations domains. This study was designed to address this knowledge gap by examining…

Left Brain/Right Brain Theory: Implications for Developmental Math Instruction.

ERIC Educational Resources Information Center

Kitchens, Anita N.; And Others

1991-01-01

Perhaps the most dramatic failure in postsecondary education has been in the teaching of mathematical skills. The different functions of the right and left hemispheres of the brain require different approaches to education. Due to their emphasis on language and verbal processing, schools have failed to give adequate stimulation to the right side…

The Study of an Intervention Summer Bridge Program Learning Community: Remediation, Retention, and Graduation

ERIC Educational Resources Information Center

McEvoy, Suzanne

2012-01-01

With the changing U.S. demographics, higher numbers of diverse, low-income, first-generation students are underprepared for the academic rigors of four-year institutions oftentimes requiring assistance, and remedial and/or developmental coursework in English and mathematics. Without intervention approaches these students are at high risk for…

Multidisciplinary approaches to understanding collective cell migration in developmental biology.

PubMed

Schumacher, Linus J; Kulesa, Paul M; McLennan, Rebecca; Baker, Ruth E; Maini, Philip K

2016-06-01

Mathematical models are becoming increasingly integrated with experimental efforts in the study of biological systems. Collective cell migration in developmental biology is a particularly fruitful application area for the development of theoretical models to predict the behaviour of complex multicellular systems with many interacting parts. In this context, mathematical models provide a tool to assess the consistency of experimental observations with testable mechanistic hypotheses. In this review, we showcase examples from recent years of multidisciplinary investigations of neural crest cell migration. The neural crest model system has been used to study how collective migration of cell populations is shaped by cell-cell interactions, cell-environmental interactions and heterogeneity between cells. The wide range of emergent behaviours exhibited by neural crest cells in different embryonal locations and in different organisms helps us chart out the spectrum of collective cell migration. At the same time, this diversity in migratory characteristics highlights the need to reconcile or unify the array of currently hypothesized mechanisms through the next generation of experimental data and generalized theoretical descriptions. © 2016 The Authors.

Recent insights into the Smith-Lemli-Opitz syndrome.

PubMed

Yu, H; Patel, S B

2005-11-01

Recent insights into the Smith-Lemli-Opitz syndrome. The Smith-Lemli-Opitz syndrome (SLOS) is an autosomal recessive multiple congenital anomaly/mental retardation disorder caused by an inborn error of post-squalene cholesterol biosynthesis. Deficient cholesterol synthesis in SLOS is caused by inherited mutations of 3beta-hydroxysterol-Delta7 reductase gene (DHCR7). DHCR7 deficiency impairs both cholesterol and desmosterol production, resulting in elevated 7DHC/8DHC levels, typically decreased cholesterol levels and, importantly, developmental dysmorphology. The discovery of SLOS has led to new questions regarding the role of the cholesterol biosynthesis pathway in human development. To date, a total of 121 different mutations have been identified in over 250 patients with SLOS who represent a continuum of clinical severity. Two genetic mouse models have been generated which recapitulate some of the developmental abnormalities of SLOS and have been useful in elucidating the pathogenesis. This mini review summarizes the recent insights into SLOS genetics, pathophysiology and potential therapeutic approaches for the treatment of SLOS.

[Asperger's syndrome: continuum or spectrum of autistic disorders?].

PubMed

Bryńska, Anita

2011-01-01

Pervasive Developmental Disorders (PPD) refers to the group of disorders characterised by delayed or inappropriate development of multiple basic functions including socialisation, communication, behaviour and cognitive functioning. The term,,autistic spectrum disorders" was established as a result of the magnitude of the intensity of symptoms and their proportions observed in all types of pervasive developmental disorders. Asperger's Syndrome (AS) remains the most controversial diagnosis in terms of its place within autism spectrum disorders. AS if often described as an equivalent of High Functioning Autism (HFA) or as a separate spectrum-related disorder with unique diagnostic criteria. Another important issue is the relationship between AS and speech disorders. Although it is relatively easy to draw a line between children with classical autism and speech disorders, the clear cut frontiers between them still remain to be found. The main distinguishing feature is the lack of stereotypic interests and unimpaired social interaction observed in children with speech disorders, such as semantic-pragmatic disorder.

An integrated framework for the optimisation of sport and athlete development: a practitioner approach.

PubMed

Gulbin, Jason P; Croser, Morag J; Morley, Elissa J; Weissensteiner, Juanita R

2013-01-01

This paper introduces a new sport and athlete development framework that has been generated by multidisciplinary sport practitioners. By combining current theoretical research perspectives with extensive empirical observations from one of the world's leading sport agencies, the proposed FTEM (Foundations, Talent, Elite, Mastery) framework offers broad utility to researchers and sporting stakeholders alike. FTEM is unique in comparison with alternative models and frameworks, because it: integrates general and specialised phases of development for participants within the active lifestyle, sport participation and sport excellence pathways; typically doubles the number of developmental phases (n = 10) in order to better understand athlete transition; avoids chronological and training prescriptions; more optimally establishes a continuum between participation and elite; and allows full inclusion of many developmental support drivers at the sport and system levels. The FTEM framework offers a viable and more flexible alternative for those sporting stakeholders interested in managing, optimising, and researching sport and athlete development pathways.

Mathematical skills in 3- and 5-year-olds with spina bifida and their typically developing peers: a longitudinal approach.

PubMed

Barnes, Marcia A; Stubbs, Allison; Raghubar, Kimberly P; Agostino, Alba; Taylor, Heather; Landry, Susan; Fletcher, Jack M; Smith-Chant, Brenda

2011-05-01

Preschoolers with spina bifida (SB) were compared to typically developing (TD) children on tasks tapping mathematical knowledge at 36 months (n = 102) and 60 months of age (n = 98). The group with SB had difficulty compared to TD peers on all mathematical tasks except for transformation on quantities in the subitizable range. At 36 months, vocabulary knowledge, visual-spatial, and fine motor abilities predicted achievement on a measure of informal math knowledge in both groups. At 60 months of age, phonological awareness, visual-spatial ability, and fine motor skill were uniquely and differentially related to counting knowledge, oral counting, object-based arithmetic skills, and quantitative concepts. Importantly, the patterns of association between these predictors and mathematical performance were similar across the groups. A novel finding is that fine motor skill uniquely predicted object-based arithmetic abilities in both groups, suggesting developmental continuity in the neurocognitive correlates of early object-based and later symbolic arithmetic problem solving. Models combining 36-month mathematical ability and these language-based, visual-spatial, and fine motor abilities at 60 months accounted for considerable variance on 60-month informal mathematical outcomes. Results are discussed with reference to models of mathematical development and early identification of risk in preschoolers with neurodevelopmental disorder.

Mathematical Skills in 3- and 5-Year-Olds with Spina Bifida and Their Typically Developing Peers: A Longitudinal Approach

PubMed Central

Barnes, Marcia A.; Stubbs, Allison; Raghubar, Kimberly P.; Agostino, Alba; Taylor, Heather; Landry, Susan; Fletcher, Jack M.; Smith-Chant, Brenda

2011-01-01

Preschoolers with spina bifida (SB) were compared to typically developing (TD) children on tasks tapping mathematical knowledge at 36 months (n = 102) and 60 months of age (n = 98). The group with SB had difficulty compared to TD peers on all mathematical tasks except for transformation on quantities in the subitizable range. At 36 months, vocabulary knowledge, visual–spatial, and fine motor abilities predicted achievement on a measure of informal math knowledge in both groups. At 60 months of age, phonological awareness, visual–spatial ability, and fine motor skill were uniquely and differentially related to counting knowledge, oral counting, object-based arithmetic skills, and quantitative concepts. Importantly, the patterns of association between these predictors and mathematical performance were similar across the groups. A novel finding is that fine motor skill uniquely predicted object-based arithmetic abilities in both groups, suggesting developmental continuity in the neurocognitive correlates of early object-based and later symbolic arithmetic problem solving. Models combining 36-month mathematical ability and these language-based, visual–spatial, and fine motor abilities at 60 months accounted for considerable variance on 60-month informal mathematical outcomes. Results are discussed with reference to models of mathematical development and early identification of risk in preschoolers with neurodevelopmental disorder. PMID:21418718

Testing inferences in developmental evolution: the forensic evidence principle.

PubMed

Larsson, Hans C E; Wagner, Günter P

2012-09-01

Developmental evolution (DE) examines the influence of developmental mechanisms on biological evolution. Here we consider the question: "what is the evidence that allows us to decide whether a certain developmental scenario for an evolutionary change is in fact "correct" or at least falsifiable?" We argue that the comparative method linked with what we call the "forensic evidence principle" (FEP) is sufficient to conduct rigorous tests of DE scenarios. The FEP states that different genetically mediated developmental causes of an evolutionary transformation will leave different signatures in the development of the derived character. Although similar inference rules have been used in practically every empirical science, we expand this approach here in two ways: (1) we justify the validity of this principle with reference to a well-known result from mathematical physics, known as the symmetry principle, and (2) propose a specific form of the FEP for DE: given two or more developmental explanations for a certain evolutionary event, say an evolutionary novelty, then the evidence discriminating between these hypotheses will be found in the most proximal internal drivers of the derived character. Hence, a detailed description of the ancestral and derived states, and their most proximal developmental drivers are necessary to discriminate between various evolutionary developmental hypotheses. We discuss how this stepwise order of testing is necessary, establishes a formal test, and how skipping this order of examination may violate a more accurate examination of DE. We illustrate the approach with an example from avian digit evolution. © 2012 Wiley Periodicals, Inc.

Infantile spasms (West syndrome): update and resources for pediatricians and providers to share with parents.

PubMed

Wheless, James W; Gibson, Patricia A; Rosbeck, Kari Luther; Hardin, Maria; O'Dell, Christine; Whittemore, Vicky; Pellock, John M

2012-07-25

Infantile spasms (IS; West syndrome) is a severe form of encephalopathy that typically affects infants younger than 2 years old. Pediatricians, pediatric neurologists, and other pediatric health care providers are all potentially key early contacts for families who have an infant with IS. The objective of this article is to assist pediatric health care providers in the detection of the disease and in the counseling and guidance of families who have an infant with IS. Treatment guidelines, consensus reports, and original research studies are reviewed to provide an update regarding the diagnosis and treatment of infants with IS. Web sites were searched for educational and supportive resource content relevant to providers and families of patients with IS. Early detection of IS and pediatrician referral to a pediatric neurologist for further evaluation and initiation of treatment may improve prognosis. Family education and the establishment of a multidisciplinary continuum of care are important components of care for the majority of patients with IS. The focus of the continuum of care varies across diagnosis, initiation of treatment, and short- and long-term needs. Several on-line educational and supportive resources for families and caregivers of patients with IS were identified. Given the possibility of poor developmental outcomes in IS, including the emergence of other seizure disorders and cognitive and developmental problems, early recognition, referral, and treatment of IS are important for optimal patient outcomes. Dissemination of and access to educational and supportive resources for families and caregivers across the lifespan of the child with IS is an urgent need. Pediatric health care providers are well positioned to address these needs.

Low performance on mathematical tasks in preschoolers: the importance of domain-general and domain-specific abilities.

PubMed

Costa, H M; Nicholson, B; Donlan, C; Van Herwegen, J

2018-04-01

Different domain-specific and domain-general cognitive precursors play a key role in the development of mathematical abilities. The contribution of these domains to mathematical ability changes during development. Primary school-aged children who show mathematical difficulties form a heterogeneous group, but it is not clear whether this also holds for preschool low achievers (LAs) and how domain-specific and domain-general abilities contribute to mathematical difficulties at a young age. The aim of this study was to explore the cognitive characteristics of a sample of preschool LAs and identify sub-types of LAs. 81 children were identified as LAs from 283 preschoolers aged 3 to 5 years old and were assessed on a number of domain-general and domain-specific tasks. Cluster analysis revealed four subgroups of LAs in mathematics: (1) a weak processing sub-type; (2) a general mathematical LAs sub-type; (3) a mixed abilities sub-type; and (4) a visuo-spatial deficit sub-type. Whilst two of the groups showed specific domain-general difficulties, none showed only domain-specific difficulties. Current findings suggest that preschool LAs constitute a heterogeneous group and stress the importance of domain-general factors for the development of mathematical abilities during the preschool years. © 2018 MENCAP and International Association of the Scientific Study of Intellectual and Developmental Disabilities and John Wiley & Sons Ltd.

Duplication of the pituitary gland associated with multiple blastogenesis defects: Duplication of the pituitary gland (DPG)-plus syndrome. Case report and review of literature

PubMed Central

Manjila, Sunil; Miller, Erin A.; Vadera, Sumeet; Goel, Rishi K.; Khan, Fahd R.; Crowe, Carol; Geertman, Robert T.

2012-01-01

Background: Duplication of the pituitary gland (DPG) is a rare craniofacial developmental anomaly occurring during blastogenesis with postulated etiology such as incomplete twinning, teratogens, median cleft face syndrome or splitting of the notochord. The complex craniocaudal spectrum of blastogenesis defects associated with DPG is examined with an illustrative case. Case Description: We report for the first time in the medical literature some unique associations with DPG, such as a clival encephalocele, third cerebral peduncle, duplicate odontoid process and a double tongue with independent volitional control. This patient also has the previously reported common associations such as duplicated sella, cleft palate, hypertelorism, callosal agenesis, hypothalamic enlargement, nasopharyngeal teratoma, fenestrated basilar artery and supernumerary teeth. This study also reviews 37 cases of DPG identified through MEDLINE literature search from 1880 to 2011. It provides a detailed analysis of the current case through physical examination and imaging. Conclusion: The authors propose that the developmental deformities associated with duplication of pituitary gland (DPG) occur as part of a developmental continuum, not as chance associations. Considering the fact that DPG is uniquely and certainly present throughout the spectrum of these blastogenesis defects, we suggest the term DPG-plus syndrome. PMID:22439114

Fundamental Dimensions of Environmental Risk : The Impact of Harsh versus Unpredictable Environments on the Evolution and Development of Life History Strategies.

PubMed

Ellis, Bruce J; Figueredo, Aurelio José; Brumbach, Barbara H; Schlomer, Gabriel L

2009-06-01

The current paper synthesizes theory and data from the field of life history (LH) evolution to advance a new developmental theory of variation in human LH strategies. The theory posits that clusters of correlated LH traits (e.g., timing of puberty, age at sexual debut and first birth, parental investment strategies) lie on a slow-to-fast continuum; that harshness (externally caused levels of morbidity-mortality) and unpredictability (spatial-temporal variation in harshness) are the most fundamental environmental influences on the evolution and development of LH strategies; and that these influences depend on population densities and related levels of intraspecific competition and resource scarcity, on age schedules of mortality, on the sensitivity of morbidity-mortality to the organism's resource-allocation decisions, and on the extent to which environmental fluctuations affect individuals versus populations over short versus long timescales. These interrelated factors operate at evolutionary and developmental levels and should be distinguished because they exert distinctive effects on LH traits and are hierarchically operative in terms of primacy of influence. Although converging lines of evidence support core assumptions of the theory, many questions remain unanswered. This review demonstrates the value of applying a multilevel evolutionary-developmental approach to the analysis of a central feature of human phenotypic variation: LH strategy.

Interactions of sex and early life social experiences at two developmental stages shape nonapeptide receptor profiles.

PubMed

Hiura, Lisa C; Ophir, Alexander G

2018-05-31

Early life social experiences are critical to behavioral and cognitive development, and can have a tremendous influence on developing social phenotypes. Most work has focused on outcomes of experiences at a single stage of development (e.g., perinatal, or post-weaning). Few studies have assessed the impact of social experience at multiple developmental stages and across sex. Oxytocin and vasopressin are profoundly important for modulating social behavior and these nonapeptide systems are highly sensitive to developmental social experience, particularly in brain areas important for social behavior. We investigated whether oxytocin receptor (OTR) and vasopressin receptor (V1aR) distributions of prairie voles (Microtus ochrogaster) change as a function of parental composition within the natal nest or social composition after weaning. We raised pups either in the presence or absence of their fathers. At weaning, offspring were housed either individually or with a same-sex sibling. We also examined whether changes in receptor distributions are sexually dimorphic because the impact of the developmental environment on the nonapeptide system could be sex-dependent. We found that differences in nonapeptide receptor expression were region-, sex-, and rearing condition-specific, indicating a high level of complexity in the ways that early life experiences shape the social brain. We found many more differences in V1aR density compared to OTR density, indicating that nonapeptide receptors demonstrate differential levels of neural plasticity and sensitivity to environmental and biological variables. Our data highlight that critical factors including biological sex and multiple experiences across the developmental continuum interact in complex ways to shape the social brain. This article is protected by copyright. All rights reserved. This article is protected by copyright. All rights reserved.

Primary school teachers' use of digital technology in mathematics: the complexities

NASA Astrophysics Data System (ADS)

Loong, Esther Yook-Kin; Herbert, Sandra

2018-02-01

This paper seeks to theorise primary teachers' degree of integration of digital technology in the mathematics classroom. In an age where digital technology use is ubiquitous, the issues surrounding teachers' choice, and ultimately their uptake of digital technologies in the classroom, is an area that need to be further unpacked. Cross-case analysis of the two teachers' uptake of digital technologies in their classroom, their pedagogical approaches and the reason for their choices provide insight into teachers' technological, pedagogical and content knowledge (TPACK). Differences in the way the teachers use digital technology in their classroom seem to be connected to their TPACK developmental stage.

Developmental and individual differences in pure numerical estimation.

PubMed

Booth, Julie L; Siegler, Robert S

2006-01-01

The authors examined developmental and individual differences in pure numerical estimation, the type of estimation that depends solely on knowledge of numbers. Children between kindergarten and 4th grade were asked to solve 4 types of numerical estimation problems: computational, numerosity, measurement, and number line. In Experiment 1, kindergartners and 1st, 2nd, and 3rd graders were presented problems involving the numbers 0-100; in Experiment 2, 2nd and 4th graders were presented problems involving the numbers 0-1,000. Parallel developmental trends, involving increasing reliance on linear representations of numbers and decreasing reliance on logarithmic ones, emerged across different types of estimation. Consistent individual differences across tasks were also apparent, and all types of estimation skill were positively related to math achievement test scores. Implications for understanding of mathematics learning in general are discussed. Copyright 2006 APA, all rights reserved.

Carnegie Math Pathways 2015-2016 Impact Report: A Five-Year Review. Carnegie Math Pathways Technical Report

ERIC Educational Resources Information Center

Hoang, Hai; Huang, Melrose; Sulcer, Brian; Yesilyurt, Suleyman

2017-01-01

College math is a gateway course that has become a constraining gatekeeper for tens of thousands of students annually. Every year, over 500,000 students fail developmental mathematics, preventing them from achieving their college and career goals. The Carnegie Math Pathways initiative offers students an alternative. It comprises two Pathways…

The Use of Group Quizzes in Developmental Mathematics Courses

ERIC Educational Resources Information Center

Sorensen, Ian

2012-01-01

For a period of four semesters, the possibility was explored of using a "group quiz" as a learning activity that provides a collaborative learning environment, a review of the previous week's material, and a formative assessment for both the student and the instructor. Using both quantitative (i.e., student surveys) and qualitative (i.e., student…

A Comparative Analysis of the Reading Levels of Community College Introductory English and College Skills Students.

ERIC Educational Resources Information Center

Hartman-Haas, Hope J.

A study was conducted at Rockland Community College (New York) to determine the adequacy of the reading criterion that determined entry into its intensive freshman English classes from the college skills program, a developmental program designed to improve skills in communication, mathematics, reading, and studying. A group of 746 freshman English…

A Mathematical Model of the Evolution of Individual Differences in Developmental Plasticity Arising through Parental Bet-Hedging

ERIC Educational Resources Information Center

Frankenhuis, Willem E.; Panchanathan, Karthik; Belsky, Jay

2016-01-01

Children vary in the extent to which their development is shaped by particular experiences (e.g. maltreatment, social support). This variation raises a question: Is there no single level of plasticity that maximizes biological fitness? One influential hypothesis states that when different levels of plasticity are optimal in different environmental…

Studies in Mathematics, Volume V. Concepts of Informal Geometry. Preliminary Edition.

ERIC Educational Resources Information Center

Anderson, Richard D.

The main purpose of this book is to provide background material in geometry for teachers or prospective teachers who know little or no geometry. It should be suitable as a text for a one-semester course for teachers of junior high school or upper elementary school students. Chapters contain developmental material and exercises. Chapters include:…

Quantitative Measures for Assessing Learning Centers: An Agenda and Exploration

ERIC Educational Resources Information Center

Berkopes, Kevin; Abshire, Stacey

2016-01-01

The national trend of requiring all college students to engage with tertiary-level mathematics has created the need to rethink how students can be supported at this level. Current trends in higher education show a decreased reliance on remedial developmental education courses and expanded reliance on learning centers. It is important to look at…

The Act and Artifact of Drawing(s): Observing Geometric Thinking with, in, and through Children's Drawings

ERIC Educational Resources Information Center

Thom, Jennifer S.; McGarvey, Lynn M.

2015-01-01

In mathematics education, as in other domains, drawing serves as means to access, assess, and attend to children's understanding. While theoretical accounts of drawings are often based on developmental stage theories, we examine insights gained by considering children's geometric thinking and reasoning from embodied cognitive perspectives. We ask,…

Conference on Non-linear Phenomena in Mathematical Physics: Dedicated to Cathleen Synge Morawetz on her 85th Birthday. The Fields Institute, Toronto, Canada September 18-20, 2008. Sponsors: Association for Women in Mathematics, Inc. and The Fields Institute

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lewis, Jennifer

2012-10-15

This scientific meeting focused on the legacy of Cathleen S. Morawetz and the impact that her scientific work on transonic flow and the non-linear wave equation has had in recent progress on different aspects of analysis for non-linear wave, kinetic and quantum transport problems associated to mathematical physics. These are areas where the elements of continuum, statistical and stochastic mechanics, and their interplay, have counterparts in the theory of existence, uniqueness and stability of the associated systems of equations and geometric constraints. It was a central event for the applied and computational analysis community focusing on Partial Differential Equations. Themore » goal of the proposal was to honor Cathleen Morawetz, a highly successful woman in mathematics, while encouraging beginning researchers. The conference was successful in show casing the work of successful women, enhancing the visibility of women in the profession and providing role models for those just beginning their careers. The two-day conference included seven 45-minute lectures and one day of six 45-minute lectures, and a poster session for junior participants. The conference program included 19 distinguished speakers, 10 poster presentations, about 70 junior and senior participants and, of course, the participation of Cathleen Synge Morawetz. The conference celebrated Morawetz's paramount contributions to the theory of non-linear equations in gas dynamics and their impact in the current trends of nonlinear phenomena in mathematical physics, but also served as an awareness session of current women's contribution to mathematics.« less

Autism genetics: Methodological issues and experimental design.

PubMed

Sacco, Roberto; Lintas, Carla; Persico, Antonio M

2015-10-01

Autism is a complex neuropsychiatric disorder of developmental origin, where multiple genetic and environmental factors likely interact resulting in a clinical continuum between "affected" and "unaffected" individuals in the general population. During the last two decades, relevant progress has been made in identifying chromosomal regions and genes in linkage or association with autism, but no single gene has emerged as a major cause of disease in a large number of patients. The purpose of this paper is to discuss specific methodological issues and experimental strategies in autism genetic research, based on fourteen years of experience in patient recruitment and association studies of autism spectrum disorder in Italy.

The Cosmologic continuum from physics to consciousness.

PubMed

Torday, John S; Miller, William B

2018-04-13

Reduction of developmental biology to self-referential cell-cell communication offers a portal for understanding fundamental mechanisms of physiology as derived from physics through quantum mechanics. It is argued that self-referential organization is implicit to the Big Bang and its further expression is a recoil reaction to that Singularity. When such a frame is considered, in combination with experimental evidence for the importance of epigenetic inheritance, the unicellular state can be reappraised as the primary object of selection. This framework provides a significant shift in understanding the relationship between physics and biology, providing novel insights to the nature and origin of consciousness. Copyright © 2018. Published by Elsevier Ltd.

Behavioral Economic Factors Related to Pediatric Obesity

PubMed Central

Greenwald, Mark K.

2016-01-01

Summary The field of behavioral economics suggests that food and activity choices are governed by costs, available alternatives, and reinforcement. Here, we review basic and translational research using a behavioral economic (BE) framework with overweight or obese children up to age 18. We address BE concepts and methods, discuss developmental issues, the continuum of BE intervention approaches, findings of studies focused on increasing the cost of unwanted behaviors (i.e., energy-dense food intake and sedentary behavior) and decreasing the cost of desired behaviors (i.e., healthy food intake and PA), and our team's recent basic behavioral studies using BE approaches with minority adolescents. PMID:27261543

Perspectives in active liquid crystals

PubMed Central

Majumdar, Apala; Cristina, Marchetti M.; Virga, Epifanio G.

2014-01-01

Active soft matter is a young, growing field, with potential applications to a wide variety of systems. This Theme Issue explores this emerging new field by highlighting active liquid crystals. The collected contributions bridge theory to experiment, mathematical theories of passive and active nematics, spontaneous flows to defect dynamics, microscopic to continuum levels of description, spontaneous activity to biological activation. While the perspectives offered here only span a small part of this rapidly evolving field, we trust that they might provide the interested reader with a taste for this new class of non-equilibrium systems and their rich behaviour. PMID:25332386

Experimental and theoretical research of the interaction between high-strength supercavitation impactors and monolithic barriers in water

NASA Astrophysics Data System (ADS)

Ishchenko, A. N.; Afanas'eva, S. A.; Burkin, V. V.; Diachkovskii, A. S.; Zykova, A. I.; Khabibullin, M. V.; Chupashev, A. V.; Yugov, N. T.

2017-09-01

The article describes experimental and theoretical research of the interaction between supercavitating impactors and underwater aluminum alloy and steel barriers. Strong alloys are used for making impactors. An experimental research technique based on a high-velocity hydro-ballistic complex was developed. Mathematical simulation of the collision the impactor and barrier is based on the continuum mechanics inclusive of the deformation and destruction of interacting bodies. Calculated and experimental data on the ultimate penetration thickness of barriers made of aluminum alloy D16T and steel for the developed supercavitating impactor are obtained.

A poroelastic medium saturated by a two-phase capillary fluid

NASA Astrophysics Data System (ADS)

Shelukhin, V. V.

2014-09-01

By Landau's approach developed for description of superfluidity of 2He, we derive a mathematical model for a poroelastic medium saturated with a two-phase capillary fluid. The model describes a three-velocity continuum with conservation laws which obey the basic principles of thermodynamics and which are consistent with the Galilean transformations. In contrast to Biot' linear theory, the equations derived allow for finite deformations. As the acoustic analysis reveals, there is one more longitudinal wave in comparison with the poroelastic medium saturated with a one-phase fluid. We prove that such a result is due to surface tension.

Discrete and continuous models for tissue growth and shrinkage.

PubMed

Yates, Christian A

2014-06-07

The incorporation of domain growth into stochastic models of biological processes is of increasing interest to mathematical modellers and biologists alike. In many situations, especially in developmental biology, the growth of the underlying tissue domain plays an important role in the redistribution of particles (be they cells or molecules) which may move and react atop the domain. Although such processes have largely been modelled using deterministic, continuum models there is an increasing appetite for individual-based stochastic models which can capture the fine details of the biological movement processes which are being elucidated by modern experimental techniques, and also incorporate the inherent stochasticity of such systems. In this work we study a simple stochastic model of domain growth. From a basic version of this model, Hywood et al. (2013) were able to derive a Fokker-Plank equation (FPE) (in this case an advection-diffusion partial differential equation on a growing domain) which describes the evolution of the probability density of some tracer particles on the domain. We extend their work so that a variety of different domain growth mechanisms can be incorporated and demonstrate a good agreement between the mean tracer density and the solution of the FPE in each case. In addition we incorporate domain shrinkage (via element death) into our individual-level model and demonstrate that we are able to derive coefficients for the FPE in this case as well. For situations in which the drift and diffusion coefficients are not readily available we introduce a numerical coefficient estimation approach and demonstrate the accuracy of this approach by comparing it with situations in which an analytical solution is obtainable. Copyright © 2014 Elsevier Ltd. All rights reserved.

Meso-scale turbulence in living fluids

NASA Astrophysics Data System (ADS)

Dunkel, Jorn; Wensink, Rik; Heidenreich, Sebastian; Drescher, Knut; Goldstein, Ray; Loewen, Hartmut; Yeomans, Julia

2012-11-01

The mathematical characterization of turbulence phenomena in active non-equilibrium fluids proves even more difficult than for conventional liquids or gases. It is not known which features of turbulent phases in living matter are universal or system-specific, or which generalizations of the Navier-Stokes equations are able to describe them adequately. We combine experiments, particle simulations, and continuum theory to identify the statistical properties of self-sustained meso-scale turbulence in active systems. To study how dimensionality and boundary conditions affect collective bacterial dynamics, we measured energy spectra and structure functions in dense Bacillus subtilis suspensions in quasi-2D and 3D geometries. Our experimental results for the bacterial flow statistics agree well with predictions from a minimal model for self-propelled rods, suggesting that at high concentrations the collective motion of the bacteria is dominated by short-range interactions. To provide a basis for future theoretical studies, we propose a minimal continuum model for incompressible bacterial flow. A detailed numerical analysis of the 2D case shows that this theory can reproduce many of the experimentally observed features of self-sustained active turbulence. Supported by the ERC, EPSRC and DFG.

Convoluted Quasi Sturmian basis for the two-electron continuum

NASA Astrophysics Data System (ADS)

Ancarani, Lorenzo Ugo; Zaytsev, A. S.; Zaytsev, S. A.

2016-09-01

In the construction of solutions for the Coulomb three-body scattering problem one encounters a series of mathematical and numerical difficulties, one of which are the cumbersome boundary conditions the wave function should obey. We propose to describe a Coulomb three-body system continuum with a set of two-particle functions, named Convoluted Quasi Sturmian (CQS) in. They are built using recently introduced Quasi Sturmian (QS) functions which have the merit of possessing a closed form. Unlike a simple product of two one-particle functions, by construction, the CQS functions look asymptotically like a six-dimensional outgoing spherical wave. The proposed CQS basis is tested through the study of the double ionization of helium by high-energy electron impact in the framework of the Temkin-Poet model. An adequate logarithmic-like phase factor is further included in order to take into account the Coulomb interelectronic interaction and formally build the correct asymptotic behavior when all interparticle distances are large. With such a phase-factor (that can be easily extended to take into account higher partial waves) rapid convergence of the expansion can be obtained.

Predictive Models of Cognitive Outcomes of Developmental Insults

NASA Astrophysics Data System (ADS)

Chan, Yupo; Bouaynaya, Nidhal; Chowdhury, Parimal; Leszczynska, Danuta; Patterson, Tucker A.; Tarasenko, Olga

2010-04-01

Representatives of Arkansas medical, research and educational institutions have gathered over the past four years to discuss the relationship between functional developmental perturbations and their neurological consequences. We wish to track the effect on the nervous system by developmental perturbations over time and across species. Except for perturbations, the sequence of events that occur during neural development was found to be remarkably conserved across mammalian species. The tracking includes consequences on anatomical regions and behavioral changes. The ultimate goal is to develop a predictive model of long-term genotypic and phenotypic outcomes that includes developmental insults. Such a model can subsequently be fostered into an educated intervention for therapeutic purposes. Several datasets were identified to test plausible hypotheses, ranging from evoked potential datasets to sleep-disorder datasets. An initial model may be mathematical and conceptual. However, we expect to see rapid progress as large-scale gene expression studies in the mammalian brain permit genome-wide searches to discover genes that are uniquely expressed in brain circuits and regions. These genes ultimately control behavior. By using a validated model we endeavor to make useful predictions.

Development of intuitive rules: evaluating the application of the dual-system framework to understanding children's intuitive reasoning.

PubMed

Osman, Magda; Stavy, Ruth

2006-12-01

Theories of adult reasoning propose that reasoning consists of two functionally distinct systems that operate under entirely different mechanisms. This theoretical framework has been used to account for a wide range of phenomena, which now encompasses developmental research on reasoning and problem solving. We begin this review by contrasting three main dual-system theories of adult reasoning (Evans & Over, 1996; Sloman, 1996; Stanovich & West, 2000) with a well-established developmental account that also incorporates a dual-system framework (Brainerd & Reyna, 2001). We use developmental studies of the formation and application of intuitive rules in science and mathematics to evaluate the claims that these theories make. Overall, the evidence reviewed suggests that what is crucial to understanding how children reason is the saliency of the features that are presented within a task. By highlighting the importance of saliency as a way of understanding reasoning, we aim to provide clarity concerning the benefits and limitations of adopting a dual-system framework to account for evidence from developmental studies of intuitive reasoning.

A Model for Predicting Thermoelectric Properties of Bi2Te3

NASA Technical Reports Server (NTRS)

Lee, Seungwon; VonAllmen, Paul

2009-01-01

A parameterized orthogonal tight-binding mathematical model of the quantum electronic structure of the bismuth telluride molecule has been devised for use in conjunction with a semiclassical transport model in predicting the thermoelectric properties of doped bismuth telluride. This model is expected to be useful in designing and analyzing Bi2Te3 thermoelectric devices, including ones that contain such nano - structures as quantum wells and wires. In addition, the understanding gained in the use of this model can be expected to lead to the development of better models that could be useful for developing other thermoelectric materials and devices having enhanced thermoelectric properties. Bi2Te3 is one of the best bulk thermoelectric materials and is widely used in commercial thermoelectric devices. Most prior theoretical studies of the thermoelectric properties of Bi2Te3 have involved either continuum models or ab-initio models. Continuum models are computationally very efficient, but do not account for atomic-level effects. Ab-initio models are atomistic by definition, but do not scale well in that computation times increase excessively with increasing numbers of atoms. The present tight-binding model bridges the gap between the well-scalable but non-atomistic continuum models and the atomistic but poorly scalable ab-initio models: The present tight-binding model is atomistic, yet also computationally efficient because of the reduced (relative to an ab-initio model) number of basis orbitals and flexible parameterization of the Hamiltonian.

Finite Element Method-Based Kinematics and Closed-Loop Control of Soft, Continuum Manipulators.

PubMed

Bieze, Thor Morales; Largilliere, Frederick; Kruszewski, Alexandre; Zhang, Zhongkai; Merzouki, Rochdi; Duriez, Christian

2018-06-01

This article presents a modeling methodology and experimental validation for soft manipulators to obtain forward kinematic model (FKM) and inverse kinematic model (IKM) under quasi-static conditions (in the literature, these manipulators are usually classified as continuum robots. However, their main characteristic of interest in this article is that they create motion by deformation, as opposed to the classical use of articulations). It offers a way to obtain the kinematic characteristics of this type of soft robots that is suitable for offline path planning and position control. The modeling methodology presented relies on continuum mechanics, which does not provide analytic solutions in the general case. Our approach proposes a real-time numerical integration strategy based on finite element method with a numerical optimization based on Lagrange multipliers to obtain FKM and IKM. To reduce the dimension of the problem, at each step, a projection of the model to the constraint space (gathering actuators, sensors, and end-effector) is performed to obtain the smallest number possible of mathematical equations to be solved. This methodology is applied to obtain the kinematics of two different manipulators with complex structural geometry. An experimental comparison is also performed in one of the robots, between two other geometric approaches and the approach that is showcased in this article. A closed-loop controller based on a state estimator is proposed. The controller is experimentally validated and its robustness is evaluated using Lypunov stability method.

Combined discrete particle and continuum model predicting solid-state fermentation in a drum fermentor.

PubMed

Schutyser, M A I; Briels, W J; Boom, R M; Rinzema, A

2004-05-20

The development of mathematical models facilitates industrial (large-scale) application of solid-state fermentation (SSF). In this study, a two-phase model of a drum fermentor is developed that consists of a discrete particle model (solid phase) and a continuum model (gas phase). The continuum model describes the distribution of air in the bed injected via an aeration pipe. The discrete particle model describes the solid phase. In previous work, mixing during SSF was predicted with the discrete particle model, although mixing simulations were not carried out in the current work. Heat and mass transfer between the two phases and biomass growth were implemented in the two-phase model. Validation experiments were conducted in a 28-dm3 drum fermentor. In this fermentor, sufficient aeration was provided to control the temperatures near the optimum value for growth during the first 45-50 hours. Several simulations were also conducted for different fermentor scales. Forced aeration via a single pipe in the drum fermentors did not provide homogeneous cooling in the substrate bed. Due to large temperature gradients, biomass yield decreased severely with increasing size of the fermentor. Improvement of air distribution would be required to avoid the need for frequent mixing events, during which growth is hampered. From these results, it was concluded that the two-phase model developed is a powerful tool to investigate design and scale-up of aerated (mixed) SSF fermentors. Copyright 2004 Wiley Periodicals, Inc.

Early childhood numeracy in a multiage setting

NASA Astrophysics Data System (ADS)

Wood, Karen; Frid, Sandra

2005-10-01

This research is a case study examining numeracy teaching and learning practices in an early childhood multiage setting with Pre-Primary to Year 2 children. Data were collected via running records, researcher reflection notes, and video and audio recordings. Video and audio transcripts were analysed using a mathematical discourse and social interactions coding system designed by MacMillan (1998), while the running records and reflection notes contributed to descriptions of the children's interactions with each other and with the teachers. Teachers used an `assisted performance' approach to instruction that supported problem solving and inquiry processes in mathematics activities, and this, combined with a child-centred pedagogy and specific values about community learning, created a learning environment designed to stimulate and foster learning. The mathematics discourse analysis showed a use of explanatory language in mathematics discourse, and this language supported scaffolding among children for new mathematics concepts. These and other interactions related to peer sharing, tutoring and regulation also emerged as key aspects of students' learning practices. However, the findings indicated that multiage grouping alone did not support learning. Rather, effective learning was dependent upon the teacher's capacities to develop productive discussion among children, as well as implement developmentally appropriate curricula that addressed the needs of the different children.

Developmental dyscalculia in children and adolescents with idiopathic epilepsies in a Brazilian sample.

PubMed

Thomé, Ursula; Paixão Alves, Sandra Regina da; Guerreiro, Sabrina Mendonça; Machado da Costa, Célia Regina Carvalho; Souza Moreira, Fernanda de; Bandeira Lima, Andrea; Ferreira Tavares, Maria Rita; Souza Maia Filho, Heber

2014-04-01

Epilepsy is one of the most prevalent chronic disorders of childhood which can threaten child development and mental health. Among cognitive disorders, dyscalculia is one of the most important. In this study, 39 children and adolescents with idiopathic epilepsy underwent clinical and neuropsychological assessment to determine the intellectual level, math skills, reading and writing performance and neuropsychological profile. It was observed that the mathematical ability was below schooling expectations in a higher frequency than expected. There were no significant differences in mathematical performance among groups divided by number of antiepileptic drugs used, duration of disease and types and frequency of seizures. There was a positive correlation with intelligence quotient and attentional and reading level. These results suggest the existence not only of dyscalculia, but the concurrence of attentional and reading problems for the poor mathematical performance in this population.

Evaluating the Effectiveness of the 2000-2001 NASA "Why?" Files Program

NASA Technical Reports Server (NTRS)

Pinelli, Thomas E.; Frank, Kari Lou; Ashcroft, Scott B.; Williams, Amy C.

2002-01-01

NASA 'Why?' Files, a research and standards-based, Emmy-award winning series of 60-minute instructional programs for grades 3-5, introduces students to NASA; integrates mathematics, science, and technology by using Problem-Based Learning (PBL), scientific inquiry, and the scientific method; and motivates students to become critical thinkers and active problem solvers. All four 2000-2001 NASA 'Why?' Files programs include an instructional broadcast, a lesson guide, an interactive web site, plus numerous instructional resources. In March 2001, 1,000 randomly selected program registrants participated in a survey. Of these surveys, 185 (154 usable) met the established cut-off date. Respondents reported that (1) they used the four programs in the 2000-2001 NASA 'Why?' Files series; (2) series goals and objectives were met; (3) programs met national mathematics, science, and technology standards; (4) program content was developmentally appropriate for grade level; and (5) programs enhanced/enriched the teaching of mathematics, science, and technology.

NASA Langley/CNU Distance Learning Programs

NASA Technical Reports Server (NTRS)

Caton, Randall; Pinelli, Thomas E.

2002-01-01

NASA Langley Research Center and Christopher Newport University (CNU) provide, free to the public, distance learning programs that focus on math, science, and/or technology over a spectrum of education levels from K-adult. The effort started in 1997, and we currently have a suite of five distance-learning programs. We have around 450,000 registered educators and 12.5 million registered students in 60 countries. Partners and affiliates include the American Institute of Aeronautics and Astronautics (AIAA), the Aerospace Education Coordinating Committee (AECC), the Alliance for Community Media, the National Educational Telecommunications Association, Public Broadcasting System (PBS) affiliates, the NASA Learning Technologies Channel, the National Council of Teachers of Mathematics (NCTM), the Council of the Great City Schools, Hampton City Public Schools, Sea World Adventure Parks, Busch Gardens, ePALS.com, and Riverdeep. Our mission is based on the "Horizon of Learning," a vision for inspiring learning across a continuum of educational experiences. The programs form a continuum of educational experiences for elementary youth through adult learners. The strategic plan for the programs will evolve to reflect evolving national educational needs, changes within NASA, and emerging system initiatives. Plans for each program component include goals, objectives, learning outcomes, and rely on sound business models. It is well documented that if technology is used properly it can be a powerful partner in education. Our programs employ both advances in information technology and in effective pedagogy to produce a broad range of materials to complement and enhance other educational efforts. Collectively, the goals of the five programs are to increase educational excellence; enhance and enrich the teaching of mathematics, science, and technology; increase scientific and technological literacy; and communicate the results of NASA discovery, exploration, innovation and research. All pre-college distance learning programs support the national mathematics, science, and technology standards; support K-12 systemic change; involve educators in their development, implementation, and evaluation; and are based on alliances and partnerships. In addition the programs seek to invoke a sense of geographic, ethnic and cultural diversity by featuring schools from all over the U.S.; schools from urban, suburban, and rural areas; public, private, and religious schools; and schools with large populations of African-American, Asian and Hispanic students.

A Look at the Impact of Raising Standards in Developmental Mathematics

ERIC Educational Resources Information Center

Guy, G. Michael; Puri, Karan; Cornick, Jonathan

2016-01-01

In this paper, we assess the effect of higher entry and exit standards at a community college in New York City. A complex set of university and college-wide policy modifications led to an increase in placement test cut-scores as well as increased requirements to complete remediation. The implementation of this policy change allows us to utilize…

A Quantitative Study Examining the Differences in Motivation and Achievement between Traditional versus Team-Based Learning

ERIC Educational Resources Information Center

Ku, James Yu-Fan

2016-01-01

Obtaining a degree from a community college could be the opportunity for students to advance their education or career. Nevertheless, nearly two-thirds of first-time community college students in the U.S. were required to take developmental mathematics courses. The problem was that approximately three-fourth of those students did not successfully…