Social Risk Takers: Understanding Bilingualism in Mathematical Discussions

ERIC Educational Resources Information Center

Dominguez, Higinio

2017-01-01

The teaching and research communities in mathematics education agree that mathematical discussions pose challenges in elementary classrooms. These challenges continue to motivate research on mathematical discussions, with a focus on how students use talk in discussions. This study addresses the question, "What can teachers and researchers…

Classroom Challenge: A 3D Snapshot of Student Learning in Mathematics

ERIC Educational Resources Information Center

Wilder, Sandra

2015-01-01

This article aims to describe a type of formative assessment, MAP Classroom Challenge, which has been introduced in mathematics classrooms in recent years. MAP, or the Mathematics Assessment Project Classroom Challenges (formerly known as Formative Assessment Lessons), are developed by teams of math educators from the Shell Centre for Mathematical…

Mastering Reading and Mathematics in the Early Grades. Challenge to Lead Series

ERIC Educational Resources Information Center

Lord, Joan; Wade, Robin; Creech, Joseph

2004-01-01

The "Challenge to Lead" goal for early grades students is first about student achievement in reading and mathematics. The goal is that students in the early grades, regardless of their economic status, school location, ethnicity or gender will be as proficient in reading and mathematics as youngsters anywhere in the nation. "Challenge to Lead"…

On the bending of structural materials with plastic anisotropic effect

NASA Astrophysics Data System (ADS)

Lachugin, D. V.; Pavilaynen, G. V.

2018-05-01

The study of a deformation features of metal alloys which are sensitive to tension or compression loading is an important technical challenge in the design and creation of a new shipbuilding and aircraft constructions. We use a mathematical model for the elastic-plastic bending of such material where SD(strength-different) parameter is taken into account. The problem is solved analytically and numerically. As an example of the material with the SD-effect the steel alloy is considered.

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

Keyes, D.; McInnes, L. C.; Woodward, C.

This report is an outcome of the workshop Multiphysics Simulations: Challenges and Opportunities, sponsored by the Institute of Computing in Science (ICiS). Additional information about the workshop, including relevant reading and presentations on multiphysics issues in applications, algorithms, and software, is available via https://sites.google.com/site/icismultiphysics2011/. We consider multiphysics applications from algorithmic and architectural perspectives, where 'algorithmic' includes both mathematical analysis and computational complexity and 'architectural' includes both software and hardware environments. Many diverse multiphysics applications can be reduced, en route to their computational simulation, to a common algebraic coupling paradigm. Mathematical analysis of multiphysics coupling in this form is not alwaysmore » practical for realistic applications, but model problems representative of applications discussed herein can provide insight. A variety of software frameworks for multiphysics applications have been constructed and refined within disciplinary communities and executed on leading-edge computer systems. We examine several of these, expose some commonalities among them, and attempt to extrapolate best practices to future systems. From our study, we summarize challenges and forecast opportunities. We also initiate a modest suite of test problems encompassing features present in many applications.« less

Perceived mathematical ability under challenge: a longitudinal perspective on sex segregation among STEM degree fields.

PubMed

Nix, Samantha; Perez-Felkner, Lara; Thomas, Kirby

2015-01-01

Students' perceptions of their mathematics ability vary by gender and seem to influence science, technology, engineering, and mathematics (STEM) degree choice. Related, students' perceptions during academic difficulty are increasingly studied in educational psychology, suggesting a link between such perceptions and task persistence. Despite interest in examining the gender disparities in STEM, these concepts have not been considered in tandem. In this manuscript, we investigate how perceived ability under challenge-in particular in mathematics domains-influences entry into the most sex-segregated and mathematics-intensive undergraduate degrees: physics, engineering, mathematics, and computer science (PEMC). Using nationally representative Education Longitudinal Study of 2002 (ELS) data, we estimate the influence of perceived ability under challenging conditions on advanced high school science course taking, selection of an intended STEM major, and specific major type 2 years after high school. Demonstrating the importance of specificity when discussing how gender influences STEM career pathways, the intersecting effects of gender and perceived ability under mathematics challenge were distinct for each scientific major category. Perceived ability under challenge in secondary school varied by gender, and was highly predictive of selecting PEMC and health sciences majors. Notably, women's 12th grade perceptions of their ability under mathematics challenge increased their probability of selecting PEMC majors over and above biology. In addition, gender moderated the effect of growth mindset on students' selection of health science majors. Perceptions of ability under challenge in general and verbal domains also influenced retention in and declaration of certain STEM majors. The implications of these results are discussed, with particular attention to access to advanced scientific coursework in high school and interventions aimed at enhancing young women's perceptions of their ability, in particular in response to the potentially inhibiting influence of stereotype threat on their pathways to scientific degrees.

The (Mathematical) Modeling Process in Biosciences

PubMed Central

Torres, Nestor V.; Santos, Guido

2015-01-01

In this communication, we introduce a general framework and discussion on the role of models and the modeling process in the field of biosciences. The objective is to sum up the common procedures during the formalization and analysis of a biological problem from the perspective of Systems Biology, which approaches the study of biological systems as a whole. We begin by presenting the definitions of (biological) system and model. Particular attention is given to the meaning of mathematical model within the context of biology. Then, we present the process of modeling and analysis of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model. All along this work the main features and shortcomings of the process are analyzed and a set of rules that could help in the task of modeling any biological system are presented. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that modeling is posing to current biology. PMID:26734063

Linguistic Challenges in the Mathematical Register for EFL Learners: Linguistic and Multimodal Strategies to Help Learners Tackle Mathematics Word Problems

ERIC Educational Resources Information Center

Chan, Simon

2015-01-01

In learning mathematics through English, one of the major challenges facing English as a Foreign Language (EFL) learners is understanding the language used to present word problems in mathematics texts. Without comprehending such language, learners are not able to carry out the targeted calculations no matter how familiar they are with the…

Examining the design features of a communication-rich, problem-centred mathematics professional development

NASA Astrophysics Data System (ADS)

de Araujo, Zandra; Orrill, Chandra Hawley; Jacobson, Erik

2018-04-01

While there is considerable scholarship describing principles for effective professional development, there have been few attempts to examine these principles in practice. In this paper, we identify and examine the particular design features of a mathematics professional development experience provided for middle grades teachers over 14 weeks. The professional development was grounded in a set of mathematical tasks that each had one right answer, but multiple solution paths. The facilitator engaged participants in problem solving and encouraged participants to work collaboratively to explore different solution paths. Through analysis of this collaborative learning environment, we identified five design features for supporting teacher learning of important mathematics and pedagogy in a problem-solving setting. We discuss these design features in depth and illustrate them by presenting an elaborated example from the professional development. This study extends the existing guidance for the design of professional development by examining and operationalizing the relationships among research-based features of effective professional development and the enacted features of a particular design.

"Connectivism"--A New Paradigm for the Mathematics Anxiety Challenge?

ERIC Educational Resources Information Center

Klinger, Christopher M.

2011-01-01

A major challenge for practitioners in adult mathematics education is to achieve effective learning outcomes in the face of prevailing negative attitudes in their students, often present as a consequence of unsatisfactory early mathematics learning experience and flowing from the wellestablished connection between adult innumeracy and mathematics…

Raising Concerns about Sharing and Reusing Large-Scale Mathematics Classroom Observation Video Data

ERIC Educational Resources Information Center

Ing, Marsha; Samkian, Artineh

2018-01-01

There are great opportunities and challenges to sharing large-scale mathematics classroom observation data. This Research Commentary describes the methodological opportunities and challenges and provides a specific example from a mathematics education research project to illustrate how the research questions and framework drove observational…

Current Challenges in Integrating Educational Technology into Elementary and Middle School Mathematics Education

ERIC Educational Resources Information Center

Okita, Sandra Y.; Jamalian, Azadeh

2011-01-01

Developing curriculum and instruction for mathematics education and designing technologically enhanced learning environments are often pursued separately, but may need to be addressed together to effectively link the strengths of technology to performance in mathematics and conceptual understanding. This paper addresses current challenges with…

Challenges and Opportunities in Teaching Mathematics

ERIC Educational Resources Information Center

Goos, Merrilyn

2016-01-01

At the special conference celebrating the 50th anniversary of the Australian Association of Mathematics Teachers (AAMT), the author was asked to speak about the challenges and opportunities in teaching mathematics as a stimulus for discussion of AAMT's "future directions". With an open invitation to be a little provocative, the author…

Reshaping Assessment Practices: Mathematics Assessment under Challenge. Proceedings from the National Conference on Assessment in the Mathematical Sciences (1st, Geelong, Victoria, Australia November 20-24, 1991).

ERIC Educational Resources Information Center

Stephens, Max, Ed.; Izard, John, Ed.

The purpose of the Australian conference on mathematical assessment was to address the challenges to traditional methods of assessment that have resulted as part of the call for reform in the mathematics curriculum. The 28 papers presented were: "Who Assesses Whom and To What Purpose?" (Leone Burton; "Assessment of the Learned…

Perceived mathematical ability under challenge: a longitudinal perspective on sex segregation among STEM degree fields

PubMed Central

Nix, Samantha; Perez-Felkner, Lara; Thomas, Kirby

2015-01-01

Students' perceptions of their mathematics ability vary by gender and seem to influence science, technology, engineering, and mathematics (STEM) degree choice. Related, students' perceptions during academic difficulty are increasingly studied in educational psychology, suggesting a link between such perceptions and task persistence. Despite interest in examining the gender disparities in STEM, these concepts have not been considered in tandem. In this manuscript, we investigate how perceived ability under challenge—in particular in mathematics domains—influences entry into the most sex-segregated and mathematics-intensive undergraduate degrees: physics, engineering, mathematics, and computer science (PEMC). Using nationally representative Education Longitudinal Study of 2002 (ELS) data, we estimate the influence of perceived ability under challenging conditions on advanced high school science course taking, selection of an intended STEM major, and specific major type 2 years after high school. Demonstrating the importance of specificity when discussing how gender influences STEM career pathways, the intersecting effects of gender and perceived ability under mathematics challenge were distinct for each scientific major category. Perceived ability under challenge in secondary school varied by gender, and was highly predictive of selecting PEMC and health sciences majors. Notably, women's 12th grade perceptions of their ability under mathematics challenge increased their probability of selecting PEMC majors over and above biology. In addition, gender moderated the effect of growth mindset on students' selection of health science majors. Perceptions of ability under challenge in general and verbal domains also influenced retention in and declaration of certain STEM majors. The implications of these results are discussed, with particular attention to access to advanced scientific coursework in high school and interventions aimed at enhancing young women's perceptions of their ability, in particular in response to the potentially inhibiting influence of stereotype threat on their pathways to scientific degrees. PMID:26113823

Examining Fourth-Grade Mathematics Writing: Features of Organization, Mathematics Vocabulary, and Mathematical Representations

ERIC Educational Resources Information Center

Hebert, Michael A.; Powell, Sarah R.

2016-01-01

Increasingly, students are expected to write about mathematics. Mathematics writing may be informal (e.g., journals, exit slips) or formal (e.g., writing prompts on high-stakes mathematics assessments). In order to develop an effective mathematics-writing intervention, research needs to be conducted on how students organize mathematics writing and…

Challenges in Implementing Strategies for Gender-Aware Teaching.

ERIC Educational Resources Information Center

Gilbert, Melissa C.; Gilbert, Lucia Albino

2002-01-01

Discusses the negative consequences of gender stereotyping in the mathematics classroom, especially for girls. Addresses possible challenges associated with creating a safe learning environment and combating gender stereotypes. Describes difficulties in various settings in the mathematics classroom and explores challenges associated with…

Connecting Pre-Service Teachers with Contemporary Mathematics Practices: Selecting and Sequencing Students' Work Samples

ERIC Educational Resources Information Center

Livy, Sharyn; Muir, Tracey; Downton, Ann

2017-01-01

One of the challenges facing teacher educators is providing our pre-service teachers (PSTs) with authentic experiences that cross the boundaries between Initial Teacher Education (ITE) and the classroom. An additional challenge facing the mathematics teacher educator, is addressing and deepening PSTs' mathematical content knowledge (MCK), which…

Amidst Multiple Theories of Learning in Mathematics Education

ERIC Educational Resources Information Center

Simon, Martin A.

2009-01-01

Currently, there are more theories of learning in use in mathematics education research than ever before (Lerman & Tsatsaroni, 2004). Although this is a positive sign for the field, it also has brought with it a set of challenges. In this article, I identify some of these challenges and consider how mathematics education researchers might think…

78 FR 70303 - Announcement of Requirements and Registration for the Predict the Influenza Season Challenge

Federal Register 2010, 2011, 2012, 2013, 2014

2013-11-25

... public. Mathematical and statistical models can be useful in predicting the timing and impact of the... applying any mathematical, statistical, or other approach to predictive modeling. This challenge will... Services (HHS) region level(s) in the United States by developing mathematical and statistical models that...

NASA Astrophysics Data System (ADS)

2018-05-01

Eigenvalues and eigenvectors, together, constitute the eigenstructure of the system. The design of vibrating systems aimed at satisfying specifications on eigenvalues and eigenvectors, which is commonly known as eigenstructure assignment, has drawn increasing interest over the recent years. The most natural mathematical framework for such problems is constituted by the inverse eigenproblems, which consist in the determination of the system model that features a desired set of eigenvalues and eigenvectors. Although such a problem is intrinsically challenging, several solutions have been proposed in the literature. The approaches to eigenstructure assignment can be basically divided into passive control and active control.

Teaching by Open-Approach Method in Japanese Mathematics Classroom.

ERIC Educational Resources Information Center

Nohda, Nobuhiko

Mathematics educators in Japan have traditionally emphasized mathematical perspectives in research and practice. This paper features an account of changes in mathematics education in Japan that focus on the possibilities of individual students as well as their mathematical ways of thinking. Students' mathematical thinking, mathematical…

Dilemma in Teaching Mathematics

ERIC Educational Resources Information Center

Md Kamaruddin, Nafisah Kamariah; Md Amin, Zulkarnain

2012-01-01

The challenge in mathematics education is finding the best way to teach mathematics. When students learn the reasoning and proving in mathematics, they will be proficient in mathematics. Students must know mathematics before they can apply it. Symbolism and logic is the key to both the learning of mathematics and its effective application to…

The Challenge of Learning Physics before Mathematics: A Case Study of Curriculum Change in Taiwan

ERIC Educational Resources Information Center

Chiu, Mei-Shiu

2016-01-01

The aim of this study was to identify challenges in implementing a physics-before- 10 mathematics curriculum. Obviously, students need to learn necessary mathematics skills in order to develop advanced physics knowledge. In the 2010 high school curriculum in Taiwan, however, grade 11 science students study two-dimensional motion in physics without…

Sandy Point Fun Run: A Context for Understanding and Using Scale

ERIC Educational Resources Information Center

Roche, Anne

2013-01-01

In the middle years of school, it is important that mathematics is challenging, engaging and focuses on worthwhile mathematics. In this article, Anne Roche describes a lesson that seemed to have all three of these characteristics, as students grappled with issues of scale to create a fun run, given a range of challenging mathematical constraints.…

A Classroom Perspective on the Principle of Moderate Challenge in Mathematics.

ERIC Educational Resources Information Center

Turner, Julianne C.; Meyer, Debra K.

2004-01-01

The authors reviewed the research on challenge as a motivator, with a view toward application in mathematics classrooms. The authors conclude that traditional motivational research, with its focus on individual differences and decontextualized tasks, is not readily applicable to classrooms. They argue that a combination of challenging instruction…

Supporting Teachers in Structuring Mathematics Lessons Involving Challenging Tasks

ERIC Educational Resources Information Center

Sullivan, Peter; Askew, Mike; Cheeseman, Jill; Clarke, Doug; Mornane, Angela; Roche, Anne; Walker, Nadia

2015-01-01

The following is a report on an investigation into ways of supporting teachers in converting challenging mathematics tasks into classroom lessons and supporting students in engaging with those tasks. Groups of primary and secondary teachers, respectively, were provided with documentation of ten lessons built around challenging tasks. Teachers…

How Does Lesson Structure Shape Teacher Perceptions of Teaching with Challenging Tasks?

ERIC Educational Resources Information Center

Russo, James; Hopkins, Sarah

2017-01-01

Despite reforms in mathematics education, many teachers remain reluctant to incorporate challenging (i.e., more cognitively demanding) tasks into their mathematics instruction. The current study examines how lesson structure shapes teacher perceptions of teaching with challenging tasks. Participants included three Year 1/2 classroom teachers who…

Truth & Beauty: Mathematics in Literature

ERIC Educational Resources Information Center

Cohen, Marion D.

2013-01-01

Today there are many categories of mathematics literature, including fiction and poetry. Mathematics fiction appears in such anthologies as "Fantasia Mathematica" (Fadiman 1958, 1997) and "The Mathematical Magpie" (Fadiman 1962, 1997). In addition, mathematics fiction is featured at http://kasmana.people.cofc.edu/MATHFICT.…

Elaine Hale | NREL

Science.gov Websites

Analysis Center. Areas of Expertise Mathematical modeling, simulation, and optimization of complex Industrial and Applied Mathematics Mathematical Optimization Society Featured Publications Stoll, Brady

The Music of Mathematics: Toward a New Problem Typology

NASA Astrophysics Data System (ADS)

Quarfoot, David

Halmos (1980) once described problems and their solutions as "the heart of mathematics". Following this line of thinking, one might naturally ask: "What, then, is the heart of problems?". In this work, I attempt to answer this question using techniques from statistics, information visualization, and machine learning. I begin the journey by cataloging the features of problems delineated by the mathematics and mathematics education communities. These dimensions are explored in a large data set of students working thousands of problems at the Art of Problem Solving, an online company that provides adaptive mathematical training for students around the world. This analysis is able to concretely show how the fabric of mathematical problems changes across different subjects, difficulty levels, and students. Furthermore, it locates problems that stand out in the crowd -- those that synergize cognitive engagement, learning, and difficulty. This quantitatively-heavy side of the dissertation is partnered with a qualitatively-inspired portion that involves human scoring of 105 problems and their solutions. In this setting, I am able to capture elusive features of mathematical problems and derive a fuller picture of the space of mathematical problems. Using correlation matrices, principal components analysis, and clustering techniques, I explore the relationships among those features frequently discussed in mathematics problems (e.g., difficulty, creativity, novelty, affective engagement, authenticity). Along the way, I define a new set of uncorrelated features in problems and use these as the basis for a New Mathematical Problem Typology (NMPT). Grounded in the terminology of classical music, the NMPT works to quickly convey the essence and value of a problem, just as terms like "etude" and "mazurka" do for musicians. Taken together, these quantitative and qualitative analyses seek to terraform the landscape of mathematical problems and, concomitantly, the current thinking about that world. Most importantly, this work highlights and names the panoply of problems that exist, expanding the myopic vision of contemporary mathematical problem solving.

The Identification, Implementation, and Evaluation of Critical User Interface Design Features of Computer-Assisted Instruction Programs in Mathematics for Students with Learning Disabilities

ERIC Educational Resources Information Center

Seo, You-Jin; Woo, Honguk

2010-01-01

Critical user interface design features of computer-assisted instruction programs in mathematics for students with learning disabilities and corresponding implementation guidelines were identified in this study. Based on the identified features and guidelines, a multimedia computer-assisted instruction program, "Math Explorer", which delivers…

Teaching Mathematics in Open Distance Learning (ODL): A Challenge to Quality Instruction?

ERIC Educational Resources Information Center

Kaino, L. M.

2012-01-01

Teaching mathematics through Open Distance Learning (ODL) has been a challenge to educators due to the nature of communication with learners and material delivery during instruction. In this paper, as a case study, we look at one mathematics module offered through ODL and the performance in the course for the past four years. A sample of 50…

Using Mathematics-Curriculum Based Measures to Predict Outcomes on the Mathematics Portion of the Mississippi Curriculum Test, Second Edition

ERIC Educational Resources Information Center

Hogan-Samuel, Eutrophia Lenora

2012-01-01

The nation is challenged with improving the mathematics achievement of its students. No Child Left Behind holds schools, districts, and states accountable for improving student achievement. Because high stakes tests are given at the end of the school year, schools are presented with the challenging task of developing or purchasing reliable…

Spreadsheets as a Transparent Resource for Learning the Mathematics of Annuities

ERIC Educational Resources Information Center

Pournara, Craig

2009-01-01

The ability of mathematics teachers to decompress mathematics and to move between representations are two key features of mathematical knowledge that is usable for teaching. This article reports on four pre-service secondary mathematics teachers learning the mathematics of annuities. In working with spreadsheets students began to make sense of…

Challenges in Responding to Scaffolding Opportunities in the Mathematics Classroom

ERIC Educational Resources Information Center

Ferguson, Sarah

2012-01-01

This paper reports on a study that explored the use of cognitively challenging tasks with low-attaining mathematics students and in particular, their teachers' attempts at scaffolding. A major finding was that responding appropriately to scaffolding opportunities was challenging for the teachers. In this paper two main factors are discussed which…

Gendered Pathways: How Mathematics Ability Beliefs Shape Secondary and Postsecondary Course and Degree Field Choices

PubMed Central

Perez-Felkner, Lara; Nix, Samantha; Thomas, Kirby

2017-01-01

Do mathematics ability beliefs explain gender gaps in the physical science, engineering, mathematics, and computer science fields (PEMC) and other science fields? We leverage U.S. nationally representative longitudinal data to estimate gendered differences in girls' and boys' perceptions of mathematics ability with the most difficult or challenging material. Our analyses examine the potentially interacting effects of gender and these ability beliefs on students' pathways to scientific careers. Specifically, we study how beliefs about ability with challenging mathematics influence girls' and boys' choices to pursue PEMC degrees, evaluating educational milestones over a 6-year period: advanced science course completion in secondary school and postsecondary major retention and selection. Our findings indicate even at the same levels of observed ability, girls' mathematics ability beliefs under challenge are markedly lower than those of boys. These beliefs matter over time, potentially tripling girls' chances of majoring in PEMC sciences, over and above biological science fields, all else being equal. Implications and potential interventions are discussed. PMID:28428762

Gendered Pathways: How Mathematics Ability Beliefs Shape Secondary and Postsecondary Course and Degree Field Choices.

PubMed

Perez-Felkner, Lara; Nix, Samantha; Thomas, Kirby

2017-01-01

Do mathematics ability beliefs explain gender gaps in the physical science, engineering, mathematics, and computer science fields (PEMC) and other science fields? We leverage U.S. nationally representative longitudinal data to estimate gendered differences in girls' and boys' perceptions of mathematics ability with the most difficult or challenging material. Our analyses examine the potentially interacting effects of gender and these ability beliefs on students' pathways to scientific careers. Specifically, we study how beliefs about ability with challenging mathematics influence girls' and boys' choices to pursue PEMC degrees, evaluating educational milestones over a 6-year period: advanced science course completion in secondary school and postsecondary major retention and selection. Our findings indicate even at the same levels of observed ability, girls' mathematics ability beliefs under challenge are markedly lower than those of boys. These beliefs matter over time, potentially tripling girls' chances of majoring in PEMC sciences, over and above biological science fields, all else being equal. Implications and potential interventions are discussed.

Mathematics disorder

MedlinePlus

... this page: //medlineplus.gov/ency/article/001534.htm Mathematics disorder To use the sharing features on this page, please enable JavaScript. Mathematics disorder is a condition in which a child's ...

Contrasts in Mathematical Challenges in A-Level Mathematics and Further Mathematics, and Undergraduate Mathematics Examinations

ERIC Educational Resources Information Center

Darlington, Ellie

2014-01-01

This article describes part of a study which investigated the role of questions in students' approaches to learning mathematics at the secondary-tertiary interface, focussing on the enculturation of students at the University of Oxford. Use of the Mathematical Assessment Task Hierarchy taxonomy revealed A-level Mathematics and Further Mathematics…

Instructional Quality Features in Videotaped Biology Lessons: Content-Independent Description of Characteristics

NASA Astrophysics Data System (ADS)

Dorfner, Tobias; Förtsch, Christian; Boone, William; Neuhaus, Birgit J.

2017-09-01

A number of studies on single instructional quality features have been reported for mathematics and science instruction. For summarizing single instructional quality features, researchers have created a model of three basic dimensions (classroom management, supportive climate, and cognitive activation) of instructional quality mainly through observing mathematics instruction. Considering this model as valid for all subjects and as usable for describing instruction, we used it in this study which aimed to analyze characteristics of instructional quality in biology lessons of high-achieving and low-achieving classes, independently of content. Therefore, we used the data of three different previous video studies of biology instruction conducted in Germany. From each video study, we selected three high-achieving and three low-achieving classes (N = 18 teachers; 35 videos) for our multiple-case study, in which conspicuous characteristics of instructional quality features were qualitatively identified and qualitatively analyzed. The amount of these characteristics was counted in a quantitative way in all the videos. The characteristics we found could be categorized using the model of three basic dimensions of instructional quality despite some subject-specific differences for biology instruction. Our results revealed that many more characteristics were observable in high-achieving classes than in low-achieving classes. Thus, we believe that this model could be used to describe biology instruction independently of the content. We also make the claims about the qualities for biology instruction—working with concentration in a content-structured environment, getting challenged in higher order thinking, and getting praised for performance—that could have positive influence on students' achievement.

Notes on an Outreach Forum for High School Chemistry Teachers - An Unexpected Success

NASA Astrophysics Data System (ADS)

Mayfield, Darwin L.

1997-05-01

Public realization in the United States of deficiencies in understanding basic facts and processes in science and mathematics is mounting. Teachers in these areas at all levels are key players in the challenges to come. This paper describes the activities of one small group of high school chemistry teachers as they have explored these challenges. The group of approximately sixteen has met regularly on the campus of California State University, Long Beach during the past seven years. The meetings (two or three each semester) are informal three-hour sessions over the dinner hour (box dinners are provided). A feature of each meeting is discussion of articles selected from the Journal of Chemical Education including retesting with variation of "Tested Demonstrations". Subscriptions to the Journal are provided to members. No fees are charged nor course credit given. The article outlines many of the program features, describes recruitment and changes in membership over time, examines possibilities for replication and emphasizes the great desire of secondary level chemistry teachers for exchange of ideas with peers. It explores the question "what did we do right?" in launching this successful forum.

Back in Time on a Mathematics Trail

ERIC Educational Resources Information Center

Moffett, Pamela

2010-01-01

The recently revised "Northern Ireland Primary Curriculum" recommends that teachers make use of the environment to extend children's understanding of mathematics. One approach to using the environment in mathematics is to take children on a mathematics trail. A mathematics trail uses the resources and features within the environment as a…

Grounded Blends and Mathematical Gesture Spaces: Developing Mathematical Understandings via Gestures

ERIC Educational Resources Information Center

Yoon, Caroline; Thomas, Michael O. J.; Dreyfus, Tommy

2011-01-01

This paper examines how a person's gesture space can become endowed with mathematical meaning associated with mathematical spaces and how the resulting mathematical gesture space can be used to communicate and interpret mathematical features of gestures. We use the theory of grounded blends to analyse a case study of two teachers who used gestures…

Using Mathematics in Science: Working with Your Mathematics Department

ERIC Educational Resources Information Center

Lyon, Steve

2014-01-01

Changes to the mathematics and science curriculums are designed to increase rigour in mathematics, and place greater emphasis on mathematical content in science subjects at key stages 3, 4 and 5 (ages 11-18). One way to meet the growing challenge of providing increased emphasis on mathematics in the science curriculum is greater collaboration…

Knowledge and Knowing in Mathematics and Pedagogy: A Case Study of Mathematics Student Teachers' Epistemological Beliefs

ERIC Educational Resources Information Center

Löfström, Erika; Pursiainen, Tuomas

2015-01-01

This study focuses on mathematics student teachers' epistemological beliefs in mathematics and education. The study aimed at gaining insight into the challenges that students experience in the consolidation of knowledge in the two disciplines. The case study with three mathematics pre-service teachers utilised mathematical and pedagogical…

Fostering German-Language Learners' Constructions of Meanings for Fractions--Design and Effects of a Language-and Mathematics-Integrated Intervention

ERIC Educational Resources Information Center

Prediger, Susanne; Wessel, Lena

2013-01-01

Learning situations that concentrate on conceptual understanding are particularly challenging for learners with limited proficiency in the language of instruction. This article presents an intervention on fractions for Grade 7 in which linguistic challenges and conceptual mathematical challenges were treated in an integrated way. The quantitative…

CLASS Challenging Tasks: Using Cognitive Load Theory to Inform the Design of Challenging Mathematical Tasks

ERIC Educational Resources Information Center

Russo, James; Hopkins, Sarah

2017-01-01

This paper outlines a seven-step process for developing problem-solving tasks informed by cognitive load theory. Through an example of a task developed for Year 2 students, we show how this approach can be used to produce challenging mathematical tasks that aim to optimise cognitive load for each student.

Mathematics Teaching Today

ERIC Educational Resources Information Center

Martin, Tami S.; Speer, William R.

2009-01-01

This article describes features, consistent messages, and new components of "Mathematics Teaching Today: Improving Practice, Improving Student Learning" (NCTM 2007), an updated edition of "Professional Standards for Teaching Mathematics" (NCTM 1991). The new book describes aspects of high-quality mathematics teaching; offers a model for observing,…

Mathematics teachers' conceptions about modelling activities and its reflection on their beliefs about mathematics

NASA Astrophysics Data System (ADS)

Shahbari, Juhaina Awawdeh

2018-07-01

The current study examines whether the engagement of mathematics teachers in modelling activities and subsequent changes in their conceptions about these activities affect their beliefs about mathematics. The sample comprised 52 mathematics teachers working in small groups in four modelling activities. The data were collected from teachers' Reports about features of each activity, interviews and questionnaires on teachers' beliefs about mathematics. The findings indicated changes in teachers' conceptions about the modelling activities. Most teachers referred to the first activity as a mathematical problem but emphasized only the mathematical notions or the mathematical operations in the modelling process; changes in their conceptions were gradual. Most of the teachers referred to the fourth activity as a mathematical problem and emphasized features of the whole modelling process. The results of the interviews indicated that changes in the teachers' conceptions can be attributed to structure of the activities, group discussions, solution paths and elicited models. These changes about modelling activities were reflected in teachers' beliefs about mathematics. The quantitative findings indicated that the teachers developed more constructive beliefs about mathematics after engagement in the modelling activities and that the difference was significant, however there was no significant difference regarding changes in their traditional beliefs.

Mathematical Modeling: Challenging the Figured Worlds of Elementary Mathematics

ERIC Educational Resources Information Center

Wickstrom, Megan H.

2017-01-01

This article is a report on a teacher study group that focused on three elementary teachers' perceptions of mathematical modeling in contrast to typical mathematics instruction. Through the theoretical lens of figured worlds, I discuss how mathematics instruction was conceptualized across the classrooms in terms of artifacts, discourse, and…

Mathematical Sciences in Australia

ERIC Educational Resources Information Center

Thomas, Jan; Muchatuta, Michelle; Wood, Leigh

2009-01-01

This article investigates enrolment trends in mathematical sciences in Australian universities. Data has been difficult to extract and the coding for mathematical disciplines has made investigation challenging. We show that the number of mathematics major undergraduates in Australia is steadily declining though the number studying…

When Mathematics and Statistics Collide in Assessment Tasks

ERIC Educational Resources Information Center

Bargagliotti, Anna; Groth, Randall

2016-01-01

Because the disciplines of mathematics and statistics are naturally intertwined, designing assessment questions that disentangle mathematical and statistical reasoning can be challenging. We explore the writing statistics assessment tasks that take into consideration potential mathematical reasoning they may inadvertently activate.

The AMATYC Review. 1994-1995.

ERIC Educational Resources Information Center

Browne, Joseph, Ed.

1995-01-01

Designed as an avenue of communication for mathematics educators concerned with the views, ideas, and experiences of two-year college students and teachers, this journal contains articles on mathematics exposition and education, and regular features presenting book and software reviews and math problems. In addition to regular features such as…

Tailoring Modified Moore Method Techniques to Liberal Arts Mathematics Courses

ERIC Educational Resources Information Center

Hitchman, Theron J.; Shaw, Douglas

2015-01-01

Inquiry-based learning (IBL) techniques can be used in mathematics courses for non-majors, such as courses required for liberal arts majors to fulfill graduation requirements. Unique challenges are discussed, followed by adaptations of IBL techniques to overcome those challenges.

First 65nm tape-out using inverse lithography technology (ILT)

NASA Astrophysics Data System (ADS)

Hung, Chi-Yuan; Zhang, Bin; Tang, Deming; Guo, Eric; Pang, Linyong; Liu, Yong; Moore, Andrew; Wang, Kechang

2005-11-01

This paper presents SMIC's first 65nm tape out results, in particularly, using ILT. ILT mathematically determines the mask features that produce the desired on-wafer results with best wafer pattern fidelity, largest process window or both. SMIC applied it to its first 65nm tape-out to study ILT performance and benefits for deep sub-wavelength lithography. SMIC selected 3 SRAM designs as the first test case, because SRAM bit-cells contain features which are challenging lithographically. Mask patterns generated from both conventional OPC and ILT were placed on the mask side-by-side. Mask manufacturability (including fracturing, writing time, inspection, and metrology) and wafer print performance of ILT were studied. The results demonstrated that ILT achieved better CD accuracy, produced substantially larger process window than conventional OPC, and met SMIC's 65nm process window requirements.

A Walsh Function Module Users' Manual

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2014-01-01

The solution of partial differential equations (PDEs) with Walsh functions offers new opportunities to simulate many challenging problems in mathematical physics. The approach was developed to better simulate hypersonic flows with shocks on unstructured grids. It is unique in that integrals and derivatives are computed using simple matrix multiplication of series representations of functions without the need for divided differences. The product of any two Walsh functions is another Walsh function - a feature that radically changes an algorithm for solving PDEs. A FORTRAN module for supporting Walsh function simulations is documented. A FORTRAN code is also documented with options for solving time-dependent problems: an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the usage of the Walsh function module including such features as operator overloading, Fast Walsh Transforms in multi-dimensions, and a Fast Walsh reciprocal.

Hyperspectral feature mapping classification based on mathematical morphology

NASA Astrophysics Data System (ADS)

Liu, Chang; Li, Junwei; Wang, Guangping; Wu, Jingli

2016-03-01

This paper proposed a hyperspectral feature mapping classification algorithm based on mathematical morphology. Without the priori information such as spectral library etc., the spectral and spatial information can be used to realize the hyperspectral feature mapping classification. The mathematical morphological erosion and dilation operations are performed respectively to extract endmembers. The spectral feature mapping algorithm is used to carry on hyperspectral image classification. The hyperspectral image collected by AVIRIS is applied to evaluate the proposed algorithm. The proposed algorithm is compared with minimum Euclidean distance mapping algorithm, minimum Mahalanobis distance mapping algorithm, SAM algorithm and binary encoding mapping algorithm. From the results of the experiments, it is illuminated that the proposed algorithm's performance is better than that of the other algorithms under the same condition and has higher classification accuracy.

Mathematics for What? High School Students Reflect on Mathematics as a Tool for Social Inquiry

ERIC Educational Resources Information Center

Brelias, Anastasia

2015-01-01

This study examines high school students' views of mathematics as a tool for social inquiry in light of their classroom experiences using mathematics to explore social issues. A critical theoretical perspective on mathematics literacy is used to ascertain the ways in which their views challenge or affirm the dominant image of mathematics in…

A Critical Discourse Analysis of Practical Problems in a Foundation Mathematics Course at a South African University

ERIC Educational Resources Information Center

le Roux, Kate; Adler, Jill

2016-01-01

Mathematical problems that make links to the everyday and to disciplines other than mathematics--variously referred to as practical, realistic, real-world or applied problems in the literature--feature in school and undergraduate mathematics reforms aimed at increasing mathematics participation in contexts of inequity and diversity. In this…

New Challenges in the Teaching of Mathematics.

ERIC Educational Resources Information Center

Bourguignon, Jean Pierre

The manifold but discrete presence of mathematics in many objects or services imposes new constraints to the teaching of mathematics. If citizens need to be comfortable in various situations with a variety of mathematical tools, the learning of mathematics requires that one starts with simple concepts. This paper proposes some solutions to solve…

Interesting and Difficult Mathematical Problems: Changing Teachers' Views by Employing Multiple-Solution Tasks

ERIC Educational Resources Information Center

Guberman, Raisa; Leikin, Roza

2013-01-01

The study considers mathematical problem solving to be at the heart of mathematics teaching and learning, while mathematical challenge is a core element of any educational process. The study design addresses the complexity of teachers' knowledge. It is aimed at exploring the development of teachers' mathematical and pedagogical conceptions…

Need for Equipping Student Teachers with Language of Mathematics

ERIC Educational Resources Information Center

Gafoor, K. Abdul; Sarabi, M. K.

2015-01-01

The significance of curriculum in building up language of mathematics which enables learners to construct and communicate knowledge of mathematics has not received due attention even as the pedagogical challenges faced by the students in learning mathematics have been discussed for years. Learning language of mathematics is not only valuable in…

The Preparation Experiences of Elementary Mathematics Specialists: Examining Influences on Beliefs, Content Knowledge, and Teaching Practices

ERIC Educational Resources Information Center

Swars, Susan L.; Smith, Stephanie Z.; Smith, Marvin E.; Carothers, Jody; Myers, Kayla

2018-01-01

Many in the field of mathematics education call for elementary schools to have elementary mathematics specialists (EMSs) who provide needed mathematical expertise and support for children and teachers. EMSs serve as a reasonable, immediate alternative to the challenges generated by elementary teachers needing improved mathematical knowledge for…

Pre-Service Teachers' Mathematics Language and Reflection in the Context of an Early Childhood Mathematics Methods Course

ERIC Educational Resources Information Center

Boyd, Soleil

2016-01-01

Preschool teachers are expected to engage young children in challenging and supportive mathematics learning. Rich and responsive language experiences in mathematics support children's language acquisition and engagement related to mathematics, however, such engaging experiences may be minimally available to many young children. Professional…

A Survey Transition Course

ERIC Educational Resources Information Center

Johnston, William; McAllister, Alex M.

2012-01-01

Successful outcomes for a "Transition Course in Mathematics" have resulted from two unique design features. The first is to run the course as a "survey course" in mathematics, introducing sophomore-level students to a broad set of mathematical fields. In this single mathematics course, undergraduates benefit from an introduction of proof…

The mathematics of cancer: integrating quantitative models.

PubMed

Altrock, Philipp M; Liu, Lin L; Michor, Franziska

2015-12-01

Mathematical modelling approaches have become increasingly abundant in cancer research. The complexity of cancer is well suited to quantitative approaches as it provides challenges and opportunities for new developments. In turn, mathematical modelling contributes to cancer research by helping to elucidate mechanisms and by providing quantitative predictions that can be validated. The recent expansion of quantitative models addresses many questions regarding tumour initiation, progression and metastases as well as intra-tumour heterogeneity, treatment responses and resistance. Mathematical models can complement experimental and clinical studies, but also challenge current paradigms, redefine our understanding of mechanisms driving tumorigenesis and shape future research in cancer biology.

Challenges in Math.

ERIC Educational Resources Information Center

Feng, Chengde

1992-01-01

Fourteen mathematics problems from the 1987 Chinese Primary School Mathematics Examination for fifth and sixth grade students are presented. The word problems, accompanied by answers, involve algebra, division, ratios, areas, and other mathematical processes. (JDD)

Grand Challenges and Opportunities in Mathematics Education Research

ERIC Educational Resources Information Center

Stephan, Michelle L.; Chval, Kathryn B.; Wanko, Jeffrey J.; Civil, Marta; Fish, Michael C.; Herbel-Eisenmann, Beth; Konold, Clifford; Wilkerson, Trena L.

2015-01-01

Mathematics education researchers seek answers to important questions that will ultimately result in the enhancement of mathematics teaching, learning, curriculum, and assessment, working toward ensuring that all students attain mathematics proficiency and increasing the numbers of students from all racial, ethnic, gender, and socioeconomic groups…

Perception of mathematics teachers on cooperative learning method in the 21st century

NASA Astrophysics Data System (ADS)

Taufik, Nurshahira Alwani Mohd; Maat, Siti Mistima

2017-05-01

Mathematics education is one of the branches to be mastered by students to help them compete with the upcoming challenges that are very challenging. As such, all parties should work together to help increase student achievement in Mathematics education in line with the Malaysian Education Blueprint (MEB) 2010-2025. Teaching methods play a very important role in attracting and fostering student understanding and interested in learning Mathematics. Therefore, this study was conducted to identify the perceptions of teachers in carrying out cooperative methods in the teaching and learning of mathematics. Participants of this study involving 4 teachers who teach Mathematics in primary schools around the state of Negeri Sembilan. Interviews are used as a method for gathering data. The findings indicate that cooperative methods help increasing interest and understanding in the teaching and learning of mathematics. In conclusion, the teaching methods affect the interest and understanding of students in the learning of Mathematics in the classroom.

Minimalism as a Guiding Principle: Linking Mathematical Learning to Everyday Knowledge

ERIC Educational Resources Information Center

Inoue, Noriyuki

2008-01-01

Studies report that students often fail to consider familiar aspects of reality in solving mathematical word problems. This study explored how different features of mathematical problems influence the way that undergraduate students employ realistic considerations in mathematical problem solving. Incorporating familiar contents in the word…

Core-Plus Mathematics. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2010

2010-01-01

"Core-Plus Mathematics" is a four-year curriculum that replaces the traditional sequence with courses that each feature interwoven strands of algebra and functions, statistics and probability, geometry and trigonometry, and discrete mathematics. The first three courses in the series provide a common core of broadly useful mathematics,…

Kindergarten Children's Interactions with Touchscreen Mathematics Virtual Manipulatives: An Innovative Mixed Methods Analysis

ERIC Educational Resources Information Center

Tucker, Stephen I.; Lommatsch, Christina W.; Moyer-Packenham, Patricia S.; Anderson-Pence, Katie L.; Symanzik, Jürgen

2017-01-01

The purpose of this study was to examine patterns of mathematical practices evident during children's interactions with touchscreen mathematics virtual manipulatives. Researchers analyzed 33 Kindergarten children's interactions during activities involving apps featuring mathematical content of early number sense or quantity in base ten, recorded…

A Guideline to Univariate Statistical Analysis for LC/MS-Based Untargeted Metabolomics-Derived Data

PubMed Central

Vinaixa, Maria; Samino, Sara; Saez, Isabel; Duran, Jordi; Guinovart, Joan J.; Yanes, Oscar

2012-01-01

Several metabolomic software programs provide methods for peak picking, retention time alignment and quantification of metabolite features in LC/MS-based metabolomics. Statistical analysis, however, is needed in order to discover those features significantly altered between samples. By comparing the retention time and MS/MS data of a model compound to that from the altered feature of interest in the research sample, metabolites can be then unequivocally identified. This paper reports on a comprehensive overview of a workflow for statistical analysis to rank relevant metabolite features that will be selected for further MS/MS experiments. We focus on univariate data analysis applied in parallel on all detected features. Characteristics and challenges of this analysis are discussed and illustrated using four different real LC/MS untargeted metabolomic datasets. We demonstrate the influence of considering or violating mathematical assumptions on which univariate statistical test rely, using high-dimensional LC/MS datasets. Issues in data analysis such as determination of sample size, analytical variation, assumption of normality and homocedasticity, or correction for multiple testing are discussed and illustrated in the context of our four untargeted LC/MS working examples. PMID:24957762

A Guideline to Univariate Statistical Analysis for LC/MS-Based Untargeted Metabolomics-Derived Data.

PubMed

Vinaixa, Maria; Samino, Sara; Saez, Isabel; Duran, Jordi; Guinovart, Joan J; Yanes, Oscar

2012-10-18

Several metabolomic software programs provide methods for peak picking, retention time alignment and quantification of metabolite features in LC/MS-based metabolomics. Statistical analysis, however, is needed in order to discover those features significantly altered between samples. By comparing the retention time and MS/MS data of a model compound to that from the altered feature of interest in the research sample, metabolites can be then unequivocally identified. This paper reports on a comprehensive overview of a workflow for statistical analysis to rank relevant metabolite features that will be selected for further MS/MS experiments. We focus on univariate data analysis applied in parallel on all detected features. Characteristics and challenges of this analysis are discussed and illustrated using four different real LC/MS untargeted metabolomic datasets. We demonstrate the influence of considering or violating mathematical assumptions on which univariate statistical test rely, using high-dimensional LC/MS datasets. Issues in data analysis such as determination of sample size, analytical variation, assumption of normality and homocedasticity, or correction for multiple testing are discussed and illustrated in the context of our four untargeted LC/MS working examples.

Mathematical Perspectives

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

Glimm, J.

2009-10-14

Progress for the past decade or so has been extraordinary. The solution of Fermat's Last Theorem [11] and of the Poincare Conjecture [1] have resolved two of the most outstanding challenges to mathematics. For both cases, deep and advanced theories and whole subfields of mathematics came into play and were developed further as part of the solutions. And still the future is wide open. Six of the original seven problems from the Clay Foundation challenge remain open, the 23 DARPA challenge problems are open. Entire new branches of mathematics have been developed, including financial mathematics and the connection between geometrymore » and string theory, proposed to solve the problems of quantized gravity. New solutions of the Einstein equations, inspired by shock wave theory, suggest a cosmology model which fits accelerating expansion of the universe possibly eliminating assumptions of 'dark matter'. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. We see a broadening of the intellectual and professional opportunities and responsibilities for mathematicians. These trends are also occuring across all of science. The response can be at the level of the professional societies, which can work to deepen their interactions, not only within the mathematical sciences, but also with other scientific societies. At a deeper level, the choices to be made will come from individual mathematicians. Here, of course, the individual choices will be varied, and we argue for respect and support for this diversity of responses. In such a manner, we hope to preserve the best of the present while welcoming the best of the new.« less

Developing Teaching Material Software Assisted for Numerical Methods

NASA Astrophysics Data System (ADS)

Handayani, A. D.; Herman, T.; Fatimah, S.

2017-09-01

The NCTM vision shows the importance of two things in school mathematics, which is knowing the mathematics of the 21st century and the need to continue to improve mathematics education to answer the challenges of a changing world. One of the competencies associated with the great challenges of the 21st century is the use of help and tools (including IT), such as: knowing the existence of various tools for mathematical activity. One of the significant challenges in mathematical learning is how to teach students about abstract concepts. In this case, technology in the form of mathematics learning software can be used more widely to embed the abstract concept in mathematics. In mathematics learning, the use of mathematical software can make high level math activity become easier accepted by student. Technology can strengthen student learning by delivering numerical, graphic, and symbolic content without spending the time to calculate complex computing problems manually. The purpose of this research is to design and develop teaching materials software assisted for numerical method. The process of developing the teaching material starts from the defining step, the process of designing the learning material developed based on information obtained from the step of early analysis, learners, materials, tasks that support then done the design step or design, then the last step is the development step. The development of teaching materials software assisted for numerical methods is valid in content. While validator assessment for teaching material in numerical methods is good and can be used with little revision.

Experiencing Socially Relevant Applications in the High School Mathematics Curriculum: Students' Perspectives on Mathematics as a Tool for Social Inquiry

ERIC Educational Resources Information Center

Brelias, Anastasia

2009-01-01

The purpose of this study was to examine the use of socially relevant mathematics applications in high school mathematics classrooms and students' views of mathematics in light of their experiences with these applications. Also, the study sought to determine whether inquiries afforded by these applications incorporated features that promoted…

How Does Self-Regulation Impact Student's Use of Mathematical Strategies in a Remedial Mathematics Course

ERIC Educational Resources Information Center

Heron, Michele Lynn

2011-01-01

In order to improve teaching strategies in a college level remedial mathematics course, this study seeks to investigate student perception while they attempt challenging mathematics tasks. The participants were 72 students enrolled in a mid-western university remedial mathematics course. A qualitative case study methodology was used to investigate…

What Mathematics Education Can Learn from Art: The Assumptions, Values, and Vision of Mathematics Education

ERIC Educational Resources Information Center

Dietiker, Leslie

2015-01-01

Elliot Eisner proposed that educational challenges can be met by applying an artful lens. This article draws from Eisner's proposal to consider the assumptions, values, and vision of mathematics education by theorizing mathematics curriculum as an art form. By conceptualizing mathematics curriculum (both in written and enacted forms) as stories…

What Is Mathematics? An Exploration of Teachers' Philosophies of Mathematics during a Time of Curriculum Reform

ERIC Educational Resources Information Center

White-Fredette, Kimberly

2009-01-01

Current reform in mathematics teaching and learning is rooted in a changing vision of school mathematics, one that includes constructivist learning, student-centered pedagogy, and the use of worthwhile tasks (National Council of Teachers of Mathematics, 1989, 1991, 2000). This changing vision not only challenges teachers' beliefs about mathematics…

Situated Mathematics Teaching within Electrical Engineering Courses

ERIC Educational Resources Information Center

Hennig, Markus; Mertsching, Bärbel; Hilkenmeier, Frederic

2015-01-01

The initial phase of undergraduate engineering degree programmes often comprises courses requiring mathematical expertise which in some cases clearly exceeds school mathematics, but will be imparted only later in mathematics courses. In this article, an approach addressing this challenge by way of example within a "fundamentals of electrical…

Sustaining Integrated Technology in Undergraduate Mathematics

ERIC Educational Resources Information Center

Oates, Greg

2011-01-01

The effective integration of technology into the teaching and learning of mathematics remains one of the critical challenges facing contemporary tertiary mathematics. This article reports on some significant findings of a wider study investigating the use of technology in undergraduate mathematics. It first discusses a taxonomy developed to…

Restoring Scholarship to Collegiate Mathematics.

ERIC Educational Resources Information Center

Steen, Lynn Arthur

1986-01-01

Needs of collegiate mathematics across the nation are considered, and suggestions are offered to the National Science Foundation (NSF) by a professor of Mathematics at St. Olaf College (Minnesota). Changes in mathematics content, scope, and applications have implications for the college curriculum. Problems and challenges are posed by: increased…

Investigating Teachers' Images of Mathematics

ERIC Educational Resources Information Center

Sterenberg, Gladys

2008-01-01

Research suggests that understanding new images of mathematics is very challenging and can contribute to teacher resistance. An explicit exploration of personal views of mathematics may be necessary for pedagogical change. One possible way for exploring these images is through mathematical metaphors. As metaphors focus on similarities, they can be…

Using Interactive Whiteboards in Teaching Retail Mathematics

ERIC Educational Resources Information Center

Greene, Marla; Kirpalani, Nicole

2013-01-01

Undergraduate marketing students have sometimes been found to lack mathematical skills. It can therefore be challenging for instructors to effectively teach courses that depend on mathematical problem-solving skills. This paper discusses the use of interactive whiteboards as an innovative way to teach retail mathematics effectively. The authors…

Teachers' Experiences with Middle-Level Mathematics Coaches

ERIC Educational Resources Information Center

Frost, Bernard Emmanuel

2013-01-01

Many school districts have provided support to middle school mathematics teachers who face challenges involving delivery of instruction by hiring instructional mathematics coaches. The purpose of this qualitative case study was to explore the experiences between classroom mathematics middle school teachers and their instructional coach, and to…

Implementing a reform-oriented pedagogy: challenges for novice secondary mathematics teachers

NASA Astrophysics Data System (ADS)

Lewis, Gary M.

2014-06-01

Novice secondary mathematics teachers attempting teaching consonant with the National Council of Teachers of Mathematics (1991, 2007) Professional Standards for Teaching Mathematics experience many stresses related to their attempts at student-centered instruction; prominent among those were novices' challenges when orchestrating whole-class mathematical discussions with students taking a central, substantive role. During such discussions, students offer conjectures, ideas, and solutions and use mathematical argumentation and verification processes. Such teaching can create uncertainty and stress as teachers occupy a revised teaching role. They avoid evaluating student ideas during class; instead, they ask questions to move students' thinking forward, pose problems that deepen students' mathematical understanding, and choose between competing directions the discussion may take. Ultimately, teachers decide whether to continue pursuing such teaching goals or revert back to more familiar, teacher-centered methods. Supportive networks showed promise at helping novices navigate their first few years of teaching; organized networks helped novices meet their teaching goals while limiting the impact of their challenges on their well-being and teaching goals. The results of this study may inform teacher educators, administrators, and colleagues on how to support novices in pursuing teaching better aligned with novices' teaching ideals and reformer's visions.

Designing PISA-Like Mathematics Tasks In Indonesia: Experiences and Challenges

NASA Astrophysics Data System (ADS)

Zulkardi, Z.; Kohar, A. W.

2018-01-01

The insignificant improvement of Indonesian students in PISA mathematics survey triggered researchers in Indonesia to develop PISA-like mathematics tasks. Some development studies have been conducted to produce valid and practical PISA-like problems that potentially effect on improving students’ mathematical literacy. This article describes the experiences of Indonesian task designers in developing PISA-like mathematics tasks as well as the potential future studies regarding to mathematical literacy as challenges for policy makers, researchers, and practitioners to improve students’ mathematical literacy in Indonesia. The results of this research indicate the task designers to consider domains of PISA like: context, mathematical content, and process as the first profiles of their missions. Our analysis shows that the designers mostly experienced difficulties regarding to the authenticity of context use and language structure. Interestingly, many of them used a variety of local wisdom in Indonesia as contexts for designing PISA-like tasks. In addition, the products developed were reported to be potentially effects on students’ interest and elicit students’ mathematical competencies as mentioned in PISA framework. Finally, this paper discusses future studies such as issues in bringing PISA task into an instructional practice.

Mathematics Professional Development: Critical Features for Developing Leadership Skills and Building Teachers' Capacity

ERIC Educational Resources Information Center

Koellner, Karen; Jacobs, Jennifer; Borko, Hilda

2011-01-01

This article focuses on three features of professional development (PD) programs that play an important role in developing leadership skills and building teachers' capacity: (1) fostering a professional learning community, (2) developing teachers' mathematical knowledge for teaching, and (3) adapting PD to support local needs and interests. We…

The Semiotic Structure of Geometry Diagrams: How Textbook Diagrams Convey Meaning

ERIC Educational Resources Information Center

Dimmel, Justin K.; Herbst, Patricio G.

2015-01-01

Geometry diagrams use the visual features of specific drawn objects to convey meaning about generic mathematical entities. We examine the semiotic structure of these visual features in two parts. One, we conduct a semiotic inquiry to conceptualize geometry diagrams as mathematical texts that comprise choices from different semiotic systems. Two,…

Examining the Design Features of a Communication-Rich, Problem-Centred Mathematics Professional Development

ERIC Educational Resources Information Center

de Araujo, Zandra; Orrill, Chandra Hawley; Jacobson, Erik

2018-01-01

While there is considerable scholarship describing principles for effective professional development, there have been few attempts to examine these principles in practice. In this paper, we identify and examine the particular design features of a mathematics professional development experience provided for middle grades teachers over 14 weeks. The…

Challenges of Integrating Mobile Technology into Mathematics Instruction in Secondary Schools: An Indonesian Context

ERIC Educational Resources Information Center

Abidin, Zaenal; Mathrani, Anuradha; Hunter, Roberta; Parsons, David

2017-01-01

Implementing mobile learning in curriculum-based educational settings faces challenges related to perceived ethical and learning issues. This study investigated the affordances of mobile technologies to support mathematics instruction by teachers. An exploratory study employing questionnaires and semi-structured interviews revealed that, while…

A Water-Service Challenge

ERIC Educational Resources Information Center

Roman, Harry T.

2011-01-01

It is important to let students see the value of mathematics in design--and how mathematics lends perspective to problem solving. In this article, the author describes a water-service challenge which enables students to design a water utility system that uses surface runoff into an open reservoir as the potable water source. This challenge…

Control Engineering, System Theory and Mathematics: The Teacher's Challenge

ERIC Educational Resources Information Center

Zenger, K.

2007-01-01

The principles, difficulties and challenges in control education are discussed and compared to the similar problems in the teaching of mathematics and systems science in general. The difficulties of today's students to appreciate the classical teaching of engineering disciplines, which are based on rigorous and scientifically sound grounds, are…

Challenge Beginning Teacher Beliefs

ERIC Educational Resources Information Center

Lannin, John K.; Chval, Kathryn B.

2013-01-01

As beginning teachers start to recognize the complexity of teaching mathematics in elementary school classrooms and how their new vision for teaching mathematics creates new challenges, they experience discomfort--a healthy awareness that much is to be learned. Brousseau (1997) notes that changes in the roles that are implicitly assigned to the…

The Challenges of Mathematics Education for Indigenous Teacher Training

ERIC Educational Resources Information Center

Gavarrete, Maria Elena

2015-01-01

In this article, I outline research carried out on in an Ethnomathematics course designed to train Indigenous teachers in Costa Rica, in which the following ethnic groups participated: Ngabes, Bribris, and Cabecares. The challenge is to develop a mathematical education that provides equitable conditions for the different groups within innovative…

The Use of GBL to Teach Mathematics in Higher Education

ERIC Educational Resources Information Center

Naik, Nitin

2017-01-01

Innovation in learning and teaching is an everyday requirement in contemporary higher education (HE), especially in challenging subjects such as mathematics. Teaching mathematics to students with limited experience of formal mathematical instruction is a good example of a demanding pedagogical undertaking where innovatory practice can help HE…

Exploring Primary Student's Problem-Solving Ability by Doing Tasks Like PISA's Question

ERIC Educational Resources Information Center

Novita, Rita; Zulkardi; Hartono, Yusuf

2012-01-01

Problem solving plays an important role in mathematics and should have a prominent role in the mathematics education. The term "problem solving" refers to mathematics tasks that have the potential to provide intellectual challenges for enhancing students' mathematical understanding and development. In addition, the contextual problem…

Teaching Adult Students Mathematical Investigations-6.

ERIC Educational Resources Information Center

Angiama, R. O.

Teaching Adult Students Mathematical Investigation is based on the continuing research work carried out for the last ten years of teaching on the Foundation Course in Mathematics at Goldsmiths, University of London. Teaching Mathematical Investigation to adult students is a very challenging and often rewarding experience for adult educators as…

Mathematics Education in Europe: Common Challenges and National Policies

ERIC Educational Resources Information Center

Parveva, Teodora; Noorani, Sogol; Ranguelov, Stanislav; Motiejunaite, Akvile; Kerpanova, Viera

2011-01-01

Competence in mathematics is integral to a wide range of disciplines, professions and areas of life. This Eurydice report reveals crucial elements of the policies and practices that shape mathematics instruction in European education systems, focusing on reforms of mathematics curricula, teaching and assessment methods, as well as teacher…

Gender Differences in Mathematics: Does the Story Need to Be Rewritten?

ERIC Educational Resources Information Center

Brunner, Martin; Krauss, Stefan; Kunter, Mareike

2008-01-01

Empirical studies of high school mathematics typically report small gender differences in favor of boys. The present article challenges this established finding by comparing two competing structural conceptions of mathematical ability. The standard model assumes mathematical ability alone to account for the interindividual differences observed on…

Supporting Mathematics Teachers' Development through Higher Education

ERIC Educational Resources Information Center

Prendergast, Mark; Roche, Joseph

2017-01-01

Mathematics education, both nationally and internationally, is facing a number of challenges with significant on-going shifts in the structure, content, and core principles of mathematics curricula in countries around the world. For example, in Ireland there was an ambitious reform of the post-primary mathematics curricula in 2010 with further…

What We Do: A Multiple Case Study from Mathematics Coaches' Perspectives

ERIC Educational Resources Information Center

Kane, Barbara Ann

2013-01-01

Teachers face new challenges when they teach a more rigorous mathematics curriculum than one to which they are accustomed. The rationale for this particular study originated from watching teachers struggle with understanding mathematical content and pedagogical practices. Mathematics coaches can address teachers' concerns through sustained,…

STEM Education: What Does Mathematics Have to Offer?

ERIC Educational Resources Information Center

Fitzallen, Noleine

2015-01-01

The emphasis on science, technology, engineering, and mathematics (STEM) education in recent times could be perceived as business as usual or as an opportunity for innovation and change in mathematics classrooms. Either option presents challenges for mathematics educators who are expected to contribute to the foundations of a STEM literate…

Where Have All the Mathematics Teachers Gone?

ERIC Educational Resources Information Center

Clever, George

Three basic causes for the general decline in mathematics achievement among high school graduates nationally are poor motivation to learn math, poor math curriculum, and poor or no mathematics instruction. Many Native Americans drop mathematics because of lack of challenging courses or interesting teachers in their high schools. Since American…

Review of Evidence-Based Mathematics Interventions for Students with Autism Spectrum Disorders

ERIC Educational Resources Information Center

Hart Barnett, Juliet E.; Cleary, Shannon

2015-01-01

Students with autism spectrum disorders (ASD) are being included more frequently in the general educational setting, and are therefore increasingly expected to access and master core curricular content, including mathematics. However, mathematics often presents challenges to students with ASD. Interventions to improve the mathematics skills of…

On Fences, Forms and Mathematical Modeling

ERIC Educational Resources Information Center

Lege, Jerry

2009-01-01

The white picket fence is an integral component of the iconic American townscape. But, for mathematics students, it can be a mathematical challenge. Picket fences in a variety of styles serve as excellent sources to model constant, step, absolute value, and sinusoidal functions. "Principles and Standards for School Mathematics" (NCTM 2000)…

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…

The Emergence of Mathematical Structures

ERIC Educational Resources Information Center

Hegedus, Stephen John; Moreno-Armella, Luis

2011-01-01

We present epistemological ruptures that have occurred in mathematical history and in the transformation of using technology in mathematics education in the twenty-first century. We describe how such changes establish a new form of digital semiotics that challenges learning paradigms and mathematical inquiry for learners today. We focus on drawing…

In Measure, Number, and Weight: Studies in Mathematics and Culture.

ERIC Educational Resources Information Center

Hoyrup, Jens

In this collection of essays, the content of mathematics is dealt with in general terms, concentrating on cognitive organization, modes of thought, and the way that mathematics interacts with the sociocultural setting. Chapter 1 compares features of Sumero-Babylonian, ancient Greek, and Latin medieval mathematics. Chapter 2 traces the specific…

Primary Teachers Notice the Impact of Language on Children's Mathematical Reasoning

ERIC Educational Resources Information Center

Bragg, Leicha A.; Herbert, Sandra; Loong, Esther Yoon-Kin; Vale, Colleen; Widjaja, Wanty

2016-01-01

Mathematical reasoning is now featured in the mathematics curriculum documents of many nations, but this necessitates changes to teaching practice and hence a need for professional learning. The development of children's mathematical reasoning requires appropriate encouragement and feedback from their teacher who can only do this if they recognise…

Informatics Approaches for Predicting, Understanding, and Testing Cancer Drug Combinations.

PubMed

Tang, Jing

2017-01-01

Making cancer treatment more effective is one of the grand challenges in our health care system. However, many drugs have entered clinical trials but so far showed limited efficacy or induced rapid development of resistance. We urgently need multi-targeted drug combinations, which shall selectively inhibit the cancer cells and block the emergence of drug resistance. The book chapter focuses on mathematical and computational tools to facilitate the discovery of the most promising drug combinations to improve efficacy and prevent resistance. Data integration approaches that leverage drug-target interactions, cancer molecular features, and signaling pathways for predicting, understanding, and testing drug combinations are critically reviewed.

On the limitations of standard statistical modeling in biological systems: a full Bayesian approach for biology.

PubMed

Gomez-Ramirez, Jaime; Sanz, Ricardo

2013-09-01

One of the most important scientific challenges today is the quantitative and predictive understanding of biological function. Classical mathematical and computational approaches have been enormously successful in modeling inert matter, but they may be inadequate to address inherent features of biological systems. We address the conceptual and methodological obstacles that lie in the inverse problem in biological systems modeling. We introduce a full Bayesian approach (FBA), a theoretical framework to study biological function, in which probability distributions are conditional on biophysical information that physically resides in the biological system that is studied by the scientist. Copyright © 2013 Elsevier Ltd. All rights reserved.

Building a Career Mathematics File: Challenging Students to Find the Importance of Mathematics in a Variety of Occupations

ERIC Educational Resources Information Center

Keleher, Lori A.

2006-01-01

The Career Mathematics file is an occupational problem-solving system, which includes a wide range of mathematical problems and solutions, collected from various resources and helps students establish connections between mathematics and their environment. The study shows that the problems given can be used as realistic examples to study and…

The challenge of computer mathematics.

PubMed

Barendregt, Henk; Wiedijk, Freek

2005-10-15

Progress in the foundations of mathematics has made it possible to formulate all thinkable mathematical concepts, algorithms and proofs in one language and in an impeccable way. This is not in spite of, but partially based on the famous results of Gödel and Turing. In this way statements are about mathematical objects and algorithms, proofs show the correctness of statements and computations, and computations are dealing with objects and proofs. Interactive computer systems for a full integration of defining, computing and proving are based on this. The human defines concepts, constructs algorithms and provides proofs, while the machine checks that the definitions are well formed and the proofs and computations are correct. Results formalized so far demonstrate the feasibility of this 'computer mathematics'. Also there are very good applications. The challenge is to make the systems more mathematician-friendly, by building libraries and tools. The eventual goal is to help humans to learn, develop, communicate, referee and apply mathematics.

Rescheduling nursing shifts: scoping the challenge and examining the potential of mathematical model based tools.

PubMed

Clark, Alistair; Moule, Pam; Topping, Annie; Serpell, Martin

2015-05-01

To review research in the literature on nursing shift scheduling / rescheduling, and to report key issues identified in a consultation exercise with managers in four English National Health Service trusts to inform the development of mathematical tools for rescheduling decision-making. Shift rescheduling is unrecognised as an everyday time-consuming management task with different imperatives from scheduling. Poor rescheduling decisions can have quality, cost and morale implications. A systematic critical literature review identified rescheduling issues and existing mathematic modelling tools. A consultation exercise with nursing managers examined the complex challenges associated with rescheduling. Minimal research exists on rescheduling compared with scheduling. Poor rescheduling can result in greater disruption to planned nursing shifts and may impact negatively on the quality and cost of patient care, and nurse morale and retention. Very little research examines management challenges or mathematical modelling for rescheduling. Shift rescheduling is a complex and frequent management activity that is more challenging than scheduling. Mathematical modelling may have potential as a tool to support managers to minimise rescheduling disruption. The lack of specific methodological support for rescheduling that takes into account its complexity, increases the likelihood of harm for patients and stress for nursing staff and managers. © 2013 John Wiley & Sons Ltd.

Towards a Theory of Identity and Agency in Coming to Learn Mathematics

ERIC Educational Resources Information Center

Grootenboer, Peter; Jorgensen, Robyn

2009-01-01

In writing this paper we draw considerably on the work of Jo Boaler and Leone Burton. Boaler's studies of classrooms have been particularly poignant in alerting the mathematics education community to a number of key features of successful classrooms, and how such features can turn around the successes for students who traditionally perform poorly…

Using Challenging Tasks for Formative Assessment on Quadratic Functions with Senior Secondary Students

ERIC Educational Resources Information Center

Wilkie, Karina J.

2016-01-01

Senior secondary mathematics students who develop conceptual understanding that moves them beyond "rules without reasons" to connections between related concepts are in a strong place to tackle the more difficult mathematics application problems. Current research is examining how the use of challenging tasks at different levels of…

Teaching 5- and 6-Year-Olds to Count: Knowledge of South African Educators

ERIC Educational Resources Information Center

Feza, Nosisi N.

2016-01-01

Mathematics learning and teaching continues to be a challenge in the South African education system. This challenge is observed in the poor performance of students in national and international assessments. Research suggests that teachers' content knowledge and knowledge of teaching mathematics contribute significantly to students' performance. In…

Traffic Flow - USMES Teacher Resource Book. Fourth Edition. Trial Edition.

ERIC Educational Resources Information Center

Keskulla, Jean

This Unified Sciences and Mathematics for Elementary Schools (USMES) unit challenges students to improve traffic flow at a problem location. The challenge is general enough to apply to many problem-solving situations in mathematics, science, social science, and language arts at any elementary school level (grades 1-8). The Teacher Resource Book…

Pedestrian Crossings - USMES Teacher Resource Book. Fifth Edition. Trial Edition.

ERIC Educational Resources Information Center

Keskulla, Jean

This Unified Sciences and Mathematics for Elementary Schools (USMES) unit challenges students to improve the safety and convenience of a pedestrian crossing near a school. The challenge is general enough to apply to many problem-solving situations in mathematics, science, social science, and language arts at any elementary school level (grades…

Protecting Property - USMES Teacher Resource Book. First Edition. Trial Edition.

ERIC Educational Resources Information Center

Bussey, Margery Koo

This Unified Sciences and Mathematics for Elementary Schools (USMES) unit challenges students to find good ways to protect property (property in desks or lockers; animals; bicycles; tools). The challenge is general enough to apply to many problem-solving situations in mathematics, science, social science, and language arts at any elementary school…

Manufacturing - USMES Teacher Resource Book. Second Edition. Trial Edition.

ERIC Educational Resources Information Center

Agro, Sally

This Unified Sciences and Mathematics for Elementary Schools (USMES) unit challenges students to find the best way to produce an item in quantities needed. The challenge is general enough to apply to many problem-solving situations in mathematics, science, social science, and language arts at any elementary school level (grades 1-8). The Teacher…

Exploring Student Reflective Practice during a Mathematical Modelling Challenge

ERIC Educational Resources Information Center

Redmond, Trevor; Sheehy, Joanne; Brown, Raymond; Kanasa, Harry

2012-01-01

This paper seeks to compare the reflective writings of two cohorts of students (Year 4/5 and Year 8/9) participating in mathematical modelling challenges. Whilst the reflections of the younger cohort were results oriented, the older cohort's reflections spoke more to the affective domain, group processes, the use of technology and the acquisition…

Feature and contrast enhancement of mammographic image based on multiscale analysis and morphology.

PubMed

Wu, Shibin; Yu, Shaode; Yang, Yuhan; Xie, Yaoqin

2013-01-01

A new algorithm for feature and contrast enhancement of mammographic images is proposed in this paper. The approach bases on multiscale transform and mathematical morphology. First of all, the Laplacian Gaussian pyramid operator is applied to transform the mammography into different scale subband images. In addition, the detail or high frequency subimages are equalized by contrast limited adaptive histogram equalization (CLAHE) and low-pass subimages are processed by mathematical morphology. Finally, the enhanced image of feature and contrast is reconstructed from the Laplacian Gaussian pyramid coefficients modified at one or more levels by contrast limited adaptive histogram equalization and mathematical morphology, respectively. The enhanced image is processed by global nonlinear operator. The experimental results show that the presented algorithm is effective for feature and contrast enhancement of mammogram. The performance evaluation of the proposed algorithm is measured by contrast evaluation criterion for image, signal-noise-ratio (SNR), and contrast improvement index (CII).

Feature and Contrast Enhancement of Mammographic Image Based on Multiscale Analysis and Morphology

PubMed Central

Wu, Shibin; Xie, Yaoqin

2013-01-01

A new algorithm for feature and contrast enhancement of mammographic images is proposed in this paper. The approach bases on multiscale transform and mathematical morphology. First of all, the Laplacian Gaussian pyramid operator is applied to transform the mammography into different scale subband images. In addition, the detail or high frequency subimages are equalized by contrast limited adaptive histogram equalization (CLAHE) and low-pass subimages are processed by mathematical morphology. Finally, the enhanced image of feature and contrast is reconstructed from the Laplacian Gaussian pyramid coefficients modified at one or more levels by contrast limited adaptive histogram equalization and mathematical morphology, respectively. The enhanced image is processed by global nonlinear operator. The experimental results show that the presented algorithm is effective for feature and contrast enhancement of mammogram. The performance evaluation of the proposed algorithm is measured by contrast evaluation criterion for image, signal-noise-ratio (SNR), and contrast improvement index (CII). PMID:24416072

A Multifaceted Mathematical Approach for Complex Systems

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

Alexander, F.; Anitescu, M.; Bell, J.

2012-03-07

Applied mathematics has an important role to play in developing the tools needed for the analysis, simulation, and optimization of complex problems. These efforts require the development of the mathematical foundations for scientific discovery, engineering design, and risk analysis based on a sound integrated approach for the understanding of complex systems. However, maximizing the impact of applied mathematics on these challenges requires a novel perspective on approaching the mathematical enterprise. Previous reports that have surveyed the DOE's research needs in applied mathematics have played a key role in defining research directions with the community. Although these reports have had significantmore » impact, accurately assessing current research needs requires an evaluation of today's challenges against the backdrop of recent advances in applied mathematics and computing. To address these needs, the DOE Applied Mathematics Program sponsored a Workshop for Mathematics for the Analysis, Simulation and Optimization of Complex Systems on September 13-14, 2011. The workshop had approximately 50 participants from both the national labs and academia. The goal of the workshop was to identify new research areas in applied mathematics that will complement and enhance the existing DOE ASCR Applied Mathematics Program efforts that are needed to address problems associated with complex systems. This report describes recommendations from the workshop and subsequent analysis of the workshop findings by the organizing committee.« less

Enhancing Teacher Education in Primary Mathematics with Mobile Technologies

ERIC Educational Resources Information Center

Schuck, Sandy

2016-01-01

A challenge of teacher education is to produce graduate primary school teachers who are confident and competent teachers of mathematics. Various approaches to primary school teacher education in mathematics have been investigated, but primary teacher education graduates still tend to be diffident in their teaching of mathematics. In an age where…

Mathematics-Literacy Checklists: A Pedagogical Innovation to Support Teachers as They Implement the Common Core

ERIC Educational Resources Information Center

del Prado Hill, Pixita; Friedland, Ellen S.; McMillen, Susan

2016-01-01

This article presents two innovative tools--the Mathematics-Literacy Planning Framework and Mathematics-Literacy Implementation Checklist--which are designed to help instructional coaches and specialists support teachers to meet the challenges of the mathematics-literacy integration goals of the Common Core. Developed with teacher input, these…

For the Technologically Challenged: Four Free Online Tools to Liven up a Mathematics Classroom

ERIC Educational Resources Information Center

Northcote, Maria

2015-01-01

Use of technology in the mathematics classroom has the potential to advance children's learning of mathematics and enhance their attitudes about mathematics. When used in conjunction with purposeful planning, teachers can use technological tools to reinforce their pedagogical intentions and to facilitate relevant learning activities for students.…

Views on Adults Re-Learning Mathematics: A Comparative Study.

ERIC Educational Resources Information Center

Angiama, R. O.

This paper is based on the on-going research, work, and teaching carried out in the Mathematics Foundations Course (MFC) at Goldsmiths College, University of London. Teaching is a very intimate and rewarding experience for the mathematics lecturer as well as for the adult student. Mathematics lecturers and adults should be challenged by their…

Projects, Puzzles and Other Pedagogies: Working with Kids to Solve Local Problems

ERIC Educational Resources Information Center

Marshman, Margaret

2012-01-01

Engaging and extending middle years students in mathematics is a continual challenge. One of the aims of the "Australian Curriculum: Mathematics" is to ensure that students are "confident, creative users and communicators of mathematics" (ACARA, 2011). Use of mathematical models and/or problems has been suggested as methods of…

Integrating Mathematics and Science: Ecology and Venn Diagrams

ERIC Educational Resources Information Center

Leszczynski, Eliza; Munakata, Mika; Evans, Jessica M.; Pizzigoni, Francesca

2014-01-01

Efforts to integrate mathematics and science have been widely recognized by mathematics and science educators. However, successful integration of these two important school disciplines remains a challenge. In this article, a mathematics and science activity extends the use of Venn diagrams to a life science context and then circles back to a…

Challenging a Teacher's Perceptions of Mathematical Smartness through Reflections on Students' Thinking

ERIC Educational Resources Information Center

Wickstrom, Megan H.

2015-01-01

Creating equitable opportunities so all students can learn and succeed mathematically has been a key focus of mathematics education across several decades. Central to student achievement are students' mathematical identity and their feelings of success during instruction. Researchers (e.g., Boaler & Staples, 2008) have shown that teachers can…

Mathematically Rich, Investigative Tasks for Teaching Algebra

ERIC Educational Resources Information Center

Day, Lorraine

2015-01-01

A challenge for teachers is to incorporate the Standards for Mathematical Practice (CCSSI 2010) throughout their teaching of mathematics so that the Common Core Standards do not revert back to a purely content-driven curriculum. One way to achieve this is through the use of mathematically rich, investigative tasks. These tasks encourage students…

Attitudes of Pre-Service Mathematics Teachers towards Modelling: A South African Inquiry

ERIC Educational Resources Information Center

Jacobs, Gerrie J.; Durandt, Rina

2017-01-01

This study explores the attitudes of mathematics pre-service teachers, based on their initial exposure to a model-eliciting challenge. The new Curriculum and Assessment Policy Statement determines that mathematics students should be able to identify, investigate and solve problems via modelling. The unpreparedness of mathematics teachers in…

Effects of Mathematics Integration in a Teaching Methods Course on Self-Efficacy of Preservice Agricultural Education Teachers

ERIC Educational Resources Information Center

Stripling, Christopher T.; Roberts, T. Grady

2013-01-01

Teachers who are efficacious persevere through challenges in the learning environment and put forth more effort in designing learning activities. The purpose of this study was to determine the effects of mathematics teaching and integration strategies (MTIS) on preservice agricultural teachers' personal mathematics efficacy, mathematics teaching…

Molecular modeling: An open invitation for applied mathematics

NASA Astrophysics Data System (ADS)

Mezey, Paul G.

2013-10-01

Molecular modeling methods provide a very wide range of challenges for innovative mathematical and computational techniques, where often high dimensionality, large sets of data, and complicated interrelations imply a multitude of iterative approximations. The physical and chemical basis of these methodologies involves quantum mechanics with several non-intuitive aspects, where classical interpretation and classical analogies are often misleading or outright wrong. Hence, instead of the everyday, common sense approaches which work so well in engineering, in molecular modeling one often needs to rely on rather abstract mathematical constraints and conditions, again emphasizing the high level of reliance on applied mathematics. Yet, the interdisciplinary aspects of the field of molecular modeling also generates some inertia and perhaps too conservative reliance on tried and tested methodologies, that is at least partially caused by the less than up-to-date involvement in the newest developments in applied mathematics. It is expected that as more applied mathematicians take up the challenge of employing the latest advances of their field in molecular modeling, important breakthroughs may follow. In this presentation some of the current challenges of molecular modeling are discussed.

The affordances of using a flipped classroom approach in the teaching of mathematics: a case study of a grade 10 mathematics class

NASA Astrophysics Data System (ADS)

Muir, Tracey; Geiger, Vince

2016-03-01

Teaching secondary mathematics has a number of challenges, including the expectations that teachers cover the prescribed curriculum, help students learn difficult concepts, prepare students for future studies, and, increasingly, that they do so incorporating digital technologies. This study investigates a teacher's, and his students', perceptions of the benefits or otherwise of a flipped classroom approach in meeting these challenges, within a prescribed curriculum context. Data collection instruments included a survey designed to investigate the nature of students' engagement with the flipped approach and semi-structured student and teacher interviews. Analysis of these data indicated that the teacher and students were positive about their experiences with a flipped classroom approach and that students were motivated to engage with the teacher-created online mathematics resources. The study adds to the limited research literature related to student and teacher perceptions of the affordances of the flipped classroom approach and has implications for secondary mathematics teachers who face the challenge of the twin demands of covering the prescribed curriculum and catering for a range of students' learning needs.

Using Video as a Stimulus to Reveal Elementary Teachers' Mathematical Knowledge for Teaching

ERIC Educational Resources Information Center

Barlow, Angela T.; Gaddy, Angeline K.; Baxter, Wesley A.

2017-01-01

The purpose of this article is to explore the usefulness of a video-based tool for measuring teachers' mathematical knowledge for teaching. Unique to this tool is the use of a video featuring a mathematical disagreement that occurred in an elementary classroom. The authors define mathematical disagreements as instances in which students challenge…

Mathematics Teachers' Response to the Reform Agenda: Results of the 1993 National Survey of Science and Mathematics Education.

ERIC Educational Resources Information Center

Weiss, Iris R.

The NCTM Standards call for the introduction of challenging mathematics content for all students beginning in the early grades. If teachers are to guide students in their exploration of mathematics concepts, they must themselves have a firm grasp of powerful mathematics concepts. This paper uses data from the 1993 National Survey of Science and…

A Framework for Examining How Mathematics Teachers Evaluate Technology

ERIC Educational Resources Information Center

Smith, Ryan C.; Shin, Dongjo; Kim, Somin

2016-01-01

Our mathematics cognitive technology noticing framework is based on professional noticing and curricular noticing frameworks and data collected in a study that explored how secondary mathematics teachers evaluate technology. Our participants displayed three categories of noticing: attention to features of technology, interpretation of the…

Studying Challenges in Integrating Technology in Secondary Mathematics with Technological Pedagogical and Content Knowledge (TPACK)

ERIC Educational Resources Information Center

Stoilescu, Dorian

2014-01-01

This paper describes challenges encountered by two secondary mathematics teachers when they try to integrate ICT devices in their classes. These findings are based on using the Technological Pedagogical and Content Knowledge (TPACK) context, the four dimension framework developed by Niess: 1) overarching conceptions of integrating ICT, 2)…

Debates on the Basic Education Curriculum Reform and Teachers' Challenges in China: The Case of Mathematics

ERIC Educational Resources Information Center

Li, Qiong; Ni, Yu-jing

2012-01-01

Focusing on the case of mathematics, this paper reviews debates on China's new Basic Education Curriculum Reform program, including the status of knowledge within the reformed curriculum, the arrangement of the curriculum system, and the push toward real-life applicability and hands-on participation. It discusses the related challenges that…

Challenges in Mathematics and Statistics Teaching Underpinned by Student-Lecturer Expectations

ERIC Educational Resources Information Center

Parashar, Deepak

2014-01-01

This study is motivated by the desire to address some of the enormous challenges faced by the students as well as the lecturer in fulfilling their respective expectations and duties demanded by the process of learning--teaching of mathematics and statistics within the framework of the constraining schedules laid down by the academic institutions…

Designing for Human Proportions - USMES Teacher Resource Book. Fourth Edition. Trial Edition.

ERIC Educational Resources Information Center

Bussey, Margery Koo

Designing or making changes in things students use or wear is the challenge of this Unified Sciences and Mathematics for Elementary Schools (USMES) unit. The challenge is general enough to apply to many problem-solving situations in mathematics, science, social science, and language arts at any elementary school level (grades 1-8). The Teacher…

When Districts Encounter Teacher Shortages: The Challenges of Recruiting and Retaining Mathematics Teachers in Urban Districts

ERIC Educational Resources Information Center

Liu, Edward; Rosenstein, Joseph G.; Swan, Aubrie E.; Khalil, Deena

2008-01-01

Administrators in six urban districts were interviewed to understand the nature and extent of their problems with recruiting and retaining high quality mathematics teachers. Findings suggest that the math staffing challenge is quite complex, and administrators have had to make difficult compromises because of deficiencies in the quantity and…

First-Year Urban Mathematics and Science Middle School Teachers: Classroom Challenges and Reflective Solutions

ERIC Educational Resources Information Center

Kelly, Angela M.; Gningue, Serigne M.; Qian, Gaoyin

2015-01-01

This study explored the challenges facing 1st-year alternatively certified teachers of mathematics and science in urban middle schools. Four teachers, participants in a National Science Foundation (NSF)-funded Robert Noyce Scholarship Program, were followed from preservice training through their 1st year of teaching, having taken part in…

Opportunities and Challenges: Integration of ICT in Teaching and Learning Mathematics in Secondary Schools, Nairobi, Kenya

ERIC Educational Resources Information Center

Amuko, Sheila; Miheso, Marguerite; Ndeuthi, Sophie

2015-01-01

This presentation is based on a larger study whose purpose was to explore the various opportunities and challenges influencing integration of ICT in teaching and learning Mathematics in secondary schools in Nairobi County. The study, adopted a descriptive survey design. Three instruments questionnaires', a structured interview schedule and an…

Challenges of Blended E-Learning Tools in Mathematics: Students' Perspectives University of Uyo

ERIC Educational Resources Information Center

Umoh, Joseph B.; Akpan, Ekemini T.

2014-01-01

An in-depth knowledge of pedagogical approaches can help improve the formulation of effective and efficient pedagogy, tools and technology to support and enhance the teaching and learning of Mathematics in higher institutions. This study investigated students' perceptions of the challenges of blended e-learning tools in the teaching and learning…

Factors Influencing Teacher Career Satisfaction, Teacher Collaboration and Everyday Challenges: An Exploratory Factor Analysis

ERIC Educational Resources Information Center

Narayan, Nilesh Anish

2016-01-01

The main purpose of this study is to assess the construct validity of Australian eighth grade mathematics teachers' perceptions towards their career satisfaction, their teaching practice and the everyday challenges encountered in schools. The data were utilised from the Trends in International Mathematics and Science Study where a total of 802…

An Evolutionary Approach to Mathematics Education: Enhancing Learning through Contextual Modification

ERIC Educational Resources Information Center

Abate, Charles J.; Cantone, Kathleen A.

2005-01-01

Contemporary mathematics education is at a crossroads. It has become exposed to forces, both static and dynamic, that pose a challenge to its traditional place in academia. Mathematics has a long-established status as perhaps the most critical foundation for analytical knowledge. But the manner in which mathematics instructors choose to respond to…

Variations of Reasoning in Equal Sharing of Children Who Experience Low Achievement in Mathematics: Competence in Context

ERIC Educational Resources Information Center

Hunt, Jessica; Westenskow, Arla; Moyer-Packenham, Patricia S.

2017-01-01

For children with persistent mathematics difficulties, research and practice espouses that an altered kind of mathematics instruction is necessary due to sustained performance differences. Yet, a critical issue in mathematics education rests in the question of why research locates the problem within these children. In this paper, we challenge a…

"Walking in a Foreign and Unknown Landscape": Studying the History of Mathematics in Initial Teacher Education

ERIC Educational Resources Information Center

Povey, Hilary

2014-01-01

This article develops the argument that students in initial teacher education benefit in terms of who they are becoming from developing awareness of and engagement in the history of mathematics. Initially, current school mathematics practices in the UK are considered and challenged. Then the role of teachers' relationship to mathematical subject…

Mathematical Investigations for Supporting Pre-Service Primary Teachers Repeating a Mathematics Education Course

ERIC Educational Resources Information Center

Bailey, Judy

2014-01-01

Preparing to become an effective primary school mathematics teacher is a challenging and complex task; and is influenced by one's past experiences, personal knowledge of, and beliefs and attitudes towards mathematics. This paper examines the experiences of a small group of pre-service teachers who did not pass their first year mathematics…

Loving and Hating Mathematics: Challenging the Myths of Mathematical Life

ERIC Educational Resources Information Center

Hersh, Reuben; John-Steiner, Vera

2010-01-01

Mathematics is often thought of as the coldest expression of pure reason. But few subjects provoke hotter emotions--and inspire more love and hatred--than mathematics. And although math is frequently idealized as floating above the messiness of human life, its story is nothing if not human; often, it is all too human. "Loving and Hating…

Tablet Technology to Facilitate Improved Interaction and Communication with Students Studying Mathematics at a Distance

ERIC Educational Resources Information Center

Galligan, Linda; Hobohm, Carola; Loch, Birgit

2012-01-01

Teaching and learning of mathematics is challenging when lecturer and students are separated geographically. While student engagement and interaction with the course, with other students and with the lecturer is vital to mathematics learning, it is difficult to facilitate this electronically, because of the nature of mathematics. With tablet…

Unpacking the Male Superiority Myth and Masculinization of Mathematics at the Intersections: A Review of Research on Gender in Mathematics Education

ERIC Educational Resources Information Center

Leyva, Luis A.

2017-01-01

Gender research in mathematics education has experienced methodological and theoretical shifts over the past 45 years. Although achievement studies have used assessment tools to explore and subsequently challenge the assumption of male superiority on mathematics assessments, research on participation has unpacked these studies' sex-based…

Teachers' Views of the Challenges of Teaching Grade 9 Applied Mathematics in Toronto Schools

ERIC Educational Resources Information Center

Stoilescu, Dorian; McDougall, Douglas; Egodawatte, Gunawardena

2016-01-01

Mathematics teachers, mathematics department heads, curriculum leaders, and administrators from 11 schools in four school boards from Toronto, Ontario, Canada, participated in a project to improve the teaching and learning in grade 9 mathematics classrooms. In each of these schools, an implementation team was created, so that at least three…

Meet Me at the Crossroads: Over-Fishing to Meet the Standards

ERIC Educational Resources Information Center

Donovan, John E., II

2008-01-01

To achieve the vision of mathematics set forth in "Crossroads" ("AMATYC," 1995), students must experience mathematics as a sensemaking endeavor that informs their world. Embedding the study of mathematics into the real world is a challenge, particularly because it was not the way that many of us learned mathematics in the first place. This article…

Teaching Assistants Who Instruct Preparatory Mathematics to Academically-Challenged First-Year College Students

ERIC Educational Resources Information Center

Tawfeeq, Dante A. L.

2011-01-01

Teaching preparatory mathematics to first-time college students--who come from economically impoverished high schools that have not prepared their students to do college level mathematics--can be a daunting task for teaching assistants (TAs). The preparation of TAs to assist such students in the mastery of mathematical content is a complex…

Influence of Linguistic Challenges on Attitude towards Mathematics Learning among Upper Primary Students of Kerala

ERIC Educational Resources Information Center

Sarabi, M. K.; Gafoor, K. Abdul

2017-01-01

Aspects that influences mathematics learning is widely studied and language factors have been identified as a key backer to difficulties in learning Mathematics. It is evidenced that not only cognitive factors but also affective factors have vital role in learning mathematics. Such affective beliefs sources from various aspects of mathematics…

Challenging Transitions and Crossing Borders: Preparing Novice Mathematics Teacher Educators to Support Novice K-12 Mathematics Teachers

ERIC Educational Resources Information Center

Yow, Jan A.; Eli, Jennifer A.; Beisiegel, Mary; McCloskey, Andrea; Welder, Rachael M.

2016-01-01

Sixty-nine recently graduated doctoral students in mathematics education completed a survey to determine their perceptions of transitioning from a doctoral program into an academic position at an institution of higher education. Research literature for novice mathematics school teachers was also reviewed to document their experiences transitioning…

Connecting Theory and Practice: Preservice Teachers' Construction of Practical Tools for Teaching Mathematics

ERIC Educational Resources Information Center

Jacobbe, Tim; Ross, Dorene D.; Caron, D. Alvarez; Barko, Timothy; Busi, Rich

2014-01-01

The National Council of Teachers of Mathematics (NCTM) has called for changes in mathematics teaching from a procedural to conceptual focus since 1980, yet the way mathematics is taught in many classrooms continues to contradict the recommended practices. The pervasiveness of this challenge has led some educators to suggest changes in university…

Automated method for the systematic interpretation of resonance peaks in spectrum data

DOEpatents

Damiano, B.; Wood, R.T.

1997-04-22

A method is described for spectral signature interpretation. The method includes the creation of a mathematical model of a system or process. A neural network training set is then developed based upon the mathematical model. The neural network training set is developed by using the mathematical model to generate measurable phenomena of the system or process based upon model input parameter that correspond to the physical condition of the system or process. The neural network training set is then used to adjust internal parameters of a neural network. The physical condition of an actual system or process represented by the mathematical model is then monitored by extracting spectral features from measured spectra of the actual process or system. The spectral features are then input into said neural network to determine the physical condition of the system or process represented by the mathematical model. More specifically, the neural network correlates the spectral features (i.e. measurable phenomena) of the actual process or system with the corresponding model input parameters. The model input parameters relate to specific components of the system or process, and, consequently, correspond to the physical condition of the process or system. 1 fig.

Automated method for the systematic interpretation of resonance peaks in spectrum data

DOEpatents

Damiano, Brian; Wood, Richard T.

1997-01-01

A method for spectral signature interpretation. The method includes the creation of a mathematical model of a system or process. A neural network training set is then developed based upon the mathematical model. The neural network training set is developed by using the mathematical model to generate measurable phenomena of the system or process based upon model input parameter that correspond to the physical condition of the system or process. The neural network training set is then used to adjust internal parameters of a neural network. The physical condition of an actual system or process represented by the mathematical model is then monitored by extracting spectral features from measured spectra of the actual process or system. The spectral features are then input into said neural network to determine the physical condition of the system or process represented by the mathematical. More specifically, the neural network correlates the spectral features (i.e. measurable phenomena) of the actual process or system with the corresponding model input parameters. The model input parameters relate to specific components of the system or process, and, consequently, correspond to the physical condition of the process or system.

A control theoretical approach to crowd management. Comment on "Human behaviours in evacuation crowd dynamics: From modelling to "big data" toward crisis management" by Nicola Bellomo et al.

NASA Astrophysics Data System (ADS)

Borzí, Alfio; Caponigro, Marco

2016-09-01

The formulation of mathematical models for crowd dynamics is one current challenge in many fields of applied sciences. It involves the modelization of the complex behavior of a large number of individuals. In particular, the difficulty lays in describing emerging collective behaviors by means of a relatively small number of local interaction rules between individuals in a crowd. Clearly, the individual's free will involved in decision making processes and in the management of the social interactions cannot be described by a finite number of deterministic rules. On the other hand, in large crowds, this individual indeterminacy can be considered as a local fluctuation averaged to zero by the size of the crowd. While at the microscopic scale, using a system of coupled ODEs, the free will should be included in the mathematical description (e.g. with a stochastic term), the mesoscopic and macroscopic scales, modeled by PDEs, represent a powerful modelling tool that allows to neglect this feature and provide a reliable description. In this sense, the work by Bellomo, Clarke, Gibelli, Townsend, and Vreugdenhil [2] represents a mathematical-epistemological contribution towards the design of a reliable model of human behavior.

Progress in recognizing typeset mathematics

NASA Astrophysics Data System (ADS)

Fateman, Richard J.; Tokuyasu, Taku A.

1996-03-01

Printed mathematics has a number of features which distinguish it from conventional text. These include structure in two dimensions (fractions, exponents, limits), frequent font changes, symbols with variable shape (quotient bars), and substantially differing notational conventions from source to source. When compounded with more generic problems such as noise and merged or broken characters, printed mathematics offers a challenging arena for recognition. Our project was initially driven by the goal of scanning and parsing some 5,000 pages of elaborate mathematics (tables of definite integrals). While our prototype system demonstrates success on translating noise-free typeset equations into Lisp expressions appropriate for further processing, a more semantic top-down approach appears necessary for higher levels of performance. Such an approach may benefit the incorporation of these programs into a more general document processing viewpoint. We intend to release to the public our somewhat refined prototypes as utility programs in the hope that they will be of general use in the construction of custom OCR packages. These utilities are quite fast even as originally prototyped in Lisp, where they may be of particular interest to those working on 'intelligent' optical processing. Some routines have been re-written in C++ as well. Additional programs providing formula recognition and parsing also form a part of this system. It is important however to realize that distinct conflicting grammars are needed to cover variations in contemporary and historical typesetting, and thus a single simple solution is not possible.

Mathematics Programming on the Apple II and IBM PC.

ERIC Educational Resources Information Center

Myers, Roy E.; Schneider, David I.

1987-01-01

Details the features of BASIC used in mathematics programming and provides the information needed to translate between the Apple II and IBM PC computers. Discusses inputing a user-defined function, setting scroll windows, displaying subscripts and exponents, variable names, mathematical characters and special symbols. (TW)

Earth's Rotation: A Challenging Problem in Mathematics and Physics

NASA Astrophysics Data System (ADS)

Ferrándiz, José M.; Navarro, Juan F.; Escapa, Alberto; Getino, Juan

2015-01-01

A suitable knowledge of the orientation and motion of the Earth in space is a common need in various fields. That knowledge has been ever necessary to carry out astronomical observations, but with the advent of the space age, it became essential for making observations of satellites and predicting and determining their orbits, and for observing the Earth from space as well. Given the relevant role it plays in Space Geodesy, Earth rotation is considered as one of the three pillars of Geodesy, the other two being geometry and gravity. Besides, research on Earth rotation has fostered advances in many fields, such as Mathematics, Astronomy and Geophysics, for centuries. One remarkable feature of the problem is in the extreme requirements of accuracy that must be fulfilled in the near future, about a millimetre on the tangent plane to the planet surface, roughly speaking. That challenges all of the theories that have been devised and used to-date; the paper makes a short review of some of the most relevant methods, which can be envisaged as milestones in Earth rotation research, emphasizing the Hamiltonian approach developed by the authors. Some contemporary problems are presented, as well as the main lines of future research prospected by the International Astronomical Union/International Association of Geodesy Joint Working Group on Theory of Earth Rotation, created in 2013.

Blended particle filters for large-dimensional chaotic dynamical systems

PubMed Central

Majda, Andrew J.; Qi, Di; Sapsis, Themistoklis P.

2014-01-01

A major challenge in contemporary data science is the development of statistically accurate particle filters to capture non-Gaussian features in large-dimensional chaotic dynamical systems. Blended particle filters that capture non-Gaussian features in an adaptively evolving low-dimensional subspace through particles interacting with evolving Gaussian statistics on the remaining portion of phase space are introduced here. These blended particle filters are constructed in this paper through a mathematical formalism involving conditional Gaussian mixtures combined with statistically nonlinear forecast models compatible with this structure developed recently with high skill for uncertainty quantification. Stringent test cases for filtering involving the 40-dimensional Lorenz 96 model with a 5-dimensional adaptive subspace for nonlinear blended filtering in various turbulent regimes with at least nine positive Lyapunov exponents are used here. These cases demonstrate the high skill of the blended particle filter algorithms in capturing both highly non-Gaussian dynamical features as well as crucial nonlinear statistics for accurate filtering in extreme filtering regimes with sparse infrequent high-quality observations. The formalism developed here is also useful for multiscale filtering of turbulent systems and a simple application is sketched below. PMID:24825886

Free-Form Region Description with Second-Order Pooling.

PubMed

Carreira, João; Caseiro, Rui; Batista, Jorge; Sminchisescu, Cristian

2015-06-01

Semantic segmentation and object detection are nowadays dominated by methods operating on regions obtained as a result of a bottom-up grouping process (segmentation) but use feature extractors developed for recognition on fixed-form (e.g. rectangular) patches, with full images as a special case. This is most likely suboptimal. In this paper we focus on feature extraction and description over free-form regions and study the relationship with their fixed-form counterparts. Our main contributions are novel pooling techniques that capture the second-order statistics of local descriptors inside such free-form regions. We introduce second-order generalizations of average and max-pooling that together with appropriate non-linearities, derived from the mathematical structure of their embedding space, lead to state-of-the-art recognition performance in semantic segmentation experiments without any type of local feature coding. In contrast, we show that codebook-based local feature coding is more important when feature extraction is constrained to operate over regions that include both foreground and large portions of the background, as typical in image classification settings, whereas for high-accuracy localization setups, second-order pooling over free-form regions produces results superior to those of the winning systems in the contemporary semantic segmentation challenges, with models that are much faster in both training and testing.

Maximum entropy methods for extracting the learned features of deep neural networks.

PubMed

Finnegan, Alex; Song, Jun S

2017-10-01

New architectures of multilayer artificial neural networks and new methods for training them are rapidly revolutionizing the application of machine learning in diverse fields, including business, social science, physical sciences, and biology. Interpreting deep neural networks, however, currently remains elusive, and a critical challenge lies in understanding which meaningful features a network is actually learning. We present a general method for interpreting deep neural networks and extracting network-learned features from input data. We describe our algorithm in the context of biological sequence analysis. Our approach, based on ideas from statistical physics, samples from the maximum entropy distribution over possible sequences, anchored at an input sequence and subject to constraints implied by the empirical function learned by a network. Using our framework, we demonstrate that local transcription factor binding motifs can be identified from a network trained on ChIP-seq data and that nucleosome positioning signals are indeed learned by a network trained on chemical cleavage nucleosome maps. Imposing a further constraint on the maximum entropy distribution also allows us to probe whether a network is learning global sequence features, such as the high GC content in nucleosome-rich regions. This work thus provides valuable mathematical tools for interpreting and extracting learned features from feed-forward neural networks.

Manipulative Apps to Support Students with Disabilities in Mathematics

ERIC Educational Resources Information Center

Bouck, Emily C.; Working, Christopher; Bone, Erin

2018-01-01

Understanding mathematical concepts is important for all students, although often challenging for many students with disabilities. Historically, educators have used concrete manipulatives to support and build conceptual understanding. Mobile devices provide a valuable option to support students with disabilities in mathematics through app-based…

Mathematically Gifted Third Graders--A Challenge in the Classroom.

ERIC Educational Resources Information Center

Wolfle, Jane A.

1988-01-01

The third-grade classroom teacher can identify mathematically gifted students and can provide them with opportunities for extending their understanding and enjoyment of mathematics through use of such techniques as content sophistication, enrichment, peer tutoring, curriculum compacting, puzzles, and math centers. (Author/JDD)

Fostering Perseverance

ERIC Educational Resources Information Center

Lewis, Jennifer M.; Özgün-Koca, S. Asli

2016-01-01

Sustaining engagement with a mathematics task is not a novel suggestion for effective mathematics teaching. "Principles and Standards for School Mathematics" (2000) specified that "students need to know that a challenging problem will take some time and that perseverance is an important aspect of the problem-solving process and of…

Multiple Paths to Mathematics Practice in Al-Kashi's "Key to Arithmetic"

ERIC Educational Resources Information Center

Taani, Osama

2014-01-01

In this paper, I discuss one of the most distinguishing features of Jamshid al-Kashi's pedagogy from his "Key to Arithmetic", a well-known Arabic mathematics textbook from the fifteenth century. This feature is the multiple paths that he includes to find a desired result. In the first section light is shed on al-Kashi's life…

A School-Based Professional Development Programme for Teachers of Mathematical Modelling in Singapore

ERIC Educational Resources Information Center

Tan, Liang Soon; Ang, Keng Cheng

2016-01-01

A school-based professional development programme (SBPD) aimed at developing secondary school mathematics teachers' competencies to teach mathematical modelling in Singapore is presented and evaluated in this article. The SBPD is characterized by two key features--content elements to develop teachers' knowledge and skills, and transformative…

Mathematics Education and the Objectivist Programme in HPS

ERIC Educational Resources Information Center

Glas, Eduard

2013-01-01

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…

Design Features of Pedagogically-Sound Software in Mathematics.

ERIC Educational Resources Information Center

Haase, Howard; And Others

Weaknesses in educational software currently available in the domain of mathematics are discussed. A technique that was used for the design and production of mathematics software aimed at improving problem-solving skills which combines sound pedagogy and innovative programming is presented. To illustrate the design portion of this technique, a…

Opening Mathematics Texts: Resisting the Seduction

ERIC Educational Resources Information Center

Wagner, David

2012-01-01

This analysis of the writing in a grade 7 mathematics textbook distinguishes between closed texts and open texts, which acknowledge multiple possibilities. I use tools that have recently been applied in mathematics contexts, focussing on grammatical features that include personal pronouns, modality, and types of imperatives, as well as on…

Progress Monitoring in Middle School Mathematics: Options and Issues

ERIC Educational Resources Information Center

Foegen, Anne

2008-01-01

This study investigated the technical features of six potential progress-monitoring measures in mathematics appropriate for use at the middle school level, including two commercially available measures for sixth-grade mathematics, two measures used in previous middle school studies, and two new measures of numeracy concepts. Five hundred…

A Primary Classroom Inquiry: Estimating the Height of a Tree

ERIC Educational Resources Information Center

Brown, Natalie; Watson, Jane; Wright, Suzie; Skalicky, Jane

2011-01-01

Measurement is one of the key areas of study in mathematics and features prominently in the "Australian Curriculum: Mathematics" (ACARA, 2010). In this set of investigations requiring students to estimate indirectly the height of a tree they are encouraged to use the "power of mathematical reasoning" and "apply their…

Good Morning, Numbers Day: Motivating for Mathematics

ERIC Educational Resources Information Center

Ramentol, Salvador Vidal

2011-01-01

The aversion that many girls and boys experience towards mathematics has been one of the author's major concerns since he started teaching. In this article, he describes a project called "Numbers Day" that was designed to improve students' attitudes toward mathematics. There are many features of Numbers Day that teachers might…

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…

Prof. Hanna Neumann's Inaugural Presidential Address, 1966

ERIC Educational Resources Information Center

Neumann, Hanna

2017-01-01

Prof. Hanna Neumann gave the Presidential Address at Australian Association of Mathematics Teachers inaugural conference in 1966. The conference was held at Monash University and had the theme of "mathematical unity". In this address, Prof. Neumann described some features of the teaching of mathematics in schools. While she did not know…

Gestures and Insight in Advanced Mathematical Thinking

ERIC Educational Resources Information Center

Yoon, Caroline; Thomas, Michael O. J.; Dreyfus, Tommy

2011-01-01

What role do gestures play in advanced mathematical thinking? We argue that the role of gestures goes beyond merely communicating thought and supporting understanding--in some cases, gestures can help generate new mathematical insights. Gestures feature prominently in a case study of two participants working on a sequence of calculus activities.…

Establishing Mathematics for Teaching within Classroom Interactions in Teacher Education

ERIC Educational Resources Information Center

Ryve, Andreas; Nilsson, Per; Mason, John

2012-01-01

Teacher educators' processes of establishing "mathematics for teaching" in teacher education programs have been recognized as an important area for further research. In this study, we examine how two teacher educators establish and make explicit features of mathematics for teaching within classroom interactions. The study shows how the…

Connecting Social and Mathematical Thinking: The Use of "Real Life" Contexts

ERIC Educational Resources Information Center

Sawatzki, Carly

2014-01-01

This paper reports the findings of research into an educational intervention featuring open-ended mathematical problems situated in "real life" contexts and associated pedagogies. "Money and financial mathematics" is the topic in focus, with tasks termed "financial dilemmas" being trialled by 35 teachers in 16…

Mathematical Communication in State Standards before the Common Core

ERIC Educational Resources Information Center

Kosko, Karl Wesley; Gao, Yang

2017-01-01

Mathematical communication has been an important feature of standards documents since National Council of Teachers of Mathematics' (NCTM) (1989) "Curriculum and Evaluation Standards." Such an emphasis has influenced content standards of states from then to present. This study examined how effective the prevalence of various forms of…

A Dynamic Theory of Mathematical Understanding: Some Features and Implications.

ERIC Educational Resources Information Center

Pirie, Susan; Kieren, Thomas

Given the current and widespread practical interest in mathematical understanding, particularly with respect to higher order thinking skills, curriculum reform advocates in many countries cite the need for teaching mathematics with understanding. However, the characterization of understanding in ways that highlight its growth, as well as the…

Limited Knowledge of Fraction Representations Differentiates Middle School Students with Mathematics Learning Disability (Dyscalculia) versus Low Mathematics Achievement

ERIC Educational Resources Information Center

Mazzocco, Michele M. M.; Myers, Gwen F.; Lewis, Katherine E.; Hanich, Laurie B.; Murphy, Melissa M.

2013-01-01

Fractions pose significant challenges for many children, but for some children those challenges persist into high school. Here we administered a fractions magnitude comparison test to 122 children, from Grades 4 to 8, to test whether their knowledge of fractions typically learned early in the sequence of formal math instruction (e.g., fractions…

Why Mathematics (Education) Was Late to the Backlash Party: The Need for a Revolution

ERIC Educational Resources Information Center

Gutiérrez, Rochelle

2017-01-01

When the pedagogy or scholarship involves challenging the status quo, the author argues, especially on behalf of students of color, there tends to an extreme backlash to silence it in recent years. She recalls her experience and provides examples of other academic challenges. However in this commentary, she argues that mathematics was late to the…

What the United States Can Learn From Singapore's World-Class Mathematics System (and What Singapore Can Learn from the United States): An Exploratory Study

ERIC Educational Resources Information Center

Ginsburg, Alan; Leinwand, Steven; Anstrom, Terry; Pollock, Elizabeth

2005-01-01

This exploratory study compares key features of the Singapore and U.S. mathematics systems in the primary grades, when students need to build a strong mathematics foundation. It identifies major differences between the mathematics frameworks, textbooks, assessments, and teachers in Singapore and the United States. It also presents initial results…

Pedagogical issues for effective teaching of biosignal processing and analysis.

PubMed

Sandham, William A; Hamilton, David J

2010-01-01

Biosignal processing and analysis is generally perceived by many students to be a challenging topic to understand, and to become adept with the necessary analytical skills. This is a direct consequence of the high mathematical content involved, and the many abstract features of the topic. The MATLAB and Mathcad software packages offer an excellent algorithm development environment for teaching biosignal processing and analysis modules, and can also be used effectively in many biosignal, and indeed bioengineering, research areas. In this paper, traditional introductory and advanced biosignal processing (and analysis) syllabi are reviewed, and the use of MATLAB and Mathcad for teaching and research is illustrated with a number of examples.

Mayr, mathematics and the study of evolution

PubMed Central

Crow, James F

2009-01-01

In 1959 Ernst Mayr challenged the relevance of mathematical models to evolutionary studies and was answered by JBS Haldane in a witty and convincing essay. Fifty years on, I conclude that the importance of mathematics has in fact increased and will continue to do so. PMID:19291256

Supporting Common Core Sense Making

ERIC Educational Resources Information Center

Keazer, Lindsay; Gerberry, Carla

2017-01-01

Imagine a mathematics classroom in which students engage in sharing ideas and reasoning through solutions to interesting mathematical problems. They are excited about mathematics and working on challenging problems that encourage collaboration and critical thinking. These are things that teachers want, but sometimes they do not know how to achieve…

Mathematical Caring Relations: A Challenging Case

ERIC Educational Resources Information Center

Hackenberg, Amy

2010-01-01

Developed from Noddings's (2002) care theory, von Glasersfeld's (1995) constructivism, and Ryan and Frederick's (1997) notion of subjective vitality, a mathematical caring relation (MCR) is a quality of interaction between a student and a mathematics teacher that conjoins affective and cognitive realms in the process of aiming for mathematical…

Meeting the Challenge of Mathematics Reform for Students with LD.

ERIC Educational Resources Information Center

Woodward, John; Montague, Marjorie

2002-01-01

This article discusses forces driving mathematics reform: shifting theoretical paradigms, disappointing levels of mathematics performance of students in the United States, and the impact of rapidly changing technologies. Concerns about this reform from the special education community are discussed, and synthesized special education research…

Preparing Mathematics Teachers for Technology-Rich Environments

ERIC Educational Resources Information Center

Sturdivant, Rodney X.; Dunham, Penelope; Jardine, Richard

2009-01-01

This article describes key elements for faculty development programs to prepare mathematics teachers for technology-rich environments. We offer practical examples from our experiences in teaching mathematics with technology and in teaching others to incorporate technology-based pedagogies. We address challenges faced by faculty using technology,…

Connecting Changes in Secondary Mathematics Teachers' Knowledge to Their Experiences in a Professional Development Workshop

ERIC Educational Resources Information Center

Boston, Melissa D.

2013-01-01

This investigation describes secondary mathematics teachers' learning and instructional change following their participation in a professional development workshop, the Enhancing Secondary Mathematics Teacher Preparation Project (ESP) (2004-2005), specifically focused on the selection and implementation of cognitively challenging mathematical…

Extending Students' Mathematical Thinking during Whole-Group Discussions

ERIC Educational Resources Information Center

Cengiz, Nesrin; Kline, Kate; Grant, Theresa J.

2011-01-01

Studies show that extending students' mathematical thinking during whole-group discussions is a challenging undertaking. To better understand what extending student thinking looks like and how teachers' mathematical knowledge for teaching (MKT) supports teachers in their efforts to extend student thinking, the teaching of six experienced…

Do word-problem features differentially affect problem difficulty as a function of students' mathematics difficulty with and without reading difficulty?

PubMed

Powell, Sarah R; Fuchs, Lynn S; Fuchs, Douglas; Cirino, Paul T; Fletcher, Jack M

2009-01-01

This study examined whether and, if so, how word-problem features differentially affect problem difficulty as a function of mathematics difficulty (MD) status: no MD (n = 109), MD only (n = 109), or MD in combination with reading difficulties (MDRD; n = 109). The problem features were problem type (total, difference, or change) and position of missing information in the number sentence representing the word problem (first, second, or third position). Students were assessed on 14 word problems near the beginning of third grade. Consistent with the hypothesis that mathematical cognition differs as a function of MD subtype, problem type affected problem difficulty differentially for MDRD versus MD-only students; however, the position of missing information in word problems did not. Implications for MD subtyping and for instruction are discussed.

Authentic Teaching Experiences in Secondary Mathematics Methods

ERIC Educational Resources Information Center

Stickles, Paula R.

2015-01-01

Often secondary mathematics methods courses include classroom peer teaching, but many pre-service teachers find it challenging to teach their classmate peers as there are no discipline issues and little mathematical discourse as the "students" know the content. We will share a recent change in our methods course where pre-service…

The Effect of Eliciting Repair of Mathematics Explanations of Students with Learning Disabilities

ERIC Educational Resources Information Center

Liu, Jia; Xin, Yan Ping

2017-01-01

Mathematical reasoning is important in conceptual understanding and problem solving. In current reform-based, discourse-oriented mathematics classrooms, students with learning disabilities (LD) encounter challenges articulating or explaining their reasoning processes. Enlightened by the concept of conversational repair borrowed from the field of…

Perceived Mathematical Ability under Challenge: A Longitudinal Perspective on Sex Segregation among STEM Degree Fields

ERIC Educational Resources Information Center

Nix, Samantha; Perez-Felkner, Lara; Thomas, Kirby

2015-01-01

Students' perceptions of their mathematics ability vary by gender and seem to influence science, technology, engineering, and mathematics (STEM) degree choice. Related, students' perceptions during academic difficulty are increasingly studied in educational psychology, suggesting a link between such perceptions and task persistence. Despite…

Using Portfolio Assignments to Assess Students' Mathematical Thinking

ERIC Educational Resources Information Center

Fukawa-Connelly, Timothy; Buck, Stephen

2010-01-01

Writing in mathematics can improve procedural knowledge and communication skills and may also help students better understand and then remember problems. The majority of mathematics teachers know that they ought to include some writing assignments in their instructional plans, but the challenge of covering the curriculum and the time required to…

Mathematics Diagnostic Testing in Engineering: An International Comparison between Ireland and Portugal

ERIC Educational Resources Information Center

Carr, M.; Fidalgo, C.; Bigotte de Almeida, M. E.; Branco, J. R.; Santos, V.; Murphy, E.; Ní Fhloinn, E.

2015-01-01

Concern has been expressed throughout Europe about the significant deficiencies in the basic mathematical skills of many engineering undergraduates. Mathematics diagnostic tests in the UK, Ireland and Portugal have shown these shortcomings, which provide a challenge to those striving to introduce more innovative educational practices into…

Supporting Mathematical Discussions: The Roles of Comparison and Cognitive Load

ERIC Educational Resources Information Center

Richland, Lindsey E.; Begolli, Kreshnik Nasi; Simms, Nina; Frausel, Rebecca R.; Lyons, Emily A.

2016-01-01

Mathematical discussions in which students compare alternative solutions to a problem can be powerful modes for students to engage and refine their misconceptions into conceptual understanding, as well as to develop understanding of the mathematics underlying common algorithms. At the same time, these discussions are challenging to lead…

Supporting Mathematical Discussions: The Roles of Comparison and Cognitive Load

ERIC Educational Resources Information Center

Richland, Lindsey E.; Begolli, Kreshnik Nasi; Simms, Nina; Frausel, Rebecca R.; Lyons, Emily A.

2017-01-01

Mathematical discussions in which students compare alternative solutions to a problem can be powerful modes for students to engage and refine their misconceptions into conceptual understanding, as well as to develop understanding of the mathematics underlying common algorithms. At the same time, these discussions are challenging to lead…

Alternative Secondary Mathematics Programs for Migrant Students: Cultural and Linguistic Considerations.

ERIC Educational Resources Information Center

Celedon-Pattichis, Sylvia

This chapter describes various programs providing secondary mathematics curricula to migrant students and discusses some challenges of integrating the cultural and linguistic experiences of migrant students learning mathematics. Among the distance-education programs designed for migrant students, the University of Texas Migrant Program delivers 22…

Foundation Content Knowledge: Pre-Service Teachers as Half-Empty or Becoming Fluent?

ERIC Educational Resources Information Center

Anakin, Megan; Linsell, Chris

2014-01-01

The concept of a growth-oriented disposition framed the analysis of theoretical and practical dimensions of pre-service teachers' mathematics content knowledge. We identify historical hangovers, tacit habits, and pedagogical strangleholds that present challenges to the way mathematics education researchers interact with the mathematics content…

Inhibiting Intuitive Thinking in Mathematics Education

ERIC Educational Resources Information Center

Thomas, Michael O. J.

2015-01-01

The papers in this issue describe recent collaborative research into the role of inhibition of intuitive thinking in mathematics education. This commentary reflects on this research from a mathematics education perspective and draws attention to some of the challenges that arise in collaboration between research fields with different cultures,…

The Mathematics Education of Elementary Teachers: Issues and Strategies for Content Courses

ERIC Educational Resources Information Center

Hart, Lynn C., Ed.; Oesterle, Susan, Ed.; Auslander, Susan Swars, Ed.; Kajander, Ann, Ed.

2016-01-01

This book is an edited volume addressing specific issues of significance for individuals involved with the undergraduate mathematics content preparation of prospective elementary teachers (PSTs). Teaching mathematics content courses to this group of students presents unique challenges. While some PSTs enter their teacher preparation with weak…

Mathematical Thinking: Challenging Prospective Teachers to Do More than "Talk the Talk"

ERIC Educational Resources Information Center

Prendergast, Mark; Johnson, Patrick; Fitzmaurice, Olivia; Liston, Miriam; O'Keeffe, Lisa; O'Meara, Niamh

2014-01-01

This paper reports on a research project which aims to improve prospective mathematics teachers' relational understanding and pedagogical beliefs for teaching in second-level Irish classrooms. Prospective mathematics teachers complete their teacher education training with varying pedagogical beliefs, and often little relational understanding of…

Reading the News: The Statistical Preparation of Pre-Service Secondary Mathematics Teachers

ERIC Educational Resources Information Center

Chesler, Joshua

2015-01-01

Undergraduate mathematics programs must prepare teachers for the challenges of teaching statistical thinking as advocated in standards documents and statistics education literature. This study investigates the statistical thinking of pre-service secondary mathematics teachers at the end of their undergraduate educations. Although all had completed…

Elementary Administrators' Mathematics Supervision and Self-Efficacy Development

ERIC Educational Resources Information Center

Johnson, Kelly M. Gomez

2017-01-01

Mathematics curriculum reform is changing the content and resources in today's elementary classrooms as well as the culture of mathematics teaching and learning. Administrators face the challenge of leading large-scale curricular change efforts with limited prior knowledge or experiences with reform curricula structures. Administrators, as the…

CASMI: Virtual Learning Collaborative Environment for Mathematical Enrichment

ERIC Educational Resources Information Center

Freiman, Viktor; Manuel, Dominic; Lirette-Pitre, Nicole

2007-01-01

Challenging problems can make mathematics more attractive to all learners, including the gifted. Application problems that one still finds in regular textbooks often can be resolved by applying a single mathematical concept, operation, or formula. These problems do not require a higher order of thinking. They are, therefore, less cognitively and…

Improving Elementary Mathematics and Science Teaching and Learning: Lessons from a School-University Partnership

ERIC Educational Resources Information Center

Norman, Patricia J.; Nordine, Jeffrey

2016-01-01

The challenges of teaching elementary mathematics and science, particularly in urban settings, have been well documented. While evidence exists that sustained professional development in mathematics and science can promote inquiry-oriented instruction and bolster student achievement, little has been written about the particular challenges…

Exploring Iconic Interpretation and Mathematics Teacher Development through Clinical Simulations

ERIC Educational Resources Information Center

Dotger, Benjamin; Masingila, Joanna; Bearkland, Mary; Dotger, Sharon

2015-01-01

Field placements serve as the traditional "clinical" experience for prospective mathematics teachers to immerse themselves in the mathematical challenges of students. This article reports data from a different type of learning experience, that of a clinical simulation with a standardized individual. We begin with a brief background on…

Developing Culturally Responsive Mathematics Teachers: Secondary Teachers' Evolving Conceptions of Knowing Students

ERIC Educational Resources Information Center

Parker, Frieda; Bartell, Tonya Gau; Novak, Jodie D.

2017-01-01

Research advances in teaching, learning, curriculum, and assessment have not changed the continued underperformance of marginalized students in mathematics education. Culturally responsive teaching is a means of addressing the needs of these students. It is sometimes challenging, however, to convince secondary mathematics teachers about the…

Under Threes' Mathematical Learning

ERIC Educational Resources Information Center

Franzén, Karin

2015-01-01

The article focuses on mathematics for toddlers in preschool, with the aim of challenging a strong learning discourse that mainly focuses on cognitive learning. By devoting more attention to other perspectives on learning, the hope is to better promote children's early mathematical development. Sweden is one of few countries to have a curriculum…

Special Educators and Mathematics Phobia: An Initial Qualitative Investigation

ERIC Educational Resources Information Center

Humphrey, Michael; Hourcade, Jack J.

2010-01-01

Special educators are uniquely challenged to be content experts in all curricular areas, including mathematics, because students in their caseloads may require academic instruction in any area. However, special educators with math phobia may be limited in their ability to provide effective instruction to their students with mathematical deficits…

The Use of Questions within In-the-Moment Coaching in Initial Mathematics Teacher Education: Enhancing Participation, Reflection, and Co-Construction in Rehearsals of Practice

ERIC Educational Resources Information Center

Averill, Robin; Drake, Michael; Anderson, Dayle; Anthony, Glenda

2016-01-01

Managing mathematical discussion is known to be challenging for novice teachers. Coaching within student teacher rehearsals of teaching has been shown to develop mathematics teaching practice, but can be time consuming. To examine how coaching using questions could assist novice teachers to promote mathematical thinking and discussions within…

From Challenging Assumptions to Measuring Effect: Researching the Nokia Mobile Mathematics Service in South Africa

ERIC Educational Resources Information Center

Roberts, Nicky; Spencer-Smith, Garth; Vänskä, Riitta; Eskelinen, Sanna

2015-01-01

This paper reports on the analysis of the voluntary uptake and use of the "Nokia Mobile Mathematics" service by 3,957 Grade 10 learners. It measures the effect of the service on the school Mathematics attainment of 1,950 of these learners over one academic year. The study reveals that 21% of Grade 10 Mathematics learners voluntarily and…

Perturbing the Hypothalamic Pituitary Adrenal Axis:A Mathematical Model for Interpreting PTSDAssessment Tests

DTIC Science & Technology

2017-08-15

RESEARCH Perturbing the Hypothalamic–Pituitary–Adrenal Axis: A Mathematical Model for Interpreting PTSD Assessment Tests Lae Un Kim1, Maria R...D’Orsogna2, and Tom Chou1 1Department of Biomathematics, University of California, Los Angeles, USA 2Department of Mathematics , California State University...observed features and experimental responses can arise from a bistable mathematical model containing two steady-states, rather than relying on specific

Combinatorial and Algorithmic Rigidity: Beyond Two Dimensions

DTIC Science & Technology

2012-12-01

problem. Manuscript, 2010. [35] G. Panina and I. Streinu. Flattening single-vertex origami : the non- expansive case. Computational Geometry : Theory and...in 2008, under the DARPA solicitation “Mathemat- ical Challenges, BAA 07-68”. It addressed Mathematical Challenge Ten: Al- gorithmic Origami and...a number of optimal algorithms and provided critical complexity analysis. The topic of algorithmic origami was successfully engaged from the same

The Microevolution of Mathematical Knowledge: The Case of Randomness.

ERIC Educational Resources Information Center

Pratt, Dave; Noss, Richard

2002-01-01

Explores the growth of mathematical knowledge and the relationship between abstraction and context. Builds on work to construct a viable model of the micro-evolution of mathematical knowledge in context whose central feature is the visibility of its mechanisms. Illustrates a case study of 10-11-year-old children's construction of meanings for…

Mathematics & Science in the Real World.

ERIC Educational Resources Information Center

Thorson, Annette, Ed.

2000-01-01

This issue of ENC Focus is organized around the theme of mathematics and science in the real world. It intends to provide teachers with practical resources and suggestions for science and mathematics education. Featured articles include: (1) "Real-World Learning: A Necessity for the Success of Current Reform Efforts" (Robert E. Yager); (2)…

Gender Differences in the Use and Benefit of Advanced Learning Technologies for Mathematics

ERIC Educational Resources Information Center

Arroyo, Ivon; Burleson, Winslow; Tai, Minghui; Muldner, Kasia; Woolf, Beverly Park

2013-01-01

We provide evidence of persistent gender effects for students using advanced adaptive technology while learning mathematics. This technology improves each gender's learning and affective predispositions toward mathematics, but specific features in the software help either female or male students. Gender differences were seen in the students' style…

Proposing a Mathematical Software Tool in Physics Secondary Education

ERIC Educational Resources Information Center

Baltzis, Konstantinos B.

2009-01-01

MathCad® is a very popular software tool for mathematical and statistical analysis in science and engineering. Its low cost, ease of use, extensive function library, and worksheet-like user interface distinguish it among other commercial packages. Its features are also well suited to educational process. The use of natural mathematical notation…

A Reconceptualized Framework for "Opportunity to Learn" in School Mathematics

ERIC Educational Resources Information Center

Walkowiak, Temple A.; Pinter, Holly H.; Berry, Robert Q.

2017-01-01

We present a reconceptualized framework for opportunity to learn (OTL) in school mathematics that builds on previous conceptualizations of OTL and includes features related to both quantity (i.e., time) and quality. Our framework draws on existing literature and on our own observational research of mathematics teaching practices. Through the…

Becoming Competent, Confident and Critically Aware: Tracing Academic Numeracy Development in Nursing

ERIC Educational Resources Information Center

Galligan, Linda

2013-01-01

This paper describes the mathematical journey of a mature aged nursing student as she struggles to become more academically numerate. Within the paper, academic numeracy is defined around three features: competence, confidence and critical awareness of both the context of mathematics and students' own relationship with mathematics. It then uses…

A Mathematics Support Programme for First-Year Engineering Students

ERIC Educational Resources Information Center

Hillock, Poh Wah; Jennings, Michael; Roberts, Anthony; Scharaschkin, Victor

2013-01-01

This article describes a mathematics support programme at the University of Queensland, targeted at first-year engineering students identified as having a high risk of failing a first-year mathematics course in calculus and linear algebra. It describes how students were identified for the programme and the main features of the programme. The…

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.

Final Technical Report: Mathematical Foundations for Uncertainty Quantification in Materials Design

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

Plechac, Petr; Vlachos, Dionisios G.

We developed path-wise information theory-based and goal-oriented sensitivity analysis and parameter identification methods for complex high-dimensional dynamics and in particular of non-equilibrium extended molecular systems. The combination of these novel methodologies provided the first methods in the literature which are capable to handle UQ questions for stochastic complex systems with some or all of the following features: (a) multi-scale stochastic models such as (bio)chemical reaction networks, with a very large number of parameters, (b) spatially distributed systems such as Kinetic Monte Carlo or Langevin Dynamics, (c) non-equilibrium processes typically associated with coupled physico-chemical mechanisms, driven boundary conditions, hybrid micro-macro systems,more » etc. A particular computational challenge arises in simulations of multi-scale reaction networks and molecular systems. Mathematical techniques were applied to in silico prediction of novel materials with emphasis on the effect of microstructure on model uncertainty quantification (UQ). We outline acceleration methods to make calculations of real chemistry feasible followed by two complementary tasks on structure optimization and microstructure-induced UQ.« less

Community structure in networks of functional connectivity: resolving functional organization in the rat brain with pharmacological MRI.

PubMed

Schwarz, Adam J; Gozzi, Alessandro; Bifone, Angelo

2009-08-01

In the study of functional connectivity, fMRI data can be represented mathematically as a network of nodes and links, where image voxels represent the nodes and the connections between them reflect a degree of correlation or similarity in their response. Here we show that, within this framework, functional imaging data can be partitioned into 'communities' of tightly interconnected voxels corresponding to maximum modularity within the overall network. We evaluated this approach systematically in application to networks constructed from pharmacological MRI (phMRI) of the rat brain in response to acute challenge with three different compounds with distinct mechanisms of action (d-amphetamine, fluoxetine, and nicotine) as well as vehicle (physiological saline). This approach resulted in bilaterally symmetric sub-networks corresponding to meaningful anatomical and functional connectivity pathways consistent with the purported mechanism of action of each drug. Interestingly, common features across all three networks revealed two groups of tightly coupled brain structures that responded as functional units independent of the specific neurotransmitter systems stimulated by the drug challenge, including a network involving the prefrontal cortex and sub-cortical regions extending from the striatum to the amygdala. This finding suggests that each of these networks includes general underlying features of the functional organization of the rat brain.

Defining Computational Thinking for Mathematics and Science Classrooms

NASA Astrophysics Data System (ADS)

Weintrop, David; Beheshti, Elham; Horn, Michael; Orton, Kai; Jona, Kemi; Trouille, Laura; Wilensky, Uri

2016-02-01

Science and mathematics are becoming computational endeavors. This fact is reflected in the recently released Next Generation Science Standards and the decision to include "computational thinking" as a core scientific practice. With this addition, and the increased presence of computation in mathematics and scientific contexts, a new urgency has come to the challenge of defining computational thinking and providing a theoretical grounding for what form it should take in school science and mathematics classrooms. This paper presents a response to this challenge by proposing a definition of computational thinking for mathematics and science in the form of a taxonomy consisting of four main categories: data practices, modeling and simulation practices, computational problem solving practices, and systems thinking practices. In formulating this taxonomy, we draw on the existing computational thinking literature, interviews with mathematicians and scientists, and exemplary computational thinking instructional materials. This work was undertaken as part of a larger effort to infuse computational thinking into high school science and mathematics curricular materials. In this paper, we argue for the approach of embedding computational thinking in mathematics and science contexts, present the taxonomy, and discuss how we envision the taxonomy being used to bring current educational efforts in line with the increasingly computational nature of modern science and mathematics.

Project-Based Learning Environments: Challenging Preservice Teachers to Act in the Moment

ERIC Educational Resources Information Center

Wilhelm, Jennifer; Sherrod, Sonya; Walters, Kendra

2008-01-01

In this design study, the authors documented means by which preservice teachers experienced mathematics and science associated with understanding the Moon and sky as they participated in project work within their mathematics and science methods course. The authors examined the way preservice teachers applied mathematics needed to accomplish…

The Mathematics of Skateboarding: A Relevant Application of the 5Es of Constructivism

ERIC Educational Resources Information Center

Robertson, William H.; Meyer, Rachelle D.; Wilkerson, Trena L.

2012-01-01

Getting high school students to enjoy mathematics and to connect concepts to their daily lives is a challenge for many educators. The Mathematics of Skateboarding demonstrated innovative and creative ways to engage students in content and skills mapped to state requirements for high school students in Algebra and Geometry.

Experiences of Visually Impaired Students in Community College Math Courses

ERIC Educational Resources Information Center

Swan, S. Tomeka

2017-01-01

Blind and visually impaired students who attend community colleges face challenges in learning mathematics (Forrest, 2010). Scoy, McLaughlin, Walls, and Zuppuhaur (2006) claim these students are at a disadvantage in studying mathematics due to the visual and interactive nature of the subject, and by the way mathematics is taught. In this…

Mathematics Education & Digital Technologies: Facing the Challenge of Networking European Research Teams

ERIC Educational Resources Information Center

Bottino, Rosa Maria; Kynigos, Chronis

2009-01-01

This paper introduces the "IJCML" Special Issue dedicated to digital technologies and mathematics education and, in particular, to the work performed by the European Research Team TELMA (Technology Enhanced Learning in Mathematics). TELMA was one of the initiatives of the Kaleidoscope Network of Excellence established by the European…

The Challenge to Situate Digital Learning Technologies in Preservice Teacher Mathematics Education

ERIC Educational Resources Information Center

McDonald, Susan

2012-01-01

This paper focuses on how preservice primary teachers can be supported to embrace digital learning technologies (DLTs) in their teaching of mathematics. The nature of the instruction and the assessment in the final mathematics unit of the bachelor of education program were changed. Despite being tagged as "tech-savvy," preservice…

Note-Taking in a Mathematics Classroom

ERIC Educational Resources Information Center

Hoong, Leong Yew; Guan, Tay Eng; Seng, Quek Khiok; Fwe, Yap Sook; Luen, Tong Cherng; Toh, Wei Yeng Karen; Chia, Alexander; Teck, Ong Yao

2014-01-01

The authors are a team of teachers and teacher educators who are deeply interested in helping mathematically-challenged students improve in their learning of mathematics. In Singapore, depending on their performance at the end of a nationwide Year 6 examination, students are channelled into three ability streams for Years 7 to 10: Express (60%),…

More Good Questions: Great Ways to Differentiate Secondary Mathematics Instruction

ERIC Educational Resources Information Center

Small, Marian; Lin, Amy

2010-01-01

Teachers know that Differentiated Instruction (DI) helps all students to learn. Yet DI challenges teachers, and nowhere more than in mathematics. In this new book, written specifically for secondary mathematics teachers, the authors cut through the difficulties with two powerful and universal strategies that teachers can use across all math…

Goldilocks Discourse--Math Scaffolding That's Just Right

ERIC Educational Resources Information Center

Dale, Rachel; Scherrer, Jimmy

2015-01-01

The Common Core has brought a sharp shift in what it means to be mathematically literate. Becoming mathematically literate is now as much a matter of acquiring mathematical practices as of acquiring any defined set of content standards. This more ambitious definition of literacy presents a challenge not only for students, but also for teachers who…

Preparing and Supporting Black Students to Enroll and Achieve in Advanced Mathematics Classes in Middle School: A Case Study

ERIC Educational Resources Information Center

Cobbs, Joyce Bernice

2014-01-01

The literature on minority student achievement indicates that Black students are underrepresented in advanced mathematics courses. Advanced mathematics courses offer students the opportunity to engage with challenging curricula, experience rigorous instruction, and interact with quality teachers. The middle school years are particularly…

Perceptions of Challenging Tasks and Achievement by New Zealand Students

ERIC Educational Resources Information Center

Linsell, Chris; Holmes, Marilyn; Sullivan, Peter

2016-01-01

This paper examines the learning by students who were participating in a project designed to promote persistence while working on mathematical tasks. We examined their learning of mathematics concepts and learning about the processes of engaging in mathematical tasks. There were substantial increases in students' knowledge of angles and also…

Enhancing Formative Assessment Practice and Encouraging Middle School Mathematics Engagement and Persistence

ERIC Educational Resources Information Center

Beesley, Andrea D.; Clark, Tedra F.; Dempsey, Kathleen; Tweed, Anne

2018-01-01

In the transition to middle school, and during the middle school years, students' motivation for mathematics tends to decline from what it was during elementary school. Formative assessment strategies in mathematics can help support motivation by building confidence for challenging tasks. In this study, the authors developed and piloted a…

Modeling in the Common Core State Standards

ERIC Educational Resources Information Center

Tam, Kai Chung

2011-01-01

The inclusion of modeling and applications into the mathematics curriculum has proven to be a challenging task over the last fifty years. The Common Core State Standards (CCSS) has made mathematical modeling both one of its Standards for Mathematical Practice and one of its Conceptual Categories. This article discusses the need for mathematical…

Playing with Mathematics: How Play Supports Learning and the Common Core State Standards

ERIC Educational Resources Information Center

Zosh, Jennifer Mary; Hassinger-Das, Brenna; Toub, Tamara Spiewak; Hirsh-Pasek, Kathy; Golinkof, Roberta

2016-01-01

International rankings show children in the United States perform well below average in mathematics. There are also large mathematics achievement gaps between children of lower- and higher-socioeconomic status. As today's teachers face these challenges, they are also faced with the pressures of sweeping educational reforms that arrived with the…

Mentoring Mathematical Minds: An Innovative Program to Develop Math Talent

ERIC Educational Resources Information Center

Gavin, M. Katherine; Casa, Tutita M.; Adelson, Jill L.

2006-01-01

Meeting the needs of mathematically talented elementary students has always been a real challenge due to the lack of appropriate curricular resources and training for teachers. Mathematics is not generally a strength area for elementary or gifted/talented teachers; rather, their talents and interests often lie in the language arts realm. This is…

Student Perception of the Impact of Mathematics Support in Higher Education

ERIC Educational Resources Information Center

Ní Fhloinn, E.; Fitzmaurice, O.; Mac an Bhaird, C.; O'Sullivan, C.

2014-01-01

Mathematics support in higher education has become increasingly widespread over the past two decades, particularly in the UK, Ireland and Australia. Despite this, reliable evaluation of mathematics support continues to present challenges for those working in this area. One reason is because ideally, properly structured support should function as…

What Mathematics Do High School Teachers Need to Know?

ERIC Educational Resources Information Center

Gilbert, Michael J.; Coomes, Jacqueline

2010-01-01

Erin has been teaching at Centennial High School for five years. Always an excellent mathematics student, she is nonetheless surprised at the amount of mathematics she has learned since she began teaching. She recently assigned what she thought was a fairly straightforward proportional reasoning task, only to be challenged to understand the…

Engaging Life-Sciences Students with Mathematical Models: Does Authenticity Help?

ERIC Educational Resources Information Center

Poladian, Leon

2013-01-01

Compulsory mathematics service units for the life sciences present unique challenges: even students who learn some specific skills maintain a negative attitude to mathematics and do not see the relevance of the unit towards their degree. The focus on authentic content and the presentation and teaching of global or qualitative methods before…

Promising Practices to Meet Global Challenges in Science and Mathematics Education

ERIC Educational Resources Information Center

Berlin, Donna F., Ed.; White, Arthur L., Ed.

2010-01-01

The chapters in this book reflect the work of science and mathematics educators who have worked for many years at the international level. As members of the International Consortium for Research in Science and Mathematics Education, their work provides readers with issues, models, practices, and research results that have applicability and…

Integrating Language and Content: Challenges in a Japanese Supplementary School in Victoria

ERIC Educational Resources Information Center

Okumura, Shinji; Obara, Yumi

2017-01-01

The Melbourne International School of Japanese (MISJ) is a supplementary Saturday school which offers Japanese language and mathematics taught in Japanese from kindergarten to senior secondary level. Classes are scheduled on Saturdays from 9am to 3pm and approximately half of the program is dedicated to mathematics. While mathematics education…

The Mathematics Syllabus and Adult Learners in Community Colleges: Integrating Technique with Content.

ERIC Educational Resources Information Center

Baker, Robert N.

2001-01-01

Presents a brief discussion of the challenges presented to mathematics education by changes in social dependence on mathematics, in professional response to the needs of students, in institutional expectations of students and teachers, and in student demographics and expectations. Provides an extended outline for a syllabus used to clearly…

Professional Development of Mathematics Teachers Implementing Probabilistic Simulations in Elementary School Classrooms

ERIC Educational Resources Information Center

de Oliveira Souza, Leandro; Lopes, Celi Espasandin; de Oliveira Mendonça, Luzinete

2014-01-01

The inclusion of statistics and probability in the mathematics curriculum has always generated challenges to mathematics teachers of elementary schools. This article discusses activities that promote the professional development of such teachers. We present part of a doctoral research study of 16 teachers in which we discuss two case studies of…

Effects of Causal Attributions Following Mathematics Tasks on Student Cognitions about a Subsequent Task

ERIC Educational Resources Information Center

Seegers, Gerard; Van Putten, Cornelis M.; Vermeer, Harriet J.

2004-01-01

The authors investigated the effects of former learning experiences on how students adapt to challenging mathematics tasks. A distinction has been made between domain-specific variables (goal orientation, self-concept of mathematics ability) and task- (or context-) specific appraisals (estimated competence for, attractiveness and relevance of the…

Mathematically Gifted in the Heterogeneously Grouped Mathematics Classroom: What Is a Teacher to Do?

ERIC Educational Resources Information Center

Reed, Catherine Finlayson

2004-01-01

Differentiation provides one method by which teachers can provide appropriate challenges at appropriate levels for all learners in a heterogeneously grouped mathematics classroom, where the range of abilities and interests can be wide. This article considers a heterogeneously grouped high school geometry class where differentiation is practiced.…

Good Questions: Great Ways to Differentiate Mathematics Instruction. Second Edition

ERIC Educational Resources Information Center

Small, Marian

2012-01-01

Expanded to include connections to Common Core State Standards, as well as National Council of Teachers of Mathematics (NCTM) standards, this critically acclaimed book will help every teacher and coach to meet the challenges of differentiating mathematics instruction in the K-8 classroom. In this bestseller, math education expert Marian Small…

The Instructor Experience of Fully Online Tertiary Mathematics: A Challenge and an Opportunity

ERIC Educational Resources Information Center

Trenholm, Sven; Alcock, Lara; Robinson, Carol

2016-01-01

As part of a dramatic recent shift in tertiary education, many undergraduate students now learn mathematics via fully online courses. At present, the mathematics education research community knows very little about this shift. The authors consider implications of an investigation into the instructor experience of fully online undergraduate…

Main Road Extraction from ZY-3 Grayscale Imagery Based on Directional Mathematical Morphology and VGI Prior Knowledge in Urban Areas

PubMed Central

Liu, Bo; Wu, Huayi; Wang, Yandong; Liu, Wenming

2015-01-01

Main road features extracted from remotely sensed imagery play an important role in many civilian and military applications, such as updating Geographic Information System (GIS) databases, urban structure analysis, spatial data matching and road navigation. Current methods for road feature extraction from high-resolution imagery are typically based on threshold value segmentation. It is difficult however, to completely separate road features from the background. We present a new method for extracting main roads from high-resolution grayscale imagery based on directional mathematical morphology and prior knowledge obtained from the Volunteered Geographic Information found in the OpenStreetMap. The two salient steps in this strategy are: (1) using directional mathematical morphology to enhance the contrast between roads and non-roads; (2) using OpenStreetMap roads as prior knowledge to segment the remotely sensed imagery. Experiments were conducted on two ZiYuan-3 images and one QuickBird high-resolution grayscale image to compare our proposed method to other commonly used techniques for road feature extraction. The results demonstrated the validity and better performance of the proposed method for urban main road feature extraction. PMID:26397832

Towards the Construction of a Framework to Deal with Routine Problems to Foster Mathematical Inquiry

ERIC Educational Resources Information Center

Santos-Trigo, Manuel; Camacho-Machin, Matias

2009-01-01

To what extent does the process of solving textbook problems help students develop a way of thinking that is consistent with mathematical practice? Can routine problems be transformed into problem solving activities that promote students' mathematical reflection? These questions are used to outline and discuss features of an inquiry framework…

Estimating the Distance to the Moon--Its Relevance to Mathematics. Core-Plus Mathematics Project.

ERIC Educational Resources Information Center

Stern, David P.

This document features an activity for estimating the distance from the earth to the moon during a solar eclipse based on calculations performed by the ancient Greek astronomer Hipparchus. Historical, mathematical, and scientific details about the calculation are provided. Internet resources for teachers to obtain more information on the subject…

The Impact of Tier 2 Mathematics Instruction on Second Graders with Mathematics Difficulties

ERIC Educational Resources Information Center

Dennis, Minyi Shih; Bryant, Brian R.; Drogan, Robin

2015-01-01

Although research on Tier 2 interventions for early mathematics is accumulating, such efforts remain far behind those for reading, especially regarding specific features such as the ideal time to begin an intervention. The present study investigated the effectiveness of a Tier 2 intervention using a single subject multiple baseline, across-groups…

ESL through Content-Area Instruction: Mathematics, Science, Social Studies. Language in Education: Theory and Practice, No. 69.

ERIC Educational Resources Information Center

Crandall, JoAnn, Ed.; And Others

Three essays focus on integrating subject matter and the English used to communicate it as a technique for teaching limited-English-proficient students. "Integrating Language and Mathematics Learning," by Theresa Corasaniti Dale and Gilberto J. Cuevas, discusses the vocabulary, syntax, semantics, and discourse features of mathematics;…

"Ms. Martin Is Secretly Teaching Us!" High School Mathematics Practices of a Teacher Striving toward Equity

ERIC Educational Resources Information Center

Dunleavy, Teresa Kathleen

2013-01-01

Attention to the pursuit of equity has been a growing priority for mathematics classrooms in the last two and a half decades. While classroom discourse has become a central feature of classrooms that strive toward equity, one continuing concern for classroom researchers in mathematics education involves understanding how and when group…

Design Approach of Mathematics Learning Activities in a Digital Environment for Children with Autism Spectrum Disorders

ERIC Educational Resources Information Center

Santos, Maria Isabel; Breda, Ana; Almeida, Ana Margarida

2017-01-01

Learning environment on mathematics for autistic children is a prototype of a digital environment with dynamic adaptation features designed to offer activities towards the development of mathematical reasoning in children aged 6-12 years, diagnosed with autism spectrum disorders (ASD), a neurodevelopmental disorder characterized by deficits in…

Student reflections on learning with challenging tasks: `I think the worksheets were just for practice, and the challenges were for maths'

NASA Astrophysics Data System (ADS)

Russo, James; Hopkins, Sarah

2017-09-01

The current study considered young students' (7 and 8 years old) experiences and perceptions of mathematics lessons involving challenging (i.e. cognitively demanding) tasks. We used the Constant Comparative Method to analyse the interview responses ( n = 73) regarding what work artefacts students were most proud of creating and why. Five themes emerged that characterised student reflections: enjoyment, effort, learning, productivity and meaningful mathematics. Overall, there was evidence that students embraced struggle and persisted when engaged in mathematics lessons involving challenging tasks and, moreover, that many students enjoyed the process of being challenged. In the second section of the paper, the lesson structure preferences of a subset of participants ( n = 23) when learning with challenging tasks are considered. Overall, more students preferred the teach-first lesson structure to the task-first lesson structure, primarily because it activated their cognition to prepare them for work on the challenging task. However, a substantial minority of students (42 %) instead endorsed the task-first lesson structure, with several students explaining they preferred this structure precisely because it was so cognitively demanding. Other reasons for preferring the task-first structure included that it allowed the focus of the lesson to be on the challenging task and the subsequent discussion of student work. A key implication of these combined findings is that, for many students, work on challenging tasks appeared to remain cognitively demanding irrespective of the structure of the lesson.

Mathematical calibration procedure of a capacitive sensor-based indexed metrology platform

NASA Astrophysics Data System (ADS)

Brau-Avila, A.; Santolaria, J.; Acero, R.; Valenzuela-Galvan, M.; Herrera-Jimenez, V. M.; Aguilar, J. J.

2017-03-01

The demand for faster and more reliable measuring tasks for the control and quality assurance of modern production systems has created new challenges for the field of coordinate metrology. Thus, the search for new solutions in coordinate metrology systems and the need for the development of existing ones still persists. One example of such a system is the portable coordinate measuring machine (PCMM), the use of which in industry has considerably increased in recent years, mostly due to its flexibility for accomplishing in-line measuring tasks as well as its reduced cost and operational advantages compared to traditional coordinate measuring machines. Nevertheless, PCMMs have a significant drawback derived from the techniques applied in the verification and optimization procedures of their kinematic parameters. These techniques are based on the capture of data with the measuring instrument from a calibrated gauge object, fixed successively in various positions so that most of the instrument measuring volume is covered, which results in time-consuming, tedious and expensive verification and optimization procedures. In this work the mathematical calibration procedure of a capacitive sensor-based indexed metrology platform (IMP) is presented. This calibration procedure is based on the readings and geometric features of six capacitive sensors and their targets with nanometer resolution. The final goal of the IMP calibration procedure is to optimize the geometric features of the capacitive sensors and their targets in order to use the optimized data in the verification procedures of PCMMs.

Mathematical models of lignin biosynthesis

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

Faraji, Mojdeh; Fonseca, Luis; Escamilla-Trevino, Luis

Lignin is a natural polymer that is interwoven with cellulose and hemicellulose within plant cell walls. Due to this molecular arrangement, lignin is a major contributor to the recalcitrance of plant materials with respect to the extraction of sugars and their fermentation into ethanol, butanol, and other potential bioenergy crops. The lignin biosynthetic pathway is similar, but not identical in different plant species. It is in each case comprised of a moderate number of enzymatic steps, but its responses to manipulations, such as gene knock-downs, are complicated by the fact that several of the key enzymes are involved in severalmore » reaction steps. This feature poses a challenge to bioenergy production, as it renders it difficult to select the most promising combinations of genetic manipulations for the optimization of lignin composition and amount.Here, we present several computational models than can aid in the analysis of data characterizing lignin biosynthesis. While minimizing technical details, we focus on the questions of what types of data are particularly useful for modeling and what genuine benefits the biofuel researcher may gain from the resulting models. We demonstrate our analysis with mathematical models for black cottonwood (Populus trichocarpa), alfalfa (Medicago truncatula), switchgrass (Panicum virgatum) and the grass Brachypodium distachyon. Despite commonality in pathway structure, different plant species show different regulatory features and distinct spatial and topological characteristics. The putative lignin biosynthes pathway is not able to explain the plant specific laboratory data, and the necessity of plant specific modeling should be heeded.« less

Mathematical models of lignin biosynthesis

DOE PAGES

Faraji, Mojdeh; Fonseca, Luis; Escamilla-Trevino, Luis; ...

2018-02-09

Lignin is a natural polymer that is interwoven with cellulose and hemicellulose within plant cell walls. Due to this molecular arrangement, lignin is a major contributor to the recalcitrance of plant materials with respect to the extraction of sugars and their fermentation into ethanol, butanol, and other potential bioenergy crops. The lignin biosynthetic pathway is similar, but not identical in different plant species. It is in each case comprised of a moderate number of enzymatic steps, but its responses to manipulations, such as gene knock-downs, are complicated by the fact that several of the key enzymes are involved in severalmore » reaction steps. This feature poses a challenge to bioenergy production, as it renders it difficult to select the most promising combinations of genetic manipulations for the optimization of lignin composition and amount.Here, we present several computational models than can aid in the analysis of data characterizing lignin biosynthesis. While minimizing technical details, we focus on the questions of what types of data are particularly useful for modeling and what genuine benefits the biofuel researcher may gain from the resulting models. We demonstrate our analysis with mathematical models for black cottonwood (Populus trichocarpa), alfalfa (Medicago truncatula), switchgrass (Panicum virgatum) and the grass Brachypodium distachyon. Despite commonality in pathway structure, different plant species show different regulatory features and distinct spatial and topological characteristics. The putative lignin biosynthes pathway is not able to explain the plant specific laboratory data, and the necessity of plant specific modeling should be heeded.« less

Fuzzy Performance between Surface Fitting and Energy Distribution in Turbulence Runner

PubMed Central

Liang, Zhongwei; Liu, Xiaochu; Ye, Bangyan; Brauwer, Richard Kars

2012-01-01

Because the application of surface fitting algorithms exerts a considerable fuzzy influence on the mathematical features of kinetic energy distribution, their relation mechanism in different external conditional parameters must be quantitatively analyzed. Through determining the kinetic energy value of each selected representative position coordinate point by calculating kinetic energy parameters, several typical algorithms of complicated surface fitting are applied for constructing microkinetic energy distribution surface models in the objective turbulence runner with those obtained kinetic energy values. On the base of calculating the newly proposed mathematical features, we construct fuzzy evaluation data sequence and present a new three-dimensional fuzzy quantitative evaluation method; then the value change tendencies of kinetic energy distribution surface features can be clearly quantified, and the fuzzy performance mechanism discipline between the performance results of surface fitting algorithms, the spatial features of turbulence kinetic energy distribution surface, and their respective environmental parameter conditions can be quantitatively analyzed in detail, which results in the acquirement of final conclusions concerning the inherent turbulence kinetic energy distribution performance mechanism and its mathematical relation. A further turbulence energy quantitative study can be ensured. PMID:23213287

The fractional volatility model: An agent-based interpretation

NASA Astrophysics Data System (ADS)

Vilela Mendes, R.

2008-06-01

Based on the criteria of mathematical simplicity and consistency with empirical market data, a model with volatility driven by fractional noise has been constructed which provides a fairly accurate mathematical parametrization of the data. Here, some features of the model are reviewed and extended to account for leverage effects. Using agent-based models, one tries to find which agent strategies and (or) properties of the financial institutions might be responsible for the features of the fractional volatility model.

Establishment of the mathematical model for diagnosing the engine valve faults by genetic programming

NASA Astrophysics Data System (ADS)

Yang, Wen-Xian

2006-05-01

Available machine fault diagnostic methods show unsatisfactory performances on both on-line and intelligent analyses because their operations involve intensive calculations and are labour intensive. Aiming at improving this situation, this paper describes the development of an intelligent approach by using the Genetic Programming (abbreviated as GP) method. Attributed to the simple calculation of the mathematical model being constructed, different kinds of machine faults may be diagnosed correctly and quickly. Moreover, human input is significantly reduced in the process of fault diagnosis. The effectiveness of the proposed strategy is validated by an illustrative example, in which three kinds of valve states inherent in a six-cylinders/four-stroke cycle diesel engine, i.e. normal condition, valve-tappet clearance and gas leakage faults, are identified. In the example, 22 mathematical functions have been specially designed and 8 easily obtained signal features are used to construct the diagnostic model. Different from existing GPs, the diagnostic tree used in the algorithm is constructed in an intelligent way by applying a power-weight coefficient to each feature. The power-weight coefficients vary adaptively between 0 and 1 during the evolutionary process. Moreover, different evolutionary strategies are employed, respectively for selecting the diagnostic features and functions, so that the mathematical functions are sufficiently utilized and in the meantime, the repeated use of signal features may be fully avoided. The experimental results are illustrated diagrammatically in the following sections.

Dispositions in the Field: Viewing Mathematics Teacher Education through the Lens of Bourdieu's Social Field Theory

ERIC Educational Resources Information Center

Nolan, Kathleen

2012-01-01

Mathematics teacher educators are confronted with numerous challenges and complexities as they work to inspire prospective teachers to embrace inquiry-based pedagogies. The research study described in this paper asks what a teacher educator and faculty advisor can learn from prospective secondary mathematics teachers as they construct (and are…

Developing a Maori Language Mathematics Lexicon: Challenges for Corpus Planning in Indigenous Language Contexts

ERIC Educational Resources Information Center

Trinick, Tony; May, Stephen

2013-01-01

Over the last 25 years, there has been significant modernisation and elaboration of the Maori language mathematics lexicon and register to support the teaching of (Western) mathematics as a component of Maori-medium schooling. These developments are situated within the wider Maori language revitalisation movement in Aotearoa/New Zealand, of which…

Implementing Reform Curriculum: Voicing the Experiences of an ESL/Mathematics Teacher

ERIC Educational Resources Information Center

Celedon-Pattichis, Sylvia

2010-01-01

The purpose of this 18-month case study is to highlight the successes and challenges that an ESL/mathematics teacher encountered as she made a shift from traditional mathematics curriculum to a standards-based curriculum as part of a statewide systemic initiative. The study was conducted in an urban, public middle school in Central Texas that…

Development of an Interactive Mathematics Learning System Based on a Two-Tier Test Diagnostic and Guiding Strategy

ERIC Educational Resources Information Center

Yang, Tzu-Chi; Fu, Hseng-Tz; Hwang, Gwo-Jen; Yang, Stephen J. H.

2017-01-01

Mathematical skills have been recognised as a core competence for engineering and science students. However, learning mathematics has been recognised as a difficult and challenging task for most students, in particular, calculus for first-year students in university. Consequently, the development of effective learning strategies and environments…

A Modular Approach to Teaching Mathematical Modeling in Biotechnology in the Undergraduate Curriculum

ERIC Educational Resources Information Center

Larripa, Kamila R.; Mazzag, Borbala

2016-01-01

Our paper describes a solution we found to a still existing need to develop mathematical modeling courses for undergraduate biology majors. Some challenges of such courses are: (i) relatively limited exposure of biology students to higher-level mathematical and computational concepts; (ii) availability of texts that can give a flavor of how…

Exploring a Structure for Mathematics Lessons That Foster Problem Solving and Reasoning

ERIC Educational Resources Information Center

Sullivan, Peter; Walker, Nadia; Borcek, Chris; Rennie, Mick

2015-01-01

While there is widespread agreement on the importance of incorporating problem solving and reasoning into mathematics classrooms, there is limited specific advice on how this can best happen. This is a report of an aspect of a project that is examining the opportunities and constraints in initiating learning by posing challenging mathematics tasks…

Teachers' Implementation of Pre-Constructed Dynamic Geometry Tasks in Technology-Intensive Algebra 1 Classrooms

ERIC Educational Resources Information Center

Cayton, Charity Sue-Adams

2012-01-01

Technology use and a focus on 21st century skills, coupled with recent adoption of Common Core State Standards for Mathematics, marks a new challenge for mathematics teachers. Communication, discourse, and tools for enhancing discourse (NCTM, 1991, 2000) play an integral role in successful implementation of technology and mathematics standards.…

Teaching Mathematics to Secondary Students with Emotional and Behavioral Disorders: Challenges and Practical Suggestions for Teachers

ERIC Educational Resources Information Center

Mulcahy, Candace A.; Krezmien, Michael; Maccini, Paula

2014-01-01

While the Common Core State Standards and state learning standards guide teachers in what mathematical content knowledge should be addressed as well as the processes and proficiencies necessary for developing mathematical competence, several student- and teacher-related factors may hinder student access to the general education curriculum for…

The Mathematics of "Star Trek"--An Honors Colloquium

ERIC Educational Resources Information Center

Karls, Michael A.

2011-01-01

After the success of a course on cryptography for a general audience, based on Simon Singh's "The Code Book" [49], I decided to try again and create a mathematics course for a general audience based on "The Physics of Star Trek" by Lawrence Krauss [32]. This article looks at the challenges of designing a physics-based mathematics course "from…

Teachers Implementing Mathematical Problem Posing in the Classroom: Challenges and Strategies

ERIC Educational Resources Information Center

Leung, Shuk-kwan S.

2013-01-01

This paper reports a study about how a teacher educator shared knowledge with teachers when they worked together to implement mathematical problem posing (MPP) in the classroom. It includes feasible methods for getting practitioners to use research-based tasks aligned to the curriculum in order to encourage children to pose mathematical problems.…

Differentiating Instruction Using a Virtual Environment: A Study of Mathematical Problem Posing among Gifted and Talented Learners

ERIC Educational Resources Information Center

Manuel, Dominic; Freiman, Viktor

2017-01-01

Meeting the needs of mathematically gifted and talented students is a challenge for educators. To support teachers of mathematically gifted and talented students to find appropriate solutions, several innovative projects were conducted in schools using funds provided by the New Brunswick, Canada, Department of Education. This article presents one…

Content Coverage Differences across Districts/States: A Persisting Challenge for U.S. Education Policy

ERIC Educational Resources Information Center

Schmidt, William H.; Cogan, Leland S.; Houang, Richard T.; McKnight, Curtis C.

2011-01-01

This article utilizes the 1999 TIMSS-R data from U.S. states and districts to explore the consequences of variation in opportunities to learn specific mathematics content. Analyses explore the relationship between classroom mathematics content coverage and student achievement as measured by the TIMSS-R international mathematics scaled score.…

Meaningful Statistics in Professional Practices as a Bridge between Mathematics and Science: An Evaluation of a Design Research Project

ERIC Educational Resources Information Center

Dierdorp, Adri; Bakker, Arthur; van Maanen, Jan A.; Eijkelhof, Harrie M. C.

2014-01-01

Background: Creating coherence between school subjects mathematics and science and making these school subjects meaningful are still topical challenges. This study investigates how students make meaningful connections between mathematics, statistics, science and applications when they engage in a specially developed unit that is based on…

Addressing Challenges in Urban Teaching, Learning and Math Using Model-Strategy-Application with Reasoning Approach in Lingustically and Culturally Diverse Classrooms

ERIC Educational Resources Information Center

Wu, Zhonghe; An, Shuhua

2016-01-01

This study examined the effects of using the Model-Strategy-Application with Reasoning Approach (MSAR) in teaching and learning mathematics in linguistically and culturally diverse elementary classrooms. Through learning mathematics via the MSAR, students from different language ability groups gained an understanding of mathematics from creating…

Challenging Assumptions: Mobile Learning for Mathematics Project in South Africa

ERIC Educational Resources Information Center

Roberts, Nicky; Vanska, Riitta

2011-01-01

This article introduces the Nokia Mobile Learning for Mathematics Project in South Africa, which made use of mobile technology to support mathematics learning at 30 public secondary schools. It draws on the evaluation of this project from January to June 2010. The article discusses learner access to mobile devices, learner and teacher uptake and…

Comparing the Achievement Goal Orientation of Mathematics Learners with and without Attention-Deficit Hyperactivity Disorder

ERIC Educational Resources Information Center

Spangenberg, Erica Dorethea

2017-01-01

Many learners with different learning challenges are accommodated in the same classroom in South Africa, which could result in poor performance in mathematics. By reinforcing or disregarding certain goals, a teacher can influence the way in which learners learn mathematics. This study compared the achievement goal orientation of Grade Nine…

Cognitive Benefits and Costs of Bilingualism in Elementary School Students: The Case of Mathematical Word Problems

ERIC Educational Resources Information Center

Kempert, Sebastian; Saalbach, Henrik; Hardy, Ilonca

2011-01-01

Previous research has emphasized the importance of language for learning mathematics. This is especially true when mathematical problems have to be extracted from a meaningful context, as in arithmetic word problems. Bilingual learners with a low command of the instructional language thus may face challenges when dealing with mathematical…

Family Mathematics Nights: An Opportunity to Improve Preservice Teachers' Understanding of Parents' Roles and Expectations

ERIC Educational Resources Information Center

Bofferding, Laura; Kastberg, Signe; Hoffman, Andrew

2016-01-01

Providing preservice teachers with opportunities to engage with parents and begin to see them as collaborators in their children's education is a persistent challenge in mathematics methods courses and teacher preparation programs more broadly. We describe the use of family mathematics nights as a model for engaging parents and preservice…

Using a Before-During-After (BDA) Model to Plan Effective Secondary Mathematics Lessons

ERIC Educational Resources Information Center

Wilburne, Jane Murphy; Peterson, Winnie

2007-01-01

Creating effective mathematics lessons can be a challenge for any teacher. One approach to design an effective lesson is using a before-during-after (BDA) format. This article describes what a BDA format is and provides two examples of how it is implemented in high school mathematics classes. (Contains 2 tables and 5 figures.)

The Affordances of Using a Flipped Classroom Approach in the Teaching of Mathematics: A Case Study of a Grade 10 Mathematics Class

ERIC Educational Resources Information Center

Muir, Tracey; Geiger, Vince

2016-01-01

Teaching secondary mathematics has a number of challenges, including the expectations that teachers cover the prescribed curriculum, help students learn difficult concepts, prepare students for future studies, and, increasingly, that they do so incorporating digital technologies. This study investigates a teacher's, and his students', perceptions…

Preservice Teachers of High School Mathematics: Success, Failure, and Persistence in the Face of Mathematical Challenges

ERIC Educational Resources Information Center

Sinicrope, Rose; Eppler, Marion; Preston, Ronald V.; Ironsmith, Marsha

2015-01-01

The goal of this study was to identify variables related to success and resilience in an undergraduate, high school mathematics teacher education program. Over a five-year period, we tracked the academic performance and achievement motivation goals of multiple cohorts of students. Students who successfully completed their degrees had higher grade…

Responding to the Challenges of Instrumental Orchestration through Physical and Virtual Robotics

ERIC Educational Resources Information Center

Haapasalo, Lenni; Samuels, Peter

2011-01-01

It has been recognised that the general lack of enjoyment of institutional mathematics learning at the secondary level is one of the basic reasons behind the bad reputation of mathematics in society. Increasing students' motivation to learn mathematics through enjoyment and playing, especially in their free time, might therefore be a relevant…

Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 4

ERIC Educational Resources Information Center

Boaler, Jo; Munson, Jen; Williams, Cathy

2017-01-01

The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the fourth-grade level through visualization, play, and…

The Priorities and Challenges of Primary Teachers' Knowledge in Their Mathematics Planning

ERIC Educational Resources Information Center

Davidson, Aylie

2016-01-01

There is growing consensus that the process of planning mathematics lessons is as complex as teaching them, yet there is limited research on this. This paper reports on one aspect of a project examining issues in primary teachers' mathematics planning. The results, taken from a questionnaire completed by 62 primary teachers, indicate that when…

Examining Elementary Pre-Service Teachers' Capacity to Use Children's Mathematical Understanding to Select and Pose Mathematical Tasks

ERIC Educational Resources Information Center

Gichobi, Mary N.

2013-01-01

The need to design teacher preparation programs to ensure that pre-service teachers (PSTs) are prepared and equipped with knowledge, skills and practices to increase the chances that they will become effective novice mathematics teachers is of prime importance. Teacher educators are facing lingering challenges, since teacher education is…

Student Performance in Mathematics: Should We Be Concerned? Evidence from a Retail Course

ERIC Educational Resources Information Center

Enderson, Mary C.; Mann, Manveer

2018-01-01

This article describes how for many college students the transition to college-level mathematics courses presents new challenges beyond those that were part of the high school experience. In this interdisciplinary study forty-four non-mathematics and non-science majors, enrolled in a retail-buying course, were studied to examine student confidence…

A College-Level Foundational Mathematics Course: Evaluation, Challenges, and Future Directions

ERIC Educational Resources Information Center

Maciejewski, Wes

2012-01-01

Recently in Ontario, Canada, the College Math Project brought to light startling data on the achievement of students in Ontario's College of Applied Arts and Technology System related to their performance in first-year mathematics courses: one-third of the students had failed their first-year mathematics course or were at risk of not completing…

Strong Is the Silence: Challenging Interlocking Systems of Privilege and Oppression in Mathematics Teacher Education

ERIC Educational Resources Information Center

Herbel-Eisenmann, Beth; Bartell, Tonya Gau; Breyfogle, M. Lynn; Bieda, Kristen; Crespo, Sandra; Dominguez, Higinio; Drake, Corey

2013-01-01

In this essay, the authors provide a rationale for the need to break the silence of privilege and oppression in mathematics education. They begin by providing a brief rationale from their personal and professional perspectives, which includes background about planning and executing the Privilege and Oppression in the Mathematics Preparation of…

Overcoming Challenges of Being an In-Field Mathematics Teacher in Indigenous Secondary School Classrooms

ERIC Educational Resources Information Center

Sandhu, Satwant; Kidman, Gillian; Cooper, Tom

2013-01-01

Queensland rural and remote schools have difficulty in attracting experienced, in-field mathematics teachers. Thus, when such teachers arrive, much is expected of them to increase the mathematics knowledge of students. This paper looks at one such teacher who, against the high expectations placed upon him as an in-field teacher, experienced…

A non-conventional discontinuous Lagrangian for viscous flow

PubMed Central

Marner, F.

2017-01-01

Drawing an analogy with quantum mechanics, a new Lagrangian is proposed for a variational formulation of the Navier–Stokes equations which to-date has remained elusive. A key feature is that the resulting Lagrangian is discontinuous in nature, posing additional challenges apropos the mathematical treatment of the related variational problem, all of which are resolvable. In addition to extending Lagrange's formalism to problems involving discontinuous behaviour, it is demonstrated that the associated equations of motion can self-consistently be interpreted within the framework of thermodynamics beyond local equilibrium, with the limiting case recovering the classical Navier–Stokes equations. Perspectives for applying the new formalism to discontinuous physical phenomena such as phase and grain boundaries, shock waves and flame fronts are provided. PMID:28386415

A non-conventional discontinuous Lagrangian for viscous flow.

PubMed

Scholle, M; Marner, F

2017-02-01

Drawing an analogy with quantum mechanics, a new Lagrangian is proposed for a variational formulation of the Navier-Stokes equations which to-date has remained elusive. A key feature is that the resulting Lagrangian is discontinuous in nature, posing additional challenges apropos the mathematical treatment of the related variational problem, all of which are resolvable. In addition to extending Lagrange's formalism to problems involving discontinuous behaviour, it is demonstrated that the associated equations of motion can self-consistently be interpreted within the framework of thermodynamics beyond local equilibrium, with the limiting case recovering the classical Navier-Stokes equations. Perspectives for applying the new formalism to discontinuous physical phenomena such as phase and grain boundaries, shock waves and flame fronts are provided.

The Acquisition of Problem-Solving Skills in Mathematics: How Animations Can Aid Understanding of Structural Problem Features and Solution Procedures

ERIC Educational Resources Information Center

Scheiter, Katharina; Gerjets, Peter; Schuh, Julia

2010-01-01

In this paper the augmentation of worked examples with animations for teaching problem-solving skills in mathematics is advocated as an effective instructional method. First, in a cognitive task analysis different knowledge prerequisites are identified for solving mathematical word problems. Second, it is argued that so called hybrid animations…

A Snapshot of the Role of the Textbook in English Secondary Mathematics Classrooms

ERIC Educational Resources Information Center

O'Keeffe, Lisa; White, Bruce

2017-01-01

The role and function of the mathematics textbook has been widely discussed since its inclusion in the Trends in International Mathematics and Science study (TIMSS) in the late nineties. It is a common feature in many classrooms worldwide and has been identified as an important vehicle for the promotion of curricula. However, there has also been…

Mathematics for the Workplace. Applications from Machine Tool Technology (Michelin Tire Corporation). A Teacher's Guide.

ERIC Educational Resources Information Center

Wallace, Johnny M.; Stewart, Grover

This module presents a real-world context in which mathematics skills (geometry and trigonometry) are used as part of a daily routine. The context is the machine tool technology field, and the module aims to help students develop the ability to analyze diagrams in order to make mathematical computations. The modules, which features applications…

Assessing Key Epistemic Features of Didactic-Mathematical Knowledge of Prospective Teachers: The Case of The Derivative

ERIC Educational Resources Information Center

Pino-Fan, Luis R.; Godino, Juan D.; Font, Vicenç

2018-01-01

In recent years, there has been a growing interest in studying the knowledge that mathematics teachers require in order for their teaching to be effective. However, only a few studies have focused on the design and application of instruments that are capable of exploring different aspects of teachers' didactic-mathematical knowledge about specific…

Influence of Teacher Support and Personal Relevance on Academic Self-Efficacy and Enjoyment of Mathematics Lessons: A Structural Equation Modeling Approach

ERIC Educational Resources Information Center

Aldridge, Jill M.; Afari, Ernest; Fraser, Barry J.

2012-01-01

The purpose of our study was to examine the effects of two psychosocial features of the classroom environment (teacher support and personal relevance) on college students' academic self-efficacy and enjoyment of mathematics lessons. Data collected from 352 mathematics students attending three higher education institutions in the United Arab…

Geogebra Applets Design and Development for Junior High School Students to Learn Quadrilateral Mathematics Concepts

ERIC Educational Resources Information Center

Nisiyatussani; Ayuningtyas, Vidya; Fathurrohman, Maman; Anriani, Nurul

2018-01-01

This design and development research was motivated by the rapid expansion and use of GeoGebra by mathematics educators (teachers and lecturers) in Indonesia. One of GeoGebra features is GeoGebra Applet that can be used, modified, and/or developed by educators for dynamic and interactive mathematics teaching and learning. At the time of research…

"Sacred Cows Make the Best Hamburger"

ERIC Educational Resources Information Center

Barger, Rita H.; McCoy, Ann C.

2009-01-01

This article describes the authors' attempts to make a college mathematics class more hands-on and interactive. The authors challenge other college mathematics instructors to try similar approaches to enhance the learning and understanding of their students.

Rotation covariant image processing for biomedical applications.

PubMed

Skibbe, Henrik; Reisert, Marco

2013-01-01

With the advent of novel biomedical 3D image acquisition techniques, the efficient and reliable analysis of volumetric images has become more and more important. The amount of data is enormous and demands an automated processing. The applications are manifold, ranging from image enhancement, image reconstruction, and image description to object/feature detection and high-level contextual feature extraction. In most scenarios, it is expected that geometric transformations alter the output in a mathematically well-defined manner. In this paper we emphasis on 3D translations and rotations. Many algorithms rely on intensity or low-order tensorial-like descriptions to fulfill this demand. This paper proposes a general mathematical framework based on mathematical concepts and theories transferred from mathematical physics and harmonic analysis into the domain of image analysis and pattern recognition. Based on two basic operations, spherical tensor differentiation and spherical tensor multiplication, we show how to design a variety of 3D image processing methods in an efficient way. The framework has already been applied to several biomedical applications ranging from feature and object detection tasks to image enhancement and image restoration techniques. In this paper, the proposed methods are applied on a variety of different 3D data modalities stemming from medical and biological sciences.

Avian Influenza spread and transmission dynamics

USGS Publications Warehouse

Bourouiba, Lydia; Gourley, Stephen A.; Liu, Rongsong; Takekawa, John Y.; Wu, Jianhong; Chen, Dongmei; Moulin, Bernard; Wu, Jianhong

2015-01-01

The spread of highly pathogenic avian influenza (HPAI) viruses of type A of subtype H5N1 has been a serious threat to global public health. Understanding the roles of various (migratory, wild, poultry) bird species in the transmission of these viruses is critical for designing and implementing effective control and intervention measures. Developing appropriate models and mathematical techniques to understand these roles and to evaluate the effectiveness of mitigation strategies have been a challenge. Recent development of the global health surveillance (especially satellite tracking and GIS techniques) and the mathematical theory of dynamical systems combined have gradually shown the promise of some cutting-edge methodologies and techniques in mathematical biology to meet this challenge.

Handbook of applied mathematics for engineers and scientists

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

Kurtz, M.

1991-12-31

This book is intended to be reference for applications of mathematics in a wide range of topics of interest to engineers and scientists. An unusual feature of this book is that it covers a large number of topics from elementary algebra, trigonometry, and calculus to computer graphics and cybernetics. The level of mathematics covers high school through about the junior level of an engineering curriculum in a major univeristy. Throughout, the emphasis is on applications of mathematics rather than on rigorous proofs.

The research of statistical properties of colorimetric features of screens with a three-component color formation principle

NASA Astrophysics Data System (ADS)

Zharinov, I. O.; Zharinov, O. O.

2017-12-01

The problem of the research is concerned with quantitative analysis of influence of technological variation of the screen color profile parameters on chromaticity coordinates of the displayed image. Some mathematical expressions which approximate the two-dimensional distribution of chromaticity coordinates of an image, which is displayed on the screen with a three-component color formation principle were proposed. Proposed mathematical expressions show the way to development of correction techniques to improve reproducibility of the colorimetric features of displays.

Smoke Ring Physics

ERIC Educational Resources Information Center

Huggins, Elisha

2011-01-01

The behavior of smoke rings, tornados, and quantized vortex rings in superfluid helium has many features in common. These features can be described by the same mathematics we use when introducing Ampere's law in an introductory physics course. We discuss these common features. (Contains 7 figures.)

Experiences Teaching a Software Aided Mathematics Course for a General University Audience.

ERIC Educational Resources Information Center

McGivney, Raymond J., Jr.

1990-01-01

Described is a nonmajor mathematics course taught using computers and lab experiments. Included are the challenge, solution, description of the first class, problems, successes, the syllabus, student comments, and the conclusion. (KR)

The education of perception.

PubMed

Goldstone, Robert L; Landy, David H; Son, Ji Y

2010-04-01

Although the field of perceptual learning has mostly been concerned with low- to middle-level changes to perceptual systems due to experience, we consider high-level perceptual changes that accompany learning in science and mathematics. In science, we explore the transfer of a scientific principle (competitive specialization) across superficially dissimilar pedagogical simulations. We argue that transfer occurs when students develop perceptual interpretations of an initial simulation and simply continue to use the same interpretational bias when interacting with a second simulation. In arithmetic and algebraic reasoning, we find that proficiency in mathematics involves executing spatially explicit transformations to notational elements. People learn to attend mathematical operations in the order in which they should be executed, and the extent to which students employ their perceptual attention in this manner is positively correlated with their mathematical experience. For both science and mathematics, relatively sophisticated performance is achieved not by ignoring perceptual features in favor of deep conceptual features, but rather by adapting perceptual processing so as to conform with and support formally sanctioned responses. These "rigged-up perceptual systems" offer a promising approach to educational reform. Copyright © 2009 Cognitive Science Society, Inc.

The Development of Mathematical Knowledge for Teaching for Quantitative Reasoning Using Video-Based Instruction

NASA Astrophysics Data System (ADS)

Walters, Charles David

Quantitative reasoning (P. W. Thompson, 1990, 1994) is a powerful mathematical tool that enables students to engage in rich problem solving across the curriculum. One way to support students' quantitative reasoning is to develop prospective secondary teachers' (PSTs) mathematical knowledge for teaching (MKT; Ball, Thames, & Phelps, 2008) related to quantitative reasoning. However, this may prove challenging, as prior to entering the classroom, PSTs often have few opportunities to develop MKT by examining and reflecting on students' thinking. Videos offer one avenue through which such opportunities are possible. In this study, I report on the design of a mini-course for PSTs that featured a series of videos created as part of a proof-of-concept NSF-funded project. These MathTalk videos highlight the ways in which the quantitative reasoning of two high school students developed over time. Using a mixed approach to grounded theory, I analyzed pre- and postinterviews using an extant coding scheme based on the Silverman and Thompson (2008) framework for the development of MKT. This analysis revealed a shift in participants' affect as well as three distinct shifts in their MKT around quantitative reasoning with distances, including shifts in: (a) quantitative reasoning; (b) point of view (decentering); and (c) orientation toward problem solving. Using the four-part focusing framework (Lobato, Hohensee, & Rhodehamel, 2013), I analyzed classroom data to account for how participants' noticing was linked with the shifts in MKT. Notably, their increased noticing of aspects of MKT around quantitative reasoning with distances, which features prominently in the MathTalk videos, seemed to contribute to the emergence of the shifts in MKT. Results from this study link elements of the learning environment to the development of specific facets of MKT around quantitative reasoning with distances. These connections suggest that vicarious experiences with two students' quantitative reasoning over time was critical for participants' development of MKT.

Using Digital Technologies in Mathematics Teaching: Developing an Understanding of the Landscape Using Three "Grand Challenge" Themes

ERIC Educational Resources Information Center

Joubert, Marie

2013-01-01

This paper develops an understanding of the issues, interests and concerns within the mathematics education community related to the use of computers and other digital technologies in the teaching and learning of mathematics. It begins by arguing for the importance of understanding this landscape of interests and concerns, and then turns to the…

The Use of a Bar Model Drawing to Teach Word Problem Solving to Students with Mathematics Difficulties

ERIC Educational Resources Information Center

Morin, Lisa L.; Watson, Silvana M. R.; Hester, Peggy; Raver, Sharon

2017-01-01

For students with mathematics difficulties (MD), math word problem solving is especially challenging. The purpose of this study was to examine the effects of a problem-solving strategy, bar model drawing, on the mathematical problem-solving skills of students with MD. The study extended previous research that suggested that schematic-based…

Building a Community of Scholars: One University's Story of Students Engaged in Learning Science, Mathematics, and Engineering through a NSF S-STEM Grant

ERIC Educational Resources Information Center

Kalevitch, Maria; Maurer, Cheryl; Badger, Paul; Holdan, Greg; Iannelli, Joe; Sirinterlikci, Arif; Semich, George; Bernauer, James

2012-01-01

The School of Engineering, Mathematics, and Science (SEMS) at Robert Morris University (RMU) was awarded a five-year grant from the National Science Foundation (NSF) to fund scholarships to 21 academically talented but financially challenged students majoring in the disciplines of science, technology, engineering, and mathematics (STEM). Each…

Teachers Perspective of Using English as a Medium of Instruction in Mathematics and Science Subjects

ERIC Educational Resources Information Center

Mansor, Norudin; Badarudin, Mohamed Ishak; Mat, Azman Che

2011-01-01

The policy of changing the medium of instruction in the teaching of mathematics and science from Bahasa Melayu to English is an important innovation affecting teachers of mathematics and science. It poses special challenges not only for teachers who have been trained in the Malay medium but also for those trained in English. This investigation…

Self-Regulated Learning: The Role of Motivation, Emotion, and Use of Learning Strategies in Students' Learning Experiences in a Self-Paced Online Mathematics Course

ERIC Educational Resources Information Center

Cho, Moon-Heum; Heron, Michele L.

2015-01-01

Enrollment in online remedial mathematics courses has increased in popularity in institutions of higher learning; however, students unskilled in self-regulated learning (SRL) find online remedial mathematics courses particularly challenging. We investigated the role of SRL, specifically motivation, emotion, and learning strategies, in students'…

Beginning a Pre-Service Teacher's Mathematical Identity Work through Narrative Rehabilitation and Bibliotherapy

ERIC Educational Resources Information Center

Lutovac, Sonja; Kaasila, Raimo

2011-01-01

In our study, we face two challenges. First, a negative view of mathematics is a widespread phenomenon among pre-service elementary teachers. Therefore, teacher education programs should find a way to handle this phenomenon. Second, we see that identity work in the domain of mathematics education needs to be conceptualized more. Here, we apply an…

Bilingual Pre-Service Teachers Grapple with the Academic and Social Role of Language in Mathematics Discussions

ERIC Educational Resources Information Center

del Rosario Zavala, Maria

2017-01-01

Effectively engaging students in mathematics discourse is challenging, especially in a language other than the one in which you learned mathematics. Teachers must manage the academic as well as social function of language. In Spanish-English bilingual classrooms in the U.S., changing the language of instruction to Spanish may not be enough to…

A Framework to Guide the Development of a Teaching Mathematics with Technology Massive Open Online Course for Educators (MOOC-Ed)

ERIC Educational Resources Information Center

Hollebrands, Karen F.

2017-01-01

Mathematics teacher educators face a challenge of preparing teachers to use technology that is rapidly changing and easily available. Teachers have access to thousands of digital tools to use with students and need guidance about how to critically choose and use tools to support students' mathematics learning. Research provides guidance to…

An oral exam model for teaching advanced "Batchelor-level" fluid mechanics in the US

NASA Astrophysics Data System (ADS)

Freund, Jonathan

2016-11-01

A teaching model is developed to meet the challenge of teaching fluid mechanics at what might be considered a high level, at least by the current norms in the US. The initial goal was to avoid loss of concepts amidst the challenge of particular mathematical manipulations on particular assignments. However, it evolved toward fostering facile working knowledge of challenging material, such as in the books by Batchelor (e.g. streaming flow), Whitham (e.g. ship waves), and van Dyke (e.g. second-order boundary layer). To this end, the course model forgoes traditional assigned problems to focus on completion, augmentation, and in-depth understanding of the lecture material. The lectures are relatively traditional in structure, albeit with somewhat more interactive examples. The main unusual feature-again, by modern US standards-was assessment via multiple half-hour oral exams. This model has now been successful over 8 semesters for 3 different graduate courses in 2 departments. For all, students were assume to have already completed a full course at a "Navier-Stokes level". The presentation will include specifics of the course and exam structure, impressions of positive outcomes from the instructor, and a summary of the overwhelmingly positive student feedback.

Geometry and Integrability

NASA Astrophysics Data System (ADS)

Mason, Lionel; Nutku, Yavuz

2003-12-01

Based on courses held at the Feza GÜrsey Institute, this collection of survey articles introduces advanced graduate students to an exciting area on the border of mathematics and mathematical physics. Including articles by key names such as Calogero, Donagi and Mason, it features the algebro-geometric material from Donagi as well as the twistor space methods in Woodhouse's contribution, forming a bridge between the pure mathematics and the more physical approaches.

Crazing in Polymeric and Composite Systems

DTIC Science & Technology

1990-04-23

these physical variations into consideration in any mathematical modeling and formulation in analyzing the stresses from the time when crazes incept to...as boundary tractions with great strength; any governing mathematical formulation must include this feature for any adequate analysis. Crazes of...constants the mathematical model describing the crazing mechanism have been successful [25-29]. References 1 J. A. Sauer, J. Marin and C. C. Hsiao, J. App

Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (30th, Prague, Czech Republic, July 16-21, 2006). Volume 4

ERIC Educational Resources Information Center

Novotna, Jarmila, Ed.; Moraova, Hana, Ed.; Kratka, Magdalena, Ed.; Stehlikova, Nad'a, Ed.

2006-01-01

This document contains the fourth volume of the proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 59 research reports by presenters with last names beginning between Kun and…

Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (30th, Prague, Czech Republic, July 16-21, 2006). Volume 2

ERIC Educational Resources Information Center

Novotna, Jarmila, Ed.; Moraova, Hana, Ed.; Kratka, Magdalena, Ed.; Stehlikova, Nad'a, Ed.

2006-01-01

This document contains the second volume of the proceedings of the 30th Annual Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 60 research reports by presenters with last names beginning between Abr…

Mathematical methods in systems biology.

PubMed

Kashdan, Eugene; Duncan, Dominique; Parnell, Andrew; Schattler, Heinz

2016-12-01

The editors of this Special Issue of Mathematical Biosciences and Engineering were the organizers for the Third International Workshop "Mathematical Methods in System Biology" that took place on June 15-18, 2015 at the University College Dublin in Ireland. As stated in the workshop goals, we managed to attract a good mix of mathematicians and statisticians working on biological and medical applications with biologists and clinicians interested in presenting their challenging problems and looking to find mathematical and statistical tools for their solutions.

Connectivity inference from neural recording data: Challenges, mathematical bases and research directions.

PubMed

Magrans de Abril, Ildefons; Yoshimoto, Junichiro; Doya, Kenji

2018-06-01

This article presents a review of computational methods for connectivity inference from neural activity data derived from multi-electrode recordings or fluorescence imaging. We first identify biophysical and technical challenges in connectivity inference along the data processing pipeline. We then review connectivity inference methods based on two major mathematical foundations, namely, descriptive model-free approaches and generative model-based approaches. We investigate representative studies in both categories and clarify which challenges have been addressed by which method. We further identify critical open issues and possible research directions. Copyright © 2018 The Author(s). Published by Elsevier Ltd.. All rights reserved.

Meeting the Challenges of Diversity and Relevance.

ERIC Educational Resources Information Center

Schwan-Smith, Margaret; Silver, Edward A.

1995-01-01

Discusses the QUASAR Project, which has worked with middle school teachers in disadvantaged communities in order to help increase the relevance of mathematics by making connections between the mathematics taught in school and the lives of students. (16 references) (MKR)

Problem solving in the borderland between mathematics and physics

NASA Astrophysics Data System (ADS)

Jensen, Jens Højgaard; Niss, Martin; Jankvist, Uffe Thomas

2017-01-01

The article addresses the problématique of where mathematization is taught in the educational system, and who teaches it. Mathematization is usually not a part of mathematics programs at the upper secondary level, but we argue that physics teaching has something to offer in this respect, if it focuses on solving so-called unformalized problems, where a major challenge is to formalize the problems in mathematics and physics terms. We analyse four concrete examples of unformalized problems for which the formalization involves different order of mathematization and applying physics to the problem, but all require mathematization. The analysis leads to the formulation of a model by which we attempt to capture the important steps of the process of solving unformalized problems by means of mathematization and physicalization.

Statistical Teleodynamics: Toward a Theory of Emergence.

PubMed

Venkatasubramanian, Venkat

2017-10-24

The central scientific challenge of the 21st century is developing a mathematical theory of emergence that can explain and predict phenomena such as consciousness and self-awareness. The most successful research program of the 20th century, reductionism, which goes from the whole to parts, seems unable to address this challenge. This is because addressing this challenge inherently requires an opposite approach, going from parts to the whole. In addition, reductionism, by the very nature of its inquiry, typically does not concern itself with teleology or purposeful behavior. Modeling emergence, in contrast, requires the addressing of teleology. Together, these two requirements present a formidable challenge in developing a successful mathematical theory of emergence. In this article, I describe a new theory of emergence, called statistical teleodynamics, that addresses certain aspects of the general problem. Statistical teleodynamics is a mathematical framework that unifies three seemingly disparate domains-purpose-free entities in statistical mechanics, human engineered teleological systems in systems engineering, and nature-evolved teleological systems in biology and sociology-within the same conceptual formalism. This theory rests on several key conceptual insights, the most important one being the recognition that entropy mathematically models the concept of fairness in economics and philosophy and, equivalently, the concept of robustness in systems engineering. These insights help prove that the fairest inequality of income is a log-normal distribution, which will emerge naturally at equilibrium in an ideal free market society. Similarly, the theory predicts the emergence of the three classes of network organization-exponential, scale-free, and Poisson-seen widely in a variety of domains. Statistical teleodynamics is the natural generalization of statistical thermodynamics, the most successful parts-to-whole systems theory to date, but this generalization is only a modest step toward a more comprehensive mathematical theory of emergence.

Are quantum-mechanical-like models possible, or necessary, outside quantum physics?

NASA Astrophysics Data System (ADS)

Plotnitsky, Arkady

2014-12-01

This article examines some experimental conditions that invite and possibly require recourse to quantum-mechanical-like mathematical models (QMLMs), models based on the key mathematical features of quantum mechanics, in scientific fields outside physics, such as biology, cognitive psychology, or economics. In particular, I consider whether the following two correlative features of quantum phenomena that were decisive for establishing the mathematical formalism of quantum mechanics play similarly important roles in QMLMs elsewhere. The first is the individuality and discreteness of quantum phenomena, and the second is the irreducibly probabilistic nature of our predictions concerning them, coupled to the particular character of the probabilities involved, as different from the character of probabilities found in classical physics. I also argue that these features could be interpreted in terms of a particular form of epistemology that suspends and even precludes a causal and, in the first place, realist description of quantum objects and processes. This epistemology limits the descriptive capacity of quantum theory to the description, classical in nature, of the observed quantum phenomena manifested in measuring instruments. Quantum mechanics itself only provides descriptions, probabilistic in nature, concerning numerical data pertaining to such phenomena, without offering a physical description of quantum objects and processes. While QMLMs share their use of the quantum-mechanical or analogous mathematical formalism, they may differ by the roles, if any, the two features in question play in them and by different ways of interpreting the phenomena they considered and this formalism itself. This article will address those differences as well.

Case Study of a Successful Educational Partnership: University of Illinois at Urbana-Champaign and the Illinois Mathematics and Science Academy

ERIC Educational Resources Information Center

DeVol, Dave

2014-01-01

When the Illinois Mathematics and Science Academy (IMSA) was founded in 1985, the state of Illinois charged IMSA with two mandates: (1) "The primary role of the Academy shall be to offer a uniquely challenging education for students talented in the areas of mathematics and science." (2) "The Academy shall also carry a responsibility…

Conceptual and Procedural Approaches to Mathematics in the Engineering Curriculum--Comparing Views of Junior and Senior Engineering Students in Two Countries

ERIC Educational Resources Information Center

Bergsten, Christer; Engelbrecht, Johann; Kågesten, Owe

2017-01-01

One challenge for an optimal design of the mathematical components in engineering education curricula is to understand how the procedural and conceptual dimensions of mathematical work can be matched with different demands and contexts from the education and practice of engineers. The focus in this paper is on how engineering students respond to…

Building a Community of Scholars: One University's Story of Students Engaged in Learning Science, Mathematics, and Engineering through a NSF S-STEM Grant--Part II

ERIC Educational Resources Information Center

Kalevitch, Maria; Maurer, Cheryl; Badger, Paul; Holdan, Greg; Sirinterlikci, Arif

2015-01-01

The School of Engineering, Mathematics, and Science (SEMS) at Robert Morris University (RMU) was awarded a five-year grant from the National Science Foundation (NSF) to fund scholarships to 21 academically talented but financially challenged students majoring in the disciplines of science, technology, engineering, and mathematics (STEM). Each…

The Implementation and Effects of the Mathematics Design Collaborative (MDC): Early Findings from Kentucky Ninth-Grade Algebra 1 Courses. CRESST Report 845

ERIC Educational Resources Information Center

Herman, Joan L.; Matrundola, Deborah La Torre; Epstein, Scott; Leon, Seth; Dai, Yunyun; Reber, Sarah; Choi, Kilchan

2015-01-01

With support from the Bill and Melinda Gates Foundation, researchers and experts in mathematics education developed the Mathematics Design Collaborative (MDC) as a strategy to support the transition to Common Core State Standards in math. MDC provides short formative assessment lessons known as Classroom Challenges for use in middle and high…

Love It, Like It, or Leave It--Elementary Preservice Teachers' Field-Based Perspectives toward the Integration of Literature in Mathematics

ERIC Educational Resources Information Center

Nesmith, Suzanne M.; Purdum-Cassidy, Barbara; Cooper, Sandi; Rogers, Rachelle D.

2017-01-01

Integrating literature in mathematics is a powerful strategy used by many teachers to meet the reformative goals outlined by the National Council of Teachers of Mathematics. This article reports a teacher education study in which 15 elementary preservice teachers engaged in a task that challenged them to link the pedagogical strategy of…

Proceedings of the Annual Meeting of the International Group for the Psychology of Mathematics Education (PME) (28th, Bergen, Norway, July 14-18, 2004). Volume 1

ERIC Educational Resources Information Center

Hoines, Marit Johnsen, Ed.; ; Fuglestad, Anne Berit, Ed.

2004-01-01

This document contains the first volume of the proceedings of the 28th Annual Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Inclusion and Diversity". In total, 147 presentations centered around the vision of mathematics for all. This volume features eight…

Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (30th, Prague, Czech Republic, July 16-21, 2006). Volume 3

ERIC Educational Resources Information Center

Novotna, Jarmila, Ed.; Moraova, Hana, Ed.; Kratka, Magdalena, Ed.; Stehlikova, Nad'a, Ed.

2006-01-01

This document contains the third volume of the proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 60 research reports by presenters with last names beginning between Ead and Kou:…

Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (30th, Prague, Czech Republic, July 16-21, 2006). Volume 5

ERIC Educational Resources Information Center

Novotna, Jarmila, Ed.; Moraova, Hana, Ed.; Kratka, Magdalena, Ed.; Stehlikova, Nad'a, Ed.

2006-01-01

This document contains the fifth volume of the proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 59 research reports by presenters with last names beginning between Sac and Zaz:…

ACER Mathematics Profile Series: Number Test. (Test Booklet, Answer and Record Sheet, Score Key, and Teachers Handbook).

ERIC Educational Resources Information Center

Cornish, Greg; Wines, Robin

The Number Test of the ACER Mathematics Profile Series, contains 30 items, for each of three suggested grade levels: 7-8, 8-9, and 9-10. Raw scores on all tests in the ACER Mathematics Profile Series (Number, Operations, Space and Measurement) are converted to a common scale called MAPS, a major feature of the Series. Based on the Rasch Model,…

Multiscale mathematical modeling of the hypothalamo-pituitary-gonadal axis.

PubMed

Clément, Frédérique

2016-07-01

Although the fields of systems and integrative biology are in full expansion, few teams are involved worldwide into the study of reproductive function from the mathematical modeling viewpoint. This may be due to the fact that the reproductive function is not compulsory for individual organism survival, even if it is for species survival. Alternatively, the complexity of reproductive physiology may be discouraging. Indeed, the hypothalamo-pituitary-gonadal (HPG) axis involves not only several organs and tissues but also intricate time (from the neuronal millisecond timescale to circannual rhythmicity) and space (from molecules to organs) scales. Yet, mathematical modeling, and especially multiscale modeling, can renew our approaches of the molecular, cellular, and physiological processes underlying the control of reproductive functions. In turn, the remarkable dynamic features exhibited by the HPG axis raise intriguing and challenging questions to modelers and applied mathematicians. In this article, we draw a panoramic review of some mathematical models designed in the framework of the female HPG, with a special focus on the gonadal and central control of follicular development. On the gonadal side, the modeling of follicular development calls to the generic formalism of structured cell populations, that allows one to make mechanistic links between the control of cell fate (proliferation, differentiation, or apoptosis) and that of the follicle fate (ovulation or degeneration) or to investigate how the functional interactions between the oocyte and its surrounding cells shape the follicle morphogenesis. On the central, mainly hypothalamic side, models based on dynamical systems with multiple timescales allow one to represent within a single framework both the pulsatile and surge patterns of the neurohormone GnRH. Beyond their interest in basic research investigations, mathematical models can also be at the source of useful tools to study the encoding and decoding of the (neuro-) hormonal signals at play within the HPG axis and detect complex, possibly hidden rhythms, in experimental time series. Copyright © 2016 Elsevier Inc. All rights reserved.

On the interplay between mathematics and biology. Hallmarks toward a new systems biology

NASA Astrophysics Data System (ADS)

Bellomo, Nicola; Elaiw, Ahmed; Althiabi, Abdullah M.; Alghamdi, Mohammed Ali

2015-03-01

This paper proposes a critical analysis of the existing literature on mathematical tools developed toward systems biology approaches and, out of this overview, develops a new approach whose main features can be briefly summarized as follows: derivation of mathematical structures suitable to capture the complexity of biological, hence living, systems, modeling, by appropriate mathematical tools, Darwinian type dynamics, namely mutations followed by selection and evolution. Moreover, multiscale methods to move from genes to cells, and from cells to tissue are analyzed in view of a new systems biology approach.

Rotation Covariant Image Processing for Biomedical Applications

PubMed Central

Reisert, Marco

2013-01-01

With the advent of novel biomedical 3D image acquisition techniques, the efficient and reliable analysis of volumetric images has become more and more important. The amount of data is enormous and demands an automated processing. The applications are manifold, ranging from image enhancement, image reconstruction, and image description to object/feature detection and high-level contextual feature extraction. In most scenarios, it is expected that geometric transformations alter the output in a mathematically well-defined manner. In this paper we emphasis on 3D translations and rotations. Many algorithms rely on intensity or low-order tensorial-like descriptions to fulfill this demand. This paper proposes a general mathematical framework based on mathematical concepts and theories transferred from mathematical physics and harmonic analysis into the domain of image analysis and pattern recognition. Based on two basic operations, spherical tensor differentiation and spherical tensor multiplication, we show how to design a variety of 3D image processing methods in an efficient way. The framework has already been applied to several biomedical applications ranging from feature and object detection tasks to image enhancement and image restoration techniques. In this paper, the proposed methods are applied on a variety of different 3D data modalities stemming from medical and biological sciences. PMID:23710255

Teaching Secondary Mathematics. Second Edition.

ERIC Educational Resources Information Center

Brumbaugh, Douglas K.; Rock, David

This book for future mathematics teachers emphasizes technology as a teaching tool; development of teachers who are self-motivated, lifelong learners; and pedagogical features that engage and motivate students. It includes examples and activities to enhance learning. Part 1, "General Fundamentals," includes (1) "Introduction"; (2) "Learning,…

Effective Instruction: A Mathematics Coach's Perspective

ERIC Educational Resources Information Center

Nebesniak, Amy L.

2012-01-01

Effective instruction is multifaceted, dependent largely on the context and, consequently, on numerous variables. Although "effective instruction" is difficult to define, in the author's experience--and as the work of mathematics education specialists and researchers indicates--three key features of quality instruction stand out: (1) Teaching…

Progress in Modeling Nonlinear Dendritic Evolution in Two and Three Dimensions, and Its Mathematical Justification

NASA Technical Reports Server (NTRS)

Tanveer, S.; Foster, M. R.

2002-01-01

We report progress in three areas of investigation related to dendritic crystal growth. Those items include: 1. Selection of tip features dendritic crystal growth; 2) Investigation of nonlinear evolution for two-sided model; and 3) Rigorous mathematical justification.

A New Wave in Applied Mathematics.

ERIC Educational Resources Information Center

Cipra, Barry A.

1990-01-01

Discussed is wavelet theory, which provides ways to rearrange data to reveal features of a physical or mathematical system which might otherwise be hidden. This theory is compared to fourier analysis and the advantages of wavelet theory are stressed. Applications of this technique are suggested. (CW)

The Literacy Component of Mathematical and Scientific Literacy

ERIC Educational Resources Information Center

Yore, Larry D.; Pimm, David; Tuan, Hsiao-Lin

2007-01-01

This opening article of the Special Issue makes an argument for parallel definitions of scientific literacy and mathematical literacy that have shared features: importance of general cognitive and metacognitive abilities and reasoning/thinking and discipline-specific language, habits-of-mind/emotional dispositions, and information communication…

A Mathematical Model of Marine Diesel Engine Speed Control System

NASA Astrophysics Data System (ADS)

Sinha, Rajendra Prasad; Balaji, Rajoo

2018-02-01

Diesel engine is inherently an unstable machine and requires a reliable control system to regulate its speed for safe and efficient operation. Also, the diesel engine may operate at fixed or variable speeds depending upon user's needs and accordingly the speed control system should have essential features to fulfil these requirements. This paper proposes a mathematical model of a marine diesel engine speed control system with droop governing function. The mathematical model includes static and dynamic characteristics of the control loop components. Model of static characteristic of the rotating fly weights speed sensing element provides an insight into the speed droop features of the speed controller. Because of big size and large time delay, the turbo charged diesel engine is represented as a first order system or sometimes even simplified to a pure integrator with constant gain which is considered acceptable in control literature. The proposed model is mathematically less complex and quick to use for preliminary analysis of the diesel engine speed controller performance.

Mathematics and its value for engineering students: what are the implications for teaching?

NASA Astrophysics Data System (ADS)

Harris, Diane; Black, Laura; Hernandez-Martinez, Paul; Pepin, Birgit; Williams, Julian; with the TransMaths Team

2015-04-01

Mathematics has long been known to be problematic for university engineering students and their teachers, for example, Scanlan.[1] This paper presents recent data gathered from interviews with engineering students who experienced problems with mathematics and their lecturers during their transition through the first year in different programme contexts. Our interviews with the students reveal how they understand the relation between engineering and mathematics and we draw on the concept of 'use- and exchange-value' to explore this relationship more fully. This paper challenges both the pedagogical practice of teaching non-contextualized mathematics and the lack of transparency regarding the significance of mathematics to engineering. We conclude that the value of mathematics in engineering remains a central problem, and argue that mathematics should be a fundamental concern in the design and practice of first-year engineering.

Real-time quasi-3D tomographic reconstruction

NASA Astrophysics Data System (ADS)

Buurlage, Jan-Willem; Kohr, Holger; Palenstijn, Willem Jan; Joost Batenburg, K.

2018-06-01

Developments in acquisition technology and a growing need for time-resolved experiments pose great computational challenges in tomography. In addition, access to reconstructions in real time is a highly demanded feature but has so far been out of reach. We show that by exploiting the mathematical properties of filtered backprojection-type methods, having access to real-time reconstructions of arbitrarily oriented slices becomes feasible. Furthermore, we present , software for visualization and on-demand reconstruction of slices. A user of can interactively shift and rotate slices in a GUI, while the software updates the slice in real time. For certain use cases, the possibility to study arbitrarily oriented slices in real time directly from the measured data provides sufficient visual and quantitative insight. Two such applications are discussed in this article.

An RBF-based reparameterization method for constrained texture mapping.

PubMed

Yu, Hongchuan; Lee, Tong-Yee; Yeh, I-Cheng; Yang, Xiaosong; Li, Wenxi; Zhang, Jian J

2012-07-01

Texture mapping has long been used in computer graphics to enhance the realism of virtual scenes. However, to match the 3D model feature points with the corresponding pixels in a texture image, surface parameterization must satisfy specific positional constraints. However, despite numerous research efforts, the construction of a mathematically robust, foldover-free parameterization that is subject to positional constraints continues to be a challenge. In the present paper, this foldover problem is addressed by developing radial basis function (RBF)-based reparameterization. Given initial 2D embedding of a 3D surface, the proposed method can reparameterize 2D embedding into a foldover-free 2D mesh, satisfying a set of user-specified constraint points. In addition, this approach is mesh free. Therefore, generating smooth texture mapping results is possible without extra smoothing optimization.

Supporting Assessment in Undergraduate Mathematics

ERIC Educational Resources Information Center

Steen, Lynn Arthur, Ed.

2006-01-01

This publication contains 29 case studies offering lessons learned during a four year NSF-supported MAA project designed to support mathematicians and mathematics departments in the increasingly important challenge of assessing student learning. Three introductory essays set assessment in broader academic and national contexts; an appendix…

Generalization across Domains: The Relating-Forming-Extending Generalization Framework

ERIC Educational Resources Information Center

Ellis, Amy; Tillema, Erik; Lockwood, Elise; Moore, Kevin

2017-01-01

Generalization is a critical aspect of doing mathematics, with policy makers recommending that it be a central component of mathematics instruction at all levels. This recommendation poses serious challenges, however, given researchers consistently identifying students' difficulties in creating and expressing normative mathematical…

An Investigation of the Effects on Students' Attitudes, Beliefs, and Abilities in Problem Solving and Mathematics after One Year of a Systematic Approach to the Learning of Problem Solving.

ERIC Educational Resources Information Center

Higgins, Karen M.

This study investigated the effects of Oregon's Lane County "Problem Solving in Mathematics" (PSM) materials on middle-school students' attitudes, beliefs, and abilities in problem solving and mathematics. The instructional approach advocated in PSM includes: the direct teaching of five problem-solving skills, weekly challenge problems,…

The Motivation and Identity Challenges for PhD Holders in the Transition to Science and Mathematics Teaching in Secondary Education: A Pilot Study

ERIC Educational Resources Information Center

Whannell, Robert; Allen, Bill

2014-01-01

Australian secondary education has endured a chronic shortage of qualified mathematics and science teachers for a number of years, particularly in rural and remote areas. A longitudinal research project examining the capacity for the holders of PhD level qualifications in mathematics and science to be utilised as one means of addressing this…

Building innovative and creative character through mathematics

NASA Astrophysics Data System (ADS)

Suyitno, Hardi; Suyitno, Amin

2018-03-01

21st century is predicted as the century with rapid development in all aspects of life. People require creative and innovative character to exist. Specifically, mathematics has been given to students from the kindergarten until the middle school. Thus, building character through mathematics should begin since the early age. The problem is how to build creative and innovative character through mathematics education? The goal expected from this question is to build innovative and creative characters to face the challenges of the 21st century. This article discusses the values of mathematics, the values in mathematics education, innovative and creative character, and the integration of these values in teaching mathematics that support the innovative and creative character building, and applying the values in structurely programmed, measurable, and applicable learning activities.

Using Curriculum-Based Measurement To Monitor Kindergarteners' Mathematics Development

ERIC Educational Resources Information Center

Seethaler, Pamela M.; Fuchs, Lynn S.

2011-01-01

The purpose of this study was to examine technical and instructional features of a kindergarten curriculum-based measurement (CBM) tool designed to track students' mathematics progress in terms of computational concepts, procedures, and counting strategies. Students in 10 kindergarten classrooms in three elementary schools completed alternate…

TexTile Math: Multicultural Explorations through Patterns. Grades 3-6.

ERIC Educational Resources Information Center

Franco, Betsy

This book features 34 reproducible student activities exploring textile design through a combination of mathematics, art, and multicultural education. Using colorful squares and triangles, students explore geometry, numbers, area, fractions, logic, and discrete mathematics, while incorporating multicultural themes in the study. The teacher page…

Strategically Fostering Dynamic Interactive Environments

ERIC Educational Resources Information Center

Özgün-Koca, S. Asli

2016-01-01

The Common Core State Standards (CCSSI 2010) and NCTM's (2014) "Principles to Actions" agree that "for meaningful learning of mathematics, tools and technology must be indispensable features of the classroom . . . that support students in exploring mathematics as well as in making sense of concepts and procedures and engaging in…

3-D Numerical Simulations of Biofilm Dynamics with Quorum Sensing in a Flow Cell

DTIC Science & Technology

2014-01-01

resistant mutants [?]. Inspired by experimental findings, researchers have come up with some mathematical models to study biofilm formation and function...develop a full 3D mathematical model to study how quorum sensing regulates biofilm formation and development as well as the pros and cons of quorum...have given an overview of current advances in mathematical modeling of biofilms. Concerning coupling biofilm growth with quorum sensing features

Multiple Paths to Mathematics Practice in Al-Kashi's Key to Arithmetic

NASA Astrophysics Data System (ADS)

Taani, Osama

2014-01-01

In this paper, I discuss one of the most distinguishing features of Jamshid al-Kashi's pedagogy from his Key to Arithmetic, a well-known Arabic mathematics textbook from the fifteenth century. This feature is the multiple paths that he includes to find a desired result. In the first section light is shed on al-Kashi's life and his contributions to mathematics and astronomy. Section 2 starts with a brief discussion of the contents and pedagogy of the Key to Arithmetic. Al-Kashi's multiple approaches are discussed through four different examples of his versatility in presenting a topic from multiple perspectives. These examples are multiple definitions, multiple algorithms, multiple formulas, and multiple methods for solving word problems. Section 3 is devoted to some benefits that can be gained by implementing al-Kashi's multiple paths approach in modern curricula. For this discussion, examples from two teaching modules taken from the Key to Arithmetic and implemented in Pre-Calculus and mathematics courses for preservice teachers are discussed. Also, the conclusions are supported by some aspects of these modules. This paper is an attempt to help mathematics educators explore more benefits from reading from original sources.

The first international workshop on the role and impact of mathematics in medicine: A collective account

PubMed Central

Artzrouni, Marc; Begg, Colin; Chabiniok, Radomir; Clairambault, Jean; Foss, AJE; Hargrove, John; Lee, Eva K; Siggers, Jennifer H; Tindall, Marcus

2011-01-01

The First International Workshop on The Role and Impact of Mathematics in Medicine (RIMM) convened in Paris in June 2010. A broad range of researchers discussed the difficulties, challenges and opportunities faced by those wishing to see mathematical methods contribute to improved medical outcomes. Finding mechanisms for interdisciplinary meetings, developing a common language, staying focused on the medical problem at hand, deriving realistic mathematical solutions, obtaining high quality data and seeing things through “by the bedside” are some of the issues discussed by the participants.

Can modeling of HIV treatment processes improve outcomes? Capitalizing on an operations research approach to the global pandemic

PubMed Central

Xiong, Wei; Hupert, Nathaniel; Hollingsworth, Eric B; O'Brien, Megan E; Fast, Jessica; Rodriguez, William R

2008-01-01

Background Mathematical modeling has been applied to a range of policy-level decisions on resource allocation for HIV care and treatment. We describe the application of classic operations research (OR) techniques to address logistical and resource management challenges in HIV treatment scale-up activities in resource-limited countries. Methods We review and categorize several of the major logistical and operational problems encountered over the last decade in the global scale-up of HIV care and antiretroviral treatment for people with AIDS. While there are unique features of HIV care and treatment that pose significant challenges to effective modeling and service improvement, we identify several analogous OR-based solutions that have been developed in the service, industrial, and health sectors. Results HIV treatment scale-up includes many processes that are amenable to mathematical and simulation modeling, including forecasting future demand for services; locating and sizing facilities for maximal efficiency; and determining optimal staffing levels at clinical centers. Optimization of clinical and logistical processes through modeling may improve outcomes, but successful OR-based interventions will require contextualization of response strategies, including appreciation of both existing health care systems and limitations in local health workforces. Conclusion The modeling techniques developed in the engineering field of operations research have wide potential application to the variety of logistical problems encountered in HIV treatment scale-up in resource-limited settings. Increasing the number of cross-disciplinary collaborations between engineering and public health will help speed the appropriate development and application of these tools. PMID:18680594

Methods of Mathematical and Computational Physics for Industry, Science, and Technology

NASA Astrophysics Data System (ADS)

Melnik, Roderick V. N.; Voss, Frands

2006-11-01

Many industrial problems provide scientists with important and challenging problems that need to be solved today rather than tomorrow. The key role of mathematical physics, modelling, and computational methodologies in addressing such problems continues to increase. Science has never been exogenous to applied research. Gigantic ships and steam engines, repeating catapult of Dionysius and the Antikythera `computer' invented around 80BC are just a few examples demonstrating a profound link between theoretical and applied science in the ancient world. Nowadays, many industrial problems are typically approached by groups of researchers who are working as a team bringing their expertise to the success of the entire enterprise. Since the late 1960s several groups of European mathematicians and scientists have started organizing regular meetings, seeking new challenges from industry and contributing to the solution of important industrial problems. In particular, this often took the format of week-long workshops originally initiated by the Oxford Study Groups with Industry in 1968. Such workshops are now held in many European countries (typically under the auspices of the European Study Groups with Industry - ESGI), as well as in Australia, Canada, the United States, and other countries around the world. Problems given by industrial partners are sometimes very difficult to complete within a week. However, during a week of brainstorming activities these problems inevitably stimulate developing fruitful new ideas, new approaches, and new collaborations. At the same time, there are cases where as soon as the problem is formulated mathematically, it is relatively easy to solve. Hence, putting the industrial problem into a mathematical framework, based on physical laws, often provides a key element to the success. In addition to this important first step, the value in such cases is the real, practical applicability of the results obtained for an industrial partner who presents the problem. Under both outlined scenarios, scientists and mathematicians are provided with an opportunity to challenge themselves with real-world problems and to work together in a team on important industrial issues. This issue is a result of selected contributions by participants of the meeting that took place in the Sønderborg area of Denmark, one of the most important centers for information technology, telecommunication and electronics in the country. The meeting was hosted by the University of Southern Denmark in a picturesque area of Southern Jutland. It brought together about 65 participants, among whom were professional mathematicians, engineers, physicists, and industrial participants. The meeting was a truly international one, with delegates from four major Danish Universities, the UK, Norway, Italy, Czech Republic, Turkey, China, Germany, Latvia, Canada, the United States, and Finland. Five challenging projects were presented by leading industrial companies, including Grundfos, Danfoss Industrial Control, Unisensor, and Danfoss Flow Division (now Siemens). The meeting featured also the Mathematics for Industry Workshop with several distinguished international speakers. This volume of Journal of Physics: Conference Series on `Methods of Mathematical and Computational Physics for Industry, Science, and Technology' contains contributions from some of the participants of the workshop as well as the papers produced as a result of collaborative efforts with the above mentioned industrial companies. We would like to thank all authors and participants for their contributions and for bearing with us during the review process and preparation of this issue. We thank also all our referees for their timely and detailed reports. The publication of the proceedings of this meeting in Denmark was delayed due to problems with a previous publisher. We are very grateful that Journal of Physics: Conference Series kindly agreed to publish the proceedings rapidly at this late stage. As industrial problems become increasingly multidisciplinary, their successful solutions are often contingent on effective collaborative efforts between scientists, mathematicians, industrialists, and engineers. This volume has provided several examples of such collaborative efforts in the context of real-world industrial problems along with the analysis of important physics-based mathematical models applicable in a range of industrial contexts. Roderick V N Melnik, Professor of Mathematical Modelling, Syddansk Universitet (Denmark) and Professor and Canada Research Chair, Wilfrid Laurier University, Waterloo, Canada E-mail: rmelnik@wlu.ca Frands Voss, Director of the Mads Clausen Institute, Syddansk Universitet (Denmark)

Supporting metacognitive monitoring in mathematics learning for young people with autism spectrum disorder: A classroom-based study.

PubMed

Maras, Katie; Gamble, Tim; Brosnan, Mark

2017-10-01

Previous research suggests impaired metacognitive monitoring and mathematics under-achievement in autism spectrum disorder. Within educational settings, metacognitive monitoring is supported through the provision of feedback (e.g. with goal reminders and by explicitly correcting errors). Given the strength of the relationship between metacognition, learning and educational attainment, this research tested new computer-based metacognitive support (the 'Maths Challenge') for mathematics learners with autism spectrum disorder within the context of their classroom. The Maths Challenge required learners to engage in metacognitive monitoring before and after answering each question (e.g. intentions and judgements of accuracy) and negotiate with the system the level of difficulty. Forty secondary school children with autism spectrum disorder and 95 typically developing learners completed the Maths Challenge in either a Feedback condition, with metacognitive monitoring support regarding the accuracy of their answers, goal reminders and strategy support, or with No Feedback. Contrary to previous findings, learners with autism showed an undiminished ability to detect errors. They did, however, demonstrate reduced cohesion between their pre- and post-test intentions. Crucially, support from the Feedback condition significantly improved task performance for both groups. Findings highlight important implications for educational interventions regarding the provision of metacognitive support for learners with autism to ameliorate under-performance in mathematics within the classroom.

Social Justice in the Mathematics Classroom

ERIC Educational Resources Information Center

Wright, Pete

2016-01-01

Despite increases in educational attainment in London, too many mathematics lessons remain focused on factual recall and procedural understanding,resulting in disaffection among learners. This study reports on the establishment of a research group, comprising five teacher researchers and myself, which aimed to challenge this situation through…

Making STEM Real

ERIC Educational Resources Information Center

Hoachlander, Gary; Yanofsky, Dave

2011-01-01

In too many schools, science and mathematics are taught separately with little or no attention to technology and engineering. Also, science and mathematics tend to function in isolation from other core subjects. In California, Linked Learning: Pathways to College and Career Success connects core academics to challenging professional and technical…

This Rock 'n' Roll Video Teaches Math

ERIC Educational Resources Information Center

Niess, Margaret L.; Walker, Janet M.

2009-01-01

Mathematics is a discipline that has significantly advanced through the use of digital technologies with improved computational, graphical, and symbolic capabilities. Digital videos can be used to present challenging mathematical questions for students. Video clips offer instructional possibilities for moving students from a passive mode of…

Nurturing Young Student Mathematicians

ERIC Educational Resources Information Center

Gavin, M. Katherine; Casa, Tutita M.

2013-01-01

Developing mathematical talent in our students should be of primary consideration in education today as nations respond to the challenges of economic crises and ever-changing technological advances. This paper describes two U.S. federally funded curriculum projects, Project M[superscript 3], Mentoring Mathematical Minds, and Project M[superscript…

5 Strategies for Discourse Scaffolding ELLs

ERIC Educational Resources Information Center

Banse, Holland W.; Palacios, Natalia A.; Merritt, Eileen G.; Rimm-Kaufman, Sara E.

2016-01-01

Facilitating productive discussions in the mathematics classroom is a challenge for many teachers. Discourse--student communication of mathematical ideas with teachers and peers--provides a platform on which students share their understanding, clarify misperceptions, and evaluate ideas. If students are unable to access and participate in…

Using Scaffolding to Scale-up Justifications

ERIC Educational Resources Information Center

James, Carolyn; Casas, Ana; Grant, Douglas

2016-01-01

Open-ended mathematical tasks provide great opportunities for students to engage in authentic mathematical practices, such as conjecturing, generalizing, and justifying. Supporting students in open-ended tasks can be challenging. Appropriate scaffolding of a task has been linked to more opportunities for student learning and better student…

Recreating History with Archimedes and Pi

ERIC Educational Resources Information Center

Santucci, Lora C.

2011-01-01

Using modern technology to examine classical mathematics problems at the high school level can reduce difficult computations and encourage generalizations. When teachers combine historical context with access to technology, they challenge advanced students to think deeply, spark interest in students whose primary interest is not mathematics, and…

Engineering Education in K-12 Schools

NASA Astrophysics Data System (ADS)

Spence, Anne

2013-03-01

Engineers rely on physicists as well as other scientists and mathematicians to explain the world in which we live. Engineers take this knowledge of the world and use it to create the world that never was. The teaching of physics and other sciences as well as mathematics is critical to maintaining our national workforce. Science and mathematics education are inherently different, however, from engineering education. Engineering educators seek to enable students to develop the habits of mind critical for innovation. Through understanding of the engineering design process and how it differs from the scientific method, students can apply problem and project based learning to solve the challenges facing society today. In this talk, I will discuss the elements critical to a solid K-12 engineering education that integrates science and mathematics to solve challenges throughout the world.

Detecting double compressed MPEG videos with the same quantization matrix and synchronized group of pictures structure

NASA Astrophysics Data System (ADS)

Aghamaleki, Javad Abbasi; Behrad, Alireza

2018-01-01

Double compression detection is a crucial stage in digital image and video forensics. However, the detection of double compressed videos is challenging when the video forger uses the same quantization matrix and synchronized group of pictures (GOP) structure during the recompression history to conceal tampering effects. A passive approach is proposed for detecting double compressed MPEG videos with the same quantization matrix and synchronized GOP structure. To devise the proposed algorithm, the effects of recompression on P frames are mathematically studied. Then, based on the obtained guidelines, a feature vector is proposed to detect double compressed frames on the GOP level. Subsequently, sparse representations of the feature vectors are used for dimensionality reduction and enrich the traces of recompression. Finally, a support vector machine classifier is employed to detect and localize double compression in temporal domain. The experimental results show that the proposed algorithm achieves the accuracy of more than 95%. In addition, the comparisons of the results of the proposed method with those of other methods reveal the efficiency of the proposed algorithm.

The AMATYC Review, Volume 10, Number 1, Fall 1988.

ERIC Educational Resources Information Center

Cohen, Don, Ed.

1988-01-01

Designed as an avenue of communication for all mathematics educators concerned with the views, ideas, and experiences pertinent to two-year college teachers and students, this journal presents articles and regular features related to mathematical and pedagogical themes. This issue includes the following articles: (1) "Fractals for Freshmen? Or,…

The AMATYC Review, Volume 18, Numbers 1-2, Fall 1996-Spring 1997.

ERIC Educational Resources Information Center

Browne, Joseph, Ed.

1997-01-01

Designed as an avenue of communication for mathematics educators concerned with the views, ideas, and experiences of two-year college students and teachers, this journal contains articles on mathematics exposition and education and regular features presenting book and software reviews, classroom activities, instructor experiences, and math…

Probability: A Matter of Life and Death

ERIC Educational Resources Information Center

Hassani, Mehdi; Kippen, Rebecca; Mills, Terence

2016-01-01

Life tables are mathematical tables that document probabilities of dying and life expectancies at different ages in a society. Thus, the life table contains some essential features of the health of a population. Probability is often regarded as a difficult branch of mathematics. Life tables provide an interesting approach to introducing concepts…

Proceedings, Conference on the Computing Environment for Mathematical Software

NASA Technical Reports Server (NTRS)

1981-01-01

Recent advances in software and hardware technology which make it economical to create computing environments appropriate for specialized applications are addressed. Topics included software tools, FORTRAN standards activity, and features of languages, operating systems, and hardware that are important for the development, testing, and maintenance of mathematical software.

The AMATYC Review, Volume 17. Numbers 1-2, Fall 1995-Spring 1996.

ERIC Educational Resources Information Center

Browne, Joseph, Ed.

1996-01-01

Designed as an avenue of communication for mathematics educators concerned with the views, ideas, and experiences of two-year college students and teachers, this journal contains articles on mathematics exposition and education and regular features presenting book and software reviews, classroom activities, instructor experiences, and math…

Peer Mentoring: Stories of Three Mathematics Teachers

ERIC Educational Resources Information Center

Kensington-Miller, Barbara

2011-01-01

Mentoring is a professional development strategy well documented. Peer mentoring however, is relatively new and was provided as a professional development strategy for a group of secondary school mathematics teachers working in low socio-economic schools. Through the stories of three teachers, the year-long study identifies the features critical…

Common Features of Professional Development Activities for Mathematics and Science Teachers

ERIC Educational Resources Information Center

Moyer-Packenham, Patricia S.; Bolyard, Johnna J.; Oh, Hana; Cerar, Nancy Irby

2011-01-01

This study examines professional development activities provided for mathematics and science teachers in the National Science Foundation's Math and Science Partnership Program by analyzing a cross-sectional sample of over 2000 professional development (PD) activities in the program. Data were gathered from secondary source documents and surveys to…

Fostering Students' Preparation and Achievement in Upper Level Mathematics Courses

ERIC Educational Resources Information Center

Celik, Mehmet; Shaqlaih, Ali

2017-01-01

This study describes an intervention to address both motivation, student engagement and preparation in upper-level mathematics courses. The effect of the intervention regarding students' achievements is investigated via students' opinions and data analysis from students' assessments. The results of this study show the featured intervention…

Students' Use of Technological Features while Solving a Mathematics Problem

ERIC Educational Resources Information Center

Lee, Hollylynne Stohl; Hollebrands, Karen F.

2006-01-01

The design of technology tools has the potential to dramatically influence how students interact with tools, and these interactions, in turn, may influence students' mathematical problem solving. To better understand these interactions, we analyzed eighth grade students' problem solving as they used a java applet designed to specifically accompany…

Student perception of the impact of mathematics support in higher education

NASA Astrophysics Data System (ADS)

Fhloinn, E. Ní; Fitzmaurice, O.; Bhaird, C. Mac an; O'Sullivan, C.

2014-10-01

Mathematics support in higher education has become increasingly widespread over the past two decades, particularly in the UK, Ireland and Australia. Despite this, reliable evaluation of mathematics support continues to present challenges for those working in this area. One reason is because ideally, properly structured support should function as an integral part of the overall educational experience of the student, in tandem with lectures and tutorials. When this occurs, it makes it difficult to isolate the impact of mathematics support from these other entities. In this paper, the results of a large-scale nationwide survey conducted with first-year service mathematics students in nine higher education institutes in Ireland are considered, exploring students' perceptions of the impact of mathematics support upon their retention, mathematical confidence, examination performance and overall ability to cope with the mathematical demands they face. Students were extremely positive about the effectiveness of mathematics support in all of these areas, providing valuable insights into the value of learning support in mathematics.

Teaching Mathematics in Primary Schools with Challenging Tasks: The Big (Not So) Friendly Giant

ERIC Educational Resources Information Center

Russo, James

2016-01-01

The use of enabling and extending prompts allows tasks to be both accessible and challenging within a classroom. This article provides an example of how to use enabling and extending prompts effectively when employing a challenging task in Year 2.

Evolving Scale-Free Networks by Poisson Process: Modeling and Degree Distribution.

PubMed

Feng, Minyu; Qu, Hong; Yi, Zhang; Xie, Xiurui; Kurths, Jurgen

2016-05-01

Since the great mathematician Leonhard Euler initiated the study of graph theory, the network has been one of the most significant research subject in multidisciplinary. In recent years, the proposition of the small-world and scale-free properties of complex networks in statistical physics made the network science intriguing again for many researchers. One of the challenges of the network science is to propose rational models for complex networks. In this paper, in order to reveal the influence of the vertex generating mechanism of complex networks, we propose three novel models based on the homogeneous Poisson, nonhomogeneous Poisson and birth death process, respectively, which can be regarded as typical scale-free networks and utilized to simulate practical networks. The degree distribution and exponent are analyzed and explained in mathematics by different approaches. In the simulation, we display the modeling process, the degree distribution of empirical data by statistical methods, and reliability of proposed networks, results show our models follow the features of typical complex networks. Finally, some future challenges for complex systems are discussed.

Graphing Calculator Mini Course

NASA Technical Reports Server (NTRS)

Karnawat, Sunil R.

1996-01-01

The "Graphing Calculator Mini Course" project provided a mathematically-intensive technologically-based summer enrichment workshop for teachers of American Indian students on the Turtle Mountain Indian Reservation. Eleven such teachers participated in the six-day workshop in summer of 1996 and three Sunday workshops in the academic year. The project aimed to improve science and mathematics education on the reservation by showing teachers effective ways to use high-end graphing calculators as teaching and learning tools in science and mathematics courses at all levels. In particular, the workshop concentrated on applying TI-82's user-friendly features to understand the various mathematical and scientific concepts.

On the interplay between mathematics and biology: hallmarks toward a new systems biology.

PubMed

Bellomo, Nicola; Elaiw, Ahmed; Althiabi, Abdullah M; Alghamdi, Mohammed Ali

2015-03-01

This paper proposes a critical analysis of the existing literature on mathematical tools developed toward systems biology approaches and, out of this overview, develops a new approach whose main features can be briefly summarized as follows: derivation of mathematical structures suitable to capture the complexity of biological, hence living, systems, modeling, by appropriate mathematical tools, Darwinian type dynamics, namely mutations followed by selection and evolution. Moreover, multiscale methods to move from genes to cells, and from cells to tissue are analyzed in view of a new systems biology approach. Copyright © 2014 Elsevier B.V. All rights reserved.

"I Hate Maths: Why Do We Need to Do Maths?" Using iPad Video Diaries to Investigate Attitudes and Emotions towards Mathematics in Year 3 and Year 6 Students

ERIC Educational Resources Information Center

Larkin, Kevin; Jorgensen, Robyn

2016-01-01

Accessing children's feelings and attitudes towards mathematics is a challenging proposition since methods for data collection may be fraught in terms of bias and power relations. This article explores a method of collecting information from young students about their attitudes towards mathematics using iPads, and a video diary technique not…

A Study of Visualization for Mathematics Education

NASA Technical Reports Server (NTRS)

Daugherty, Sarah C.

2008-01-01

Graphical representations such as figures, illustrations, and diagrams play a critical role in mathematics and they are equally important in mathematics education. However, graphical representations in mathematics textbooks are static, Le. they are used to illustrate only a specific example or a limited set. of examples. By using computer software to visualize mathematical principles, virtually there is no limit to the number of specific cases and examples that can be demonstrated. However, we have not seen widespread adoption of visualization software in mathematics education. There are currently a number of software packages that provide visualization of mathematics for research and also software packages specifically developed for mathematics education. We conducted a survey of mathematics visualization software packages, summarized their features and user bases, and analyzed their limitations. In this survey, we focused on evaluating the software packages for their use with mathematical subjects adopted by institutions of secondary education in the United States (middle schools and high schools), including algebra, geometry, trigonometry, and calculus. We found that cost, complexity, and lack of flexibility are the major factors that hinder the widespread use of mathematics visualization software in education.

Ancient Paradoxes Can Extend Mathematical Thinking

ERIC Educational Resources Information Center

Czocher, Jennifer A.; Moss, Diana L.

2017-01-01

This article presents the Snail problem, a relatively simple challenge about motion that offers engaging extensions involving the notion of infinity. It encourages students in grades 5-9 to connect mathematics learning to logic, history, and philosophy through analyzing the problem, making sense of quantitative relationships, and modeling with…

Problem Solving through Paper Folding

ERIC Educational Resources Information Center

Wares, Arsalan

2014-01-01

The purpose of this article is to describe a couple of challenging mathematical problems that involve paper folding. These problem-solving tasks can be used to foster geometric and algebraic thinking among students. The context of paper folding makes some of the abstract mathematical ideas involved relatively concrete. When implemented…

Indigenous Languages and Mathematics in Elementary Schools

ERIC Educational Resources Information Center

Edmonds-Wathen, Cris; Owens, Kay; Sakopa, Priscilla; Bino, Vagi

2014-01-01

Indigenous languages are used for instruction in elementary schools in Papua New Guinea, but teachers have generally received their own education in English. The challenges of identifying terminology to use in mathematics include many-to-one correspondences between English and the vernacular languages, and different grammatical structures.…

An Introduction to Inferentialism in Mathematics Education

ERIC Educational Resources Information Center

Derry, Jan

2017-01-01

This paper introduces the philosophical work of Robert Brandom, termed inferentialism, which underpins this collection and argues that it offers rich theoretical resources for reconsidering many of the challenges and issues that have arisen in mathematics education. Key to inferentialism is the privileging of the inferential over the…

Connecting Slope, Steepness, and Angles

ERIC Educational Resources Information Center

Nagle, Courtney R.; Moore-Russo, Deborah

2013-01-01

All teachers, especially high school teachers, face the challenge of ensuring that students have opportunities to relate and connect the various representations and notions of mathematics concepts developed over the course of the pre-K-12 mathematics curriculum. NCTM's (2000) Representation Standard emphasizes the importance of students being…

Supporting Secondary Novices' Efforts to Implement Student- and Discourse-Centred Pedagogical Practices

ERIC Educational Resources Information Center

Lewis, Gary

2012-01-01

Novice secondary mathematics teachers attempting teaching consonant with NCTM (1991) Professional Standards for Teaching Mathematics experience stresses related to those attempts. Foremost among those stresses are challenges while orchestrating student-centred, whole-class discussions. Such discussions can create uncertainty and stress as novices…

The Applied Mathematics for Power Systems (AMPS)

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

Chertkov, Michael

2012-07-24

Increased deployment of new technologies, e.g., renewable generation and electric vehicles, is rapidly transforming electrical power networks by crossing previously distinct spatiotemporal scales and invalidating many traditional approaches for designing, analyzing, and operating power grids. This trend is expected to accelerate over the coming years, bringing the disruptive challenge of complexity, but also opportunities to deliver unprecedented efficiency and reliability. Our Applied Mathematics for Power Systems (AMPS) Center will discover, enable, and solve emerging mathematics challenges arising in power systems and, more generally, in complex engineered networks. We will develop foundational applied mathematics resulting in rigorous algorithms and simulation toolboxesmore » for modern and future engineered networks. The AMPS Center deconstruction/reconstruction approach 'deconstructs' complex networks into sub-problems within non-separable spatiotemporal scales, a missing step in 20th century modeling of engineered networks. These sub-problems are addressed within the appropriate AMPS foundational pillar - complex systems, control theory, and optimization theory - and merged or 'reconstructed' at their boundaries into more general mathematical descriptions of complex engineered networks where important new questions are formulated and attacked. These two steps, iterated multiple times, will bridge the growing chasm between the legacy power grid and its future as a complex engineered network.« less

Visualizing Uncertainty of Point Phenomena by Redesigned Error Ellipses

NASA Astrophysics Data System (ADS)

Murphy, Christian E.

2018-05-01

Visualizing uncertainty remains one of the great challenges in modern cartography. There is no overarching strategy to display the nature of uncertainty, as an effective and efficient visualization depends, besides on the spatial data feature type, heavily on the type of uncertainty. This work presents a design strategy to visualize uncertainty con-nected to point features. The error ellipse, well-known from mathematical statistics, is adapted to display the uncer-tainty of point information originating from spatial generalization. Modified designs of the error ellipse show the po-tential of quantitative and qualitative symbolization and simultaneous point based uncertainty symbolization. The user can intuitively depict the centers of gravity, the major orientation of the point arrays as well as estimate the ex-tents and possible spatial distributions of multiple point phenomena. The error ellipse represents uncertainty in an intuitive way, particularly suitable for laymen. Furthermore it is shown how applicable an adapted design of the er-ror ellipse is to display the uncertainty of point features originating from incomplete data. The suitability of the error ellipse to display the uncertainty of point information is demonstrated within two showcases: (1) the analysis of formations of association football players, and (2) uncertain positioning of events on maps for the media.

Unravelling Student Challenges with Quadratics: A Cognitive Approach

ERIC Educational Resources Information Center

Kotsopoulos, Donna

2007-01-01

The author's secondary school mathematics students have often reported to her that quadratic relations are one of the most conceptually challenging aspects of the high school curriculum. From her own classroom experiences there seemed to be several aspects to the students' challenges. Many students, even in their early secondary education, have…

The Smarties-Box Challenge: Supporting Systematic Approaches to Problem Solving

ERIC Educational Resources Information Center

Russo, James

2016-01-01

The Smarties-Box Challenge encourages students to apply several different mathematical capabilities and concepts--such as, estimation, multiplication, and the notion of being systematic--to solve a complex, multistep problem. To effectively engage in the Smarties-Box Challenge, students are required to demonstrate aspects of all four proficiency…

Geometric Series via Probability

ERIC Educational Resources Information Center

Tesman, Barry

2012-01-01

Infinite series is a challenging topic in the undergraduate mathematics curriculum for many students. In fact, there is a vast literature in mathematics education research on convergence issues. One of the most important types of infinite series is the geometric series. Their beauty lies in the fact that they can be evaluated explicitly and that…

Good Questions: Great Ways to Differentiate Mathematics Instruction

ERIC Educational Resources Information Center

Small, Marian

2009-01-01

Using differentiated instruction in the classroom can be a challenge, especially when teaching mathematics. This book cuts through the difficulties with two powerful and universal strategies that teachers can use across all math content: Open Questions and Parallel Tasks. Specific strategies and examples for grades Kindergarten - 8 are organized…

Conceptualizing Perseverance in Problem Solving as Collective Enterprise

ERIC Educational Resources Information Center

Sengupta-Irving, Tesha; Agarwal, Priyanka

2017-01-01

Students are expected to learn mathematics such that when they encounter challenging problems they will persist. Creating opportunities for students to persist in problem solving is therefore argued as essential to effective teaching and to children developing positive dispositions in mathematical learning. This analysis takes a novel approach to…

Exploring the Possibility of Introducing Supplemental Instruction at Secondary School Level

ERIC Educational Resources Information Center

Naidoo, Jayaluxmi; Paideya, Vinodhani

2015-01-01

Globally, mathematics and science pass rates at school level have been a much discussed and researched issue. Teachers are tasked with the responsibility of alleviating learners' challenges associated with the learning of mathematics and science. Thus, teachers are pursuing innovative techniques for improving the understanding of and increasing…

The Amazing Mathematical Race

ERIC Educational Resources Information Center

Noblitt, Bethany A.; Buckley, Brooke E.

2011-01-01

Teams, pit stops, clues, time limits, fast forwards, challenges, and prizes are all components of the CBS hit show "The Amazing Race." They were also elements of the Amazing Mathematical Race sponsored by the Math and Stats Club at Northern Kentucky University in April 2009. Held in recognition of Math Awareness Month, which is advocated…

Hoop Hoop Hooray!

ERIC Educational Resources Information Center

Tomsett, Ruth

2008-01-01

The author believes that Venn diagrams are a useful, yet hugely underused resource, to encourage purposeful talk, reasoning and logical thinking both within mathematics and across the curriculum. Here, she describes ways in which Venn diagrams can be used to add challenge and develop reasoning, discussion and mathematical thinking at Key Stage 2.…

Promoting Student Collaboration in a Detracked, Heterogeneous Secondary Mathematics Classroom

ERIC Educational Resources Information Center

Staples, Megan E.

2008-01-01

Detracking and heterogeneous groupwork are two educational practices that have been shown to have promise for affording all students needed learning opportunities to develop mathematical proficiency. However, teachers face significant pedagogical challenges in organizing productive groupwork in these settings. This study offers an analysis of one…

The Search for Hidden Structure

ERIC Educational Resources Information Center

Matsuura, Ryota; Sword, Sarah; Finkelstein, Tatyana

2017-01-01

How does one look for mathematical structure? Finding structure is a challenging yet accessible activity for all students. This article describes a lesson in which seventh graders engaged with mathematical structure. The setting was a seventh-grade prealgebra classroom in a suburban school. The classroom teacher was co-author Tatyana Finkelstein.…

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…

Reading the World with Calculus

ERIC Educational Resources Information Center

Verzosa, Debbie

2015-01-01

It is now increasingly recognized that mathematics is not a neutral value-free subject. Rather, mathematics can challenge students' taken-for-granted realities and promote action. This article describes two issues, namely deforestation and income inequality. These were specifically chosen because they can be related to a range of calculus concepts…

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…

The Contribution of Domain-Specific Knowledge in Predicting Students' Proportional Word Problem Solving Performance

ERIC Educational Resources Information Center

Jitendra, Asha K.; Lein, Amy E.; Star, Jon R.; Dupuis, Danielle N.

2013-01-01

Proportional thinking, which requires understanding fractions, ratios, and proportions, is an area of mathematics that is cognitively challenging for many children and adolescents (Fujimura, 2001; Lamon, 2007; Lobato, Ellis, Charles, & Zbiek, 2010; National Mathematics Advisory Panel [NMAP], 2008) and "transcends topical barriers in adult…

TIMMS Advanced 2015 Assessment Frameworks

ERIC Educational Resources Information Center

Mullis, Ina V. S., Ed.; Martin, Michael O., Ed.

2014-01-01

It is critical for countries to ensure that capable secondary school students receive further preparation in advanced mathematics and science, so that they are ready to enter challenging university-level studies that prepare them for careers in science, technology, engineering, and mathematics (STEM) fields. This group of students will become the…

Gender Mainstreaming of Adult Mathematics Education: Opportunities and Challenges

ERIC Educational Resources Information Center

Henningsen, Inge

2008-01-01

Mainstreaming as a strategy for equality has been widely adopted by the international community. Mainstreaming of adult mathematics education entails that gender, ethnicity, social class and other difference defining categories are included consciously and explicitly in all activities. A growing body of research explore how pluralism and…

Primary Students' Perceptions of Their Mathematics Learning

ERIC Educational Resources Information Center

Cheeseman, Jill; Mornane, Angela

2014-01-01

A survey was given to 87 primary students in Years 3 and 4 at a school participating in the "Encouraging Persistence Maintaining Challenge" project. Its purpose was to give an overview of students' attitudes and beliefs about learning mathematics, their motivation, and their self-awareness. Findings indicate that most students believe…

Exploring Elementary Mathematics Teachers' Opportunities to Learn to Teach

ERIC Educational Resources Information Center

Cavanna, Jillian M.; Drake, Corey; Pak, Byungeun

2017-01-01

Mathematics teacher education is faced with the challenge of preparing new teachers for ambitious instruction, but we have limited understandings of what happens within the courses where this preparation occurs. This paper draws on interview data from of a larger investigation of novices' enactment of ambitious instruction in elementary…

Getting a Bead on It

ERIC Educational Resources Information Center

Ferrucci, Beverly J.; McDougall, Jennifer; Carter, Jack

2009-01-01

One challenge that middle school teachers commonly face is finding insightful, hands-on applications when teaching basic mathematical concepts. One concept that is a foundation of middle school mathematics is the notion of "linear functions." Although a variety of models can be used for linear equations, such as temperature conversions,…

The Ideology of Certainty in Mathematics Education.

ERIC Educational Resources Information Center

Borba, Marcelo C.; Skovsmose, Ole

1997-01-01

Presents one aspect that makes mathematics the final word in many discussions, the ideology of certainty. Argues that one way of challenging the ideology of certainty is to change classroom practice by introducing a landscape of discussion on chaotic nature where relativity, provisional starting points, different points of view, and uncertainty…

Challenging Teacher Beliefs about Student Engagement in Mathematics

ERIC Educational Resources Information Center

Bobis, Janette; Way, Jennifer; Anderson, Judy; Martin, Andrew J.

2016-01-01

This study explored the beliefs about student engagement in mathematics of three Year 5 and 6 teachers, focusing on the shifts that occurred during a 10-week intervention. Data obtained from teacher surveys, interviews, video-recorded workshop observations and artefacts from teachers' classrooms reveal variations in their reactions to the…

Teachers' Perceptions of Examining Students' Thinking: Changing Mathematics Instructional Practice

ERIC Educational Resources Information Center

Anderson-Pence, Katie L.

2015-01-01

This paper seeks to illuminate teachers' perceptions of the challenges and benefits of systematically examining students' thinking as part of a professional development program in elementary mathematics education. Using a framework of models of conceptual change and principles of discomfort, three elementary teachers' perceptions of their…

Changing the Subject: The Challenge to Teacher Professionalism of Innovation in OECD Countries.

ERIC Educational Resources Information Center

Olson, John; James, Edwyn; Lang, Manfred

The Organization for Economic Cooperation and Development (OECD) study, "Innovations in Science, Mathematics and Technology Education" (SMTE), documents 23 projects aimed at enhancing the appeal of science, mathematics, and technology education. The projects began in 13 OECD countries that believed that curricula must be more…

Colloquy on Minority Males in Science, Technology, Engineering, and Mathematics

ERIC Educational Resources Information Center

Didion, Catherine; Fortenberry, Norman L.; Cady, Elizabeth

2012-01-01

On August 8-12, 2010 the National Academy of Engineering (NAE), with funding from the National Science Foundation (NSF), convened the Colloquy on Minority Males in Science, Technology, Engineering, and Mathematics (STEM), following the release of several reports highlighting the educational challenges facing minority males. The NSF recognized the…

Laboratory Barriers in Science, Engineering, and Mathematics for Students with Disabilities.

ERIC Educational Resources Information Center

Heidari, Farzin

This report addresses the barriers college students with disabilities face in the laboratory setting. In engineering, mathematics, and science education most courses require laboratory work which may pose challenges to those with disabilities. Instructors should be aware of the individual needs of students with disabilities and make necessary…

Planning Questions and Persevering in the Practices

ERIC Educational Resources Information Center

Gurl, Theresa J.; Fox, Ryan; Dabovic, Nikolina; Leavitt, Arielle Eager

2016-01-01

The implementation of the Common Core's Standards for Mathematical Practice can pose a challenge to all teachers of mathematics but especially to preservice teachers. These standards require teaching in a way that often differs from what preservice teachers have experienced as learners. Standard 1--"Make sense of problems and persevere in…

Challenging Students' Beliefs about Mathematics: The Use of Documentary to Alter Perceptions of Efficacy

ERIC Educational Resources Information Center

Hekimoglu, Serkan; Kittrell, Emily

2010-01-01

This study investigates whether seeing a documentary on how mathematicians do mathematics improves students' math "self-efficacy beliefs." The analysis of students' written reflections and classroom observations suggests that watching the documentary may help students' math anxiety decrease and positive self-efficacy toward learning mathematics…

Regular Numbers and Mathematical Worlds

ERIC Educational Resources Information Center

Whitacre, Ian; Bouhjar, Khalid; Bishop, Jessica Pierson; Philipp, Randolph; Schappelle, Bonnie P.

2016-01-01

Rather than describing the challenges of integer learning in terms of a transition from positive to negative numbers, we have arrived at a different perspective: We view students as inhabiting distinct mathematical worlds consisting of particular types of numbers (as construed by the students). These worlds distinguish and illuminate students'…

Examining Individual and Collective Level Mathematical Progress

ERIC Educational Resources Information Center

Rasmussen, Chris; Wawro, Megan; Zandieh, Michelle

2015-01-01

A challenge in mathematics education research is to coordinate different analyses to develop a more comprehensive account of teaching and learning. We contribute to these efforts by expanding the constructs in Cobb and Yackel's (Educational Psychologist 31:175-190, 1996) interpretive framework that allow for coordinating social and individual…

A Provably Necessary Symbiosis

ERIC Educational Resources Information Center

Hochberg, Robert; Gabric, Kathleen

2010-01-01

The "new biology" of the 21st century is increasingly dependent on mathematics, and preparing high school students to have both strong science and math skills has created major challenges for both disciplines. Researchers and educators in biology and mathematics have been working long hours on a project to create high school teaching modules…

Produce Intrigue with Crypto!

ERIC Educational Resources Information Center

Avila, Cheryl L.; Ortiz, Enrique

2012-01-01

Learning mathematics is challenging. It requires discipline, logic, precision, perseverance, and accuracy. It can also be fun. When mathematics is set in a context that inspires students to want to solve interesting problems, students will have an intrinsic desire to learn the necessary skills to accomplish a specific goal. The game of Crypto! was…

Understanding the dynamics of sustainable social-ecological systems: human behavior, institutions, and regulatory feedback networks.

PubMed

Anderies, John M

2015-02-01

I present a general mathematical modeling framework that can provide a foundation for the study of sustainability in social- ecological systems (SESs). Using basic principles from feedback control and a sequence of specific models from bioeconomics and economic growth, I outline several mathematical and empirical challenges associated with the study of sustainability of SESs. These challenges are categorized into three classes: (1) the social choice of performance measures, (2) uncertainty, and (3) collective action. Finally, I present some opportunities for combining stylized dynamical systems models with empirical data on human behavior and biophysical systems to address practical challenges for the design of effective governance regimes (policy feedbacks) for highly uncertain natural resource systems.

Girls back off mathematics again: the views and experiences of girls in computer-based mathematics

NASA Astrophysics Data System (ADS)

Vale, Colleen

2002-12-01

The views and experiences of girls in two co-educational mathematics classrooms in which computers were regularly used were researched. Data were collected by observation and videotaping of lessons, questionnaire, and interviews of students and the teachers. In this paper case studies of six girls are presented. Their `stories' reveal a diversity of experiences and views and multiple gender identities. High achieving girls persisted as "outsiders within," other girls "backed off", and exceptional girls challenged gender stereotypes. Implications for social justice in mathematics in the age of the super highway are discussed.

Space-Based Astronomy: An Educator Guide with Activities for Science, Mathematics, and Technology Education.

ERIC Educational Resources Information Center

Vogt, Gregory L.

This educator's guide features activities for science, mathematics, and technology education. The activities in this curriculum guide were developed based on the hands-on approach. The guide starts with introductory information and is followed by five units: (1) "The Atmospheric Filter"; (2) "The Electromagnetic Spectrum"; (3)…

Relations of Instructional Tasks to Teacher-Student Discourse in Mathematics Classrooms of Chinese Primary Schools

ERIC Educational Resources Information Center

Ni, Yujing; Zhou, Dehui; Li, Xiaoqing; Li, Qiong

2014-01-01

This study, based on observation of 90 fifth-grade mathematics classes in Chinese elementary schools, examined how the task features, high cognitive demand, multiple representations, and multiple solution methods may relate to classroom discourse. Results indicate that high cognitive demand tasks were associated with teachers' use higher order…

The AMATYC Review, Fall 1992-Spring 1993.

ERIC Educational Resources Information Center

Cohen, Don, Ed.; Browne, Joseph, Ed.

1993-01-01

Designed as an avenue of communication for mathematics educators concerned with the views, ideas, and experiences of two-year college students and teachers, this journal contains articles on mathematics exposition and education, as well as regular features presenting book and software reviews and math problems. The first of two issues of volume 14…

Development of Intellectual Activity in Solving Exponential Inequalities

ERIC Educational Resources Information Center

Alpyssov, Akan; Mukanova, Zhazira; Kireyeva, Assel; Sakenov, Janat; Kervenev, Kabylgazy

2016-01-01

The article describes the possibilities and the main directions of development of intellectual activity in teaching mathematics in school. The aims and specific features of application of international comparative TIMSS and PISA studies, as well as their results in the field of mathematics education in relation to the pupils in Kazakhstan are…

Learner-Centered Pedagogy in a Liberal Arts Mathematics Course

ERIC Educational Resources Information Center

Rufatto, Robin; Dickin, Holly; Florescu, Alina; Lorch, Crystal; Bremigan, Ralph; Lorch, John

2016-01-01

We discuss the pedagogical redesign of a liberal arts mathematics course that enrolls roughly 3000 students per year. Flipping the classroom is a prominent feature of the new pedagogical approach. We describe the nature of this redesign, course resources, and how students are assessed for both preparation and understanding. We also indicate how…

Common Grounds for Modelling Mathematics in Educational Software

ERIC Educational Resources Information Center

Neuper, Walther

2010-01-01

Two kinds of software, CAS and DGS, are starting to work towards mutual integration. This paper envisages common grounds for such integration based on principles of computer theorem proving (CTP). Presently, the CTP community seems to lack awareness as to which of their products' features might serve mathematics education from high-school to…

The Spirit of Investigation: Modifying Pascal and Fibonacci

ERIC Educational Resources Information Center

Lopez-Real, Francis

2008-01-01

Using investigations in teaching mathematics has for many years become an established feature of most curricula around the world. Investigations can be a vehicle for enabling children to experience the genuine excitement that comes from mathematical discovery. The true spirit of inquiry and investigation lies in the mind-set that continually asks…

Culturally and Linguistically Responsive Schema Intervention: Improving Word Problem Solving for English Language Learners with Mathematics Difficulty

ERIC Educational Resources Information Center

Driver, Melissa K.; Powell, Sarah R.

2017-01-01

Word problems are prevalent on high-stakes assessments, and success on word problems has implications for grade promotion and graduation. Unfortunately, English Language Learners (ELLs) continue to perform significantly below their native English-speaking peers on mathematics assessments featuring word problems. Little is known about the…

The AMATYC Review, Volume 15, Numbers 1-2, Fall 1993-Spring 1994.

ERIC Educational Resources Information Center

Browne, Joseph, Ed.

1994-01-01

Designed as a avenue of communication for mathematics educators concerned with the views, ideas, and experiences of two-year college students and teachers, this journal contains articles on mathematics exposition and education, and regular features presenting book and software reviews and math problems. Volume 15 includes the following articles:…

Preschool Drawing and School Mathematics: The Nature of the Association

ERIC Educational Resources Information Center

Malanchini, Margherita; Tosto, Maria G.; Garfield, Victoria; Dirik, Aysegul; Czerwik, Adrian; Arden, Rosalind; Malykh, Sergey; Kovas, Yulia

2016-01-01

The study examined the etiology of individual differences in early drawing and of its longitudinal association with school mathematics. Participants (N = 14,760), members of the Twins Early Development Study, were assessed on their ability to draw a human figure, including number of features, symmetry, and proportionality. Human figure drawing was…

Designing and Incorporating Mathematics-Based Video Cases Highlighting Virtual and Physical Tool Use

ERIC Educational Resources Information Center

Kurz, Terri L.; Kokic, Ivana Batarelo

2012-01-01

As there has recently been an onslaught of video cases being developed and implemented with preservice teachers, it is important to evaluate how we should use these cases. This research investigates the features elementary preservice teachers consider valuable when using video cases in mathematics education. The researchers used hierarchical…

The AMATYC Review, Fall 1987, Spring 1988.

ERIC Educational Resources Information Center

Cohen, Don, Ed.

1988-01-01

Designed as an avenue of communication for mathematics educators concerned with the views, ideas, and experiences of two-year college students and teachers, this journal contains articles on mathematics exposition and education, and regular features that present book and software reviews and math problems. The first of two issues of volume 9…

Developing a TI-92 Manual Generator Based on Computer Algebra Systems

ERIC Educational Resources Information Center

Jun, Youngcook

2004-01-01

The electronic medium suitable for mathematics learning and teaching is often designed with a notebook interface provided in a computer algebra system. Such a notebook interface facilitates a workspace for mathematical activities along with an online help system. In this paper, the proposed feature is implemented in the Mathematica's notebook…

Some Implications of a Behavioral Analysis of Verbal Behavior for Logic and Mathematics

PubMed Central

2013-01-01

The evident power and utility of the formal models of logic and mathematics pose a puzzle: Although such models are instances of verbal behavior, they are also essentialistic. But behavioral terms, and indeed all products of selection contingencies, are intrinsically variable and in this respect appear to be incommensurate with essentialism. A distinctive feature of verbal contingencies resolves this puzzle: The control of behavior by the nonverbal environment is often mediated by the verbal behavior of others, and behavior under control of verbal stimuli is blind to the intrinsic variability of the stimulating environment. Thus, words and sentences serve as filters of variability and thereby facilitate essentialistic model building and the formal structures of logic, mathematics, and science. Autoclitic frames, verbal chains interrupted by interchangeable variable terms, are ubiquitous in verbal behavior. Variable terms can be substituted in such frames almost without limit, a feature fundamental to formal models. Consequently, our fluency with autoclitic frames fosters generalization to formal models, which in turn permit deduction and other kinds of logical and mathematical inference. PMID:28018038

Mathematical modeling of swirled flows in industrial applications

NASA Astrophysics Data System (ADS)

Dekterev, A. A.; Gavrilov, A. A.; Sentyabov, A. V.

2018-03-01

Swirled flows are widely used in technological devices. Swirling flows are characterized by a wide range of flow regimes. 3D mathematical modeling of flows is widely used in research and design. For correct mathematical modeling of such a flow, it is necessary to use turbulence models, which take into account important features of the flow. Based on the experience of computational modeling of a wide class of problems with swirling flows, recommendations on the use of turbulence models for calculating the applied problems are proposed.

Categorization and analysis of explanatory writing in mathematics

NASA Astrophysics Data System (ADS)

Craig, Tracy S.

2011-10-01

The aim of this article is to present a scheme for coding and categorizing students' written explanations of mathematical problem-solving activities. The scheme was used successfully within a study project carried out to determine whether student problem-solving behaviour could be positively affected by writing explanatory strategies to mathematical problem-solving processes. The rationale for the study was the recognized importance of mathematical problem-solving, the widely acknowledged challenge of teaching problem-solving skills directly and the evidence in the literature that writing in mathematics provides a tool for learning. The study was carried out in a first-year mathematics course at the University of Cape Town, South Africa. Students' written submissions were categorized and analysed through use of an adaptation of a journal entry classification scheme. The scheme successfully observed positive changes over the experimental period in students' level of engagement with the mathematical material and with their stance towards knowledge.

Academic Preparedness as a Predictor of Achievement in an Engineering Design Challenge

ERIC Educational Resources Information Center

Mentzer, Nathan; Becker, Kurt

2010-01-01

The purpose of this study was to determine if a student's academic success, measured by grade point average (GPA) in mathematics, science, and communication courses, is correlated with student change in achievement during an engineering design challenge. Engineering design challenges have been implemented and researched in K-16 environments where…

Adult Numeracy Development: Theory, Research, Practice. Series on Literacy: Research, Policy, and Practice.

ERIC Educational Resources Information Center

Gal, Iddo, Ed.

This book contains 16 papers on the theory, research, and practice of adult numeracy development. The following papers are included: "The Numeracy Challenge" (Iddo Gal); "Numeracy, Mathematics, and Adult Learning" (Diane Coben); "Building a Problem-Solving Environment for Teaching Mathematics" (Peter Kloosterman, Bin Hassan Mohamad-Ali, Lynda R.…

Partial Derivative Games in Thermodynamics: A Cognitive Task Analysis

ERIC Educational Resources Information Center

Kustusch, Mary Bridget; Roundy, David; Dray, Tevian; Manogue, Corinne A.

2014-01-01

Several studies in recent years have demonstrated that upper-division students struggle with the mathematics of thermodynamics. This paper presents a task analysis based on several expert attempts to solve a challenging mathematics problem in thermodynamics. The purpose of this paper is twofold. First, we highlight the importance of cognitive task…

The Development of a Cognitively-Diagnostic Formative Assessment of the Early Concept of Angle

ERIC Educational Resources Information Center

Khasanova, Elvira

2016-01-01

Students' development of conceptual understandings is a central goal of mathematics education (CCSS-Mathematics, 2010). Such a challenging, yet ambiguous, goal cannot be achieved without empowering teachers with the knowledge and tools critical for their ability to adequately convey the content, and assess and interpret students' performance. This…

A Naturalistic Study of Executive Function and Mathematical Problem-Solving

ERIC Educational Resources Information Center

Kotsopoulos, Donna; Lee, Joanne

2012-01-01

Our goal in this research was to understand the specific challenges middle-school students face when engaging in mathematical problem-solving by using executive function (i.e., shifting, updating, and inhibiting) of working memory as a functional construct for the analysis. Using modified talk-aloud protocols, real-time naturalistic analysis of…

The Effect of Mathematical Games on On-Task Behaviours in the Primary Classroom

ERIC Educational Resources Information Center

Bragg, Leicha A.

2012-01-01

A challenge for primary classroom teachers is to maintain students' engagement with learning tasks while catering for their diverse needs, capabilities and interests. Multiple pedagogical approaches are employed to promote on-task behaviours in the mathematics classroom. There is a general assumption by educators that games ignite children's…

Preservice Primary Teachers' Geometric Thinking: Is Pre-Tertiary Mathematics Education Building Sufficiently Strong Foundations?

ERIC Educational Resources Information Center

Hourigan, Mairéad; Leavy, Aisling M.

2017-01-01

Teacher knowledge is a critical focus of educational research in light of the potential impact of teacher knowledge on student learning. The dearth of research exploring entry-level preservice teachers' geometric knowledge poses an onerous challenge for mathematics educators in initial teacher education (ITE) when designing experiences that…

Teaching Mathematics by Comparison: Analog Visibility as a Double-Edged Sword

ERIC Educational Resources Information Center

Begolli, Kreshnik Nasi; Richland, Lindsey Engle

2016-01-01

Comparing multiple solutions to a single problem is an important mode for developing flexible mathematical thinking, yet instructionally leading this activity is challenging (Stein, Engle, Smith, & Hughes, 2008). We test 1 decision teachers must make after having students solve a problem: whether to only verbally discuss students' solutions or…

Algebraic Functions, Computer Programming, and the Challenge of Transfer

ERIC Educational Resources Information Center

Schanzer, Emmanuel Tanenbaum

2015-01-01

Students' struggles with algebra are well documented. Prior to the introduction of functions, mathematics is typically focused on applying a set of arithmetic operations to compute an answer. The introduction of functions, however, marks the point at which mathematics begins to focus on building up abstractions as a way to solve complex problems.…

Factors Influencing Elementary Teachers' Positioning of African American Girls as Science and Mathematics Learners

ERIC Educational Resources Information Center

Pringle, Rose M.; Brkich, Katie Milton; Adams, Thomasenia Lott; West-Olatunii, Cirecie; Archer-Banks, Diane A.

2012-01-01

Despite recent progress toward gender equity in science and mathematics education, the underachievement of low-income African American girls remains a challenge when compared with their white counterparts. Furthermore, the causes of this persistent underachievement have not been explored thoroughly. We have initiated a three-year longitudinal…

Bridging Algebra & Geometry with "n"-Gram Proofs

ERIC Educational Resources Information Center

Craven, Joshua D.

2010-01-01

For many students, geometry is the first course in which mathematical proof takes center stage. To help ease students into writing proofs, the author tries to create lessons and activities throughout the year that challenge students to prove their own conjectures by using tools learned in previous mathematics courses. Teachers cannot get all…

Challenging the Western Approach to Cultural Comparisons: Young Pupils' Affective Structures Regarding Mathematics in Finland and Chile

ERIC Educational Resources Information Center

Tuohilampi, Laura; Hannula, Markku S.; Varas, Leonor; Giaconi, Valentina; Laine, Anu; Näveri, Liisa; i Nevado, Laia Saló

2015-01-01

Large-scale studies measure mathematics-related affect using questionnaires developed by researchers in primarily English-based countries and according to Western-based theories. Influential comparative conclusions about different cultures and countries are drawn based on such measurements. However, there are certain premises involved in these…

Computational Modeling and Mathematics Applied to the Physical Sciences.

ERIC Educational Resources Information Center

National Academy of Sciences - National Research Council, Washington, DC.

One aim of this report is to show and emphasize that in the computational approaches to most of today's pressing and challenging scientific and technological problems, the mathematical aspects cannot and should not be considered in isolation. Following an introductory chapter, chapter 2 discusses a number of typical problems leading to…

Stirring the Pot: Supporting and Challenging General Education Science, Technology, Engineering, and Mathematics Faculty to Change Teaching and Assessment Practice

ERIC Educational Resources Information Center

Stieha, Vicki; Shadle, Susan E.; Paterson, Sharon

2016-01-01

Evidence-based instructional practices (ebips) have been associated with positive student outcomes; however, institutions struggle to catalyze widespread adoption of these practices in general education science, technology, engineering, and mathematics (stem) courses. Further, linking ebips with integrated learning assessment is rarely discussed…

Every Teacher Is a Teacher of Mathematics

ERIC Educational Resources Information Center

Steen, Lynn Arthur

2007-01-01

Even under the best of circumstances, teaching mathematics is a daunting challenge. However, in today's society, it is increasingly important. Basic numeracy is one of the few essential skills that students absolutely must master, both for their own good and for the benefit of the nation's democracy and economic well-being. Unfortunately, numeracy…

SUPERSTARS III: 6-8.

ERIC Educational Resources Information Center

North Carolina State Dept. of Public Education, Raleigh.

SUPERSTARS III is a K-8 program designed as an enrichment opportunity for self-directed learners in mathematics. The basic purpose of SUPERSTARS III is to provide the extra challenge that self-motivated students need in mathematics and to do so in a structured, long-term program that does not impinge on the normal classroom routine or the…

How Inquiry Pedagogy Enables Teachers to Facilitate Growth Mindsets in Mathematics Classrooms

ERIC Educational Resources Information Center

O'Brien, Mia; Fielding-Wells, Jill; Makar, Katie; Hillman, Jude

2015-01-01

Growth mindsets are vital for effective lifelong learning. Students with growth mindsets are more willing to learn new things, take risks, and embrace challenges. Students with fixed mindsets have limiting beliefs about their abilities, and will attribute success in learning to factors beyond their control. Inquiry in mathematics classrooms may…

Going with the Flow: Challenging Students to Make Assumptions

ERIC Educational Resources Information Center

Felton, Mathew D.; Anhalt, Cynthia O.; Cortez, Ricardo

2015-01-01

Many current and future teachers have little experience with modeling and how to integrate it into their teaching. However, with the introduction of the Common Core State Standards for Mathematics (CCSSM) and its emphasis on mathematical modeling in all grades (CCSSI 2010), this integration has become paramount. Therefore, middle-grades teachers…

Mathematical Learning Disabilities in Special Populations: Phenotypic Variation and Cross-Disorder Comparisons

ERIC Educational Resources Information Center

Dennis, Maureen; Berch, Daniel B.; Mazzocco, Michele M. M.

2009-01-01

What is mathematical learning disability (MLD)? The reviews in this special issue adopt different approaches to defining the construct of MLD. Collectively, they demonstrate the current status of efforts to establish a consensus definition and the challenges faced in this endeavor. In this commentary, we reflect upon the proposed pathways to…

Infrastructure Redesign and Instructional Reform in Mathematics: Formal Structure and Teacher Leadership

ERIC Educational Resources Information Center

Hopkins, Megan; Spillane, James P.; Jakopovic, Paula; Heaton, Ruth M.

2013-01-01

Designing infrastructures to support instruction remains a challenge in educational reform. This article reports on a study of one school system's efforts to redesign its infrastructure for mathematics instruction by promoting teacher leadership. Using social network and interview data from 12 elementary schools, we explore how the district's…