Role Playing Based on Multicultural for Understanding Fraction in Primary School

NASA Astrophysics Data System (ADS)

Aryanto, S.; Budiarti, T.; Rahmatullah, R.; Utami, S. R.; Jupri, A.

2017-09-01

Multicultural serve as a reference in the development of innovative mathematical learning materials and is expected to be a solution in improving the ability of students in understanding the fraction matter based on social and mathematical approach, so this study aims to determine the improvement of students’ understanding in fraction matter through role playing by integrating multicultural concepts as development learning content. Classroom Action Research conducted on 34 students in elementary school class proves that students’ understanding in fraction matter shows improvement in cycle II as much as 67% of students are able to apply the concept or formula exactly when compared with the result of cycles I of 33%. This research is expected to be the reference of teachers in developing innovative mathematical learning, let alone explicitly, this concept not only emphasizes the cognitive abilities of students, but implicitly can develop their social skills in mathematical perspective.

A structural equation modeling analysis of students' understanding in basic mathematics

NASA Astrophysics Data System (ADS)

Oktavia, Rini; Arif, Salmawaty; Ferdhiana, Ridha; Yuni, Syarifah Meurah; Ihsan, Mahyus

2017-11-01

This research, in general, aims to identify incoming students' understanding and misconceptions of several basic concepts in mathematics. The participants of this study are the 2015 incoming students of Faculty of Mathematics and Natural Science of Syiah Kuala University, Indonesia. Using an instrument that were developed based on some anecdotal and empirical evidences on students' misconceptions, a survey involving 325 participants was administered and several quantitative and qualitative analysis of the survey data were conducted. In this article, we discuss the confirmatory factor analysis using Structural Equation Modeling (SEM) on factors that determine the new students' overall understanding of basic mathematics. The results showed that students' understanding on algebra, arithmetic, and geometry were significant predictors for their overall understanding of basic mathematics. This result supported that arithmetic and algebra are not the only predictors of students' understanding of basic mathematics.

Development and Validation of the Mathematics Teachers' Beliefs about English Language Learners Survey (MTBELL)

ERIC Educational Resources Information Center

Gann, Linda; Bonner, Emily P.; Moseley, Christine

2016-01-01

Given the increasing number of English Language Learners (ELLs) in secondary mathematics classrooms, it is imperative that mathematics teacher educators develop measures for determining how and why secondary mathematics teachers (SMTs) understand and respond instructionally to these students. This paper reports on the initial development and…

Taking the Guesswork out of Computational Estimation

ERIC Educational Resources Information Center

Cochran, Jill; Dugger, Megan Hartmann

2013-01-01

Computational estimation is an important skill necessary for students' mathematical development. Students who can estimate well for computations rely on an understanding of many mathematical topics, including a strong number sense, which facilitates understanding the mathematical operations and contextual evidence within a problem. In turn, good…

Children's Mathematical Reasoning: Opportunities for Developing Understanding and Creative Thinking

ERIC Educational Resources Information Center

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

2017-01-01

Reasoning underpins students' mathematical understanding and promotes creative thinking. It is regarded as a key mathematical proficiency. This article discusses the reasoning actions that primary children employed and teachers noticed for the "What else belongs?" task focused on forming and testing conjectures.

Mathematics for the New Millennium

ERIC Educational Resources Information Center

Gordon, Sheldon P.

2004-01-01

Courses below calculus need to be refocused to emphasise conceptual understanding and realistic applications via mathematical modelling rather than an overarching focus on developing algebraic skills that may be needed for calculus. Without understanding the concepts, students will not be able to transfer the mathematics to new situations or to…

"Mathematics Is Just 1 + 1 = 2, What Is There to Argue About?": Developing a Framework for Argument-Based Mathematical Inquiry

ERIC Educational Resources Information Center

Fielding-Wells, Jill

2016-01-01

One potential means to develop students' contextual and conceptual understanding of mathematics is through Inquiry Learning. However, introducing a problem context can distract from mathematical content. Incorporating argumentation practices into Inquiry may address this through providing a stronger reliance on mathematical evidence and reasoning.…

Helping Students with Mathematics Difficulties Understand Ratios and Proportions

ERIC Educational Resources Information Center

Dougherty, Barbara; Bryant, Diane Pedrotty; Bryant, Brian R.; Shin, Mikyung

2016-01-01

Ratios and proportions are foundational to student understanding across multiple topics in mathematics and science. In mathematics, they are central to developing concepts and skills related to slope, constant rate of change, and similar figures, which are all fundamental to algebraic concepts and skills. This article examines the importance of…

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…

Developing Understanding of Mathematical Modeling in Secondary Teacher Preparation

ERIC Educational Resources Information Center

Anhalt, Cynthia Oropesa; Cortez, Ricardo

2016-01-01

This study examines the evolution of 11 prospective teachers' understanding of mathematical modeling through the implementation of a modeling module within a curriculum course in a secondary teacher preparation program. While the prospective teachers had not previously taken a course on mathematical modeling, they will be expected to include…

Professional Learning in Mathematical Reasoning: Reflections of a Primary Teacher

ERIC Educational Resources Information Center

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

2016-01-01

Reasoning is an important aspect in the understanding and learning of mathematics. This paper reports on a case study presenting one Australian primary teacher's reflections regarding the role played by a professional learning program in her developing understanding of mathematical reasoning. Examination of the transcripts of two interviews…

Fear, Loathing and Ambivalence toward Learning and Teaching Mathematics: Preservice Teachers' Perspectives

ERIC Educational Resources Information Center

Itter, Diane; Meyers, Noel

2017-01-01

Preservice teachers graduate from an education system that shapes their mathematical understandings, beliefs and attitudes, and then re-enter that system to shape their own students' mathematical understandings, beliefs, and attitudes. Unfortunately, many of our future teachers have developed negative attitudes symptomatic of a self-perpetuating…

"Weigh" to Go! Exploring Mathematical Language

ERIC Educational Resources Information Center

Adams, Thomasenia Lott; Thangata, Fiona; King, Cindy

2005-01-01

This article focuses on the dynamics of language in the context of mathematics. The interaction of everyday words and specialized mathematics vocabulary impacts students' development of mathematical understanding. (Contains 4 tables and 1 figure.)

Intangible heritage for sustainable future: mathematics in the paddy field

NASA Astrophysics Data System (ADS)

Dewanto, Stanley P.; Kusuma, Dianne A.; Nurani Ruchjana, Budi; Setiawan Abdullah, Atje

2017-10-01

Mathematics, as the only general language, can describe all phenomena on earth. Mathematics not only helps us to understand these phenomena, but it also can sustain human activities, consequently ensure that the future development is sustainable. Indonesia, with high cultural diversity, should aware to have its understanding, skills, and philosophies developed by certain societies, with long histories of interaction with their natural surroundings, which will provide a foundation for locally appropriate sustainable development. This paper discussed the condition and situation on certain area in Cigugur, Indonesia, and what skills, knowledge, and concept can be transmitted, regarding simple mathematics (arithmetic). Some examples are provided.

Reflective Modeling in Teacher Education.

ERIC Educational Resources Information Center

Shealy, Barry E.

This paper describes mathematical modeling activities from a secondary mathematics teacher education course taken by fourth-year university students. Experiences with mathematical modeling are viewed as important in helping teachers develop a more intuitive understanding of mathematics, generate and evaluate mathematical interpretations, and…

Math Autobiographies: A Window into Teachers' Identities as Mathematics Learners

ERIC Educational Resources Information Center

McCulloch, Allison W.; Marshall, Patricia L.; DeCuir-Gunby, Jessica T.; Caldwell, Ticola S.

2013-01-01

Mathematics autobiographies have the potential to help teachers reflect on their identities as mathematics learners and to understand their role in the development of their students' mathematics identities. This paper reports on a professional development project for K-2 teachers (n = 41), in which participants were asked to write mathematics…

How Syntactic Reasoners Can Develop Understanding, Evaluate Conjectures, and Generate Counterexamples in Advanced Mathematics

ERIC Educational Resources Information Center

Weber, Keith

2009-01-01

This paper presents a case study of a highly successful student whose exploration of an advanced mathematical concept relies predominantly on syntactic reasoning, such as developing formal representations of mathematical ideas and making logical deductions. This student is observed as he learns a new mathematical concept and then completes…

SPATIAL VISUALIZATION ABILITIES OF CENTRAL WASHINGTON STATE COLLEGE PROSPECTIVE ELEMENTARY AND SECONDARY TEACHERS OF MATHEMATICS.

ERIC Educational Resources Information Center

MARTIN, BERNARD LOYAL

INVESTIGATED WAS THE EXTENT TO WHICH STUDENTS COMPLETING PLANNED MATHEMATICS EDUCATION PROGRAMS (1) WERE PROFICIENT IN SPATIAL VISUALIZATION ABILITIES, AND (2) HAD DEVELOPED MATHEMATICAL UNDERSTANDINGS. THE EFFECTS OF THE MATHEMATICS CURRICULA UPON SUCH DEVELOPMENT WERE INVESTIGATED BY COMPARING GROUP MEAN TEST SCORES OF PROSPECTIVE ELEMENTARY AND…

Mapping Children's Understanding of Mathematical Equivalence

ERIC Educational Resources Information Center

Taylor, Roger S.; Rittle-Johnson, Bethany; Matthews, Percival G.; McEldoon, Katherine L.

2009-01-01

The focus of this research is to develop an initial framework for assessing and interpreting students' level of understanding of mathematical equivalence. Although this topic has been studied for many years, there has been no systematic development or evaluation of a valid measure of equivalence knowledge. A powerful method for accomplishing this…

An Examination of the Statistical Problem-Solving Process as a Potential Means for Developing an Understanding of Argumentation

ERIC Educational Resources Information Center

Smith Baum, Brittany Deshae

2017-01-01

As part of the recent history of the mathematics curriculum, reasoning and argument have been emphasized throughout mathematics curriculum standards. Specifically, as part of the Common Core State Standards for Mathematics, the Standards for Mathematical Practice were presented, which included the expectation that students develop arguments and…

Understanding the Technological, Pedagogical, and Mathematical Issues That Emerge as Secondary Mathematics Teachers Design Lessons That Integrate Technology

ERIC Educational Resources Information Center

Gonzalez, Marggie Denise

2016-01-01

This multiple case study examines four groups of secondary mathematics teachers engaged in a Lesson Study approach to professional development where they planned and taught lessons that integrate technology. Informed by current literature, a framework was developed to focus on the dimensions of teacher's knowledge to teach mathematics with…

Using confirmatory factor analysis to understand executive control in preschool children: sources of variation in emergent mathematic achievement

PubMed Central

Bull, Rebecca; Espy, Kimberly Andrews; Wiebe, Sandra A.; Sheffield, Tiffany D.; Nelson, Jennifer Mize

2010-01-01

Latent variable modeling methods have demonstrated utility for understanding the structure of executive control (EC) across development. These methods are utilized to better characterize the relation between EC and mathematics achievement in the preschool period, and to understand contributing sources of individual variation. Using the sample and battery of laboratory tasks described in Wiebe, Espy and Charak (2008), latent EC was related strongly to emergent mathematics achievement in preschool, and was robust after controlling for crystallized intellectual skills. The relation between crystallized skills and emergent mathematics differed between girls and boys, although the predictive association between EC and mathematics did not. Two dimensions of the child’s social environment contributed to mathematics achievement: social network support through its relation to EC and environmental stressors through its relation with crystallized skills. These findings underscore the need to examine the dimensions, mechanisms, and individual pathways that influence the development of early competence in basic cognitive processes that underpin early academic achievement. PMID:21676089

Using confirmatory factor analysis to understand executive control in preschool children: sources of variation in emergent mathematic achievement.

PubMed

Bull, Rebecca; Espy, Kimberly Andrews; Wiebe, Sandra A; Sheffield, Tiffany D; Nelson, Jennifer Mize

2011-07-01

Latent variable modeling methods have demonstrated utility for understanding the structure of executive control (EC) across development. These methods are utilized to better characterize the relation between EC and mathematics achievement in the preschool period, and to understand contributing sources of individual variation. Using the sample and battery of laboratory tasks described in Wiebe, Espy and Charak (2008), latent EC was related strongly to emergent mathematics achievement in preschool, and was robust after controlling for crystallized intellectual skills. The relation between crystallized skills and emergent mathematics differed between girls and boys, although the predictive association between EC and mathematics did not. Two dimensions of the child 's social environment contributed to mathematics achievement: social network support through its relation to EC and environmental stressors through its relation with crystallized skills. These findings underscore the need to examine the dimensions, mechanisms, and individual pathways that influence the development of early competence in basic cognitive processes that underpin early academic achievement. © 2010 Blackwell Publishing Ltd.

Growing Mathematical Understanding through Collective Image Making, Collective Image Having, and Collective Property Noticing

ERIC Educational Resources Information Center

Martin, Lyndon C.; Towers, Jo

2015-01-01

In the research reported in this paper, we develop a theoretical perspective to describe and account for the growth of collective mathematical understanding. We discuss collective processes in mathematics, drawing in particular on theoretical work in the domains of improvisational jazz and theatre. Using examples of data from a study of elementary…

Effectiveness of a Language Based Program in School Mathematics on Students' Understanding of Statistics

ERIC Educational Resources Information Center

Wekesa, Duncan Wasike

2006-01-01

Mathematical knowledge and understanding is important not only for scientific progress and development but also for its day-to-day application in social sciences and arts, government, business and management studies and household chores. But the general performance in school mathematics in Kenya has been poor over the years. There is evidence that…

Using Mathematical Software to Introduce Fourier Transforms in Physical Chemistry to Develop Improved Understanding of Their Applications in Analytical Chemistry

ERIC Educational Resources Information Center

Miller, Tierney C.; Richardson, John N.; Kegerreis, Jeb S.

2016-01-01

This manuscript presents an exercise that utilizes mathematical software to explore Fourier transforms in the context of model quantum mechanical systems, thus providing a deeper mathematical understanding of relevant information often introduced and treated as a "black-box" in analytical chemistry courses. The exercise is given to…

Learning To Teach: Constructing Meaningful Understanding of Mathematical Content. Craft Paper 89-3.

ERIC Educational Resources Information Center

Lappan, Glenda; Even, Ruhama

This paper discusses the development of the mathematical experiences which make up the three-term sequence of mathematics courses taken by participants in the Elementary Mathematics Project (EMP), a longitudinal study of change in preservice teachers' perceptions and beliefs about mathematics. For the mathematics courses, both content and teaching…

Calling for Research Collaborations and the Use of Dis/ability Studies in Mathematics Education

ERIC Educational Resources Information Center

Tan, Paulo; Kastberg, Signe

2017-01-01

In this commentary, the authors find that despite discussions of "mathematics for all," opportunities that support the development of mathematical reasoning and understanding of mathematics as a human endeavor often do not exist for mathematics learners identified in schools as having dis/abilities. Indeed, mathematics for all is…

Students' Perceptions and Development of Conceptual Understanding Regarding Trigonometry and Trigonometric Function

ERIC Educational Resources Information Center

Cetin, Omer Faruk

2015-01-01

This study aims to analyse university level mathematics education students' perceptions on conceptual understanding of trigonometry and trigonometric functions and their content development of these concepts. A case study was conducted with 90 freshman students of Elementary Mathematics Department. The data were gathered via a scale; they included…

Advanced Mathematical Study and the Development of Conditional Reasoning Skills

PubMed Central

Attridge, Nina; Inglis, Matthew

2013-01-01

Since the time of Plato, philosophers and educational policy-makers have assumed that the study of mathematics improves one's general ‘thinking skills’. Today, this argument, known as the ‘Theory of Formal Discipline’ is used in policy debates to prioritize mathematics in school curricula. But there is no strong research evidence which justifies it. We tested the Theory of Formal Discipline by tracking the development of conditional reasoning behavior in students studying post-compulsory mathematics compared to post-compulsory English literature. In line with the Theory of Formal Discipline, the mathematics students did develop their conditional reasoning to a greater extent than the literature students, despite them having received no explicit tuition in conditional logic. However, this development appeared to be towards the so-called defective conditional understanding, rather than the logically normative material conditional understanding. We conclude by arguing that Plato may have been correct to claim that studying advanced mathematics is associated with the development of logical reasoning skills, but that the nature of this development may be more complex than previously thought. PMID:23869241

Life on the Number Line: Routes to Understanding Fraction Magnitude for Students with Difficulties Learning Mathematics

ERIC Educational Resources Information Center

Gersten, Russell; Schumacher, Robin F.; Jordan, Nancy C.

2017-01-01

Magnitude understanding is critical for students to develop a deep understanding of fractions and more advanced mathematics curriculum. The research reports in this special issue underscore magnitude understanding for fractions and emphasize number lines as both an assessment and an instructional tool. In this commentary, we discuss how number…

Developing Essential Understanding of Rational Numbers for Teaching Mathematics in Grades 3-5. Essential Understandings

ERIC Educational Resources Information Center

Clarke, Carne; Fisher, William; Marks, Rick; Ross, Sharon; Zbiek, Rose Mary

2010-01-01

This book focuses on essential knowledge for teachers about rational numbers. It is organized around four big ideas, supported by multiple smaller, interconnected ideas--essential understandings. Taking teachers beyond a simple introduction to rational numbers, the book will broaden and deepen their mathematical understanding of one of the most…

Effecting Affect: Developing a Positive Attitude to Primary Mathematics Learning

ERIC Educational Resources Information Center

Sparrow, Len; Hurst, Chris

2010-01-01

Most adults' attitudes to mathematics come from their experiences of mathematics in school when they were children. Children's mathematical worlds are complex places containing both cognitive and affective elements. One cannot ignore the affective domain if one wishes to understand children's mathematical learning. Teacher education students…

Asynchronous Discourse in a Web-Assisted Mathematics Education Course

ERIC Educational Resources Information Center

Li, Zhongxiao

2009-01-01

Fall term of 2006, a web-assisted undergraduate mathematics course was taught at the University of Idaho: Math 235 Mathematics for Elementary Teachers I. The course goals were: To foster a deep understanding of critical mathematical content; and to promote the development of mathematical communication and collaboration concepts, skills, and…

Graphing Calculator Exposure of Mathematics Learning in a Partially Technology Incorporated Environment

ERIC Educational Resources Information Center

Kharuddin, Azrul Fazwan; Ismail, Noor Azina

2017-01-01

Integrating technology in the mathematics curriculum has become a necessary task for curriculum developers as well as mathematics practitioners across the world and time. In general research studies seeking a better understanding of how best to integrate mathematics analysis tools with mathematics subject matter normally observe mathematics…

Communication and Representation as Elements in Mathematical Literacy

ERIC Educational Resources Information Center

Thompson, Denisse R.; Chappell, Michaele F.

2007-01-01

The process standards of communication and representation in the "Principles and Standards for School Mathematics" are critical tools to help students develop mathematical literacy. In the mathematics classroom, students need to be encouraged to use speaking, listening, reading, and writing to communicate their understanding of mathematics words,…

The Language of Mathematics: The Importance of Teaching and Learning Mathematical Vocabulary

ERIC Educational Resources Information Center

Riccomini, Paul J.; Smith, Gregory W.; Hughes, Elizabeth M.; Fries, Karen M.

2015-01-01

Vocabulary understanding is a major contributor to overall comprehension in many content areas, including mathematics. Effective methods for teaching vocabulary in all content areas are diverse and long standing. Teaching and learning the language of mathematics is vital for the development of mathematical proficiency. Students' mathematical…

Using Problem Solving to Assess Young Children's Mathematics Knowledge

ERIC Educational Resources Information Center

Charlesworth, Rosalind; Leali, Shirley A.

2012-01-01

Mathematics problem solving provides a means for obtaining a view of young children's understanding of mathematics as they move through the early childhood concept development sequence. Assessment information can be obtained through observations and interviews as children develop problem solutions. Examples of preschool, kindergarten, and primary…

Business Mathematics Curriculum Guide.

ERIC Educational Resources Information Center

Ebersole, Benjamin P., Comp.; And Others

This revised course in business mathematics emphasizes computations needed for problem solving, but greater attention is focused on mathematical principles that were developed in previous grades. In addition, the course aims to develop further an understanding of business principles and practices which can be used in gainful employment and in the…

A Case Study Using CRA to Teach Students with Disabilities to Count Using Flexible Numbers: Applying Skip Counting to Multiplication

ERIC Educational Resources Information Center

Gibbs, Anna S.; Hinton, Vanessa M.; Flores, Margaret M.

2018-01-01

Children who struggle in mathematics have a limited understanding of the foundational processes of mathematics. A lack of conceptual understanding causes students to fall behind as they progress through the core curriculum. Children at high risk for developing mathematics disabilities fail to gain numeracy knowledge. The purpose of this case study…

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…

STEM Gives Meaning to Mathematics

ERIC Educational Resources Information Center

Hefty, Lukas J.

2015-01-01

The National Council of Teachers of Mathematics' (NCTM's) "Principles and Standards for School Mathematics" (2000) outlines fi ve Process Standards that are essential for developing deep understanding of mathematics: (1) Problem Solving; (2) Reasoning and Proof; (3) Communication; (4) Connections; and (5) Representation. The Common Core…

Making the Most of Mathematical Discussions

ERIC Educational Resources Information Center

Staples, Megan; Colonis, Melissa M.

2007-01-01

The importance of mathematical discourse and its connection to developing conceptual understanding, communication, and reasoning is well documented throughout the National Council of Teachers of Mathematics (NCTM's) "Principles and Standards for School Mathematics" (2000). This article highlights the differences between two kinds of discussions:…

Variation and Mathematics Pedagogy

ERIC Educational Resources Information Center

Leung, Allen

2012-01-01

This discussion paper put forwards variation as a theme to structure mathematical experience and mathematics pedagogy. Patterns of variation from Marton's Theory of Variation are understood and developed as types of variation interaction that enhance mathematical understanding. An idea of a discernment unit comprising mutually supporting variation…

Implementing an Effective Mathematics Fact Fluency Practice Activity

ERIC Educational Resources Information Center

Riccomini, Paul J.; Stocker, James D., Jr.; Morano, Stephanie

2017-01-01

Proficiency in mathematics involves the seamless synchronization of conceptual understanding, procedural knowledge, computational fluency, and problem solving (NMAP, 2008). Clearly, fluency with mathematics facts is one element embedded within mathematical proficiency and important for students with disabilities to develop. As more and more…

How to Develop Teachers' Mathematical Molding Teaching Skills

ERIC Educational Resources Information Center

Mrayyan, Salwa

2016-01-01

This study aimed at developing some of the mathematical modelling skills necessary for the student teachers in mathematics education College. Modeling involves making genuine choices, modeling problems have many possible justifiable answers, modeling problems matter to the end-user who needs to understand something or make a decision. Modeling…

Opportunities to Promote Mathematical Content Knowledge for Primary Teaching

ERIC Educational Resources Information Center

Livy, Sharyn; Herbert, Sandra

2014-01-01

Understanding the development of pre-service teachers' mathematical content knowledge (MCK) is important for improving primary mathematics' teacher education. This paper reports on a case study, Rose and her opportunities to develop MCK during the four years of her program. Program opportunities to promote MCK when planning and practicing primary…

Developing Mathematical Practices through Reflection Cycles

ERIC Educational Resources Information Center

Reinholz, Daniel L.

2016-01-01

This paper focuses on reflection in learning mathematical practices. While there is a long history of research on reflection in mathematics, it has focused primarily on the development of conceptual understanding. Building on notion of learning as participation in social practices, this paper broadens the theory of reflection in mathematics…

Beyond the Write Answer: Mathematical Connections

ERIC Educational Resources Information Center

Haltiwanger, Leigh; Simpson, Amber M.

2013-01-01

As math teachers, the authors often encountered students who could ace a test but not explain their reasoning. This phenomenon was disturbing to them, and they fought for years to help students both understand mathematical concepts and develop meaning for them. Since their primary goal was to develop mathematically literate students, their…

Students' Understanding of Mathematical Expressions in Physical Chemistry Contexts: An Analysis Using Sherin's Symbolic Forms

ERIC Educational Resources Information Center

Becker, Nicole; Towns, Marcy

2012-01-01

Undergraduate physical chemistry courses require students to be proficient in calculus in order to develop an understanding of thermodynamics concepts. Here we present the findings of a study that examines student understanding of mathematical expressions, including partial derivative expressions, in two undergraduate physical chemistry courses.…

Unlocking Mathematics Teaching. Second Edition

ERIC Educational Resources Information Center

Koshy, Valsa, Ed.; Murray, Jean, Ed.

2011-01-01

Now in a fully updated second edition, "Unlocking Mathematics Teaching" is a comprehensive guide to teaching mathematics in the primary school. Combining theory and practice, selected experts outline the current context of mathematics education. They suggest strategies, activities and examples to help develop readers understanding and confidence…

Clinical Assessment in Mathematics: Learning the Craft.

ERIC Educational Resources Information Center

Hunting, Robert P.; Doig, Brian A.

1997-01-01

Discusses a professional development program called Clinical Approaches to Mathematics Assessment. Argues for the advanced training of mathematics teachers who understand knowledge construction processes of students; can use clinical tools for evaluating a student's unique mathematical "fingerprint"; and can create or adapt problems, tasks, or…

DOE Fundamentals Handbook: Mathematics, Volume 1

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

Not Available

1992-06-01

The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclearmore » facility operations.« less

DOE Fundamentals Handbook: Mathematics, Volume 2

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

Not Available

1992-06-01

The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclearmore » facility operations.« less

Critical Relationships between Teachers and Learners of School Mathematics

ERIC Educational Resources Information Center

Wright, Pete

2017-01-01

This article draws on critical theories and perspectives on mathematics education to explain the tendency of mathematics teaching worldwide to remain focused on developing procedural understanding, despite repeated calls from the mathematics education community for a more relevant and engaging curriculum. It highlights how conventional approaches…

Research Mathematicians' Practices in Selecting Mathematical Problems

ERIC Educational Resources Information Center

Misfeldt, Morten; Johansen, Mikkel Willum

2015-01-01

Developing abilities to create, inquire into, qualify, and choose among mathematical problems is an important educational goal. In this paper, we elucidate how mathematicians work with mathematical problems in order to understand this mathematical process. More specifically, we investigate how mathematicians select and pose problems and discuss to…

Student Teachers' Mathematics Attitudes, Authentic Investigations and Use of Metacognitive Tools

ERIC Educational Resources Information Center

Afamasaga-Fuata'i, Karoline; Sooaemalelagi, Lumaava

2014-01-01

Based on findings from a semester-long study, this article examines the development of Samoan prospective teachers' mathematical understandings and mathematics attitudes when investigating authentic contexts and applying working mathematically processes, mental computations and problem-solving strategies to find solutions of problems. The…

Understanding the Chinese Approach to Creative Teaching in Mathematics Classrooms

ERIC Educational Resources Information Center

Niu, Weihua; Zhou, Zheng; Zhou, Xinlin

2017-01-01

Using Amabile's componential theory of creativity as a framework, this paper analyzes how Chinese mathematics teachers achieve creative teaching through acquiring in-depth domain-specific knowledge in mathematics, developing creativity-related skills, as well as stimulating student interest in learning mathematics, through well-crafted,…

Developing and Piloting the Planning for Facilitating Mathematical Processes and Strategies for Preschool Learners

ERIC Educational Resources Information Center

Botha, M.; Maree, J. G.; de Witt, M. W.

2005-01-01

From an early age young children actively engage informally in acquiring fundamental concepts and process skills that form a basis for mathematical understanding. Quite logically, questions will arise during planning when young children first encounter a more formal learning environment: what strategy should one use to develop mathematical …

Life on the Number Line: Routes to Understanding Fraction Magnitude for Students With Difficulties Learning Mathematics.

PubMed

Gersten, Russell; Schumacher, Robin F; Jordan, Nancy C

Magnitude understanding is critical for students to develop a deep understanding of fractions and more advanced mathematics curriculum. The research reports in this special issue underscore magnitude understanding for fractions and emphasize number lines as both an assessment and an instructional tool. In this commentary, we discuss how number lines broaden the concept of fractions for students who are tied to the more general part-whole representations of area models. We also discuss how number lines, compared to other representations, are a superior and more mathematically correct way to explain fraction concepts.

Using Confirmatory Factor Analysis to Understand Executive Control in Preschool Children: Sources of Variation in Emergent Mathematic Achievement

ERIC Educational Resources Information Center

Bull, Rebecca; Espy, Kimberly Andrews; Wiebe, Sandra A.; Sheffield, Tiffany D.; Nelson, Jennifer Mize

2011-01-01

Latent variable modeling methods have demonstrated utility for understanding the structure of executive control (EC) across development. These methods are utilized to better characterize the relation between EC and mathematics achievement in the preschool period, and to understand contributing sources of individual variation. Using the sample and…

Learning Mathematics in High School Courses beyond Mathematics: Combating the Need for Post-Secondary Remediation in Mathematics

ERIC Educational Resources Information Center

Young, R. Brent; Hodge, Angie; Edwards, M. Craig; Leising, James G.

2012-01-01

The purpose of this study was to empirically test the posit that students who participated in a contextualized, mathematics-enhanced high school agricultural power and technology (APT) curriculum and aligned instructional approach would develop a deeper and more sustained understanding of selected mathematics concepts than those students who…

Understanding the Development of Mathematical Work in the Context of the Classroom

ERIC Educational Resources Information Center

Kuzniak, Alain; Nechache, Assia; Drouhard, J. P.

2016-01-01

According to our approach to mathematics education, the optimal aim of the teaching of mathematics is to assist students in achieving efficient mathematical work. But, what does efficient exactly mean in that case? And how can teachers reach this objective? The model of Mathematical Working Spaces with its three dimensions--semiotic, instrumental,…

An Analysis of Pre-Service Mathematics Teachers' Performance in Modelling Tasks in Terms of Spatial Visualisation Ability

ERIC Educational Resources Information Center

Tasova, Halil Ibrahim; Delice, Ali

2012-01-01

Mathematical modelling involves mathematical constructions chosen to represent some real world situations and the relationships among them; it is the process of expressing a real world situation mathematically. Visualisation can play a significant role in the development of thinking or understanding mathematical concepts, and also makes abstract…

Towards Understanding the Origins of Children's Difficulties in Mathematics Learning

ERIC Educational Resources Information Center

Mulligan, Joanne

2011-01-01

Contemporary research from a psychology of mathematics education perspective has turned increasing attention to the structural development of mathematics as an explanation for the wide differences in mathematical competence shown upon school entry and in the early school years. Patterning, multiplicative reasoning and spatial structuring are three…

Winning Women into Mathematics.

ERIC Educational Resources Information Center

Kenschaft, Patricia Clark, Ed.; Keith, Sandra Zaroodny, Ed.

Mathematics is an auspicious discipline for young people of both sexes and all ethnic groups. This booklet aims to help members of the Mathematical Association of America (MAA) and others to increase future participation of women in mathematics, to better understand their present roles, and to develop a vision of a world with greater equal…

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…

Investigative Approaches to Teaching Mathematics and "Getting through the Curriculum": The Example of Pendulums

ERIC Educational Resources Information Center

Beswick, Kim; Muir, Tracey; Callingham, Rosemary

2014-01-01

The benefits of rich tasks, project-based learning, and other inquiry-based approaches in terms of student understanding and engagement with mathematics are well documented. Such pedagogies are consistent with the development of mathematical proficiencies as described in the "Australian Curriculum: Mathematics" (Australian Curriculum…

Teaching Gifted Children Mathematics in Grades Four Through Six.

ERIC Educational Resources Information Center

Gensley, Juliana T.

Intended for teachers of gifted students in grades 4-6, the guide emphasizes the need for specialized instruction in mathematics, suggests methods for teaching mathematical facts and concepts, describes approaches and materials to develop students' understanding of mathematical principles, and explores ways to build skills and creativity. Stressed…

Examining the Efficacy of a Tier 2 Kindergarten Mathematics Intervention

ERIC Educational Resources Information Center

Clarke, Ben; Doabler, Christian T.; Smolkowski, Keith; Baker, Scott K.; Fien, Hank; Cary, Mari Strand

2016-01-01

This study examined the efficacy of a Tier 2 kindergarten mathematics intervention program, ROOTS, focused on developing whole number understanding for students at risk in mathematics. A total of 29 classrooms were randomly assigned to treatment (ROOTS) or control (standard district practices) conditions. Measures of mathematics achievement were…

Mathematical Modeling with Middle School Students: The Robot Art Model-Eliciting Activity

ERIC Educational Resources Information Center

Stohlmann, Micah S.

2017-01-01

Internationally mathematical modeling is garnering more attention for the benefits associated with it. Mathematical modeling can develop students' communication skills and the ability to demonstrate understanding through different representations. With the increased attention on mathematical modeling, there is a need for more curricula to be…

Missing the Promise of Mathematical Modeling

ERIC Educational Resources Information Center

Meyer, Dan

2015-01-01

The Common Core State Standards for Mathematics (CCSSM) have exerted enormous pressure on every participant in a child's education. Students are struggling to meet new standards for mathematics learning, and parents are struggling to understand how to help them. Teachers are growing in their capacity to develop new mathematical competencies, and…

Mathematics education and students with learning disabilities: introduction to the special series.

PubMed

Rivera, D P

1997-01-01

The prevalence of students with mathematics learning disabilities has triggered an interest among special education researchers and practitioners in developing an understanding of the needs of this group of students, and in identifying effective instructional programming to foster their mathematical performance during the school years and into adulthood. Research into the characteristics of students with mathematics learning disabilities is being approached from different perspectives, including developmental, neurological and neuropsychological, and educational. This diversity helps us develop a broader understanding of students' learning needs and difficulties. Special education assessment practices encompass a variety of approaches, including norm-referenced, criterion-referenced, and nonstandardized procedures, depending on the specific assessment questions professionals seek to answer. Students' mathematical knowledge and conceptual understanding must be examined to determine their strengths and weaknesses, curriculum-based progress, and use of cognitive strategies to arrive at mathematical solutions. Research findings have identified empirically validated interventions for teaching mathematics curricula to students with mathematics learning disabilities. Research studies have been grounded in behavioral theory and cognitive psychology, with an emergent interest in the constructivist approach. Although research studies have focused primarily on computational performance, more work is being conducted in the areas of story-problem solving and technology. These areas as well as other math curricular skills require further study. Additionally, the needs of adults with math LD have spurred educators to examine the elementary and secondary math curricula and determine ways to infuse them with life skills instruction accordingly. As the field of mathematics special education continues to evolve, special educators must remain cognizant of the developments in and influences on the field of mathematics education. Reform efforts have shaped the field significantly since the 1950s, contributing to the curriculum offered in mathematics textbooks and the pedagogical practices taught in higher education courses. Mathematics educators continue to search for a better understanding of how children learn mathematics; this process is shaped by the prevailing theoretical orientations and research methodologies. This special series in mathematics special education provides readers with information about the characteristics of students with mathematics learning disabilities, assessment procedures, mathematics programming, teacher preparation, and future directions for the field. The series originated as a result of discussions with Dr. Lee Wiederholt and Dr. Judith K. Voress, who saw a need for the compilation of recent research and best practices in mathematics special education. I thank them for their support of and thoughtful insights about the development of this series. I also appreciate the support of Dr. George Hynd and his editorial assistant, Kathryn Black, in finalizing the details for publication. Finally, I am most appreciative of the authors' contributions to this series; their work continues to significantly influence the development of the field of mathematics special education and programming for students with mathematics learning disabilities.

What Should Common Core Assessments Measure?

ERIC Educational Resources Information Center

Chandler, Kayla; Fortune, Nicholas; Lovett, Jennifer N.; Scherrer, Jimmy

2016-01-01

The Common Core State Standards for mathematics promote ideals about learning mathematics by providing specific standards focused on conceptual understanding and incorporating practices in which students must participate to develop conceptual understanding. Thus, how we define learning is pivotal because our current definition isn't aligned with…

Tracing the Construction of Mathematical Activity with an Advanced Graphing Calculator to Understand the Roles of Technology Developers, Teachers and Students

ERIC Educational Resources Information Center

Hillman, Thomas

2014-01-01

This article examines mathematical activity with digital technology by tracing it from its development through its use in classrooms. Drawing on material-semiotic approaches from the field of Science and Technology Studies, it examines the visions of mathematical activity that developers had for an advanced graphing calculator. It then follows the…

Supporting Teachers' Understandings of Function through Online Professional Development

ERIC Educational Resources Information Center

Silverman, Jason

2017-01-01

This article explores one segment of an extended research and development project that was conducted to better understand the ways online teacher professional development can support teachers' development of deep and connected mathematical understandings. In particular, this article discusses teachers' understandings of the concept of…

Impact of the Developing Mathematical Ideas Professional Development Program on Grade 4 Students' and Teachers' Understanding of Fractions. REL 2017-256

ERIC Educational Resources Information Center

Jayanthi, Madhavi; Gersten, Russell; Taylor, Mary Jo; Smolkowski, Keith; Dimino, Joseph

2017-01-01

Contemporary state math standards emphasize that students must demonstrate an understanding of the mathematical ideas underlying the computations that have typically been the core of the elementary school math curriculum. The standards have put an increased emphasis on the study of fractions in upper elementary grades, which are the years during…

The Development and Publication of Elementary Mathematics Textbooks: Let the Buyer Beware!

ERIC Educational Resources Information Center

Reys, Barbara J.; Reys, Robert E.

2006-01-01

Mathematics textbooks are critical tools for student learning in American classrooms. Teachers use them daily to plan and deliver lessons, and students use them in class to explore and learn mathematics. Given textbooks' potential to support student learning, it is important to understand how they are developed. While pressure is growing on…

Impacts of Professional Development on High School Mathematics Teachers as They Implement Common Core State Standards

ERIC Educational Resources Information Center

Saucedo, Ana A.

2017-01-01

The purpose of this qualitative study was to understand the perceptions of high school mathematics teachers regarding the support provided through professional development (PD) as they engage in the implementation of the Common Core State Standards (CCSS). By means of a qualitative instrumental case study, eight high school mathematics teachers…

Gesture Recognition for Educational Games: Magic Touch Math

NASA Astrophysics Data System (ADS)

Kye, Neo Wen; Mustapha, Aida; Azah Samsudin, Noor

2017-08-01

Children nowadays are having problem learning and understanding basic mathematical operations because they are not interested in studying or learning mathematics. This project proposes an educational game called Magic Touch Math that focuses on basic mathematical operations targeted to children between the age of three to five years old using gesture recognition to interact with the game. Magic Touch Math was developed in accordance to the Game Development Life Cycle (GDLC) methodology. The prototype developed has helped children to learn basic mathematical operations via intuitive gestures. It is hoped that the application is able to get the children motivated and interested in mathematics.

(Re)Envisioning Mathematics Education: Examining Equity and Social Justice in an Elementary Mathematics Methods Course

ERIC Educational Resources Information Center

Koestler, Courtney

2010-01-01

In this dissertation, I present my attempts at designing an elementary mathematics methods course to support prospective teachers in developing an understanding of how to teach all students in learning powerful mathematics. To do this, I introduced them to teaching mathematics for equity and social justice by discussing ways to support students'…

Evaluating the Suitability of Mathematical Thinking Problems for Senior High-School Students by Including Mathematical Sense Making and Global Planning

ERIC Educational Resources Information Center

van Velzen, Joke H.

2016-01-01

The mathematics curriculum often provides for relatively few mathematical thinking problems or non-routine problems that focus on a deepening of understanding mathematical concepts and the problem-solving process. To develop such problems, methods are required to evaluate their suitability. The purpose of this preliminary study was to find such an…

Influence of Difficulty with Language of Mathematics on Perceived Self-Efficacy in Learning Mathematics among Upper Primary Students of Kerala

ERIC Educational Resources Information Center

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

2017-01-01

There is increasing realization that mathematics-related self-efficacy expectations are a strong predictor of an array of significant mathematics outcomes. It is also evident that the curricular practice in schools largely neglects development of a student understanding in the unique language of mathematics. Consequently, this study probes how…

Analyzing the Teaching of Advanced Mathematics Courses via the Enacted Example Space

ERIC Educational Resources Information Center

Fukawa-Connelly, Timothy Patrick; Newton, Charlene

2014-01-01

Examples are believed to be very important in developing conceptual understanding of mathematical ideas, useful both in mathematics research and instruction (Bills & Watson in "Educational Studies in Mathematics" 69:77-79, 2008; Mason & Watson, 2008; Bills & Tall, 1998; Tall & Vinner, 1981). In this study, we draw on the…

Motivating Prospective Elementary School Teachers to Learn Mathematics by Focusing upon Children's Mathematical Thinking

ERIC Educational Resources Information Center

Philipp, Randolph A.

2008-01-01

Elementary school children in the United States are not developing acceptable levels of mathematical proficiency (National Center for Education Statistics, 1999), and a major concern of teacher educators is that teachers lack the depth and flexibility of mathematical understanding and the corresponding beliefs they need to teach for proficiency…

Understanding Prospective Teachers' Mathematical Modeling Processes in the Context of a Mathematical Modeling Course

ERIC Educational Resources Information Center

Zeytun, Aysel Sen; Cetinkaya, Bulent; Erbas, Ayhan Kursat

2017-01-01

This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…

Improving Primary School Prospective Teachers' Understanding of the Mathematics Modeling Process

ERIC Educational Resources Information Center

Bal, Aytgen Pinar; Doganay, Ahmet

2014-01-01

The development of mathematical thinking plays an important role on the solution of problems faced in daily life. Determining the relevant variables and necessary procedural steps in order to solve problems constitutes the essence of mathematical thinking. Mathematical modeling provides an opportunity for explaining thoughts in real life by making…

Examining the Process of Developing a Research-Based Mathematics Curriculum and Its Policy Implications

ERIC Educational Resources Information Center

Superfine, Alison Castro; Kelso, Catherine Randall; Beal, Susan

2010-01-01

The implementation of "research-based" mathematics curricula is increasingly becoming a central element of mathematics education reform policies. Given the recent focus on grounding mathematics curriculum policies in research, it is important to understand precisely what it means for a curriculum to be research-based. Using the Curriculum Research…

Parent-Child Mathematical Interactions: Examining Self-Report and Direct Observation

ERIC Educational Resources Information Center

Missall, Kristen N.; Hojnoski, Robin L.; Moreano, Ginna

2017-01-01

Variability in children's early-learning home environments points to the need to better understand specific mechanisms of early mathematical development. We used a sample of 66 parent-preschool child dyads to describe parent-reported mathematical activities in the home and observed parent-child mathematical activities in a semi-structured play…

The QUASAR Project: The "Revolution of the Possible" in Mathematics Instructional Reform in Urban Middle Schools.

ERIC Educational Resources Information Center

Silver, Edward A.; Stein, Mary Kay

1996-01-01

Examines critical features of the QUASAR Project, a mathematics instruction program oriented toward helping students develop a meaningful understanding of mathematical ideas through challenging mathematical tasks, and discusses findings regarding the positive impact it has had on students. Challenges and obstacles in implementing the project are…

Comparison of University Students' Understanding of Graphs in Different Contexts

ERIC Educational Resources Information Center

Planinic, Maja; Ivanjek, Lana; Susac, Ana; Milin-Sipus, Zeljka

2013-01-01

This study investigates university students' understanding of graphs in three different domains: mathematics, physics (kinematics), and contexts other than physics. Eight sets of parallel mathematics, physics, and other context questions about graphs were developed. A test consisting of these eight sets of questions (24 questions in all) was…

Community College Developmental Education Students' Understanding of Foundational Fraction Concepts

ERIC Educational Resources Information Center

Alexander, Cathleen Marie

2013-01-01

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

Implementing Mathematics Teaching That Promotes Students' Understanding through Theory-Driven Lesson Study

ERIC Educational Resources Information Center

Huang, Rongjin; Gong, Zikun; Han, Xue

2016-01-01

Lesson study (LS) has been practiced in China as an effective way to advance teachers' professional development for decades. This study explores how LS improves teaching that promotes students' understanding. A LS group including didacticians (practice-based teaching research specialist and University-based mathematics educators) and mathematics…

A Strategy for Improving US Middle School Student Mathematics Word Problem Solving Performance

NASA Technical Reports Server (NTRS)

Thomas, Valerie L.

2004-01-01

U.S. middle school students have difficulty understanding and solving mathematics word problems. Their mathematics performance on the Third International Mathematics and Science Study (TIMMS) is far below their international peers, and minority students are less likely than high socioeconomic status (SES) White/Asian students to be exposed to higher-level mathematics concepts. Research literature also indicates that when students use both In-School and Out-of-School knowledge and experiences to create authentic mathematics word problems, student achievement improves. This researcher developed a Strategy for improving mathematics problem solving performance and a Professional Development Model (PDM) to effectively implement the Strategy.

Tragic mathematics: romantic narratives and the refounding of mathematics in the early nineteenth century.

PubMed

Alexander, Amir R

2006-12-01

A new, Romantic type of mathematical story appeared in the early nineteenth century that was radically different from the sober narrative characteristic of the previous generation of mathematicians. At the same time, a new mathematical practice emerged that differed sharply from the understanding and practice of mathematics during the Enlightenment. These parallel developments are inseparable: the new type of mathematical practice went hand in hand with the new mathematical story.

A Framework for Teachers' Knowledge of Mathematical Reasoning

ERIC Educational Resources Information Center

Herbert, Sandra

2014-01-01

Exploring and developing primary teachers' understanding of mathematical reasoning was the focus of the "Mathematical Reasoning Professional Learning Research Program." Twenty-four primary teachers were interviewed after engagement in the first stage of the program incorporating demonstration lessons focused on reasoning conducted in…

Facilitating Science and Mathematics Teachers' Talk about Equity: What Are the Strengths and Limitations of Four Strategies for Professional Learning?

ERIC Educational Resources Information Center

Bianchini, Julie A.; Dwyer, Hilary A.; Brenner, Mary E.; Wearly, Alayna J.

2015-01-01

We investigated a 2.5-year professional development effort designed to support practicing science and mathematics teachers in understanding equity and enacting equitable practices. Our purpose was to inform the research base on effective equity professional development, toward the goal of better supporting science and mathematics teachers in…

Learning biology through connecting mathematics to scientific mechanisms: Student outcomes and teacher supports

NASA Astrophysics Data System (ADS)

Schuchardt, Anita

Integrating mathematics into science classrooms has been part of the conversation in science education for a long time. However, studies on student learning after incorporating mathematics in to the science classroom have shown mixed results. Understanding the mixed effects of including mathematics in science has been hindered by a historical focus on characteristics of integration tangential to student learning (e.g., shared elements, extent of integration). A new framework is presented emphasizing the epistemic role of mathematics in science. An epistemic role of mathematics missing from the current literature is identified: use of mathematics to represent scientific mechanisms, Mechanism Connected Mathematics (MCM). Building on prior theoretical work, it is proposed that having students develop mathematical equations that represent scientific mechanisms could elevate their conceptual understanding and quantitative problem solving. Following design and implementation of an MCM unit in inheritance, a large-scale quantitative analysis of pre and post implementation test results showed MCM students, compared to traditionally instructed students) had significantly greater gains in conceptual understanding of mathematically modeled scientific mechanisms, and their ability to solve complex quantitative problems. To gain insight into the mechanism behind the gain in quantitative problem solving, a small-scale qualitative study was conducted of two contrasting groups: 1) within-MCM instruction: competent versus struggling problem solvers, and 2) within-competent problem solvers: MCM instructed versus traditionally instructed. Competent MCM students tended to connect their mathematical inscriptions to the scientific phenomenon and to switch between mathematical and scientifically productive approaches during problem solving in potentially productive ways. The other two groups did not. To address concerns about teacher capacity presenting barriers to scalability of MCM approaches, the types and amount of teacher support needed to achieve these types of student learning gains were investigated. In the context of providing teachers with access to educative materials, students achieved learning gains in both areas in the absence of face-to-face teacher professional development. However, maximal student learning gains required the investment of face-to-face professional development. This finding can govern distribution of scarce resources, but does not preclude implementation of MCM instruction even where resource availability does not allow for face-to-face professional development.

Promoting Reasoning through the Magic V Task

ERIC Educational Resources Information Center

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

2015-01-01

Reasoning in mathematics plays a critical role in developing mathematical understandings. In this article, Bragg, Loong, Widjaja, Vale & Herbert explore an adaptation of the Magic V Task and how it was used in several classrooms to promote and develop reasoning skills.

Helping Mathematics Teachers Develop Noticing Skills: Utilizing Smartphone Technology for One-on-One Teacher/Student Interviews

ERIC Educational Resources Information Center

Chao, Theodore; Murray, Eileen; Star, Jon R.

2016-01-01

Teaching mathematics for understanding requires listening to each student's mathematical thinking, best elicited in a one-on-one interview. Interviews are difficult to enact in a teacher's busy schedule, however. In this study, the authors utilize smartphone technology to help mathematics teachers interview a student in a virtual one-on-one…

The Mathematics of Tithing: A Study of Religious Giving and Mathematical Development

ERIC Educational Resources Information Center

Taylor, Edd V.

2013-01-01

The purpose of this study was to examine children's mathematical understandings related to participation in tithing (giving 10% of earnings to the church). Observations of church services and events, as well as interviews with parents, children, and church leaders, were analyzed in an effort to capture the ways in which mathematical problem…

The Mathematics of Tithing: A Study of Religious Giving and Mathematical Development

ERIC Educational Resources Information Center

Taylor, Edd V.

2013-01-01

The purpose of this study was to examine children's mathematical understandings related to participation in tithing (giving 10% of earnings to the church). Observations of church services and events, as well as interviews with parents, children, and church leaders, were analyzed in an effort to capture the ways in which mathematical problem…

Preventing Early Mathematics Difficulties: The Feasibility of a Rigorous Kindergarten Mathematics Curriculum

ERIC Educational Resources Information Center

Chard, David J.; Baker, Scott K.; Clarke, Ben; Jungjohann, Kathleen; Davis, Karen; Smolkowski, Keith

2008-01-01

Concern about poor mathematics achievement in U.S. schools has increased in recent years. In part, poor achievement may be attributed to a lack of attention to early instruction and missed opportunities to build on young children's early understanding of mathematics. This study examined the development and feasibility testing of a kindergarten…

Preliminary Evaluation Report on the Los Angeles City Schools SB 28 Demonstration Program in Mathematics. CSE Working Paper No. 1.

ERIC Educational Resources Information Center

Gordon, C. Wayne

The objectives of the Los Angeles Model Mathematics Project (LAMMP) are stated by the administration as improvement of mathematical skills and understanding of mathematical concepts; improvement of the pupils' self-image; identification of specific assets and limitations relating to the learning process; development and use of special…

Preliminary Evaluation Report on the Los Angeles City Schools, SB 28 Demonstration Program in Mathematics.

ERIC Educational Resources Information Center

Gordon, C. Wayne

The purpose of this preliminary report is to describe and evaluate the Los Angeles Model Mathematics Project (LAMMP). The objectives of this project include the improvement of mathematical skills and understanding of mathematical concepts, the improvement of students' self-image, the development of instructional materials and the assessment of…

Adapting Math Instruction to Support Prospective Elementary Teachers

ERIC Educational Resources Information Center

LeSage, Ann

2012-01-01

Purpose: Elementary teachers' understanding of mathematics is a significant contributor to student success with mathematics. Consequently, teacher educators are frequently charged with the responsibility of supporting the development of prospective elementary teachers' mathematics content knowledge as they re-learn concepts in ways they are…

Reflectiveness/Impulsiveness and Mathematics Achievement

ERIC Educational Resources Information Center

Cathcart, W. George; Liedtke, Werner

1969-01-01

Report of research to test the hypothesis that reflective students would be higher achievers in mathematics than impulsive pupils. An achievement test was developed to measure understanding of mathematical concepts and applications, ability to solve verbal problems and recall basic facts. Data suggest that reflective students obtain better…

Students' Thinking and the Depth of the Mathematics Curriculum

ERIC Educational Resources Information Center

Kent, Laura B.

2014-01-01

This article explores the impact of students' thinking centered professional development on mathematics teaching and learning. Purposeful pedagogy and problem posing are examined as mechanisms by which teachers can potentially deepen students' understanding of mathematics. A classroom example comparing student generated strategies versus…

On Mathematical Understanding: Perspectives of Experienced Chinese Mathematics Teachers

ERIC Educational Resources Information Center

Cai, Jinfa; Ding, Meixia

2017-01-01

Researchers have long debated the meaning of mathematical understanding and ways to achieve mathematical understanding. This study investigated experienced Chinese mathematics teachers' views about mathematical understanding. It was found that these mathematics teachers embrace the view that understanding is a web of connections, which is a result…

Creating opportunities to learn in mathematics education: a sociocultural perspective

NASA Astrophysics Data System (ADS)

Goos, Merrilyn

2014-09-01

The notion of `opportunities to learn in mathematics education' is open to interpretation from multiple theoretical perspectives, where the focus may be on cognitive, social or affective dimensions of learning, curriculum and assessment design, issues of equity and access, or the broad policy and political contexts of learning and teaching. In this paper, I conceptualise opportunities to learn from a sociocultural perspective. Beginning with my own research on the learning of students and teachers of mathematics, I sketch out two theoretical frameworks for understanding this learning. One framework extends Valsiner's zone theory of child development, and the other draws on Wenger's ideas about communities of practice. My aim is then to suggest how these two frameworks might help us understand the learning of others who have an interest in mathematics education, such as mathematics teacher educator-researchers and mathematicians. In doing so, I attempt to move towards a synthesis of ideas to inform mathematics education research and development.

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

ERIC Educational Resources Information Center

Seeger, Falk

2011-01-01

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

Initial Understandings of Fraction Concepts Evidenced by Students with Mathematics Learning Disabilities and Difficulties: A Framework

ERIC Educational Resources Information Center

Hunt, Jessica H.; Welch-Ptak, Jasmine J.; Silva, Juanita M.

2016-01-01

Documenting how students with learning disabilities (LD) initially conceive of fractional quantities, and how their understandings may align with or differ from students with mathematics difficulties, is necessary to guide development of assessments and interventions that attach to unique ways of thinking or inherent difficulties these students…

Advancing Fourth-Grade Students' Understanding of Arithmetic Properties with Instruction That Promotes Mathematical Argumentation

ERIC Educational Resources Information Center

Rumsey, Chepina Witkowski

2012-01-01

The goals for this study were to investigate how fourth-grade students developed an understanding of the arithmetic properties when instruction promoted mathematical argumentation and to identify the characteristics of students' arguments. Using the emergent perspective as an overarching theoretical perspective helped distinguish between two…

Characterizing Student Mathematics Teachers' Levels of Understanding in Spherical Geometry

ERIC Educational Resources Information Center

Guven, Bulent; Baki, Adnan

2010-01-01

This article presents an exploratory study aimed at the identification of students' levels of understanding in spherical geometry as van Hiele did for Euclidean geometry. To do this, we developed and implemented a spherical geometry course for student mathematics teachers. Six structured, "task-based interviews" were held with eight student…

What's Missing in Teaching Probability and Statistics: Building Cognitive Schema for Understanding Random Phenomena

ERIC Educational Resources Information Center

Kuzmak, Sylvia

2016-01-01

Teaching probability and statistics is more than teaching the mathematics itself. Historically, the mathematics of probability and statistics was first developed through analyzing games of chance such as the rolling of dice. This article makes the case that the understanding of probability and statistics is dependent upon building a…

The Importance of Equal Sign Understanding in the Middle Grades

ERIC Educational Resources Information Center

Knuth, Eric J.; Alibali, Martha W.; Hattikudur, Shanta; McNeil, Nicole M.; Stephens, Ana C.

2008-01-01

The equal sign is perhaps the most prevalent symbol in school mathematics, and developing an understanding of it has typically been considered mathematically straightforward. In fact, after its initial introduction during students' early elementary school education, little, if any instructional time is explicitly spent on the concept in the later…

Development and Validation of a Scale for Measuring Mathematics Teaching Self-Efficacy for Teachers in the Sultanate of Oman

ERIC Educational Resources Information Center

Alkharusi, Hussain; Aldhafri, Said; Al-Hosni, Khoula; Al-Busaidi, Saleh; Al-Kharusi, Bader; Ambusaidi, Abdullah; Alrajhi, Marwa

2017-01-01

A scale for measuring self-efficacy for teaching mathematics in grades 5 to 10 was developed in this study for teachers in Oman. The participants were 328 mathematics teachers randomly selected from five educational governorates in the Sultanate of Oman. Factorial structure of the scale revealed three subscales: self-efficacy for understanding the…

A Primary Teacher's Developing Understanding of Mathematical Reasoning

ERIC Educational Resources Information Center

Loong, Esther Yook-Kin

2014-01-01

To support teachers in their quest to incorporate reasoning as a mathematical proficiency as espoused in the Australian Curriculum: Mathematics, a professional learning research project using demonstration lessons was carried out. This paper reports on the impact of demonstration lessons on one participating teacher's pedagogical knowledge about…

Developing a Pedagogically Useful Content Knowledge in Elementary Mathematics.

ERIC Educational Resources Information Center

Peck, Donald M.; Connell, Michael L.

Elementary school teacher candidates typically enter their professional training with deficiencies in their conceptual understanding of the topics of elementary school mathematics and with a reliance upon procedural (algorithmic) approaches to the solutions of mathematical problems. If elementary school teacher candidates are expected to teach…

Cognitive Psychology and Mathematical Thinking.

ERIC Educational Resources Information Center

Greer, Brian

1981-01-01

This review illustrates aspects of cognitive psychology relevant to the understanding of how people think mathematically. Developments in memory research, artificial intelligence, visually mediated processes, and problem-solving research are discussed. (MP)

Teaching Early Knowledge of Whole Number Concepts through Technology: Findings from a Feasibility Study of an iPad Delivered Kindergarten Mathematics Intervention

ERIC Educational Resources Information Center

Shanley, Lina; Cary, Mari Strand; Clarke, Ben; Jungjohann, Kathy

2013-01-01

Children enter kindergarten with variable levels of mathematics skill and knowledge gained from informal learning opportunities at home, preschool, and daycare. Many perform well once they receive formal mathematics instruction. However, if students do not develop an initial understanding of the most basic aspects of formal mathematics, they are…

Teaching Statistics in Middle School Mathematics Classrooms: Making Links with Mathematics but Avoiding Statistical Reasoning

ERIC Educational Resources Information Center

Savard, Annie; Manuel, Dominic

2015-01-01

Statistics is a domain that is taught in Mathematics in all school levels. We suggest a potential in using an interdisciplinary approach with this concept. Thus the development of the understanding of a situation might mean to use both mathematical and statistical reasoning. In this paper, we present two case studies where two middle school…

Using Students' Interests as Algebraic Models

ERIC Educational Resources Information Center

Whaley, Kenneth A.

2012-01-01

Fostering algebraic thinking is an important goal for middle-grades mathematics teachers. Developing mathematical reasoning requires that teachers cultivate students' habits of mind. Teachers develop students' understanding of algebra by engaging them in tasks that involve modeling and representation. This study was designed to investigate how…

Historical Objections against the Number Line

ERIC Educational Resources Information Center

Heeffer, Albrecht

2011-01-01

Historical studies on the development of mathematical concepts will help mathematics teachers to relate their students' difficulties in understanding to conceptual problems in the history of mathematics. We argue that one popular tool for teaching about numbers, the number line, may not be fit for early teaching of operations involving negative…

Teaching with the Mathematical Practices in Mind

ERIC Educational Resources Information Center

Billings, Esther M. H.; Coffey, David C.; Golden, John; Wells, Pamela J.

2013-01-01

How can the use of the Standards for Mathematical Practice in the classroom be supported? Professional developers and teacher educators strive to support teachers as they seek to answer this question. When teachers personally and intentionally experience the practices and reflect on how the practices support and promote mathematical understanding,…

Primary Trait Analysis to Assess a Learner-Centered, Upper-Level Mathematics Course

ERIC Educational Resources Information Center

Alsardary, Salar; Pontiggia, Laura; Hamid, Mohammed; Blumberg, Phyllis

2011-01-01

This study presents a primary trait analysis of a learner-centered, discrete mathematics course based on student-to-student instruction. The authors developed a scoring rubric for the primary traits: conceptual knowledge, procedural knowledge, application of understanding, and mathematical communication skills. Eleven students took an exam…

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

ERIC Educational Resources Information Center

Jaafar, Reem

2015-01-01

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

Representations in Problem Solving: A Case Study with Optimization Problems

ERIC Educational Resources Information Center

Villegas, Jose L.; Castro, Enrique; Gutierrez, Jose

2009-01-01

Introduction: Representations play an essential role in mathematical thinking. They favor the understanding of mathematical concepts and stimulate the development of flexible and versatile thinking in problem solving. Here our focus is on their use in optimization problems, a type of problem considered important in mathematics teaching and…

Refining "Teacher Design Capacity": Mathematics Teachers' Interactions with Digital Curriculum Resources

ERIC Educational Resources Information Center

Pepin, B.; Gueudet, G.; Trouche, L.

2017-01-01

The goal of this conceptual paper is to develop enhanced understandings of mathematics teacher design and design capacity when interacting with digital curriculum resources. We argue that digital resources in particular offer incentives and increasing opportunities for mathematics teachers' design, both individually and in collectives. Indeed they…

Sunny Side Up in Mathematics.

ERIC Educational Resources Information Center

LaHart, David, Ed.

Energy is a problem affecting all individuals. To help today's students understand the problem and become realistic decision-makers, materials have been developed by the Sunny Side Up (in Mathematics) program to introduce energy concepts into the mathematics curriculum. Objectives of the program are to: (1) provide highly effective practice in…

Effects of Directed Learning Groups upon Students' Ability to Understand Conceptual Ideas

ERIC Educational Resources Information Center

Johnson, Karen Gabrielle; Galluzzo, Benjamin Jason

2014-01-01

Mathematical modeling and directed learning groups were employed in a terminal mathematics course to encourage university students to conceptualize real-world mathematics problems. Multiple assessments were utilized to determine whether students' conceptual development is enhanced by participating in directed learning groups conducted in a…

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…

Mathematical Tasks as a Framework for Reflection: From Research To Practice.

ERIC Educational Resources Information Center

Stein, Mary Kay; Smith, Margaret Schwan

1998-01-01

Describes the Quantitative Understanding: Amplifying Student Achievement and Reasoning (QUASAR) national reform project aimed at studying and fostering the development and implementation of enhanced mathematics instructional programs. It is a framework for reflection based on mathematical tasks used during classroom instruction and the ways in…

Virtual Manipulatives: Tools for Teaching Mathematics to Students with Learning Disabilities

ERIC Educational Resources Information Center

Shin, Mikyung; Bryant, Diane P.; Bryant, Brian R.; McKenna, John W.; Hou, Fangjuan; Ok, Min Wook

2017-01-01

Many students with learning disabilities demonstrate difficulty in developing a conceptual understanding of mathematical topics. Researchers recommend using visual models to support student learning of the concepts and skills necessary to complete abstract and symbolic mathematical problems. Virtual manipulatives (i.e., interactive visual models)…

A Cognitive Theory Driven New Orientation of Indonesian Lessons

ERIC Educational Resources Information Center

Nowinska, Edyta

2014-01-01

The main focus of this design research was on students' mathematical thinking and skills and on their understanding of mathematical concepts and methods. The mathematical content our project starts with is the introduction of integers. For this content new learning environments have been developed, implemented and evaluated. An important question…

Creating Cultures of Participation to Promote Mathematical Discourse

ERIC Educational Resources Information Center

Bennett, Cory A.

2014-01-01

Discourse requires students to evaluate and interpret the perspectives, ideas, and mathematical arguments of others as well as construct valid arguments of their own. That is, students develop deeper understandings of mathematics when they engage in meaningful social interactions such as whole class discourse. Both the National Council of Teachers…

Examining Teachers' Understanding of the Mathematical Learning Progression through Vertical Articulation during Lesson Study

ERIC Educational Resources Information Center

Suh, Jennifer; Seshaiyer, Padmanabhan

2015-01-01

This study examines elementary- and middle-grade teachers' understanding of the mathematical learning progression as they participated in a 6-month professional learning project. Teachers participated in a professional development project that consisted of a 1-week summer content-focused institute with school-based follow-up Lesson Study cycles in…

Students' Conceptual Understanding of a Function and Its Derivative in an Experimental Calculus Course

ERIC Educational Resources Information Center

Habre, Samer; Abboud, May

2006-01-01

Calculus has been witnessing fundamental changes in its curriculum, with an increased emphasis on visualization. This mode for representing mathematical concepts is gaining more strength due to the advances in computer technology and the development of dynamical mathematical software. This paper focuses on the understanding of the function and its…

Professional Development for Mathematics Teachers: Using Task Design and Analysis

ERIC Educational Resources Information Center

Lee, Hea-Jin; Özgün-Koca, S. Asli

2016-01-01

This study is based on a Task Design and Analysis activity from a year-long professional development program. The activity was designed to increase teacher growth in several areas, including knowledge of mathematics, understanding of students' cognitive activity, knowledge of good questions, and ability to develop and improve high quality tasks.…

Modelling Mathematical Reasoning in Physics Education

NASA Astrophysics Data System (ADS)

Uhden, Olaf; Karam, Ricardo; Pietrocola, Maurício; Pospiech, Gesche

2012-04-01

Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.

Understanding Mathematics Teachers' Beliefs about Professional Learning Communities and Professional Development

ERIC Educational Resources Information Center

Garner, Arthur L., Jr.

2011-01-01

This ethnographic study utilized the theoretical frameworks of constructivism, cognitivism, and socio-cultural theories to examine how professional learning communities influenced the professional development of mathematics teacher knowledge and student achievement. This study sought to comprehend and interpret the behaviors, beliefs and values of…

Documenting Collective Development in Online Settings

ERIC Educational Resources Information Center

Dean, Chrystal; Silverman, Jason

2015-01-01

In this paper the authors explored the question of collective understanding in online mathematics education settings and presented a brief overview of traditional methods for documenting norms and collective mathematical practices. A method for documenting collective development was proposed that builds on existing methods and frameworks yet is…

Supporting Mathematical Proficiency

ERIC Educational Resources Information Center

Allsopp, David; Lovin, LouAnn H.; van Ingen, Sarah

2017-01-01

Special educators can play an essential role in the development of students' understanding of and capacity to do mathematics. Whether a special education teacher's goal is to help kindergartners develop counting skills or to support 10th graders in constructing geometric proofs and whether instruction will occur in co teaching, consulting, or…

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.

The application of brain-based learning principles aided by GeoGebra to improve mathematical representation ability

NASA Astrophysics Data System (ADS)

Priatna, Nanang

2017-08-01

The use of Information and Communication Technology (ICT) in mathematics instruction will help students in building conceptual understanding. One of the software products used in mathematics instruction is GeoGebra. The program enables simple visualization of complex geometric concepts and helps improve students' understanding of geometric concepts. Instruction applying brain-based learning principles is one oriented at the efforts of naturally empowering the brain potentials which enable students to build their own knowledge. One of the goals of mathematics instruction in school is to develop mathematical communication ability. Mathematical representation is regarded as a part of mathematical communication. It is a description, expression, symbolization, or modeling of mathematical ideas/concepts as an attempt of clarifying meanings or seeking for solutions to the problems encountered by students. The research aims to develop a learning model and teaching materials by applying the principles of brain-based learning aided by GeoGebra to improve junior high school students' mathematical representation ability. It adopted a quasi-experimental method with the non-randomized control group pretest-posttest design and the 2x3 factorial model. Based on analysis of the data, it is found that the increase in the mathematical representation ability of students who were treated with mathematics instruction applying the brain-based learning principles aided by GeoGebra was greater than the increase of the students given conventional instruction, both as a whole and based on the categories of students' initial mathematical ability.

The Nature of Scaffolding in Undergraduate Students' Transition to Mathematical Proof

ERIC Educational Resources Information Center

Blanton, Maria L.; Stylianou, Despina A.; David, Maria Manuela

2003-01-01

This paper explores the role of instructional scaffolding in the development of undergraduate students' understanding of mathematical proof during a one-year discrete mathematics course. We describe here the framework adapted for the analysis of whole-class discussion and examine how the teacher scaffolded students' thinking. Results suggest that…

Testing the Immediate and Long-Term Efficacy of a Tier 2 Kindergarten Mathematics Intervention

ERIC Educational Resources Information Center

Clarke, Ben; Doabler, Christian T.; Smolkowski, Keith; Kurtz-Nelson, Evangeline; Fien, Hank; Baker, Scott K.; Kosty, Derek

2016-01-01

This study examined the efficacy of a kindergarten mathematics intervention program, ROOTS, focused on developing whole-number understanding in the areas of counting and cardinality and operations and algebraic thinking for students at risk in mathematics. The study utilized a randomized block design with students within classrooms randomly…

Designing and Developing Assessments of Complex Thinking in Mathematics for the Middle Grades

ERIC Educational Resources Information Center

Graf, Edith Aurora; Arieli-Attali, Meirav

2015-01-01

Designing an assessment system for complex thinking in mathematics involves decisions at every stage, from how to represent the target competencies to how to interpret evidence from student performances. Beyond learning to solve particular problems in a particular area, learning mathematics with understanding involves comprehending connections…

Preparing Middle Level Preservice Teachers to Integrate Mathematics and Science: Problems and Possibilities

ERIC Educational Resources Information Center

Koirala, Hari P.; Bowman, Jacqueline K.

2003-01-01

Many members of the mathematics and science education community believe that the integration of mathematics and science enhances students' understanding of both subjects. Despite this belief, attempts to integrate these subjects have frequently been unsuccessful. This study examines the development and implementation of a team-taught integrated…

Making It Count: Strategies for Improving Mathematics Instruction for Students in Short-Term Facilities. Strategy Guide

ERIC Educational Resources Information Center

Leone, Peter; Wilson, Michael; Mulcahy, Candace

2010-01-01

This guide is designed to support the development of mathematics proficiency for youth in short-term juvenile correctional facilities. Mathematics proficiency includes mastery and fluency in foundational numeracy; an understanding of complex, grade-appropriate concepts and procedures; and application of those competencies to solve relevant,…

Mathematics Undergraduate Student Teachers' Conceptions of Guided Inductive and Deductive Teaching Approaches

ERIC Educational Resources Information Center

Ndemo, Zakaria; Zindi, Fred; Mtetwa, David

2017-01-01

This contribution aimed at developing an understanding of student teachers' conceptions of guided discovery teaching approaches. A cross-sectional survey design involving eleven secondary mathematics teachers who had enrolled for an in-service mathematics education degree was used to address the research question: What are undergraduate student…

The Differences in Scores and Self-Efficacy by Student Gender in Mathematics and Science

ERIC Educational Resources Information Center

Louis, Rachel A.; Mistele, Jean M.

2012-01-01

Typically, mathematics and science are seen as linked together, where both subjects involve numbers, critical thinking, and problem solving. Our study aims to develop a better understanding of the connections between student's achievement scores in mathematics and science, student gender, and self-efficacy. We used the Trends in International…

Evolving Polygons and Spreadsheets: Connecting Mathematics across Grade Levels in Teacher Education

ERIC Educational Resources Information Center

Abramovich, Sergei; Brouwer, Peter

2009-01-01

This paper was prepared in response to the Conference Board of Mathematical Sciences recommendations for the preparation of secondary teachers. It shows how using trigonometry as a conceptual tool in spreadsheet-based applications enables one to develop mathematical understanding in the context of constructing geometric representations of unit…

How Mathematics Propels the Development of Physical Knowledge

ERIC Educational Resources Information Center

Schwartz, Daniel L.; Martin, Taylor; Pfaffman, Jay

2005-01-01

Three studies examined whether mathematics can propel the development of physical understanding. In Experiment 1, 10-year-olds solved balance scale problems that used easy-to-count discrete quantities or hard-to-count continuous quantities. Discrete quantities led to age typical performances. Continuous quantities caused performances like those of…

The Conceptual Framework for the Development of a Mathematics Performance Assessment Instrument.

ERIC Educational Resources Information Center

Lane, Suzanne

1993-01-01

A conceptual framework is presented for the development of the Quantitative Understanding: Amplifying Student Achievement and Reasoning (QUASAR) Cognitive Assessment Instrument (QCAI) that focuses on the ability of middle-school students to problem solve, reason, and communicate mathematically. The instrument will provide programatic rather than…

Development of Understanding and Self-Confidence in Mathematics; Grades 5-8

ERIC Educational Resources Information Center

Hannula, Markku S.; Maijala, Hanna; Pehkonen, Erkki

2004-01-01

This paper presents some preliminary results of the longitudinal aspect of a research project on self-confidence and understanding in mathematics. We have collected a survey data of 3057 fifth-graders and seventh-graders and a follow-up data of ten classes (191 pupils) one and a half years later. The longitudinal data indicates that the learning…

The Effects of a Grouping by Tens Manipulative on Children's Strategy Use, Base Ten Understanding and Mathematical Knowledge

ERIC Educational Resources Information Center

Pagar, Dana

2013-01-01

Manipulatives have the potential to be powerful tools in helping children improve their number sense, develop advanced mathematical strategies, and build an understanding of the base ten number system. Physical manipulatives used in classrooms, however, are often not designed to promote efficient strategy use, such as counting on, and typically do…

Science and Mathematics in Astronomy

NASA Technical Reports Server (NTRS)

Woolack, Edward

2009-01-01

A brief historical introduction to the development of observational astronomy will be presented. The close historical relationship between the successful application of mathematical concepts and advances in astronomy will be presented. A variety of simple physical demonstrations, hands-on group activities, and puzzles will be used to understand how the properties of light can be used to understand the contents of our universe.

Learning to Teach High School Mathematics: Patterns of Growth in Understanding Right Triangle Trigonometry during Lesson Plan Study

ERIC Educational Resources Information Center

Cavey, Laurie O.; Berenson, Sarah B.

2005-01-01

"Lesson plan study" (LPS), adapted from the Japanese Lesson Study method of professional development, is a sequence of activities designed to engage prospective teachers in broadening and deepening their understanding of school mathematics and teaching strategies. LPS occurs over 5 weeks on the same lesson topic and includes four opportunities to…

Folding Back and the Dynamical Growth of Mathematical Understanding: Elaborating the Pirie-Kieren Theory

ERIC Educational Resources Information Center

Martin, Lyndon C.

2008-01-01

The study reported here extends the work of Pirie and Kieren on the nature and growth of mathematical understanding. The research examines in detail a key aspect of their theory, the process of 'folding back', and develops a theoretical framework of categories and sub-categories that more fully describe the phenomenon. This paper presents an…

The role of language in mathematical development: evidence from children with specific language impairments.

PubMed

Donlan, Chris; Cowan, Richard; Newton, Elizabeth J; Lloyd, Delyth

2007-04-01

A sample (n=48) of eight-year-olds with specific language impairments is compared with age-matched (n=55) and language matched controls (n=55) on a range of tasks designed to test the interdependence of language and mathematical development. Performance across tasks varies substantially in the SLI group, showing profound deficits in production of the count word sequence and basic calculation and significant deficits in understanding of the place-value principle in Hindu-Arabic notation. Only in understanding of arithmetic principles does SLI performance approximate that of age-matched-controls, indicating that principled understanding can develop even where number sequence production and other aspects of number processing are severely compromised.

The Impact of Problem-Based Learning on Non-Science Undergraduate Students' Attitudes towards Mathematics in an Egyptian Classroom

NASA Astrophysics Data System (ADS)

Rizkallah, Mohammed W.

While Problem-based Learning (PBL) has been established in the literature in different contexts, there remains few studies on how PBL has an impact on students' attitude towards mathematics and their conceptual understanding of it in Egyptian classrooms. This study was conducted in an international university in Egypt, and the participants were non-science undergraduate students who took a course called "Fun with Problem-Solving" as a requirement core class. The study shows that students' attitude towards mathematics developed throughout the course, and this was tested using the Fennema-Sherman Mathematics Attitude Scale, where students had a pretest and posttest. While the sample size was small, there was statistical significance in the change of the means of how students perceived mathematics as a male domain, and how teachers perceived students' achievements. This notion was coupled with students' development of conceptual understanding, which was tracked throughout the semester by mapping students' work with the Lesh Translation Model.

Inquiry based learning: a student centered learning to develop mathematical habits of mind

NASA Astrophysics Data System (ADS)

Handayani, A. D.; Herman, T.; Fatimah, S.; Setyowidodo, I.; Katminingsih, Y.

2018-05-01

Inquiry based learning is learning that based on understanding constructivist mathematics learning. Learning based on constructivism is the Student centered learning. In constructivism, students are trained and guided to be able to construct their own knowledge on the basis of the initial knowledge that they have before. This paper explained that inquiry based learning can be used to developing student’s Mathematical habits of mind. There are sixteen criteria Mathematical Habits of mind, among which are diligent, able to manage time well, have metacognition ability, meticulous, etc. This research method is qualitative descriptive. The result of this research is that the instruments that have been developed to measure mathematical habits of mind are validated by the expert. The conclusion is the instrument of mathematical habits of mind are valid and it can be used to measure student’s mathematical habits of mind.

Statistical Mechanics of Disordered Systems - Series: Cambridge Series in Statistical and Probabilistic Mathematics (No. 18)

NASA Astrophysics Data System (ADS)

Bovier, Anton

2006-06-01

Our mathematical understanding of the statistical mechanics of disordered systems is going through a period of stunning progress. This self-contained book is a graduate-level introduction for mathematicians and for physicists interested in the mathematical foundations of the field, and can be used as a textbook for a two-semester course on mathematical statistical mechanics. It assumes only basic knowledge of classical physics and, on the mathematics side, a good working knowledge of graduate-level probability theory. The book starts with a concise introduction to statistical mechanics, proceeds to disordered lattice spin systems, and concludes with a presentation of the latest developments in the mathematical understanding of mean-field spin glass models. In particular, recent progress towards a rigorous understanding of the replica symmetry-breaking solutions of the Sherrington-Kirkpatrick spin glass models, due to Guerra, Aizenman-Sims-Starr and Talagrand, is reviewed in some detail. Comprehensive introduction to an active and fascinating area of research Clear exposition that builds to the state of the art in the mathematics of spin glasses Written by a well-known and active researcher in the field

An Iceberg Model for Improving Mathematical Understanding and Mindset or Disposition: An Individualized Summer Intervention Program

ERIC Educational Resources Information Center

Westensko, Arla; Moyer-Packenham, Patricia S.; Child, Barbara

2017-01-01

This study describes 3 years of mathematics intervention research examining the effectiveness of a summer individualized tutoring program for rising fourth-, fifth-, and sixth-grade students with low mathematics achievement. Based on an iceberg model of learning, an instructional framework was developed that identified and targeted students'…

Tablet-Based Math Assessment: What Can We Learn from Math Apps?

ERIC Educational Resources Information Center

Cayton-Hodges, Gabrielle A.; Feng, Gary; Pan, Xingyu

2015-01-01

In this report, we describe a survey of mathematics education apps in the Apple App Store, conducted as part of a research project to develop a tablet-based assessment prototype for elementary mathematics. This survey was performed with the goal of understanding the design principles and techniques used in mathematics apps designed for tablets. We…

The Number Line as a Representation of Decimal Numbers: A Research with Sixth Grade Students

ERIC Educational Resources Information Center

Michaelidou, Niki; Gagatsis, Athanasios; Pitta-Pantazi, Demetra

2004-01-01

One of the aims of mathematics instruction is to achieve the understanding of mathematical concepts through the development of rich and well organized cognitive representations (Goldin, 1998; NCTM, 2000; DeWindt-King, & Goldin, 2003). In this study the term representation is interpreted as the tool used for representing mathematical ideas such…

Influence of Demographic Factors on Students' Beliefs in Learning Mathematics

ERIC Educational Resources Information Center

Tahir, Izah Mohd; Bakar, Nor Mazlina Abu

2009-01-01

Learning mathematics has been recognized by many as important. It does not only develop students' ability to think in quantitative terms but can also enhance skills such as analytical and problem solving skills. However, to enable us to tell our students how important mathematics is we have to understand students' beliefs in learning mathematics…

Refocusing on Oral Language and Rich Representations to Develop the Early Mathematical Understandings of Indigenous Students

ERIC Educational Resources Information Center

McDonald, Susan; Warren, Elizabeth; DeVries, Eva

2011-01-01

This article examines the nature of oral language and representations used by teachers as they instruct young Indigenous Australian students at the beginning of formal schooling during play-based activities in mathematics. In particular, the use of Standard Australian English (SAE), the mathematical register used, and the interplay with…

Stealing from Physics: Modeling with Mathematical Functions in Data-Rich Contexts

ERIC Educational Resources Information Center

Erickson, Tim

2006-01-01

In the course of a project to create physics education materials for secondary schools in the USA we have, not surprisingly, had insights into how students develop certain mathematical understandings. Some of these translate directly into the mathematics classroom. With our materials, students get data from a variety of sources, data that arise in…

Developing Mathematical Understanding and Students with Emotional and Behavioural Disorders: A Review of the Literature

ERIC Educational Resources Information Center

Tan, Paulo

2016-01-01

Recent shifts in focus on academic interventions for students diagnosed with emotional and behavioural disorders (EBD) create a need to evaluate existing interventional research in content areas such as mathematics. Literature reviews in the area of mathematics interventions for students with EBD have mostly focused on the outcomes and the rigour…

How Plankton Swim: An Interdisciplinary Approach for Using Mathematics & Physics to Understand the Biology of the Natural World

ERIC Educational Resources Information Center

Clay, Tansy W.; Fox, Jennifer B.; Grunbaum, Daniel; Jumars, Peter A.

2008-01-01

The authors have developed and field-tested high school-level curricular materials that guide students to use biology, mathematics, and physics to understand plankton and how these tiny organisms move in a world where their intuition does not apply. The authors chose plankton as the focus of their materials primarily because the challenges faced…

Basic mathematical cognition.

PubMed

Gaber, David; Schlimm, Dirk

2015-01-01

Mathematics is a powerful tool for describing and developing our knowledge of the physical world. It informs our understanding of subjects as diverse as music, games, science, economics, communications protocols, and visual arts. Mathematical thinking has its roots in the adaptive behavior of living creatures: animals must employ judgments about quantities and magnitudes in the assessment of both threats (how many foes) and opportunities (how much food) in order to make effective decisions, and use geometric information in the environment for recognizing landmarks and navigating environments. Correspondingly, cognitive systems that are dedicated to the processing of distinctly mathematical information have developed. In particular, there is evidence that certain core systems for understanding different aspects of arithmetic as well as geometry are employed by humans and many other animals. They become active early in life and, particularly in the case of humans, develop through maturation. Although these core systems individually appear to be quite limited in application, in combination they allow for the recognition of mathematical properties and the formation of appropriate inferences based upon those properties. In this overview, the core systems, their roles, their limitations, and their interaction with external representations are discussed, as well as possibilities for how they can be employed together to allow us to reason about more complex mathematical domains. © 2015 John Wiley & Sons, Ltd.

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…

Using Action Research to Develop a Course in Statistical Inference for Workplace-Based Adults

ERIC Educational Resources Information Center

Forbes, Sharleen

2014-01-01

Many adults who need an understanding of statistical concepts have limited mathematical skills. They need a teaching approach that includes as little mathematical context as possible. Iterative participatory qualitative research (action research) was used to develop a statistical literacy course for adult learners informed by teaching in…

Knowing and Teaching Middle School Mathematics: A Professional Development Course for In-Service Teachers

ERIC Educational Resources Information Center

Anderson, Celia Rousseau; Hoffmeister, April M.

2007-01-01

This article describes a professional development course intended to improve the content understanding of middle school mathematics teachers. The design of the course included three professional learning strategies: problem solving, examination of student thinking, and discussion of research. The concepts studied in the course included multi-digit…

Developing Students' Relational Understanding: Innovations and Insights

ERIC Educational Resources Information Center

Stump, Sheryl

2009-01-01

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

Self-Determination Theory and Middle School Mathematics Teachers: Understanding the Motivation to Attain Professional Development

ERIC Educational Resources Information Center

Crawford, Amy K.

2017-01-01

The purpose of this phenomenological research study was to use Self-Determination Theory as a framework to analyze middle school mathematics teachers' motivation to attain effective professional development concerning Ohio's Learning Standards as well as other instructional aspects that affect the classroom. Teachers are exceptionally busy meeting…

Supporting Children's Mathematical Understanding: Professional Development Focused on Out-of-School Practices

ERIC Educational Resources Information Center

Taylor, Edd V.

2012-01-01

This study describes the Reflection Connection Cycle professional development designed to support teachers' use and appreciation of students' out-of-school practices related to school mathematics. The year-long program incorporated group lesson design, readings, and video analysis for 14 elementary school (ages 5-12) teachers. Analysis of lesson…

Mathematics understanding and anxiety in collaborative teaching

NASA Astrophysics Data System (ADS)

Ansari, B. I.; Wahyu, N.

2017-12-01

This study aims to examine students’ mathematical understanding and anxiety using collaborative teaching. The sample consists of 51 students in the 7th-grade of MTs N Jeureula, one of the Islamic public junior high schools in Jeureula, Aceh, Indonesia. A test of mathematics understanding was administered to the students twice during the period of two months. The result suggests that there is a significant increase in mathematical understanding in the pre-test and post-test. We categorized the students into the high, intermediate, and low level of prior mathematics knowledge. In the high-level prior knowledge, there is no difference of mathematical understanding between the experiment and control group. Meanwhile, in the intermediate and low level of prior knowledge, there is a significant difference of mathematical understanding between the experiment and control group. The mathematics anxiety is at an intermediate level in the experiment class and at a high level in the control group. There is no interaction between the learning model and the students’ prior knowledge towards the mathematical understanding, but there are interactions towards the mathematics anxiety. It indicates that the collaborative teaching model and the students’ prior knowledge do not simultaneously impacts on the mathematics understanding but the mathematics anxiety.

An Archaeoastronomical Adventure.

ERIC Educational Resources Information Center

Russo, Richard

1997-01-01

Describes investigations in archaeoastronomy that combine modern archaeology with the mathematical precision of practical astronomy. Helps students develop an understanding of a society's astronomical systems which can lead to a knowledge of their religion, art, mathematics, writings, calendar, myths, and agricultural practices. (JRH)

Using an evaluative tool to develop effective mathscasts

NASA Astrophysics Data System (ADS)

Galligan, Linda; Hobohm, Carola; Peake, Katherine

2017-09-01

This study is situated in a course designed for both on-campus and online pre-service and in-service teachers, where student-created mathscasts provide a way for university lecturers to assess students' quality of teaching, and understanding of mathematics. Teachers and pre-service teachers, in a university course with 90% online enrolment, were asked to create mathscasts to explain mathematics concepts at middle school level. This paper describes the process of developing and refining a tool for the creation and evaluation of quality student-produced mathscasts. The study then investigates the usefulness of the tool within the context of pedagogy and mathematical understanding. Despite an abundance of mathscasts already available on the web, there is merit in creating mathscasts, not only as a tool for teaching, but also as a means of learning by doing. The premise for creating student-produced mathscasts was to capture the creators' mathematical understanding and pedagogical approach to teaching a mathematical concept, which were then peer-assessed and graded. The analysis included surveys, practice mathscasts with peer- and self-reviews, and students' final assessed mathscasts. The results indicate that the use of the evaluative tool resulted in an improvement in quality of student-created mathscasts and critiques thereof. The paper concludes with a discussion on future directions of student-produced mathscasts.

Mathematical Modeling of Renal Hemodynamics in Physiology and Pathophysiology

PubMed Central

Sgouralis, Ioannis; Layton, Anita T.

2015-01-01

In addition to the excretion of metabolic waste and toxin, the kidney plays an indispensable role in regulating the balance of water, electrolyte, acid-base, and blood pressure. For the kidney to maintain proper functions, hemodynamic control is crucial. In this review, we describe representative mathematical models that have been developed to better understand the kidney's autoregulatory processes. We consider mathematical models that simulate glomerular filtration, and renal blood flow regulation by means of the myogenic response and tubuloglomerular feedback. We discuss the extent to which these modeling efforts have expanded the understanding of renal functions in health and disease. PMID:25765886

Developing a Theoretical Framework to Inform the Design of a Teacher Professional Development Program to Enable Foundation to Year 2 Teachers of Mathematics to Build on Indigenous and Low-SES Students' Cultural Capital

ERIC Educational Resources Information Center

Anderson, Robyn; Stütz, Alexander; Cooper, Tom; Nason, Rod

2017-01-01

This paper reports on the early stages of the conceptualisation and implementation of the Accelerated Inclusive Mathematics-Early Understandings (AIM EU) project, a project whose major goals are to advance theory and practice in the improvement of Foundation to Year 2 (F-2) teachers' capacity to teach mathematics and through this to enhance F-2…

Examining the Impact of a Framework to Support Prospective Secondary Teachers' Transition from 'Doer' to 'Teacher' of Mathematics

ERIC Educational Resources Information Center

Lee, Hea-Jin; Özgün-Koca, S. Asli; Meagher, Michael; Edwards, Michael Todd

2018-01-01

A transition from "doer" to "teacher" for prospective teachers requires them to reorient from thinking about how they do mathematics to engaging with students and their work, understanding student representations, and planning instruction accordingly. To scaffold a transition, we developed a five-step mathematics as teacher…

Assessment Skills: A Case of Mathematics Examination and Its Place in Math-Teacher Development

ERIC Educational Resources Information Center

Qudah, Ahmad Hassan

2016-01-01

The research aims to reveal the specific way to evaluate learning mathematics, so that we get the "measuring tool" for the achievement of learners in mathematics that reflect their level of understanding by score (mark), which we trust it with high degree. The behavior of the learner can be measured by a professional way to build the…

Comparison of university students' understanding of graphs in different contexts

NASA Astrophysics Data System (ADS)

Planinic, Maja; Ivanjek, Lana; Susac, Ana; Milin-Sipus, Zeljka

2013-12-01

This study investigates university students’ understanding of graphs in three different domains: mathematics, physics (kinematics), and contexts other than physics. Eight sets of parallel mathematics, physics, and other context questions about graphs were developed. A test consisting of these eight sets of questions (24 questions in all) was administered to 385 first year students at University of Zagreb who were either prospective physics or mathematics teachers or prospective physicists or mathematicians. Rasch analysis of data was conducted and linear measures for item difficulties were obtained. Average difficulties of items in three domains (mathematics, physics, and other contexts) and over two concepts (graph slope, area under the graph) were computed and compared. Analysis suggests that the variation of average difficulty among the three domains is much smaller for the concept of graph slope than for the concept of area under the graph. Most of the slope items are very close in difficulty, suggesting that students who have developed sufficient understanding of graph slope in mathematics are generally able to transfer it almost equally successfully to other contexts. A large difference was found between the difficulty of the concept of area under the graph in physics and other contexts on one side and mathematics on the other side. Comparison of average difficulty of the three domains suggests that mathematics without context is the easiest domain for students. Adding either physics or other context to mathematical items generally seems to increase item difficulty. No significant difference was found between the average item difficulty in physics and contexts other than physics, suggesting that physics (kinematics) remains a difficult context for most students despite the received instruction on kinematics in high school.

Understanding for Teaching for Understanding.

ERIC Educational Resources Information Center

Kieren, Thomas E.

1990-01-01

Outlines a model of mathematical understanding as a whole, dynamic, nonlinear, recursive growing process, entailing "folding back" for the reconstruction of inner level knowing. Presents examples from seventh graders' work. Discusses teacher awareness of student level of understanding, and implications for development of mathematics…

Mathematics and Information Retrieval.

ERIC Educational Resources Information Center

Salton, Gerald

1979-01-01

Examines the main mathematical approaches to information retrieval, including both algebraic and probabilistic models, and describes difficulties which impede formalization of information retrieval processes. A number of developments are covered where new theoretical understandings have directly led to improved retrieval techniques and operations.…

I. SPATIAL SKILLS, THEIR DEVELOPMENT, AND THEIR LINKS TO MATHEMATICS.

PubMed

Verdine, Brian N; Golinkoff, Roberta Michnick; Hirsh-Pasek, Kathy; Newcombe, Nora S

2017-03-01

Understanding the development of spatial skills is important for promoting school readiness and improving overall success in STEM (science, technology, engineering, and mathematics) fields (e.g., Wai, Lubinski, Benbow, & Steiger, 2010). Children use their spatial skills to understand the world, including visualizing how objects fit together, and can practice them via spatial assembly activities (e.g., puzzles or blocks). These skills are incorporated into measures of overall intelligence and have been linked to success in subjects like mathematics (Mix & Cheng, 2012) and science (Pallrand & Seeber, 1984; Pribyl & Bodner, 1987). This monograph sought to answer four questions about early spatial skill development: 1) Can we reliably measure spatial skills in 3- and 4-year-olds?; 2) Do spatial skills measured at 3 predict spatial skills at age 5?; 3) Do preschool spatial skills predict mathematics skills at age 5?; and 4) What factors contribute to individual differences in preschool spatial skills (e.g., SES, gender, fine-motor skills, vocabulary, and executive function)? Longitudinal data generated from a new spatial skill test for 3-year-old children, called the TOSA (Test of Spatial Assembly), show that it is a reliable and valid measure of early spatial skills that provides strong prediction to spatial skills measured with established tests at age 5. New data using this measure finds links between early spatial skill and mathematics, language, and executive function skills. Analyses suggest that preschool spatial experiences may play a central role in children's mathematical skills around the time of school entry. Executive function skills provide an additional unique contribution to predicting mathematical performance. In addition, individual differences, specifically socioeconomic status, are related to spatial and mathematical skill. We conclude by exploring ways of providing rich early spatial experiences to children. © 2017 The Society for Research in Child Development, Inc.

Professional Development School Triads Inquiring about Student Work in Elementary Mathematics

ERIC Educational Resources Information Center

Coon-Kitt, Mary Jayne; Nolan, James F.; Lloyd, Gwendolyn M.; Romig, Gail

2015-01-01

This article reports on a case of cross-role triads (mentor, intern, and supervisor) in a professional development school (PDS) setting engaged in the process of looking at student work in elementary mathematics over time. The study represents a significant effort to understand what inquiry-oriented behavior looks like in this context. By…

Profile of Metacognition of Mathematics and Mathematics Education Students in Understanding the Concept of Integral Calculus

NASA Astrophysics Data System (ADS)

Misu, La; Ketut Budayasa, I.; Lukito, Agung

2018-03-01

This study describes the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. The metacognition profile is a natural and intact description of a person’s cognition that involves his own thinking in terms of using his knowledge, planning and monitoring his thinking process, and evaluating his thinking results when understanding a concept. The purpose of this study was to produce the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. This research method is explorative method with the qualitative approach. The subjects of this study are mathematics and mathematics education students who have studied integral calculus. The results of this study are as follows: (1) the summarizing category, the mathematics and mathematics education students can use metacognition knowledge and metacognition skills in understanding the concept of indefinite integrals. While the definite integrals, only mathematics education students use metacognition skills; and (2) the explaining category, mathematics students can use knowledge and metacognition skills in understanding the concept of indefinite integrals, while the definite integrals only use metacognition skills. In addition, mathematics education students can use knowledge and metacognition skills in understanding the concept of both indefinite and definite integrals.

Longitudinal mathematics development of students with learning disabilities and students without disabilities: a comparison of linear, quadratic, and piecewise linear mixed effects models.

PubMed

Kohli, Nidhi; Sullivan, Amanda L; Sadeh, Shanna; Zopluoglu, Cengiz

2015-04-01

Effective instructional planning and intervening rely heavily on accurate understanding of students' growth, but relatively few researchers have examined mathematics achievement trajectories, particularly for students with special needs. We applied linear, quadratic, and piecewise linear mixed-effects models to identify the best-fitting model for mathematics development over elementary and middle school and to ascertain differences in growth trajectories of children with learning disabilities relative to their typically developing peers. The analytic sample of 2150 students was drawn from the Early Childhood Longitudinal Study - Kindergarten Cohort, a nationally representative sample of United States children who entered kindergarten in 1998. We first modeled students' mathematics growth via multiple mixed-effects models to determine the best fitting model of 9-year growth and then compared the trajectories of students with and without learning disabilities. Results indicate that the piecewise linear mixed-effects model captured best the functional form of students' mathematics trajectories. In addition, there were substantial achievement gaps between students with learning disabilities and students with no disabilities, and their trajectories differed such that students without disabilities progressed at a higher rate than their peers who had learning disabilities. The results underscore the need for further research to understand how to appropriately model students' mathematics trajectories and the need for attention to mathematics achievement gaps in policy. Copyright © 2015 Society for the Study of School Psychology. Published by Elsevier Ltd. All rights reserved.

Six to Ten Digits Multiplication Fun Learning Using Puppet Prototype

NASA Astrophysics Data System (ADS)

Islamiah Rosli, D.'oria; Ali, Azita; Peng, Lim Soo; Sujardi, Imam; Usodo, Budi; Adie Perdana, Fengky

2017-01-01

Logic and technical subjects require students to understand basic knowledge in mathematic. For instance, addition, minus, division and multiplication operations need to be mastered by students due to mathematic complexity as the learning mathematic grows higher. Weak foundation in mathematic also contribute to high failure rate in mathematic subjects in schools. In fact, students in primary schools are struggling to learn mathematic because they need to memorize formulas, multiplication or division operations. To date, this study will develop a puppet prototyping for learning mathematic for six to ten digits multiplication. Ten participants involved in the process of developing the prototype in this study. Students involved in the study were those from the intermediate class students whilst teachers were selected based on their vast knowledge and experiences and have more than five years of experience in teaching mathematic. Close participatory analysis will be used in the prototyping process as to fulfil the requirements of the students and teachers whom will use the puppet in learning six to ten digit multiplication in mathematic. Findings showed that, the students had a great time and fun learning experience in learning multiplication and they able to understand the concept of multiplication using puppet. Colour and materials of the puppet also help to attract student attention during learning. Additionally, students able to visualized and able to calculate accurate multiplication value and the puppet help them to recall in multiplying and adding the digits accordingly.

Supporting Mathematical Thinking

ERIC Educational Resources Information Center

Houssart, Jenny; Roaf, Caroline; Watson, Anne

2005-01-01

This book looks at how practitioners have focused on the fully educational application of intellect to the problem of developing mathematical thinking among one's pupils. Each chapter demonstrates reflective minds at work, relying on close observation, willingness to understand the student's thinking processes and patient commitment to students…

Introducing geometry concept based on history of Islamic geometry

NASA Astrophysics Data System (ADS)

Maarif, S.; Wahyudin; Raditya, A.; Perbowo, K. S.

2018-01-01

Geometry is one of the areas of mathematics interesting to discuss. Geometry also has a long history in mathematical developments. Therefore, it is important integrated historical development of geometry in the classroom to increase’ knowledge of how mathematicians earlier finding and constructing a geometric concept. Introduction geometrical concept can be started by introducing the Muslim mathematician who invented these concepts so that students can understand in detail how a concept of geometry can be found. However, the history of mathematics development, especially history of Islamic geometry today is less popular in the world of education in Indonesia. There are several concepts discovered by Muslim mathematicians that should be appreciated by the students in learning geometry. Great ideas of mathematicians Muslim can be used as study materials to supplement religious character values taught by Muslim mathematicians. Additionally, by integrating the history of geometry in teaching geometry are expected to improve motivation and geometrical understanding concept.

Working with Functions without Understanding: An Assessment of the Perceptions of Basotho College Mathematics Specialists on the Idea of Function

ERIC Educational Resources Information Center

Polaki, Mokaeane Victor

2005-01-01

It is a well-known fact that the idea of function plays a unifying role in the development of mathematical concepts. Yet research has shown that many students do not understand it adequately even though they have experienced a great deal of success in performing a plethora of operations on function, and on using functions to solve various types of…

Measure for Measure: What Combining Diverse Measures Reveals about Children's Understanding of the Equal Sign as An Indicator of Mathematical Equality

ERIC Educational Resources Information Center

Matthews, Percival; Rittle-Johnson, Bethany; McEldoon, Katherine; Taylor, Roger

2012-01-01

Knowledge of the equal sign as an indicator of mathematical equality is foundational to children's mathematical development and serves as a key link between arithmetic and algebra. The current findings reaffirmed a past finding that diverse items can be integrated onto a single scale, revealed the wide variability in children's knowledge of the…

Selected Effects of a Curriculum Integration Intervention on the Mathematics Performance of Secondary Students Enrolled in an Agricultural Power and Technology Course: An Experimental Study

ERIC Educational Resources Information Center

Parr, Brian; Edwards, M. Craig; Leising, James G.

2009-01-01

The purpose of this study was to empirically test the posit that students who participated in a contextualized, mathematics-enhanced high school agricultural power and technology (APT) curriculum and aligned instructional approach would develop a deeper and more sustained understanding of selected mathematics concepts than those students who…

Mathematical Understanding of the Underprivileged Students through GeoGebra

NASA Astrophysics Data System (ADS)

Amam, A.; Fatimah, A. T.; Hartono, W.; Effendi, A.

2017-09-01

A student’s mathematical understanding in high school from poor families in the district of Ciamis is still low. After reviews the various literature and earlier research, consequently, researchers convince that learning mathematics with GeoGebra can help students improve for the better understanding. Our long-term goal of this research is to support the implementation of new curriculum, namely ICT-based learning mathematics. Another goal is to give a basic mastery skill regarding mathematics software to students from underprivileged families. Moreover, the specific objective of this study is to examine the students’ mathematical understanding from underprivileged families after the implementation of learning with GeoGebra. We use a quantitative comparative research method to determine differences in the mathematical understanding of students’ from underprivileged families before and after mathematics learning with GeoGebra. Accordingly, the students of senior high school from underprivileged family in Baregbeg, Ciamis district, are the population of this study. This research is using purposive sampling. The instrument is in the form of a test question, which is the test of mathematical understanding. Research results show that the mathematical understanding students’ from underprivileged families after the mathematics learning with GeoGebra becomes better than before. The novelty of this research is that students understand the material of trigonometry through the use of modules, aided by GeoGebra in learning activities. Thus, the understanding has an impact on improving students’ mathematical understanding. Students also master the use of GeoGebra Software. Implementing these two things will be very useful for the next lesson.

13th Annual Systems Engineering Conference: Tues- Wed

DTIC Science & Technology

2010-10-28

greater understanding/documentation of lessons learned – Promotes SE within the organization • Justification for continued funding of SE Infrastructure...educational process – Addresses the development of innovative learning tools, strategies, and teacher training • Research and Development – Promotes ...technology, and mathematics • More commitment to engaging young students in science, engineering, technology and mathematics • More rigor in defining

Brief Report: Preliminary Proposal of a Conceptual Model of a Digital Environment for Developing Mathematical Reasoning in Students with Autism Spectrum Disorders

ERIC Educational Resources Information Center

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

2015-01-01

There is clear evidence that in typically developing children reasoning and sense-making are essential in all mathematical learning and understanding processes. In children with autism spectrum disorders (ASD), however, these become much more significant, considering their importance to successful independent living. This paper presents a…

Learning within Context: Exploring Lesson Study as an Aid in Enhancing Teachers' Implementations, Conceptions, and Perceptions of the Mathematics Teaching Practices

ERIC Educational Resources Information Center

Prince, Kyle

2016-01-01

With traditional teaching methods pervasive in the U.S., it is crucial that mathematics teacher educators and professional development leaders understand what methods result in authentic changes in classroom instruction. Lesson study presents a promising approach to developing reform-oriented instruction, as it is situated within the classroom,…

Mathematical Models of Blast-Induced TBI: Current Status, Challenges, and Prospects

PubMed Central

Gupta, Raj K.; Przekwas, Andrzej

2013-01-01

Blast-induced traumatic brain injury (TBI) has become a signature wound of recent military activities and is the leading cause of death and long-term disability among U.S. soldiers. The current limited understanding of brain injury mechanisms impedes the development of protection, diagnostic, and treatment strategies. We believe mathematical models of blast wave brain injury biomechanics and neurobiology, complemented with in vitro and in vivo experimental studies, will enable a better understanding of injury mechanisms and accelerate the development of both protective and treatment strategies. The goal of this paper is to review the current state of the art in mathematical and computational modeling of blast-induced TBI, identify research gaps, and recommend future developments. A brief overview of blast wave physics, injury biomechanics, and the neurobiology of brain injury is used as a foundation for a more detailed discussion of multiscale mathematical models of primary biomechanics and secondary injury and repair mechanisms. The paper also presents a discussion of model development strategies, experimental approaches to generate benchmark data for model validation, and potential applications of the model for prevention and protection against blast wave TBI. PMID:23755039

Collaborative and Cooperative Learning in Malaysian Mathematics Education

ERIC Educational Resources Information Center

Hossain, Md. Anowar; Tarmizi, Rohani Ahmad; Ayud, Ahmad Fauzi Mohd

2012-01-01

Collaborative and cooperative learning studies are well recognized in Malaysian mathematics education research. Cooperative learning is used to serve various ability students taking into consideration of their level of understanding, learning styles, sociological backgrounds that develop students' academic achievement and skills, and breeze the…

Techniques for Small-Group Discourse

ERIC Educational Resources Information Center

Kilic, Hulya; Cross, Dionne I.; Ersoz, Filyet A.; Mewborn, Denise S.; Swanagan, Diana; Kim, Jisun

2010-01-01

The nature of mathematical discourse and its influence on the development of students' mathematical understanding has received much attention from researchers in recent years. Engaging students in discursive practices can be difficult; teachers can increase their competence in facilitating discourse through greater awareness of the impact of…

What Teachers Understand of Model Lessons

ERIC Educational Resources Information Center

Courtney, Scott A.

2017-01-01

Over the past two decades, researchers in mathematics teacher education have identified characteristics of high quality professional development (PD). This report describes an investigation of a common approach to PD with secondary mathematics teachers, providing teachers with opportunities to experience reform-oriented model lessons as students…

Social activity method (SAM): A fractal language for mathematics

NASA Astrophysics Data System (ADS)

Dowling, Paul

2013-09-01

In this paper I shall present and develop my organisational language, social activity method (SAM), and illustrate some of its applications. I shall introduce a new scheme for modes of recontextualisation that enables the analysis of the ways in which one activity - which might be school mathematics or social research or any empirically observed regularity of practice - recontextualises the practice of another and I shall also present, deploy, and develop an existing scheme - domains of action - in an analysis of school mathematics examination papers and in the structuring of what I refer to as the esoteric domain. This domain is here conceived as a hybrid domain of, first, linguistic and extralinguistic resources that are unambiguously mathematical in terms of both expression and content and, second, pedagogic theory - often tacit - that enables the mathematical gaze onto other practices and so recontextualises them. A second and more general theme that runs through the paper is the claim that there is nothing that is beyond semiosis, that there is nothing to which we have direct access, unmediated by interpretation. This state of affairs has implications for mathematics education. Specifically, insofar as an individual's mathematical semiotic system is under continuous development - the curriculum never being graspable all at once - understanding - as a stable semiotic moment - of any aspect or object of mathematics is always localised to the individual and is at best transient, and the sequencing of such moments may well also be more individualised than consistent in some correspondence with the sequencing of the curriculum. This being the case, a concentration on understanding as a goal may well serve to inhibit the pragmatic acquisition and deployment of mathematical technologies, which should be the principal aim of mathematics teaching and learning. The paper is primarily concerned with mathematics education. SAM, however, is a language that is available for recruiting and deploying in potentially any context as I have attempted to illustrate with some of the secondary illustrations in the text.

Mathematical and Computational Modeling in Complex Biological Systems

PubMed Central

Li, Wenyang; Zhu, Xiaoliang

2017-01-01

The biological process and molecular functions involved in the cancer progression remain difficult to understand for biologists and clinical doctors. Recent developments in high-throughput technologies urge the systems biology to achieve more precise models for complex diseases. Computational and mathematical models are gradually being used to help us understand the omics data produced by high-throughput experimental techniques. The use of computational models in systems biology allows us to explore the pathogenesis of complex diseases, improve our understanding of the latent molecular mechanisms, and promote treatment strategy optimization and new drug discovery. Currently, it is urgent to bridge the gap between the developments of high-throughput technologies and systemic modeling of the biological process in cancer research. In this review, we firstly studied several typical mathematical modeling approaches of biological systems in different scales and deeply analyzed their characteristics, advantages, applications, and limitations. Next, three potential research directions in systems modeling were summarized. To conclude, this review provides an update of important solutions using computational modeling approaches in systems biology. PMID:28386558

Mathematical and Computational Modeling in Complex Biological Systems.

PubMed

Ji, Zhiwei; Yan, Ke; Li, Wenyang; Hu, Haigen; Zhu, Xiaoliang

2017-01-01

The biological process and molecular functions involved in the cancer progression remain difficult to understand for biologists and clinical doctors. Recent developments in high-throughput technologies urge the systems biology to achieve more precise models for complex diseases. Computational and mathematical models are gradually being used to help us understand the omics data produced by high-throughput experimental techniques. The use of computational models in systems biology allows us to explore the pathogenesis of complex diseases, improve our understanding of the latent molecular mechanisms, and promote treatment strategy optimization and new drug discovery. Currently, it is urgent to bridge the gap between the developments of high-throughput technologies and systemic modeling of the biological process in cancer research. In this review, we firstly studied several typical mathematical modeling approaches of biological systems in different scales and deeply analyzed their characteristics, advantages, applications, and limitations. Next, three potential research directions in systems modeling were summarized. To conclude, this review provides an update of important solutions using computational modeling approaches in systems biology.

Mathematical modeling of renal hemodynamics in physiology and pathophysiology.

PubMed

Sgouralis, Ioannis; Layton, Anita T

2015-06-01

In addition to the excretion of metabolic waste and toxin, the kidney plays an indispensable role in regulating the balance of water, electrolyte, acid-base, and blood pressure. For the kidney to maintain proper functions, hemodynamic control is crucial. In this review, we describe representative mathematical models that have been developed to better understand the kidney's autoregulatory processes. We consider mathematical models that simulate glomerular filtration, and renal blood flow regulation by means of the myogenic response and tubuloglomerular feedback. We discuss the extent to which these modeling efforts have expanded the understanding of renal functions in health and disease. Copyright © 2015 Elsevier Inc. All rights reserved.

Computer-Based Mathematics Instructions for Engineering Students

NASA Technical Reports Server (NTRS)

Khan, Mustaq A.; Wall, Curtiss E.

1996-01-01

Almost every engineering course involves mathematics in one form or another. The analytical process of developing mathematical models is very important for engineering students. However, the computational process involved in the solution of some mathematical problems may be very tedious and time consuming. There is a significant amount of mathematical software such as Mathematica, Mathcad, and Maple designed to aid in the solution of these instructional problems. The use of these packages in classroom teaching can greatly enhance understanding, and save time. Integration of computer technology in mathematics classes, without de-emphasizing the traditional analytical aspects of teaching, has proven very successful and is becoming almost essential. Sample computer laboratory modules are developed for presentation in the classroom setting. This is accomplished through the use of overhead projectors linked to graphing calculators and computers. Model problems are carefully selected from different areas.

The influence of Missouri mathematics project on seventh grade students’ mathematical understanding ability

NASA Astrophysics Data System (ADS)

Rezeki, S.; Setyawan, A. A.; Amelia, S.

2018-01-01

Mathematical understanding ability is a primary goal of Indonesian national education goals. However, various sources has shown that Indonesian students’ mathematical understanding ability is still relatively low. This study used quasi-experimental research design to examine the effectiveness of the application of Missouri Mathematics Project (MMP) on students’ mathematical understanding ability. The participants of the study were seventh grade students in Pekanbaru, Riau Province, Indonesia. They were selected purposively and represented as high, medium, and low-quality schools. The result of this study indicated that there was a significant effect of MMP on the overall students’ mathematical understanding ability and in all categories, except for low school level.

Multiscale Mathematics for Biomass Conversion to Renewable Hydrogen

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

Plechac, Petr

2016-03-01

The overall objective of this project was to develop multiscale models for understanding and eventually designing complex processes for renewables. To the best of our knowledge, our work is the first attempt at modeling complex reacting systems, whose performance relies on underlying multiscale mathematics and developing rigorous mathematical techniques and computational algorithms to study such models. Our specific application lies at the heart of biofuels initiatives of DOE and entails modeling of catalytic systems, to enable economic, environmentally benign, and efficient conversion of biomass into either hydrogen or valuable chemicals.

Learning to teach mathematics with technology: A survey of professional development needs, experiences and impacts

NASA Astrophysics Data System (ADS)

Bennison, Anne; Goos, Merrilyn

2010-04-01

The potential for digital technologies to enhance students' mathematics learning is widely recognised, and use of computers and graphics calculators is now encouraged or required by secondary school mathematics curriculum documents throughout Australia. However, previous research indicates that effective integration of technology into classroom practice remains patchy, with factors such as teacher knowledge, confidence, experience and beliefs, access to resources, and participation in professional development influencing uptake and implementation. This paper reports on a large-scale survey of technology-related professional development experiences and needs of Queensland secondary mathematics teachers. Teachers who had participated in professional development were found to be more confident in using technology and more convinced of its benefits in supporting students' learning of mathematics. Experienced, specialist mathematics teachers in large metropolitan schools were more likely than others to have attended technology-related professional development, with lack of time and limited access to resources acting as hindrances to many. Teachers expressed a clear preference for professional development that helps them meaningfully integrate technology into lessons to improve student learning of specific mathematical topics. These findings have implications for the design and delivery of professional development that improves teachers' knowledge, understanding, and skills in a diverse range of contexts.

Polygon Properties: What Is Possible?

ERIC Educational Resources Information Center

Rodrigue, Paulette R.; Robichaux, Rebecca R.

2010-01-01

Sorting shapes and solving riddles develop and advance children's geometric thinking and understanding while promoting mathematical communication, cooperative learning, and numerous representations. This article presents a brief summary of how children develop an understanding of the properties of geometric shapes as well as a description of the…

Problems Identifying Independent and Dependent Variables

ERIC Educational Resources Information Center

Leatham, Keith R.

2012-01-01

This paper discusses one step from the scientific method--that of identifying independent and dependent variables--from both scientific and mathematical perspectives. It begins by analyzing an episode from a middle school mathematics classroom that illustrates the need for students and teachers alike to develop a robust understanding of…

Modeling Mathematical Ideas: Developing Strategic Competence in Elementary and Middle School

ERIC Educational Resources Information Center

Suh, Jennifer M.; Seshaiyer, Padmanabhan

2016-01-01

"Modeling Mathematical Ideas" combining current research and practical strategies to build teachers and students strategic competence in problem solving.This must-have book supports teachers in understanding learning progressions that addresses conceptual guiding posts as well as students' common misconceptions in investigating and…

Gender-Related Differential Item Functioning on a Middle-School Mathematics Performance Assessment.

ERIC Educational Resources Information Center

Lane, Suzanne; And Others

This study examined gender-related differential item functioning (DIF) using a mathematics performance assessment, the QUASAR Cognitive Assessment Instrument (QCAI), administered to middle school students. The QCAI was developed for the Quantitative Understanding: Amplifying Student Achievement and Reading (QUASAR) project, which focuses on…

GED Math for Workplace Students.

ERIC Educational Resources Information Center

Goschen, Claire

This curriculum module contains lesson plans and application activities that were developed to help adult students master the mathematics skills needed to earn a general high school equivalency diploma. Included in the module are materials designed to help students improve their understanding of mathematics and achieve the following objectives:…

Student Interactions in Technology-Rich Classrooms

ERIC Educational Resources Information Center

Fonkert, Karen L.

2010-01-01

Students are more likely to develop a deep conceptual understanding of mathematics when they interact with and discuss their thoughts with others. The National Council of Teachers of Mathematics (NCTM) (1989, 2000) has recommended that students be active learners--communicating with one another, conjecturing, exploring, and justifying claims by…

Indicators of Multiplicative Reasoning among Fourth Grade Students

ERIC Educational Resources Information Center

Carrier, James A.

2010-01-01

Many students encounter difficulty in their transition to advanced mathematical thinking. Such difficulty may be explained by a lack of understanding of many concepts taught in early school years, especially multiplicative reasoning. Advanced mathematical thinking depends on the development of multiplicative reasoning. The purpose of this study…

Brain stimulation, mathematical, and numerical training: Contribution of core and noncore skills.

PubMed

Looi, C Y; Cohen Kadosh, R

2016-01-01

Mathematical abilities that are correlated with various life outcomes vary across individuals. One approach to improve mathematical abilities is by understanding the underlying cognitive functions. Theoretical and experimental evidence suggest that mathematical abilities are subserved by "core" and "noncore" skills. Core skills are commonly regarded as the "innate" capacity to attend to and process numerical information, while noncore skills are those that are important for mathematical cognition, but are not exclusive to the mathematical domain such as executive functions, spatial skills, and attention. In recent years, mathematical training has been combined with the application of noninvasive brain stimulation to further enhance training outcomes. However, the development of more strategic training paradigms is hindered by the lack of understanding on the contributory nature of core and noncore skills and their neural underpinnings. In the current review, we will examine the effects of brain stimulation with focus on transcranial electrical stimulation on core and noncore skills, and its impact on mathematical and numerical training. We will conclude with a discussion on the theoretical and experimental implications of these studies and directions for further research. © 2016 Elsevier B.V. All rights reserved.

The Development of an Assessment Tool: Student Knowledge of the Concept of Place Value

ERIC Educational Resources Information Center

Major, Karen

2012-01-01

The importance of student understanding of the concept of place value cannot be underestimated. Place value is a "gate keeper" in developing mathematical understanding. The purpose of this study was to examine and develop a teacher-made test of place value knowledge. The questions were developed using the progressions from the Number…

GUIDE FOR COURSE OF STUDY FOR COOK (HOTEL AND RESTAURANT) (ENTRY).

ERIC Educational Resources Information Center

GUNN, VIRLAH

DESIGNED FOR TEACHER USE, THIS GUIDE FOR TRAINING COOKS IN HOTEL AND RESTAURANT OCCUPATIONS AIMS--(1) TO DEVELOP MANIPULATIVE SKILLS, (2) TO DEVELOP UNDERSTANDING OF THE BASIC PRINCIPLES OF SCIENCE, MATHEMATICS, AND RELATED KNOWLEDGE THAT CONDITION THESE SKILLS, (3) TO UNDERSTAND THE ADVANTAGES OF STEADY EMPLOYMENT, (4) TO DEVELOP HIGH STANDARDS…

Developing an Understanding of What Constitutes Mathematics Teacher Educator PCK: A Case Study of a Collaboration between Two Teacher Educators

ERIC Educational Resources Information Center

Muir, Tracey; Wells, Jill; Chick, Helen

2017-01-01

Previous research into the knowledge required for teaching has focused primarily on pre-service and in-service teachers' knowledge. What is less researched, however, is the role of the teacher educator in helping pre-service teachers (PSTs) develop the knowledge needed in order to teach mathematics to students. The focus thus shifts from examining…

How To Use the Spreadsheet as a Tool in the Secondary School Mathematics Classroom. Second Edition (for Windows and Macintosh Operating Systems).

ERIC Educational Resources Information Center

Masalski, William J.

This book seeks to develop, enhance, and expand students' understanding of mathematics by using technology. Topics covered include the advantages of spreadsheets along with the opportunity to explore the 'what if?' type of questions encountered in the problem-solving process, enhancing the user's insight into the development and use of algorithms,…

Soap films and GeoGebra in the study of Fermat and Steiner points

NASA Astrophysics Data System (ADS)

Flores, Alfinio; Park, Jungeun

2018-05-01

We discuss how mathematics and secondary mathematics education majors developed an understanding of Fermat points for the triangle as well as Steiner points for the square and regular pentagon, and also of soap film configurations between parallel plates where forces are in equilibrium. The activities included the use of soap films and the interactive geometry program GeoGebra. Students worked in small groups using these tools to investigate the properties of Fermat and Steiner points and then justified the results of their investigations using geometrical arguments. These activities are specific approaches of how to encourage prospective teachers to use physical experiments to support students' development of mathematical curiosity and mathematical justifications.

Sliding into Multiplicative Thinking: The Power of the "Marvellous Multiplier"

ERIC Educational Resources Information Center

Hurst, Chris; Hurrell, Derek

2016-01-01

Multiplicative thinking is a critical stage in mathematical learning and underpins much of the mathematics learned beyond middle primary years. Its components are complex and an inability to understand them conceptually is likely to undermine students' capacity to develop beyond additive thinking. Of particular importance are the ten times…

Pathways to Arithmetic Fact Retrieval and Percentage Calculation in Adolescents

ERIC Educational Resources Information Center

Träff, Ulf; Skagerlund, Kenny; Olsson, Linda; Östergren, Rickard

2017-01-01

Background: Developing sufficient mathematical skills is a prerequisite to function adequately in society today. Given this, an important task is to increase our understanding regarding the cognitive mechanisms underlying young people's acquisition of early number skills and formal mathematical knowledge. Aims: The purpose was to examine whether…

Understanding the Problems of Learning Mathematics.

ERIC Educational Resources Information Center

Semilla-Dube, Lilia

1983-01-01

A model is being developed to categorize problems in teaching and learning mathematics. Categories include problems due to language difficulties, lack of prerequisite knowledge, and those related to the affective domain. This paper calls on individuals to share teaching and learning episodes; those submitted will then be compiled and categorized.…

High and Low Visualization Skills and Pedagogical Decision of Preservice Secondary Mathematics Teachers

ERIC Educational Resources Information Center

Unal, Hasan

2011-01-01

The purpose of this study was to investigate the preservice secondary mathematics teachers' development of pedagogical understanding in the teaching of modular arithmetic problems. Data sources included, written assignments, interview transcripts and filed notes. Using case study and action research approaches cases of three preservice teachers…

Not Just for Computation: Basic Calculators Can Advance the Process Standards

ERIC Educational Resources Information Center

Moss, Laura J.; Grover, Barbara W.

2007-01-01

Simple nongraphing calculators can be powerful tools to enhance students' conceptual understanding of mathematics concepts. Students have opportunities to develop (1) a broad repertoire of problem-solving strategies by observing multiple solution strategies; (2) respect for other students' abilities and ways of thinking about mathematics; (3) the…

ELPSA as a Lesson Design Framework

ERIC Educational Resources Information Center

Lowrie, Tom; Patahuddin, Sitti Maesuri

2015-01-01

This paper offers a framework for a mathematics lesson design that is consistent with the way we learn about, and discover, most things in life. In addition, the framework provides a structure for identifying how mathematical concepts and understanding are acquired and developed. This framework is called ELPSA and represents five learning…

The Value of Why for Student and Teacher Learning

ERIC Educational Resources Information Center

Guarino, Jody; Sykes, Marie; Santagata, Rossella

2013-01-01

The authors believe teaching for understanding begins with the development of a few essential orientations. Teachers must have an appreciation for student centered mathematics teaching, valuing an approach that builds on student thinking. In addition, teachers must appreciate the complexity of students' mathematical thinking and ideas. Once these…

Cleared for Takeoff: Paper Airplanes in Flight

ERIC Educational Resources Information Center

Reeder, Stacy L.

2012-01-01

As middle school mathematics becomes more abstract, it is imperative for teachers to introduce concepts in ways that are interesting and meaningful to students. Since her students struggled at times to stay engaged in mathematics and seemed to have difficulty developing conceptual understanding, the author looked for ways to create learning…

Developing Classroom Formative Assessment in Dutch Primary Mathematics Education

ERIC Educational Resources Information Center

van den Berg, M.; Harskamp, E. G.; Suhre, C. J. M.

2016-01-01

In the last two decades Dutch primary school students scored below expectation in international mathematics tests. An explanation for this may be that teachers fail to adequately assess their students' understanding of learning goals and provide timely feedback. To improve the teachers' formative assessment practice, researchers, curriculum…

A Practitioner Implementation of a Tier 2 First-Grade Mathematics Intervention

ERIC Educational Resources Information Center

Strand Cary, Mari G.; Clarke, Ben; Doabler, Christian T.; Smolkowski, Keith; Fien, Hank; Baker, Scott K.

2017-01-01

We report on a practitioner implementation of Fusion, a first-grade mathematics intervention. Studies such as this evaluation of a loose implementation under realistic conditions are important to curriculum developers' understanding of how evidence-based programs and tools work under a variety of implementation scenarios. In this…

Student Engagement and Teacher Guidance in Meaningful Mathematics: Enduring Principles

ERIC Educational Resources Information Center

Freeman, Gregory D.; Lucius, Lisa B.

2008-01-01

In mathematics, developing a conceptual understanding and observing properly modeled methods rarely lead to successful student performance. The student must participate. As with bike riding, participation with monitoring and guidance makes initial efforts meaningful and beneficial. In this article, the authors share a bike riding experience and…

Building a Knowledge Base: Understanding Prospective Elementary Teachers' Mathematical Content Knowledge

ERIC Educational Resources Information Center

Thanheiser, Eva; Browning, Christine; Edson, Alden J.; Kastberg, Signe; Lo, Jane-Jane

2013-01-01

This survey of the literature summarizes and reflects on research findings regarding elementary preservice teachers' (PSTs') mathematics conceptions and the development thereof. Despite the current focus on teacher education, peer-reviewed journals offer a surprisingly sparse insight in these areas. The limited research that exists…

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

PubMed

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

2015-01-01

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

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

PubMed Central

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

2015-01-01

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

Motion sensors in mathematics teaching: learning tools for understanding general math concepts?

NASA Astrophysics Data System (ADS)

Urban-Woldron, Hildegard

2015-05-01

Incorporating technology tools into the mathematics classroom adds a new dimension to the teaching of mathematics concepts and establishes a whole new approach to mathematics learning. In particular, gathering data in a hands-on and real-time method helps classrooms coming alive. The focus of this paper is on bringing forward important mathematics concepts such as functions and rate of change with the motion detector. Findings from the author's studies suggest that the motion detector can be introduced from a very early age and used to enliven classes at any level. Using real-world data to present the main functions invites an experimental approach to mathematics and encourages students to engage actively in their learning. By emphasizing learning experiences with computer-based motion detectors and aiming to involve students in mathematical representations of real-world phenomena, six learning activities, which were developed in previous research studies, will be presented. Students use motion sensors to collect physical data that are graphed in real time and then manipulate and analyse them. Because data are presented in an immediately understandable graphical form, students are allowed to take an active role in their learning by constructing mathematical knowledge from observation of the physical world. By utilizing a predict-observe-explain format, students learn about slope, determining slope and distance vs. time graphs through motion-filled activities. Furthermore, exploring the meaning of slope, viewed as the rate of change, students acquire competencies for reading, understanding and interpreting kinematics graphs involving a multitude of mathematical representations. Consequently, the students are empowered to efficiently move among tabular, graphical and symbolic representation to analyse patterns and discover the relationships between different representations of motion. In fact, there is a need for further research to explore how mathematics teachers can integrate motion sensors into their classrooms.

The effect of mathematics anxiety on the processing of numerical magnitude.

PubMed

Maloney, Erin A; Ansari, Daniel; Fugelsang, Jonathan A

2011-01-01

In an effort to understand the origins of mathematics anxiety, we investigated the processing of symbolic magnitude by high mathematics-anxious (HMA) and low mathematics-anxious (LMA) individuals by examining their performance on two variants of the symbolic numerical comparison task. In two experiments, a numerical distance by mathematics anxiety (MA) interaction was obtained, demonstrating that the effect of numerical distance on response times was larger for HMA than for LMA individuals. These data support the claim that HMA individuals have less precise representations of numerical magnitude than their LMA peers, suggesting that MA is associated with low-level numerical deficits that compromise the development of higher level mathematical skills.

Fraction Development in Children: Importance of Building Numerical Magnitude Understanding

ERIC Educational Resources Information Center

Jordan, Nancy C.; Carrique, Jessica; Hansen, Nicole; Resnick, Ilyse

2016-01-01

This chapter situates fraction learning within the integrated theory of numerical development. We argue that the understanding of numerical magnitudes for whole numbers as well as for fractions is critical to fraction learning in particular and mathematics achievement more generally. Results from the Delaware Longitudinal Study, which examined…

The Codevelopment of Children's Fraction Arithmetic Skill and Fraction Magnitude Understanding

ERIC Educational Resources Information Center

Bailey, Drew H.; Hansen, Nicole; Jordan, Nancy C.

2017-01-01

The importance of fraction knowledge to later mathematics achievement, along with U.S. students' poor knowledge of fraction concepts and procedures, has prompted research on the development of fraction learning. In the present study, participants' (N = 536) development of fraction magnitude understanding and fraction arithmetic skills was assessed…

Helping Secondary School Students Develop a Conceptual Understanding of Refraction

ERIC Educational Resources Information Center

Ashmann, Scott; Anderson, Charles W.; Boeckman, Heather

2016-01-01

Using real-world examples, ray diagrams, and a cognitive apprenticeship cycle, this paper focuses on developing students' conceptual (not mathematical) understanding of refraction. Refraction can be a difficult concept for students to comprehend if they do not have well-designed opportunities to practice explaining situations where reflection and…

Quantitative imaging with Fucci and mathematics to uncover temporal dynamics of cell cycle progression.

PubMed

Saitou, Takashi; Imamura, Takeshi

2016-01-01

Cell cycle progression is strictly coordinated to ensure proper tissue growth, development, and regeneration of multicellular organisms. Spatiotemporal visualization of cell cycle phases directly helps us to obtain a deeper understanding of controlled, multicellular, cell cycle progression. The fluorescent ubiquitination-based cell cycle indicator (Fucci) system allows us to monitor, in living cells, the G1 and the S/G2/M phases of the cell cycle in red and green fluorescent colors, respectively. Since the discovery of Fucci technology, it has found numerous applications in the characterization of the timing of cell cycle phase transitions under diverse conditions and various biological processes. However, due to the complexity of cell cycle dynamics, understanding of specific patterns of cell cycle progression is still far from complete. In order to tackle this issue, quantitative approaches combined with mathematical modeling seem to be essential. Here, we review several studies that attempted to integrate Fucci technology and mathematical models to obtain quantitative information regarding cell cycle regulatory patterns. Focusing on the technological development of utilizing mathematics to retrieve meaningful information from the Fucci producing data, we discuss how the combined methods advance a quantitative understanding of cell cycle regulation. © 2015 Japanese Society of Developmental Biologists.

Learning over Time: Learning Trajectories in Mathematics Education

ERIC Educational Resources Information Center

Maloney, Alan P., Ed.; Confrey, Jere, Ed.; Nguyen, Kenny H., Ed.

2014-01-01

The driving forces behind mathematics learning trajectories is the need to understand how children actually learn and make sense of mathematics--how they progress from prior knowledge, through intermediate understandings, to the mathematics target understandings--and how to use these insights to improve instruction and student learning. In this…

A Recursive Theory for the Mathematical Understanding--Some Elements and Implications.

ERIC Educational Resources Information Center

Pirie, Susan; Kieren, Thomas

There has been considerable interest in mathematical understanding. Both those attempting to build, and those questioning the possibility of building intelligent artificial tutoring systems, struggle with the notions of mathematical understanding. The purpose of this essay is to show a transcendently recursive theory of mathematical understanding…

Developing Second Grade Teachers' Pedagogical Content Knowledge of Place Value

ERIC Educational Resources Information Center

Kulhanek, Stefani Michelle

2013-01-01

An understanding of whole number place value is a critical component of second-grade mathematics. This understanding of place value provides the foundational concept for operations with whole numbers. The ability to understand the concept of place value and transfer that understanding to teaching addition and subtraction are often problems…

Teaching and Assessing Polygons Using Technology

ERIC Educational Resources Information Center

Soucie, Tanja; Radovic, Nikol; Svedrec, Renata; Kokic, Ivana

2011-01-01

Studying geometry is an integral component of learning mathematics because it allows students to analyse and interpret the world they live in as well as equip them with tools they can apply in other areas of mathematics. Therefore, students need to develop an understanding of geometric concepts as well as gaining adequate geometry related skills.…

Addressing the Standards for Mathematical Practice in a Calculus Class

ERIC Educational Resources Information Center

Pilgrim, Mary E.

2014-01-01

The Common Core State Standards (CCSS) provide teachers with the expectations and requirements that are meant to prepare K-12 students for college and the workforce (CCSSI 2010b). The Common Core State Standards for Mathematical Practice (SMPs) emphasize the development of skills and conceptual understanding for students to become proficient in…

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…

Increasing Communication in Geometry by Using a Personal Math Concept Chart

ERIC Educational Resources Information Center

Friedman, Rhonda; Kazerouni, Gety; Lax, Stacey; Weisdorf, Elli

2011-01-01

The action research team developed a "Personal Math Concept Chart". This chart required students to describe the mathematical concepts that they were studying in the Geometry strand of Mathematics using their own images and words. In this study, students were encouraged to express their own understanding of geometric concepts in order to…

The Complexities of a Lesson Study in a Dutch Situation: Mathematics Teacher Learning

ERIC Educational Resources Information Center

Verhoef, Nellie; Tall, David; Coenders, Fer; van Smaalen, Daan

2014-01-01

This study combines the Japanese lesson study approach and mathematics teachers' professional development. The first year of a 4-year project in which 3 Dutch secondary school teachers worked cooperatively on introducing making sense of the calculus is reported. The analysis focusses on instrumental and relational student understanding of…

Reframing Practice: High School Mathematics Teachers' Learning through Interactions in Their Workplace Community

ERIC Educational Resources Information Center

Bannister, Nicole A.

2009-01-01

This dissertation seeks to understand how teachers learn through interactions in newly formed workplace communities by examining how mathematics teachers engaged in equity-oriented reforms frame problems of practice. It examines how teachers' framings develop over time, and how teachers' shifting frames connect to their learning in a community of…

Learning about "Half": Critical Aspects and Pedagogical Strategies in Designed Preschool Activities

ERIC Educational Resources Information Center

Björklund, Camilla

2018-01-01

This is an empirical inquiry concerning children's concept development and early mathematics teaching. The intention is to broaden the understanding of preschool children's perceptions of the concept "half" (as 1 of 2 equal parts of a whole), in designed mathematics teaching settings. Three teachers working with 4-5-year-old children…

Understanding What Makes for Productive Coaching Moves to Help Teachers Attend to Mathematical Tasks of Teaching

ERIC Educational Resources Information Center

Jakopovic, Paula M.

2017-01-01

Reforms in mathematics education call for teaching to move away from "traditional" approaches (Carpenter, Ansell, & Levi, 2001) that are focused around rote procedures and skills, and toward practice that engages students in cognitively demanding tasks, discourse, and productive struggle to develop conceptual and procedural…

Mathematical difficulties as decoupling of expectation and developmental trajectories

PubMed Central

McLean, Janet F.; Rusconi, Elena

2014-01-01

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

Mathematical modeling and numerical simulation of the mitotic spindle orientation system.

PubMed

Ibrahim, Bashar

2018-05-21

The mitotic spindle orientation and position is crucial for the fidelity of chromosome segregation during asymmetric cell division to generate daughter cells with different sizes or fates. This mechanism is best understood in the budding yeast Saccharomyces cerevisiae, named the spindle position checkpoint (SPOC). The SPOC inhibits cells from exiting mitosis until the mitotic spindle is properly oriented along the mother-daughter polarity axis. Despite many experimental studies, the mechanisms underlying SPOC regulation remains elusive and unexplored theoretically. Here, a minimal mathematical is developed to describe SPOC activation and silencing having autocatalytic feedback-loop. Numerical simulations of the nonlinear ordinary differential equations (ODEs) model accurately reproduce the phenotype of SPOC mechanism. Bifurcation analysis of the nonlinear ODEs reveals the orientation dependency on spindle pole bodies, and how this dependence is altered by parameter values. These results provide for systems understanding on the molecular organization of spindle orientation system via mathematical modeling. The presented mathematical model is easy to understand and, within the above mentioned context, can be used as a base for further development of quantitative models in asymmetric cell-division. Copyright © 2018. Published by Elsevier Inc.

The Mathematics Attitudes and Perceptions Survey: an instrument to assess expert-like views and dispositions among undergraduate mathematics students

NASA Astrophysics Data System (ADS)

Code, Warren; Merchant, Sandra; Maciejewski, Wes; Thomas, Matthew; Lo, Joseph

2016-08-01

One goal of an undergraduate education in mathematics is to help students develop a productive disposition towards mathematics. A way of conceiving of this is as helping mathematical novices transition to more expert-like perceptions of mathematics. This conceptualization creates a need for a way to characterize students' perceptions of mathematics in authentic educational settings. This article presents a survey, the Mathematics Attitudes and Perceptions Survey (MAPS), designed to address this need. We present the development of the MAPS instrument and its validation on a large (N = 3411) set of student data. Results from various MAPS implementations corroborate results from analogous instruments in other STEM disciplines. We present these results and highlight some in particular: MAPS scores correlate with course grades; students tend to move away from expert-like orientations over a semester or year of taking a mathematics course; and interactive-engagement type lectures have less of a negative impact, but no positive impact, on students' overall orientations than traditional lecturing. We include the MAPS instrument in this article and suggest ways in which it may deepen our understanding of undergraduate mathematics education.

Growth in Mathematical Understanding While Learning How To Teach: A Theoretical Perspective.

ERIC Educational Resources Information Center

Cavey, Laurie O.

This theoretical paper outlines a conceptual framework for examining growth in prospective teachers' mathematical understanding as they engage in thinking about and planning for the mathematical learning of others. The framework is based on the Pirie-Kieren (1994) Dynamical Theory for the Growth of Mathematical Understanding and extends into the…

Comparing the development of the multiplication of fractions in Turkish and American textbooks

NASA Astrophysics Data System (ADS)

Kar, Tuğrul; Güler, Gürsel; Şen, Ceylan; Özdemir, Ercan

2018-02-01

This study analyzed the methods used to teach the multiplication of fractions in Turkish and American textbooks. Two Turkish textbooks and two American textbooks, Everyday Mathematics (EM) and Connected Mathematics 3 (CM), were analyzed. The analyses focused on the content and the nature of the mathematical problems presented in the textbooks. The findings of the study showed that the American textbooks aimed at developing conceptual understanding first and then procedural fluency, whereas the Turkish textbooks aimed at developing both concurrently. The American textbooks provided more opportunities for different computational strategies. The solutions to most problems in all textbooks required a single computational step, a numerical answer, and procedural knowledge. Furthermore, compared with the Turkish textbooks, the American textbooks contained a greater number of problems that required high-level cognitive skills such as mathematical reasoning.

Improving students’ understanding of mathematical concept using maple

NASA Astrophysics Data System (ADS)

Ningsih, Y. L.; Paradesa, R.

2018-01-01

This study aimed to improve students’ understanding of mathematical concept ability through implementation of using Maple in learning and expository learning. This study used a quasi-experimental research with pretest-posttest control group design. The sample on this study was 61 students in the second semester of Mathematics Education of Universitas PGRI Palembang, South Sumatera in academic year 2016/2017. The sample was divided into two classes, one class as the experiment class who using Maple in learning and the other class as a control class who received expository learning. Data were collective through the test of mathematical initial ability and mathematical concept understanding ability. Data were analyzed by t-test and two ways ANOVA. The results of this study showed (1) the improvement of students’ mathematical concept understanding ability who using Maple in learning is better than those who using expository learning; (2) there is no interaction between learning model and students’ mathematical initial ability toward the improvement of students’ understanding of mathematical concept ability.

Abstracting Sequences: Reasoning That Is a Key to Academic Achievement.

PubMed

Pasnak, Robert; Kidd, Julie K; Gadzichowski, K Marinka; Gallington, Debbie A; Schmerold, Katrina Lea; West, Heather

2015-01-01

The ability to understand sequences of items may be an important cognitive ability. To test this proposition, 8 first-grade children from each of 36 classes were randomly assigned to four conditions. Some were taught sequences that represented increasing or decreasing values, or were symmetrical, or were rotations of an object through 6 or 8 positions. Control children received equal numbers of sessions on mathematics, reading, or social studies. Instruction was conducted three times weekly in 15-min sessions for seven months. In May, the children taught sequences applied their understanding to novel sequences, and scored as well or better on three standardized reading tests as the control children. They outscored all children on tests of mathematics concepts, and scored better than control children on some mathematics scales. These findings indicate that developing an understanding of sequences is a form of abstraction, probably involving fluid reasoning, that provides a foundation for academic achievement in early education.

Examining the Efficacy of a Tier 2 Kindergarten Mathematics Intervention.

PubMed

Clarke, Ben; Doabler, Christian T; Smolkowski, Keith; Baker, Scott K; Fien, Hank; Strand Cary, Mari

2016-01-01

This study examined the efficacy of a Tier 2 kindergarten mathematics intervention program, ROOTS, focused on developing whole number understanding for students at risk in mathematics. A total of 29 classrooms were randomly assigned to treatment (ROOTS) or control (standard district practices) conditions. Measures of mathematics achievement were collected at pretest and posttest. Treatment and control students did not differ on mathematics assessments at pretest. Gain scores of at-risk intervention students were significantly greater than those of control peers, and the gains of at-risk treatment students were greater than the gains of peers not at risk, effectively reducing the achievement gap. Implications for Tier 2 mathematics instruction in a response to intervention (RtI) model are discussed. © Hammill Institute on Disabilities 2014.

Using Classroom Scenarios to Reveal Mathematics Teachers' Understanding of Sociomathematical Norms

ERIC Educational Resources Information Center

Zembat, Ismail Ozgur; Yasa, Seyit Ali

2015-01-01

The purpose of this study was to uncover the degree to which in-service teachers understand sociomathematical norms and the nature of that understanding without having to enter and observe their classes. We therefore developed five classroom scenarios exemplifying classroom interactions shaped by certain sociomathematical norms. We then…

Developing Children's Conceptual Understanding of Area Measurement: A Curriculum and Teaching Experiment

ERIC Educational Resources Information Center

Huang, Hsin-Mei E.; Witz, Klaus G.

2011-01-01

The present study examined the effectiveness of three instructional treatments which had different combinations of mathematical elements regarding 2-dimensional (2-D) geometry and area measurement for developing 4th-grade children's understanding of the formulas for area measurement and their ability to solve area measurement problems.…

Using Spreadsheets to Discover Meaning for Parameters in Nonlinear Models

ERIC Educational Resources Information Center

Green, Kris H.

2008-01-01

This paper explores the use of spreadsheets to develop an exploratory environment where mathematics students can develop their own understanding of the parameters of commonly encountered families of functions: linear, logarithmic, exponential and power. The key to this understanding involves opening up the definition of rate of change from the…

Developing mathematics edutainment media for Android based on students’ understanding and interest: a teachers’ review

NASA Astrophysics Data System (ADS)

Setyaningrum, W.; Waryanto, N. H.

2018-03-01

This paper aimed to describe the development of interactive edutainment mathematics media using Construct 2 software for grade 7 Junior High School, and to determine the quality of the interactive edutainment media developed in regards to improve students’ understanding and interest. This research employs Research and Development design, which media was developed using ADDIE model consisting of analysing, designing, developing, implementing and evaluating. This paper focuses on the steps of development and validity of the interactive media from teachers’ point of view. The teachers review focuses on three aspects – instructional, audio-visual and operational design. The review suggested that the media was very good in regard to the three aspects, with the average score was 144.55 from the maximum score of 175. Several contexts used in the game, however, need to be adjusted to students age.

Saussurian linguistics revisited: Can it inform our interpretation of mathematical activity?

NASA Astrophysics Data System (ADS)

McNamara, O.

1995-07-01

This paper examines the basic notions of Ferdinand de Saussure (1857 1913) who was a preeminent figure in the development of linguistics and the foundation of structuralism. It suggests that a key aspect of twentieth century thought has been the growing recognition that the study of language can offer a framework through which we can develop an understanding of our world. It thus proposes that language is fundamental to the process of learning mathematics on every level whether it be through classroom discussion, group exploration, teacher exposition or individual interaction with printed material. Ensuing from this the paper investigates possible mathematical perspectives upon Saussure's ideas and explores what contribution his work can offer to enhance and enrich the interpretive framework through which we observe mathematical activity in the classroom. It takes as an example a mathematical investigation carried out by a group of 12 year old girls and develops the analysis from a Saussurian stance. The paper concludes that language is the medium through which, and in which, mathematical ideas are formed and exchanged.

Analysing the relationships between students and mathematics: a tale of two paradigms

NASA Astrophysics Data System (ADS)

Jorgensen, Robyn; Larkin, Kevin

2017-03-01

In this article, we argue the need to use inter-disciplinary paradigms to make sense of a range of findings from a research project. We developed a methodology using iPad diaries to uncover young students' thinking—mathematical, social and affective—so as to better understand their experiences of mathematics. These students, predominantly from year 3 to year 6, were drawn from economically and socially distinct schools in Queensland and New South Wales, Australia. This article builds on previous research, where we outlined the unique methodology that we developed over three iterations to collect student attitudinal comments regarding mathematics. The comments we collected gave significant insights into the experiences of, and possibilities for, the mathematics education of young learners. Here, we use these findings to explore the value of two paradigms to explain student experiences towards mathematics among primary school students from different social backgrounds. In so doing, we develop an explanatory model for the socially differentiated outcomes in students' responses and then use this explanatory model to analyse student responses from the two most socially disparate schools in our research.

Cognitive Correlates of Performance in Advanced Mathematics

ERIC Educational Resources Information Center

Wei, Wei; Yuan, Hongbo; Chen, Chuansheng; Zhou, Xinlin

2012-01-01

Background: Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic).Aims: To promote mathematical knowledge among college students, it is necessary to understand what factors…

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.

Mathematical Representation by Students in Building Relational Understanding on Concepts of Area and Perimeter of Rectangle

ERIC Educational Resources Information Center

Anwar, Rahmad Bustanul; Yuwono, Ipung; As'ari, Abdur Rahman; Sisworo; Dwi, Rahmawati

2016-01-01

Representation is an important aspect of learners in building a relational understanding of mathematical concepts. But the ability of a mathematical representation of students in building relational understanding is still very limited. The purpose of this research is to description of mathematical representation of students who appear in building…

The unique and shared contributions of arithmetic operation understanding and numerical magnitude representation to children's mathematics achievement.

PubMed

Wong, Terry Tin-Yau

2017-12-01

The current study examined the unique and shared contributions of arithmetic operation understanding and numerical magnitude representation to children's mathematics achievement. A sample of 124 fourth graders was tested on their arithmetic operation understanding (as reflected by their understanding of arithmetic principles and the knowledge about the application of arithmetic operations) and their precision of rational number magnitude representation. They were also tested on their mathematics achievement and arithmetic computation performance as well as the potential confounding factors. The findings suggested that both arithmetic operation understanding and numerical magnitude representation uniquely predicted children's mathematics achievement. The findings highlight the significance of arithmetic operation understanding in mathematics learning. Copyright © 2017 Elsevier Inc. All rights reserved.

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…

An Investigation of the Mathematics-Vocabulary Knowledge of First-Grade Students

ERIC Educational Resources Information Center

Powell, Sarah R.; Nelson, Gena

2017-01-01

Competency with mathematics requires use of numerals and symbols as well as an understanding and use of mathematics vocabulary (e.g., "add," "more," "triangle"). Currently, no measures exist in which the primary function is to gauge mathematics-vocabulary understanding. We created a 64-item mathematics-vocabulary…

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

Globalization and Its Impact on the Medium of Instruction in Higher Education in Malaysia

ERIC Educational Resources Information Center

Mohamed, Mohini

2008-01-01

Understanding bilingualism in science and mathematics education and developing a principled instruction is a pressing issue in Malaysian system of education. With the implementation of government policy of teaching science and mathematics in English starting from year 2003, an increasing number of students are affected with this policy. An initial…

Teacher-Student Dialogue during One-to-One Interactions in a Post-16 Mathematics Classroom

ERIC Educational Resources Information Center

Grandi, Clarissa

2013-01-01

Current reforms in mathematics education place dialogue at the heart of the development of conceptual understanding. Underlying these ideas is strong criticism of transmissive teaching styles, often referred to as "teaching by telling" However, there is little in terms of specific guidance for teachers about how best to achieve these…

Psychometric Properties of the RMARS Scale in High School Students

ERIC Educational Resources Information Center

García-Santillán, Arturo; Martínez-Rodríguez, Valeria; Santana, Josefina C.

2018-01-01

The purpose of this study was to determine if there is a structure of variables that allows us to understand the level of Anxiety towards Mathematics in high school students from the municipalities of Zacatal and Jamapa, Veracruz, Mexico. This was based on the seminal works of Richardson and Suinn [1972], who developed the Mathematics Anxiety…

Student Strategies Suggesting Emergence of Mental Structures Supporting Logical and Abstract Thinking: Multiplicative Reasoning

ERIC Educational Resources Information Center

Carrier, Jim

2014-01-01

For many students, developing mathematical reasoning can prove to be challenging. Such difficulty may be explained by a deficit in the core understanding of many arithmetical concepts taught in early school years. Multiplicative reasoning is one such concept that produces an essential foundation upon which higher-level mathematical thinking skills…

Norms for Participation in a Middle School Mathematics Classroom and Its Effect on Student Motivation

ERIC Educational Resources Information Center

Megowan-Romanowicz, M. Colleen; Middleton, James A.; Ganesh, Tirupalavanam; Joanou, Jamie

2013-01-01

In this article we examine how students engage in learning mathematical concepts in the middle grades of an urban public school in the Southwestern United States. In the context of a 3-year National Science Foundation-funded longitudinal study of the development of students' rational number understanding, we encountered differing levels of…

Studies in Mathematics, Volume XVIII: Puzzle Problems and Games Project. Final Report.

ERIC Educational Resources Information Center

Dilworth, R. P.; And Others

This is a self-contained manual for use by teachers in preparation for classroom presentations. One of the goals of the report is to show how games and puzzles can provide effective means for developing mathematical understanding and skills. The authors indicate that this type of activity is well adapted for discovery teaching techniques. The…

Using a Framework for Three Levels of Sense Making in a Mathematics Classroom

ERIC Educational Resources Information Center

Moss, Diana L.; Lamberg, Teruni

2016-01-01

This discussion-based lesson is designed to support Year 6 students in their initial understanding of using letters to represent numbers, expressions, and equations in algebra. The three level framework is designed for: (1) making thinking explicit, (2) exploring each other's solutions, and (3) developing new mathematical insights. In each level…

The Vital Role of Basic Mathematics in Teaching and Learning the Mole Concept

ERIC Educational Resources Information Center

Mehrotra, Alka; Koul, Anjni

2016-01-01

This article focuses on the importance of activity-based teaching in understanding the mole concept and the vital role of basic mathematical operations. It describes needs-based training for teachers in a professional development programme in India. Analysis of test results before and after the training indicates that teachers improved their…

Soap Films and GeoGebra in the Study of Fermat and Steiner Points

ERIC Educational Resources Information Center

Flores, Alfinio; Park, Jungeun

2018-01-01

We discuss how mathematics and secondary mathematics education majors developed an understanding of Fermat points for the triangle as well as Steiner points for the square and regular pentagon, and also of soap film configurations between parallel plates where forces are in equilibrium. The activities included the use of soap films and the…

Learning Fractions by Splitting: Using Learning Analytics to Illuminate the Development of Mathematical Understanding

ERIC Educational Resources Information Center

Martin, Taylor; Petrick Smith, Carmen; Forsgren, Nicole; Aghababyan, Ani; Janisiewicz, Philip; Baker, Stephanie

2015-01-01

The struggle with fraction learning in kindergarten through Grade 12 in the United States is a persistent problem and one of the major stumbling blocks to succeeding in higher mathematics. Research into this problem has identified several areas where students commonly struggle with fractions. While there are many theories of fraction learning,…

Sex Differences in Mathematics and Science Achievement: A Meta-Analysis of National Assessment of Educational Progress Assessments

ERIC Educational Resources Information Center

Reilly, David; Neumann, David L.; Andrews, Glenda

2015-01-01

Gender gaps in the development of mathematical and scientific literacy have important implications for the general public's understanding of scientific issues and for the underrepresentation of women in science, technology, engineering, and math. We subjected data from the National Assessment of Educational Progress to a meta-analysis to examine…

Examination of the Assumptions and Properties of the Graded Item Response Model: An Example Using a Mathematics Performance Assessment.

ERIC Educational Resources Information Center

Lane, Suzanne; And Others

1995-01-01

Over 5,000 students participated in a study of the dimensionality and stability of the item parameter estimates of a mathematics performance assessment developed for the Quantitative Understanding: Amplifying Student Achievement and Reasoning (QUASAR) Project. Results demonstrate the test's dimensionality and illustrate ways to examine use of the…

Teachers' Perceptions of Preparedness Related to National Common Core State Standards for Mathematics

ERIC Educational Resources Information Center

Brown, Tykier

2016-01-01

With the adoption of the National Common Core State Standards in Mathematics (CCSSM) in many states and the lack of understanding and strategies to implement the new standards by classroom teachers, implementing effective professional development is vital. The focus of this qualitative case study was to provide insight into elementary school…

Developing Conceptual Understanding and Definitional Clarity in Linear Algebra through the Three Worlds of Mathematical Thinking

ERIC Educational Resources Information Center

Hannah, John; Stewart, Sepideh; Thomas, Michael

2016-01-01

Linear algebra is one of the first abstract mathematics courses that students encounter at university. Research shows that many students find the dense presentation of definitions, theorems and proofs difficult to comprehend. Using a case study approach, we report on a teaching intervention based on Tall's three worlds (embodied, symbolic and…

Investigating Participation in Advanced Level Mathematics: A Study of Student Drop-Out

ERIC Educational Resources Information Center

Noyes, Andrew; Sealey, Paula

2012-01-01

There has, for some years, been a growing concern about participation in university-entrance level mathematics in England and across the developed world. Extensive statistical analyses present the decline but offer little to help us understand the causes. In this paper we explore a concern which cannot be explored through national data-sets,…

Mathematical and Numerical Analysis of Model Equations on Interactions of the HIV/AIDS Virus and the Immune System

NASA Astrophysics Data System (ADS)

Parumasur, N.; Willie, R.

2008-09-01

We consider a simple HIV/AIDs finite dimensional mathematical model on interactions of the blood cells, the HIV/AIDs virus and the immune system for consistence of the equations to the real biomedical situation that they model. A better understanding to a cure solution to the illness modeled by the finite dimensional equations is given. This is accomplished through rigorous mathematical analysis and is reinforced by numerical analysis of models developed for real life cases.

Developing Mathematical Resilience: Students' Voice about the Use of ICT in Classroom (El desarrollo de la capacidad de resiliencia matemática: La voz de los estudiantes sobre el uso de las TIC en la aula)

ERIC Educational Resources Information Center

Mota, Ana Isabel; Oliveira, Hélia; Henriques, Ana

2016-01-01

Introduction: Mathematical resilience is assumed as one of the most important areas in school context and whose focus should be given priority, due to the distress exhibited by students when learning and understanding basic knowledge in mathematics year after year. The main goal of this research was to study how students attending middle schools…

History of mathematics and history of science reunited?

PubMed

Gray, Jeremy

2011-09-01

For some years now, the history of modern mathematics and the history of modern science have developed independently. A step toward a reunification that would benefit both disciplines could come about through a revived appreciation of mathematical practice. Detailed studies of what mathematicians actually do, whether local or broadly based, have often led in recent work to examinations of the social, cultural, and national contexts, and more can be done. Another recent approach toward a historical understanding of the abstractness of modern mathematics has been to see it as a species of modernism, and this thesis will be tested by the raft of works on the history of modern applied mathematics currently under way.

Investigating and developing engineering students' mathematical modelling and problem-solving skills

NASA Astrophysics Data System (ADS)

Wedelin, Dag; Adawi, Tom; Jahan, Tabassum; Andersson, Sven

2015-09-01

How do engineering students approach mathematical modelling problems and how can they learn to deal with such problems? In the context of a course in mathematical modelling and problem solving, and using a qualitative case study approach, we found that the students had little prior experience of mathematical modelling. They were also inexperienced problem solvers, unaware of the importance of understanding the problem and exploring alternatives, and impeded by inappropriate beliefs, attitudes and expectations. Important impacts of the course belong to the metacognitive domain. The nature of the problems, the supervision and the follow-up lectures were emphasised as contributing to the impacts of the course, where students show major development. We discuss these empirical results in relation to a framework for mathematical thinking and the notion of cognitive apprenticeship. Based on the results, we argue that this kind of teaching should be considered in the education of all engineers.

Silent method for mathematics instruction: An overview of teaching subsets

NASA Astrophysics Data System (ADS)

Sugiman, Apino, Ezi

2017-05-01

Generally, teachers use oral communication for teaching mathematics. Taking an opposite perspective, this paper describes how instructional practices for mathematics can be carried out namely a silent method. Silent method uses body language, written, and oral communication for classroom interaction. This research uses a design research approach consisting of four phases: preliminary, prototyping and developing the instruction, and assessment. There are four stages of silent method. The first stage is conditioning stage in which the teacher introduces the method and makes agreement about the `rule of the game'. It is followed by the second one, elaborating stage, where students guess and explore alternative answers. The third stage is developing mathematical thinking by structuring and symbolizing. Finally, the method is ended by reinforcing stage which aims at strengthening and reflecting student's understanding. In this paper, every stage is described on the basis of practical experiences in a real mathematics classroom setting.

Formulating the Fibonacci Sequence: Paths or Jumps in Mathematical Understanding.

ERIC Educational Resources Information Center

Kieren, Thomas; And Others

In dynamical theory, mathematical understanding is considered to be that of a person (or group) of a topic (or problem) in a situation or setting. This paper compares the interactions between the situations and the mathematical understandings of two students by comparing the growth in understanding within a Fibonacci sequence setting in which…

Role of cognitive theory in the study of learning disability in mathematics.

PubMed

Geary, David C

2005-01-01

Gersten, Jordan, and Flojo (in this issue) provide the beginnings of an essential bridge between basic research on mathematical disabilities (MD) in young children and the application of this research for the early identification and remediation of these forms of learning disability. As they acknowledge, the field of MD is in the early stages of development, and thus recommendations regarding identification measures and remedial techniques must be considered preliminary. I discuss the importance of maintaining a tight link between theoretical and empirical research on children's developing numerical, arithmetical, and mathematical competencies and future research on learning disabilities in mathematics. This link will provide the foundation for transforming experimental procedures into assessment measures, understanding the cognitive strengths and weaknesses of children with these forms of learning disability, and developing remedial approaches based on the pattern of cognitive strengths and weaknesses for individual children.

Developing learning environments which support early algebraic reasoning: a case from a New Zealand primary classroom

NASA Astrophysics Data System (ADS)

Hunter, Jodie

2014-12-01

Current reforms in mathematics education advocate the development of mathematical learning communities in which students have opportunities to engage in mathematical discourse and classroom practices which underlie algebraic reasoning. This article specifically addresses the pedagogical actions teachers take which structure student engagement in dialogical discourse and activity which facilitates early algebraic reasoning. Using videotaped recordings of classroom observations, the teacher and researcher collaboratively examined the classroom practices and modified the participatory practices to develop a learning environment which supported early algebraic reasoning. Facilitating change in the classroom environment was a lengthy process which required consistent and ongoing attention initially to the social norms and then to the socio-mathematical norms. Specific pedagogical actions such as the use of specifically designed tasks, materials and representations and a constant press for justification and generalisation were required to support students to link their numerical understandings to algebraic reasoning.

Developing mathematical practices through reflection cycles

NASA Astrophysics Data System (ADS)

Reinholz, Daniel L.

2016-09-01

This paper focuses on reflection in learning mathematical practices. While there is a long history of research on reflection in mathematics, it has focused primarily on the development of conceptual understanding. Building on notion of learning as participation in social practices, this paper broadens the theory of reflection in mathematics learning. To do so, it introduces the concept of reflection cycles. Each cycle begins with prospective reflection, which guides one's actions during an experience, and ends with retrospective reflection, which consolidates the experience and informs the next reflection cycle. Using reflection cycles as an organizing framework, this paper synthesizes the literature on reflective practices at a variety of levels: (1) metacognition, (2) self-assessment, (3) noticing, and (4) lifelong learning. These practices represent a spectrum of reflection, ranging from the micro level (1) to macro level (4).

Science, technology, engineering, mathematics (STEM) as mathematics learning approach in 21st century

NASA Astrophysics Data System (ADS)

Milaturrahmah, Naila; Mardiyana, Pramudya, Ikrar

2017-08-01

This 21st century demands competent human resources in science, technology, engineering design and mathematics so that education is expected to integrate the four disciplines. This paper aims to describe the importance of STEM as mathematics learning approach in Indonesia in the 21st century. This paper uses a descriptive analysis research method, and the method reveals that STEM education growing in developed countries today can be a framework for innovation mathematics in Indonesia in the 21st century. STEM education integrate understanding of science, math skills, and the available technology with the ability to perform engineering design process. Implementation of mathematics learning with STEM approach makes graduates trained in using of mathematics knowledge that they have to create innovative products that are able to solve the problems that exist in society.

Enhancing Established Counting Routines to Promote Place-Value Understanding: An Empirical Study in Early Elementary Classrooms

ERIC Educational Resources Information Center

Fraivillig, Judith L.

2018-01-01

Understanding place value is a critical and foundational competency for elementary mathematics. Classroom teachers who endeavor to promote place-value development adopt a variety of established practices to varying degrees of effectiveness. In parallel, researchers have validated models of how young children acquire place-value understanding.…

Reference Framework for Describing and Assessing Students' Understanding in First Year Calculus

ERIC Educational Resources Information Center

Kannemeyer, Larry

2005-01-01

This paper presents aspects of a study that investigates the development of an instrument, a reference framework, to analyse students' written responses to non-routine problems in a first year calculus course in order to describe the complexities of their understanding and to assess their understanding of particular mathematical concepts.…

Brief Report: Preliminary Proposal of a Conceptual Model of a Digital Environment for Developing Mathematical Reasoning in Students with Autism Spectrum Disorders.

PubMed

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

2015-08-01

There is clear evidence that in typically developing children reasoning and sense-making are essential in all mathematical learning and understanding processes. In children with autism spectrum disorders (ASD), however, these become much more significant, considering their importance to successful independent living. This paper presents a preliminary proposal of a digital environment, specifically targeted to promote the development of mathematical reasoning in students with ASD. Given the diversity of ASD, the prototyping of this environment requires the study of dynamic adaptation processes and the development of activities adjusted to each user's profile. We present the results obtained during the first phase of this ongoing research, describing a conceptual model of the proposed digital environment. Guidelines for future research are also discussed.

QR-STEM: Energy and Environment as a Context for Improving QR and STEM Understandings of 6-12 Grade Teachers II. The Quantitative Reasoning

NASA Astrophysics Data System (ADS)

Mayes, R.; Lyford, M. E.; Myers, J. D.

2009-12-01

The Quantitative Reasoning in STEM (QR STEM) project is a state level Mathematics and Science Partnership Project (MSP) with a focus on the mathematics and statistics that underlies the understanding of complex global scientific issues. This session is a companion session to the QR STEM: The Science presentation. The focus of this session is the quantitative reasoning aspects of the project. As students move from understandings that range from local to global in perspective on issues of energy and environment, there is a significant increase in the need for mathematical and statistical conceptual understanding. These understandings must be accessible to the students within the scientific context, requiring the special understandings that are endemic within quantitative reasoning. The QR STEM project brings together interdisciplinary teams of higher education faculty and middle/high school teachers to explore complex problems in energy and environment. The disciplines include life sciences, physics, chemistry, earth science, statistics, and mathematics. These interdisciplinary teams develop open ended performance tasks to implement in the classroom, based on scientific concepts that underpin energy and environment. Quantitative reasoning is broken down into three components: Quantitative Literacy, Quantitative Interpretation, and Quantitative Modeling. Quantitative Literacy is composed of arithmetic concepts such as proportional reasoning, numeracy, and descriptive statistics. Quantitative Interpretation includes algebraic and geometric concepts that underlie the ability to interpret a model of natural phenomena which is provided for the student. This model may be a table, graph, or equation from which the student is to make predictions or identify trends, or from which they would use statistics to explore correlations or patterns in data. Quantitative modeling is the ability to develop the model from data, including the ability to test hypothesis using statistical procedures. We use the term model very broadly, so it includes visual models such as box models, as well as best fit equation models and hypothesis testing. One of the powerful outcomes of the project is the conversation which takes place between science teachers and mathematics teachers. First they realize that though they are teaching concepts that cross their disciplines, the barrier of scientific language within their subjects restricts students from applying the concepts across subjects. Second the mathematics teachers discover the context of science as a means of providing real world situations that engage students in the utility of mathematics as a tool for solving problems. Third the science teachers discover the barrier to understanding science that is presented by poor quantitative reasoning ability. Finally the students are engaged in exploring energy and environment in a manner which exposes the importance of seeing a problem from multiple interdisciplinary perspectives. The outcome is a democratic citizen capable of making informed decisions, and perhaps a future scientist.

Modeling the Role of Priming in Executive Control: Cognitive and Neural Constraints

DTIC Science & Technology

2012-01-24

theoretical and empirical advances in our understanding of cognitive control. We discovered new phenomena and developed theories to account for them. We...developed theories of cognitive control and visual attention that integrated mathematical psychology with cognitive science and with neuroscience. We...significant theoretical and empirical advances in our understanding of cognitive control. We discovered new phenomena and developed theories to account

The role of mathematics for physics teaching and understanding

NASA Astrophysics Data System (ADS)

Pospiech, Gesche; Eylon, BatSheva; Bagno, Esther; Lehavi, Yaron; Geyer, Marie-Annette

2016-05-01

-1That mathematics is the "language of physics" implies that both areas are deeply interconnected, such that often no separation between "pure" mathematics and "pure" physics is possible. To clarify their interplay a technical and a structural role of mathematics can be distinguished. A thorough understanding of this twofold role in physics is also important for shaping physics education especially with respect to teaching the nature of physics. Herewith the teachers and their pedagogical content knowledge play an important role. Therefore we develop a model of PCK concerning the interplay of mathematics and physics in order to provide a theoretical framework for the views and teaching strategies of teachers. In an exploratory study four teachers from Germany and four teachers from Israel have been interviewed concerning their views and its transfer to teaching physics. Here we describe the results from Germany. Besides general views and knowledge held by all or nearly all teachers we also observe specific individual focus depending on the teachers' background and experiences. The results fit well into the derived model of PCK.

Characterizing Preservice Teachers' Mathematical Understanding of Algebraic Relationships

ERIC Educational Resources Information Center

Nillas, Leah A.

2010-01-01

Qualitative research methods were employed to investigate characterization of preservice teachers' mathematical understanding. Responses on test items involving algebraic relationships were analyzed using with-in case analysis (Miles and Huberman, 1994) and Pirie and Kieren's (1994) model of growth of mathematical understanding. Five elementary…

Common Core State Standards for Mathematics: Love It or Hate It, Understand Those Who Don't

ERIC Educational Resources Information Center

Wagner, Patty Anne

2016-01-01

In this commentary, Wagner points out that the Common Core State Standards for Mathematics (CCSSM) has fueled strong reactions on either end of the spectrum, compelling its supporters and critics to argue their positions. Naturally neither side have interest in entertaining the arguments of the other. Wagner claims, however, that you develop the…

The Process of Thinking among Junior High School Students in Solving HOTS Question

ERIC Educational Resources Information Center

Bakry, Md Nor Bin Bakar

2015-01-01

Higher order thinking skills (HOTS) is one of the important aspect of teaching and learning mathematics. By using HOTS, student will be able to acquire a deep understand of mathematical concepts and can be applied in real life. Students ability to develop the capacity of the HOTS is closely related with thinking processes while solving mathematics…

Studio Mathematics: The Epistemology and Practice of Design Pedagogy as a Model for Mathematics Learning. WCER Working Paper No. 2005-3

ERIC Educational Resources Information Center

Shaffer, David Williamson

2005-01-01

This paper examines how middle school students developed understanding of transformational geometry through design activities in Escher's World, a computationally rich design experiment explicitly modeled on an architectural design studio. Escher's World was based on the theory of pedagogical praxis (Shaffer, 2004a), which suggests that preserving…

Assessing K-5 Teacher Leaders' Mathematical Understanding: What Have the Test Makers and the Test Takers Learned?

ERIC Educational Resources Information Center

Ellington, Aimee J.; Whitenack, Joy W.; Inge, Vickie L.; Murray, Megan K.; Schneider, Patti J.

2012-01-01

This article describes the design and implementation of an assessment instrument for Numbers and Operations, the first course in a program to train elementary mathematics specialists. We briefly describe the course and its content, and then we elaborate on the process we used to develop the assessment instrument and the corresponding rubric for…

A Tale of Two Metaphors: Storylines about Mathematics Education in Canadian National Media

ERIC Educational Resources Information Center

Rodney, Sheree; Rouleau, Annette; Sinclair, Nathalie

2016-01-01

Public perception about mathematics education is developed and sustained by the Canadian news media. Our goal is to understand better the nature of this public discourse by identifying what is being communicated and how it is presented. We examine a data corpus of 71 online national newspaper articles (published between 2013 and 2015, a period…

Shuffling the Deck To Ensure Fairness in Dealing: A Commentary on Some Issues of Equity and Mathematics Education from the Perspective of the QUASAR Project.

ERIC Educational Resources Information Center

Silver, Edward A.

This paper is a reaction to a plenary address, "Fairness in Dealing: Diversity, Psychology, and Mathematics Education" by Suzanne Damarin (SE 057 179). The issues of intentionality, institutional and instructional practices, identity development, and assessment are addressed in regard to the Quantitative Understanding: Amplifying Student…

Developing a "Leading Identity": The Relationship between Students' Mathematical Identities and Their Career and Higher Education Aspirations

ERIC Educational Resources Information Center

Black, Laura; Williams, Julian; Hernandez-Martinez, Paul; Davis, Pauline; Pampaka, Maria; Wake, Geoff

2010-01-01

The construct of identity has been used widely in mathematics education in order to understand how students (and teachers) relate to and engage with the subject (Kaasila, 2007; Sfard & Prusak, 2005; Boaler, 2002). Drawing on cultural historical activity theory (CHAT), this paper adopts Leont'ev's notion of "leading activity" in order to explore…

Explicating mathematical thinking in differential equations using a computer algebra system

NASA Astrophysics Data System (ADS)

Zeynivandnezhad, Fereshteh; Bates, Rachel

2018-07-01

The importance of developing students' mathematical thinking is frequently highlighted in literature regarding the teaching and learning of mathematics. Despite this importance, most curricula and instructional activities for undergraduate mathematics fail to bring the learner beyond the mathematics. The purpose of this study was to enhance students' mathematical thinking by implementing a computer algebra system and active learning pedagogical approaches. students' mathematical thinking processes were analyzed while completing specific differential equations tasks based on posed prompts and questions and Instrumental Genesis. Data were collected from 37 engineering students in a public Malaysian university. This study used the descriptive and interpretive qualitative research design to investigate the students' perspectives of emerging mathematical understanding and approaches to learning mathematics in an undergraduate differential equations course. Results of this study concluded that students used a variety of mathematical thinking processes in a non-sequential manner. Additionally, the outcomes provide justification for continued use of technologies such as computer algebra systems in undergraduate mathematics courses and the need for further studies to uncover the various processes students utilize to complete specific mathematical tasks.

The Role of Reasoning in the Australian Curriculum: Mathematics

ERIC Educational Resources Information Center

McCluskey, Catherine; Mulligan, Joanne; Mitchelmore, Mike

2016-01-01

The mathematical proficiencies in the "Australian Curriculum: Mathematics" of understanding, problem solving, reasoning, and fluency are intended to be entwined actions that work together to build generalised understandings of mathematical concepts. A content analysis identifying the incidence of key proficiency terms (KPTs) embedded in…

Examining Preservice Elementary Mathematics Teachers' Understandings about Irrational Numbers

ERIC Educational Resources Information Center

Guven, Bulent; Cekmez, Erdem; Karatas, Ilhan

2011-01-01

The purpose of this study is to provide an account of preservice elementary mathematics teachers' understandings about irrational numbers. Three dimensions of preservice mathematics teachers' understandings are examined: defining rational and irrational numbers, placing rational and irrational numbers on the number line, and operations with…

Profile of mathematical reasoning ability of 8th grade students seen from communicational ability, basic skills, connection, and logical thinking

NASA Astrophysics Data System (ADS)

Sumarsih; Budiyono; Indriati, D.

2018-04-01

This research aims to understand the students’ weaknesses in mathematical reasoning ability in junior secondary school. A set of multiple choice tests were used to measure this ability involve components mathematical communication, basic skills, connection, and logical thinking. A total of 259 respondents were determined by stratified cluster random sampling. Data were analyzed using one-way Anova test with Fobs = 109.5760 and F = 3.0000. The results show that students’ ability from schools with high National Exam in mathematics category was the best and followed by medium and low category. Mathematical connection is the most difficult component performed by students. In addition, most students also have difficulty in expressing ideas and developing logical arguments.

Modeling small cell lung cancer (SCLC) biology through deterministic and stochastic mathematical models.

PubMed

Salgia, Ravi; Mambetsariev, Isa; Hewelt, Blake; Achuthan, Srisairam; Li, Haiqing; Poroyko, Valeriy; Wang, Yingyu; Sattler, Martin

2018-05-25

Mathematical cancer models are immensely powerful tools that are based in part on the fractal nature of biological structures, such as the geometry of the lung. Cancers of the lung provide an opportune model to develop and apply algorithms that capture changes and disease phenotypes. We reviewed mathematical models that have been developed for biological sciences and applied them in the context of small cell lung cancer (SCLC) growth, mutational heterogeneity, and mechanisms of metastasis. The ultimate goal is to develop the stochastic and deterministic nature of this disease, to link this comprehensive set of tools back to its fractalness and to provide a platform for accurate biomarker development. These techniques may be particularly useful in the context of drug development research, such as combination with existing omics approaches. The integration of these tools will be important to further understand the biology of SCLC and ultimately develop novel therapeutics.

The Symbolic World of Mathematics

ERIC Educational Resources Information Center

Lingefjärd, Thomas; Farahani, Djamshid

2017-01-01

In understanding upper secondary school students' interpretations of information in symbolic representations of a distance-time-relation, little attention has been paid to the analysis of the condition of the conceptual development related to utterances. Understanding this better can help improve the teaching of attribute and information in…

The Role of Mathematical Knowledge in Children's Understanding of Geographical Concepts.

ERIC Educational Resources Information Center

Kaplan, Rochelle G.

This study examines the relationship between children's procedural and conceptual understanding of mathematics and their accuracy in reporting and interpreting geography text material containing mathematical information. It was hypothesized that (1) children's misconceptions or lack of experience with particular mathematical content areas would be…

Mathematics Education and the Objectivist Programme in HPS

NASA Astrophysics Data System (ADS)

Glas, Eduard

2013-06-01

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

What's Cooking?

ERIC Educational Resources Information Center

Routledge, Joan

1985-01-01

The role that food-preparation activities could play in developing understanding of mathematical ideas by middle school students is discussed. Measurement, computation, language, attitudes, and problem solving are addressed. (MNS)

Teaching Mathematics Understandings for Transfer

ERIC Educational Resources Information Center

Jones, Jennifer L.; Jones, Karrie A.; Vermette, Paul J.

2009-01-01

Promoting student understanding for transfer is an illusive hallmark of effective mathematics instruction. While much research has shown the necessity of promoting understanding for transfer, less attention has been paid to actual pedagogical strategies that can be used to promote transfer of mathematical ideas. Using Fogarty et al. (1992, "How to…

Science + Maths = A Better Understanding of Science!

ERIC Educational Resources Information Center

Markwick, Andy; Clark, Kris

2016-01-01

Science and mathematics share a common purpose: to explore, understand and explain the pure beauty of our universe and how it works. Using mathematics in science enquiry can enhance children's understanding of science and also provide opportunities for children to apply their mathematical knowledge to "real" contexts. The authors…

Students' Coordination of Geometric Reasoning and Measuring Strategies on a Fixed Perimeter Task: Developing Mathematical Understanding of Linear Measurement

ERIC Educational Resources Information Center

Barrett, Jeffrey E.; Clements, Douglas H.; Klanderman, David; Pennisi, Sarah-Jean; Polaki, Mokaeane V.

2006-01-01

This article examines students' development of levels of understanding for measurement by describing the coordination of geometric reasoning with measurement and numerical strategies. In analyzing the reasoning and argumentation of 38 Grade 2 through Grade 10 students on linear measure tasks, we found support for the application and elaboration of…

Developing Essential Understanding of Functions for Teaching Mathematics in Grades 9-12

ERIC Educational Resources Information Center

Lloyd, Gwendolyn; Beckmann, Sybilla; Zbiek, Rose Mary; Cooney, Thomas

2010-01-01

Are sequences functions? What can't the popular "vertical line test" be applied in some cases to determine if a relation is a function? How does the idea of rate of change connect with simpler ideas about proportionality as well as more advanced topics in calculus? Helping high school students develop a robust understanding of functions requires…

Extreme Folding

NASA Astrophysics Data System (ADS)

Demaine, Erik

2012-02-01

Our understanding of the mathematics and algorithms behind paper folding, and geometric folding in general, has increased dramatically over the past several years. These developments have found a surprisingly broad range of applications. In the art of origami, it has helped spur the technical origami revolution. In engineering and science, it has helped solve problems in areas such as manufacturing, robotics, graphics, and protein folding. On the recreational side, it has led to new kinds of folding puzzles and magic. I will give an overview of the mathematics and algorithms of folding, with a focus on new mathematics and sculpture.

Re-"Conceptualizing" Procedural Knowledge in Mathematics.

ERIC Educational Resources Information Center

Star, Jon R.

Many mathematics educators have lost sight of the critical importance of the mathematical understanding which underlies procedural competence, in part because we do not have a language to refer to this kind of understanding. The modal way of categorizing mathematical knowledge--conceptual and procedural knowledge--is limited in that: (a) it is…

Mathematical Models of Continuous Flow Electrophoresis

NASA Technical Reports Server (NTRS)

Saville, D. A.; Snyder, R. S.

1985-01-01

Development of high resolution continuous flow electrophoresis devices ultimately requires comprehensive understanding of the ways various phenomena and processes facilitate or hinder separation. A comprehensive model of the actual three dimensional flow, temperature and electric fields was developed to provide guidance in the design of electrophoresis chambers for specific tasks and means of interpreting test data on a given chamber. Part of the process of model development includes experimental and theoretical studies of hydrodynamic stability. This is necessary to understand the origin of mixing flows observed with wide gap gravitational effects. To insure that the model accurately reflects the flow field and particle motion requires extensive experimental work. Another part of the investigation is concerned with the behavior of concentrated sample suspensions with regard to sample stream stability particle-particle interactions which might affect separation in an electric field, especially at high field strengths. Mathematical models will be developed and tested to establish the roles of the various interactions.

Lily Pad Doubling: Proportional Reasoning Development

ERIC Educational Resources Information Center

Robichaux-Davis, Rebecca R.

2017-01-01

Progressing from additive to multiplicative thinking is critical for the development of middle school students' proportional reasoning abilities. Yet, many middle school mathematics teachers lack a thorough understanding of additive versus multiplicative situations. This article describes a sequence of instructional activities used to develop the…

How Do Kindergarteners Express Their Mathematics Understanding?

ERIC Educational Resources Information Center

Johns, Kyoko

2015-01-01

This article describes how kindergarten students represent their understanding of mathematical knowledge. The study examines the students' use of oral expressions, drawings, written language, and gestures when communicating mathematically with their classmates and teacher.

Using a Summer REU to Help Develop the Next Generation of Mathematical Ecologists.

PubMed

Bennie, Barbara; Eager, Eric Alan; Peirce, James P; Sandland, Gregory J

2018-04-01

Understanding the complexities of environmental issues requires individuals to bring together ideas and data from different disciplines, including ecology and mathematics. With funding from the national science foundation (NSF), scientists from the University of Wisconsin-La Crosse and the US geological survey held a research experience for undergraduates (REU) program in the summer of 2016. The goals of the program were to expose students to open problems in the area of mathematical ecology, motivate students to pursue STEM-related positions, and to prepare students for research within interdisciplinary, collaborative settings. Based on backgrounds and interests, eight students were selected to participate in one of two research projects: wind energy and wildlife conservation or the establishment and spread of waterfowl diseases. Each research program was overseen by a mathematician and a biologist. Regardless of the research focus, the program first began with formal lectures to provide students with foundational knowledge followed by student-driven research projects. Throughout this period, student teams worked in close association with their mentors to create, parameterize and evaluate ecological models to better understand their systems of interest. Students then disseminated their results at local, regional, and international meetings and through publications (one in press and one in progress). Direct and indirect measures of student development revealed that our REU program fostered a deep appreciation for and understanding of mathematical ecology. Finally, the program allowed students to gain experiences working with individuals with different backgrounds and perspectives. Taken together, this REU program allowed us to successfully excite, motivate and prepare students for future positions in the area of mathematical biology, and because of this it can be used as a model for interdisciplinary programs at other institutions.

Essential concepts and underlying theories from physics, chemistry, and mathematics for "biochemistry and molecular biology" majors.

PubMed

Wright, Ann; Provost, Joseph; Roecklein-Canfield, Jennifer A; Bell, Ellis

2013-01-01

Over the past two years, through an NSF RCN UBE grant, the ASBMB has held regional workshops for faculty members from around the country. The workshops have focused on developing lists of Core Principles or Foundational Concepts in Biochemistry and Molecular Biology, a list of foundational skills, and foundational concepts from Physics, Chemistry, and Mathematics that all Biochemistry or Molecular Biology majors must understand to complete their major coursework. The allied fields working group created a survey to validate foundational concepts from Physics, Chemistry, and Mathematics identified from participant feedback at various workshops. One-hundred twenty participants responded to the survey and 68% of the respondents answered yes to the question: "We have identified the following as the core concepts and underlying theories from Physics, Chemistry, and Mathematics that Biochemistry majors or Molecular Biology majors need to understand after they complete their major courses: 1) mechanical concepts from Physics, 2) energy and thermodynamic concepts from Physics, 3) critical concepts of structure from chemistry, 4) critical concepts of reactions from Chemistry, and 5) essential Mathematics. In your opinion, is the above list complete?" Respondents also delineated subcategories they felt should be included in these broad categories. From the results of the survey and this analysis the allied fields working group constructed a consensus list of allied fields concepts, which will help inform Biochemistry and Molecular Biology educators when considering the ASBMB recommended curriculum for Biochemistry or Molecular Biology majors and in the development of appropriate assessment tools to gauge student understanding of how these concepts relate to biochemistry and molecular biology. © 2013 by The International Union of Biochemistry and Molecular Biology.

Persisting mathematics and science high school teachers: A Q-methodology study

NASA Astrophysics Data System (ADS)

Robbins-Lavicka, Michelle M.

There is a lack of qualified mathematics and science teachers at all levels of education in Arkansas. Lasting teaching initiative programs are needed to address retention so qualified teachers remain in the classroom. The dearth of studies regarding why mathematics and science teachers persist in the classroom beyond the traditional 5-year attrition period led this Q-methodological study to evaluate the subjective perceptions of persistent mathematics and science teachers to determine what makes them stay. This study sought to understand what factors persisting mathematics and science teachers used to explain their persistence in the classroom beyond 5 years and what educational factors contributed to persisting mathematics and science teachers. Q-methodology combines qualitative and quantitative techniques and provided a systematic means to investigate personal beliefs by collecting a concourse, developing a Q-sample and a person-sample, conducting a Q-sorting process, and analyzing the data. The results indicated that to encourage longevity within mathematics and science classrooms (a) teachers should remain cognizant of their ability to influence student attitudes toward teaching; (b) administrators should provide support for teachers and emphasize the role and importance of professional development; and (c) policy makers should focus their efforts and resources on developing recruitment plans, including mentorship programs, while providing and improving financial compensation. Significantly, the findings indicate that providing mentorship and role models at every level of mathematics and science education will likely encourage qualified teachers to remain in the mathematics and science classrooms, thus increasing the chance of positive social change.

Developing an Understanding of Ions in Junior Secondary School Chemistry

ERIC Educational Resources Information Center

Waldrip, Bruce; Prain, Vaughan

2012-01-01

There is growing research interest in the challenges and opportunities learners face in representing scientific understandings, processes and reasoning. These challenges include integrating verbal, visual and mathematical modes in science discourse to make strong conceptual links between representations and classroom experiences. Our paper reports…

What Teaching for Understanding Looks Like.

ERIC Educational Resources Information Center

Unger, Chris

1994-01-01

To apply four principles of Teaching for Understanding framework developed at Harvard University, researchers worked with team of four teachers at two Massachusetts high schools. One history teacher revised Industrial Revolution unit to emphasize human progress. Mathematics teacher had students design a dance floor based on several different…

Technological pedagogical content knowledge of junior high school mathematics teachers in teaching linear equation

NASA Astrophysics Data System (ADS)

Wati, S.; Fitriana, L.; Mardiyana

2018-04-01

Linear equation is one of the topics in mathematics that are considered difficult. Student difficulties of understanding linear equation can be caused by lack of understanding this concept and the way of teachers teach. TPACK is a way to understand the complex relationships between teaching and content taught through the use of specific teaching approaches and supported by the right technology tools. This study aims to identify TPACK of junior high school mathematics teachers in teaching linear equation. The method used in the study was descriptive. In the first phase, a survey using a questionnaire was carried out on 45 junior high school mathematics teachers in teaching linear equation. While in the second phase, the interview involved three teachers. The analysis of data used were quantitative and qualitative technique. The result PCK revealed teachers emphasized developing procedural and conceptual knowledge through reliance on traditional in teaching linear equation. The result of TPK revealed teachers’ lower capacity to deal with the general information and communications technologies goals across the curriculum in teaching linear equation. The result indicated that PowerPoint constitutes TCK modal technological capability in teaching linear equation. The result of TPACK seems to suggest a low standard in teachers’ technological skills across a variety of mathematics education goals in teaching linear equation. This means that the ability of teachers’ TPACK in teaching linear equation still needs to be improved.

Mapping Changes in Support: A Longitudinal Analysis of Networks of Pre-Service Mathematics and Science Teachers

ERIC Educational Resources Information Center

Bokhove, Christian; Downey, Christopher

2018-01-01

In England teachers of secondary school mathematics and science are in short supply and it is important to understand how pre-service teachers develop and maintain networks of support during their training year and the impact these networks can have on their training outcomes. The purpose of this study is to examine how changes to the size and…

Development of Teacher Beliefs through Online Instruction: A One-Year Study of Middle School Science and Mathematics Teachers' Beliefs about Teaching and Learning

ERIC Educational Resources Information Center

Wong, Sissy S.

2016-01-01

Understanding teachers' beliefs is important because beliefs influence teacher decisions. In science, teacher beliefs have an impact on how science curriculum is interpreted and implemented in the classroom. With the push for science, technology, engineering, and mathematics (STEM) education in the United States, it is also critical to examine the…

Summary of Research Academic Departments, 1987-1988

DTIC Science & Technology

1988-12-01

quantify the computer nccring students and their faculty with roughly system’s ability to enhance learning of the course equivalent computers; one group...Sponsor: Naval Academy Instructional Development Advisory Committee To understand mathematics , a student must under- also to explain the central concepts... Mathematics Department. The project will attempt resources for in-class and extra instruction , to move toward these goals by preparing extra Students

Preparing Prospective Elementary Teachers To Foster Conceptually Based Mathematical Understandings: A Study Investigating Change in Prospective Teachers' Conceptions Related to Mathematics Teaching and Learning.

ERIC Educational Resources Information Center

Benken, Babette M.; Brown, Nancy

More than two decades of research and experience supports the idea that computer and calculator technologies can have an important role to play in supporting and effecting student learning (Heid, 1988; Kaput, 1992; Kutzler, 1996; Papert, 1980; Waits and Demana, 1999). The development of Classroom Communication Systems (CCSs) is providing new…

Balancing Considerations of Equity, Content Quality, and Technical Excellence in Designing, Validating and Implementing Performance Assessments in the Context of Mathematics Instructional Reform: The Experience of the QUASAR Project.

ERIC Educational Resources Information Center

Silver, Edward A.; Lane, Suzanne

Issues of educational equity and quality are explored in the context of the Quantitative Understanding: Amplifying Student Achievement and Reasoning (QUASAR) project, a national educational reform project aimed at fostering and studying the development and implementation of enhanced mathematics instructional programs for students attending middle…

Key Understandings in School Mathematics: 3

ERIC Educational Resources Information Center

Watson, Anne

2010-01-01

This article is the third in a series which draws on findings from Nunes, Watson and Bryant (2009): "Key understandings in school mathematics: a report to the Nuffield Foundation". In this article the author focuses on what learners have to understand and learn in order to do secondary mathematics well in general terms. She is assuming a…

Mathematical Metaphors: Problem Reformulation and Analysis Strategies

NASA Technical Reports Server (NTRS)

Thompson, David E.

2005-01-01

This paper addresses the critical need for the development of intelligent or assisting software tools for the scientist who is working in the initial problem formulation and mathematical model representation stage of research. In particular, examples of that representation in fluid dynamics and instability theory are discussed. The creation of a mathematical model that is ready for application of certain solution strategies requires extensive symbolic manipulation of the original mathematical model. These manipulations can be as simple as term reordering or as complicated as discovery of various symmetry groups embodied in the equations, whereby Backlund-type transformations create new determining equations and integrability conditions or create differential Grobner bases that are then solved in place of the original nonlinear PDEs. Several examples are presented of the kinds of problem formulations and transforms that can be frequently encountered in model representation for fluids problems. The capability of intelligently automating these types of transforms, available prior to actual mathematical solution, is advocated. Physical meaning and assumption-understanding can then be propagated through the mathematical transformations, allowing for explicit strategy development.

Old Habits Die Hard: An Uphill Struggle against Rules without Reason in Mathematics Teacher Education

ERIC Educational Resources Information Center

O'Meara, Niamh; Fitzmaurice, Olivia; Johnson, Patrick

2017-01-01

Mathematics teacher educators in the University of Limerick became aware of a lack of conceptual understanding of key mathematics concepts of prospective secondary mathematics teachers through observation on teaching placement and in pedagogy lectures. A pilot study to enhance the conceptual understanding of prospective teachers was carried out…

Orthogonal Reflections on Computer Microworlds, Constructivism, Play and Mathematical Understanding.

ERIC Educational Resources Information Center

Kieren, Thomas E.

1994-01-01

Comments on the Fractions Project presented in this same issue. Discusses two major ideas: the construction of mathematics of children and its basis and playful actions as a basis for mathematical actions. Highlights the understanding of children's mathematical concepts and schemes as they grow and are organized in the context of computer…

Flight test planning and parameter extraction for rotorcraft system identification

NASA Technical Reports Server (NTRS)

Wang, J. C.; Demiroz, M. Y.; Talbot, P. D.

1986-01-01

The present study is concerned with the mathematical modelling of aircraft dynamics on the basis of an investigation conducted with the aid of the Rotor System Research Aircraft (RSRA). The particular characteristics of RSRA make it possible to investigate aircraft properties which cannot be readily studied elsewhere, for example in the wind tunnel. The considered experiment had mainly the objective to develop an improved understanding of the physics of rotor flapping dynamics and rotor loads in maneuvers. The employed approach is based on a utilization of parameter identification methodology (PID) with application to helicopters. A better understanding of the contribution of the main rotor to the overall aircraft forces and moments is also to be obtained. Attention is given to the mathematical model of a rotorcraft system, an integrated identification method, flight data processing, and the identification of RSRA mathematical models.

Assessing Formal Knowledge of Math Equivalence among Algebra and Pre-Algebra Students

ERIC Educational Resources Information Center

Fyfe, Emily R.; Matthews, Percival G.; Amsel, Eric; McEldoon, Katherine L.; McNeil, Nicole M.

2018-01-01

A central understanding in mathematics is knowledge of "math equivalence," the relation indicating that 2 quantities are equal and interchangeable. Decades of research have documented elementary-school (ages 7 to 11) children's (mis)understanding of math equivalence, and recent work has developed a construct map and comprehensive…

Developing Children's Understanding of Fractions: An Intervention Study

ERIC Educational Resources Information Center

Gabriel, Florence; Coche, Frederic; Szucs, Denes; Carette, Vincent; Rey, Bernard; Content, Alain

2012-01-01

Fractions constitute a stumbling block in mathematics education. To improve children's understanding of fractions, we designed an intervention based on learning-by-doing activities, which focused on the representation of the magnitude of fractions. Participants were 292 Grade 4 and 5 children. Half of the classes received experimental instruction,…

Continued professional development of teachers to facilitate language used in numeracy and mathematics.

PubMed

Wium, Anna-Marie; Louw, Brenda

2012-12-01

Learners in South African schools have been found to perform poorly in mathematics because they do not understand the language used in solving mathematical problems. In order to improve academic performance teachers need to be made aware of the importance of language in the development of numeracy. A continued professional development (CPD) programme addressed this need. The purpose of the research was to understand how the participants implemented the strategies developed during the programme and how they perceived the support provided by the programme. The research was conducted over 2 years in semi-rural and urban contexts. As part of a more comprehensive mixed method study, the qualitative data referred to in this article were obtained through open-ended questions in questionnaires, focus groups,I reflections in portfolios, and a research diary. Results showed that numeracy terminology was often used by learners that differed from standard terminology prescribed by the curriculum. The participants themselves did not necessarily understand the numeracy terminology and thus found it a challenge to implement curriculum outcomes. Issues related to language use of the participants in teaching numeracy were associated with the lack of resources available in the language of learning and teaching (LoLT). Some of the participants taught numeracy in English, rather than LoLT. The results indicated low teacher expectations of the learners. The CPD programme was considered valuable and effective. SLPs in schools need to be expand their role to provide CPD opportunities for teachers.

Mathematics education graduate students' understanding of trigonometric ratios

NASA Astrophysics Data System (ADS)

Yiǧit Koyunkaya, Melike

2016-10-01

This study describes mathematics education graduate students' understanding of relationships between sine and cosine of two base angles in a right triangle. To explore students' understanding of these relationships, an elaboration of Skemp's views of instrumental and relational understanding using Tall and Vinner's concept image and concept definition was developed. Nine students volunteered to complete three paper and pencil tasks designed to elicit evidence of understanding and three students among these nine students volunteered for semi-structured interviews. As a result of fine-grained analysis of the students' responses to the tasks, the evidence of concept image and concept definition as well as instrumental and relational understanding of trigonometric ratios was found. The unit circle and a right triangle were identified as students' concept images, and the mnemonic was determined as their concept definition for trigonometry, specifically for trigonometric ratios. It is also suggested that students had instrumental understanding of trigonometric ratios while they were less flexible to act on trigonometric ratio tasks and had limited relational understanding. Additionally, the results indicate that graduate students' understanding of the concept of angle mediated their understanding of trigonometry, specifically trigonometric ratios.

WWC Review of the Report "Benefits of Practicing 4 = 2 + 2: Nontraditional Problem Formats Facilitate Children's Understanding of Mathematical Equivalence." What Works Clearinghouse Single Study Review

ERIC Educational Resources Information Center

What Works Clearinghouse, 2014

2014-01-01

The 2011 study, "Benefits of Practicing 4 = 2 + 2: Nontraditional Problem Formats Facilitate Children's Understanding of Mathematical Equivalence," examined the effects of addition practice using nontraditional problem formats on students' understanding of mathematical equivalence. In nontraditional problem formats, operations appear on…

Improving of Junior High School Visual Thinking Representation Ability in Mathematical Problem Solving by CTL

ERIC Educational Resources Information Center

Surya, Edy; Sabandar, Jozua; Kusumah, Yaya S.; Darhim

2013-01-01

The students' difficulty which was found is in the problem of understanding, drawing diagrams, reading the charts correctly, conceptual formal mathematical understanding, and mathematical problem solving. The appropriate problem representation is the basic way in order to understand the problem itself and make a plan to solve it. This research was…

Relationship between mathematics teacher subject matter knowledge, pedagogical content knowledge and professional development needs

NASA Astrophysics Data System (ADS)

Tajudin, Nor'ain Mohd; Chinnappan, Mohan; Saad, Noor Shah

2017-05-01

Two key variables emerged from the literature review is that Specific Matter Knowledge [SMK] and Pedagogical Content Knowledge [PCK] can influence the mathematics teachers' Professional Development [PD] needs. However, the key variables of SMK and PCK that were being investigated were not defined clearly. Empirical evidence that support relationship between SMK and PD and PCK and PD were not verified. In addition, how does PCK mediate SMK and PD is not clear and somewhat lacking. Therefore, the purpose of this paper was to examine the relationship between primary mathematics teacher's SMK, PCK and PD needs. Results of path analysis with SmartPLS indicated that the direct effect of SMK on PD was mediated via PCK. This data provide support for the claim that PD programs for future teachers of primary mathematics should be driven by a more nuanced understanding of the link between SMK and PCK.

Towards a Better Understanding of the Potential of Interactive Whiteboards in Stimulating Mathematics Learning

ERIC Educational Resources Information Center

De Vita, Mauro; Verschaffel, Lieven; Elen, Jan

2018-01-01

This research explored the stimulation of mathematics understanding and learning in an Interactive Whiteboard (IWB) environment. IWB affordances appear to be best used when mathematical tasks engage students in mathematical reasoning and when all students are involved in the discussion. The intent of this project was to design and implement,…

Teaching Statistics with Technology

ERIC Educational Resources Information Center

Prodromou, Theodosia

2015-01-01

The Technological Pedagogical Content Knowledge (TPACK) conceptual framework for teaching mathematics, developed by Mishra and Koehler (2006), emphasises the importance of developing integrated and interdependent understanding of three primary forms of knowledge: technology, pedagogy, and content. The TPACK conceptual framework is based upon the…

ENERGY IMBALANCE UNDERLYING THE DEVELOPMENT OF CHILDHOOD OBESITY IN HISPANIC CHILDREN

USDA-ARS?s Scientific Manuscript database

Childhood obesity arises from dysregulation of energy balance; however, the energetics for the development of childhood obesity are poorly delineated. We therefore developed a mathematical model based on empirical data and current understanding of energy balance to predict the total energy cost of w...

National Testing of Pupils in Europe: Objectives, Organisation and Use of Results. Malta 2009

ERIC Educational Resources Information Center

Vassallo, Peter

2009-01-01

At Kindergarten Level (ages 3 to 5) pupil assessment focuses on their physical development, social development, creative development, intellectual development (which includes language and mathematical development) and their understanding of the world around them. At this level there is no formal teaching; the Kindergarten practitioner is…

Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century.

PubMed

Ganusov, Vitaly V

2016-01-01

While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest "strong inference in mathematical modeling" as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century.

Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century

PubMed Central

Ganusov, Vitaly V.

2016-01-01

While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest “strong inference in mathematical modeling” as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century. PMID:27499750

Mathematical modelling in developmental biology.

PubMed

Vasieva, Olga; Rasolonjanahary, Manan'Iarivo; Vasiev, Bakhtier

2013-06-01

In recent decades, molecular and cellular biology has benefited from numerous fascinating developments in experimental technique, generating an overwhelming amount of data on various biological objects and processes. This, in turn, has led biologists to look for appropriate tools to facilitate systematic analysis of data. Thus, the need for mathematical techniques, which can be used to aid the classification and understanding of this ever-growing body of experimental data, is more profound now than ever before. Mathematical modelling is becoming increasingly integrated into biological studies in general and into developmental biology particularly. This review outlines some achievements of mathematics as applied to developmental biology and demonstrates the mathematical formulation of basic principles driving morphogenesis. We begin by describing a mathematical formalism used to analyse the formation and scaling of morphogen gradients. Then we address a problem of interplay between the dynamics of morphogen gradients and movement of cells, referring to mathematical models of gastrulation in the chick embryo. In the last section, we give an overview of various mathematical models used in the study of the developmental cycle of Dictyostelium discoideum, which is probably the best example of successful mathematical modelling in developmental biology.

Mathematical modeling of kidney transport.

PubMed

Layton, Anita T

2013-01-01

In addition to metabolic waste and toxin excretion, the kidney also plays an indispensable role in regulating the balance of water, electrolytes, nitrogen, and acid-base. In this review, we describe representative mathematical models that have been developed to better understand kidney physiology and pathophysiology, including the regulation of glomerular filtration, the regulation of renal blood flow by means of the tubuloglomerular feedback mechanisms and of the myogenic mechanism, the urine concentrating mechanism, epithelial transport, and regulation of renal oxygen transport. We discuss the extent to which these modeling efforts have expanded our understanding of renal function in both health and disease. Copyright © 2013 Wiley Periodicals, Inc.

From boring to scoring - a collaborative serious game for learning and practicing mathematical logic for computer science education

NASA Astrophysics Data System (ADS)

Schäfer, Andreas; Holz, Jan; Leonhardt, Thiemo; Schroeder, Ulrik; Brauner, Philipp; Ziefle, Martina

2013-06-01

In this study, we address the problem of low retention and high dropout rates of computer science university students in early semesters of the studies. Complex and high abstract mathematical learning materials have been identified as one reason for the dropout rate. In order to support the understanding and practicing of core mathematical concepts, we developed a game-based multitouch learning environment in which the need for a suitable learning environment for mathematical logic was combined with the ability to train cooperation and collaboration in a learning scenario. As application domain, the field of mathematical logic had been chosen. The development process was accomplished along three steps: First, ethnographic interviews were run with 12 students of computer science revealing typical problems with mathematical logic. Second, a multitouch learning environment was developed. The game consists of multiple learning and playing modes in which teams of students can collaborate or compete against each other. Finally, a twofold evaluation of the environment was carried out (user study and cognitive walk-through). Overall, the evaluation showed that the game environment was easy to use and rated as helpful: The chosen approach of a multiplayer game supporting competition, collaboration, and cooperation is perceived as motivating and "fun."

Upgrading geometry conceptual understanding and strategic competence through implementing rigorous mathematical thinking (RMT)

NASA Astrophysics Data System (ADS)

Nugraheni, Z.; Budiyono, B.; Slamet, I.

2018-03-01

To reach higher order thinking skill, needed to be mastered the conceptual understanding and strategic competence as they are two basic parts of high order thinking skill (HOTS). RMT is a unique realization of the cognitive conceptual construction approach based on Feurstein with his theory of Mediated Learning Experience (MLE) and Vygotsky’s sociocultural theory. This was quasi-experimental research which compared the experimental class that was given Rigorous Mathematical Thinking (RMT) as learning method and the control class that was given Direct Learning (DL) as the conventional learning activity. This study examined whether there was different effect of two learning model toward conceptual understanding and strategic competence of Junior High School Students. The data was analyzed by using Multivariate Analysis of Variance (MANOVA) and obtained a significant difference between experimental and control class when considered jointly on the mathematics conceptual understanding and strategic competence (shown by Wilk’s Λ = 0.84). Further, by independent t-test is known that there was significant difference between two classes both on mathematical conceptual understanding and strategic competence. By this result is known that Rigorous Mathematical Thinking (RMT) had positive impact toward Mathematics conceptual understanding and strategic competence.

Content Knowledge, Attitudes, and Self-Efficacy in the Mathematics New York City Teaching Fellows (NYCTF) Program

ERIC Educational Resources Information Center

Evans, Brian R.

2011-01-01

The purpose of this study was to understand the mathematical content knowledge new teachers have both before and after taking a mathematics methods course in the NYCTF program. Further, the purpose was to understand the attitudes toward mathematics and concepts of self-efficacy that Teaching Fellows had over the course of the semester. The sample…

Cognition, emotion, and arithmetic in primary school: A cross-cultural investigation.

PubMed

Rodic, Maja; Cui, Jiaxin; Malykh, Sergey; Zhou, Xinlin; Gynku, Elena I; Bogdanova, Elena L; Zueva, Dina Y; Y Bogdanova, Olga; Kovas, Yulia

2018-06-01

The study investigated cross-cultural differences in variability and average performance in arithmetic, mathematical reasoning, symbolic and non-symbolic magnitude processing, intelligence, spatial ability, and mathematical anxiety in 890 6- to 9-year-old children from the United Kingdom, Russia, and China. Cross-cultural differences explained 28% of the variance in arithmetic and 17.3% of the variance in mathematical reasoning, with Chinese children outperforming the other two groups. No cross-cultural differences were observed for spatial ability and mathematical anxiety. In all samples, symbolic magnitude processing and mathematical reasoning were independently related to early arithmetic. Other factors, such as non-symbolic magnitude processing, mental rotation, intelligence, and mathematical anxiety, produced differential patterns across the populations. The results are discussed in relation to potential influences of parental practice, school readiness, and linguistic factors on individual differences in early mathematics. Statement of contribution What is already known on this subject? Cross-cultural differences in mathematical ability are present in preschool children. Similar mechanisms of mathematical development operate in preschool children from the United Kingdom, Russia, and China. Tasks that require understanding of numbers are best predictors of arithmetic in preschool children. What does this study add? Cross-cultural differences in mathematical ability become greater with age/years of formal education. Similar mechanisms of mathematical development operate in early primary school children from the United Kingdom, Russia, and China. Symbolic number magnitude and mathematical reasoning are the main predictors of arithmetic in all three populations. © 2018 The Authors British Journal of Developmental Psychology published by John Wiley & Sons Ltd on behalf of British Psychological Society.

Between timelessness and historiality: on the dynamics of the epistemic objects of mathematics.

PubMed

Epple, Moritz

2011-09-01

In order to discuss the temporal structure of mathematical research, this essay offers four related definitions of a mathematical object from different times and places. It is argued that in order to appreciate the differences between these definitions, the historian needs to understand that none of them made sense in mathematical practice without a technical framework, referred to but not explained in the definitions themselves (an "epistemic configuration of research"); that the dynamics of the epistemic objects of mathematical research are secondary to the dynamics of these epistemic configurations as a whole; and that the dynamics of epistemic configurations of mathematical research do not follow law-like processes. Very different types of change may happen, and some of them link the dynamics of epistemic configurations with events and developments far beyond the bounds of the research field in question. These insights have historiographical consequences that require us to rethink the kind of temporality ascribed to mathematics.

Unwrapping Students' Ideas about Fractions

ERIC Educational Resources Information Center

Lewis, Rebecca M.; Gibbons, Lynsey K.; Kazemi, Elham; Lind, Teresa

2015-01-01

Supporting students to develop an understanding of the meaning of fractions is an important goal of elementary school mathematics. This involves developing partitioning strategies, creating representations, naming fractional quantities, and using symbolic notation. This article describes how teachers can use a formative assessment problem to…

The Layering of Mathematical Interpretations through Digital Media

ERIC Educational Resources Information Center

Calder, Nigel

2012-01-01

How might understanding emerge when learners engage mathematical phenomena through digital technologies? This paper considers the ways children's mathematical thinking was influenced by their interpretations through various pedagogical discourses and how understanding emerged through those various filters. Current research into using digital…

Authority, Identity, and Collaborative Mathematics

ERIC Educational Resources Information Center

Langer-Osuna, Jennifer M.

2017-01-01

The field of mathematics education research has seen a resurgence of interest in understanding collaborative learning because students in K-12 classrooms are increasingly expected to make sense of mathematics problems together. This Research Commentary argues for the importance of understanding student authority relations in collaborative…

Development and Validation of the Numeracy Understanding in Medicine Instrument Short Form

PubMed Central

Schapira, Marilyn M.; Walker, Cindy M.; Miller, Tamara; Fletcher, Kathlyn A; Ganschow, Pamela G.; Jacobs, Elizabeth A; Imbert, Diana; O'Connell, Maria; Neuner, Joan M.

2014-01-01

Background Health numeracy can be defined as the ability to understand and use numeric information and quantitative concepts in the context of health. We previously reported the development of the Numeracy Understanding in Medicine Instrument (NUMi); a 20-item test developed using item response theory. We now report the development and validation of a short form of the NUMi. Methods Item statistics were used to identify a subset of 8-items representing a range of difficulty and content areas. Internal reliability was evaluated with Cronbach's alpha. Divergent and convergent validity was assessed by comparing scores of the S-NUMI with existing measures of education, print and numeric health literacy, mathematic achievement, cognitive reasoning, and the original NUMi. Results The 8-item scale had adequate reliability (Cronbach's alpha: 0.72) and was strongly correlated to the 20-item NUMi (0.92). The S-NUMi scores were strongly correlated with the Lipkus numeracy test (0.62), Wide Range of Achievement Test-Mathematics (WRAT-M) (0.72), and Wonderlic cognitive reasoning test (0.76). Moderate correlation was found with education level (0.58) and print literacy as measured by the TOFHLA (0.49). Conclusion The short Numeracy Understanding in Medicine Instrument is a reliable and valid measure of health numeracy feasible for use in clinical and research settings. PMID:25315596

Recent advances in mathematical criminology. Comment on "Statistical physics of crime: A review" by M.R. D'Orsogna and M. Perc

NASA Astrophysics Data System (ADS)

Rodríguez, Nancy

2015-03-01

The use of mathematical tools has long proved to be useful in gaining understanding of complex systems in physics [1]. Recently, many researchers have realized that there is an analogy between emerging phenomena in complex social systems and complex physical or biological systems [4,5,12]. This realization has particularly benefited the modeling and understanding of crime, a ubiquitous phenomena that is far from being understood. In fact, when one is interested in the bulk behavior of patterns that emerge from small and seemingly unrelated interactions as well as decisions that occur at the individual level, the mathematical tools that have been developed in statistical physics, game theory, network theory, dynamical systems, and partial differential equations can be useful in shedding light into the dynamics of these patterns [2-4,6,12].

Mathematization in introductory physics

NASA Astrophysics Data System (ADS)

Brahmia, Suzanne M.

Mathematization is central to STEM disciplines as a cornerstone of the quantitative reasoning that characterizes these fields. Introductory physics is required for most STEM majors in part so that students develop expert-like mathematization. This dissertation describes coordinated research and curriculum development for strengthening mathematization in introductory physics; it blends scholarship in physics and mathematics education in the form of three papers. The first paper explores mathematization in the context of physics, and makes an original contribution to the measurement of physics students' struggle to mathematize. Instructors naturally assume students have a conceptual mastery of algebra before embarking on a college physics course because these students are enrolled in math courses beyond algebra. This paper provides evidence that refutes the validity of this assumption and categorizes some of the barriers students commonly encounter with quantification and representing ideas symbolically. The second paper develops a model of instruction that can help students progress from their starting points to their instructor's desired endpoints. Instructors recognize that the introductory physics course introduces new ideas at an astonishing rate. More than most physicists realize, however, the way that mathematics is used in the course is foreign to a large portion of class. This paper puts forth an instructional model that can move all students toward better quantitative and physical reasoning, despite the substantial variability of those students' initial states. The third paper describes the design and testing of curricular materials that foster mathematical creativity to prepare students to better understand physics reasoning. Few students enter introductory physics with experience generating equations in response to specific challenges involving unfamiliar quantities and units, yet this generative use of mathematics is typical of the thinking involved in doing physics. It contrasts with their more common experience with mathematics as the practice of specified procedures to improve efficiency. This paper describes new curricular materials based on invention instruction provide students with opportunities to generate mathematical relationships in physics, and the paper presents preliminary evidence of the effectiveness of this method with mathematically underprepared engineering students.

Assessing the Impact of Computer Programming in Understanding Limits and Derivatives in a Secondary Mathematics Classroom

ERIC Educational Resources Information Center

de Castro, Christopher H.

2011-01-01

This study explored the development of student's conceptual understandings of limit and derivative when utilizing specifically designed computational tools. Fourteen students from a secondary Advanced Placement Calculus AB course learned and explored the limit and derivative concepts from differential calculus using visualization tools in the…

Students' Understanding of Loops and Nested Loops in Computer Programming: An APOS Theory Perspective

ERIC Educational Resources Information Center

Cetin, Ibrahim

2015-01-01

The purpose of this study is to explore students' understanding of loops and nested loops concepts. Sixty-three mechanical engineering students attending an introductory programming course participated in the study. APOS (Action, Process, Object, Schema) is a constructivist theory developed originally for mathematics education. This study is the…

College Students' Understanding of the Domain and Range of Functions on Graphs

ERIC Educational Resources Information Center

Cho, Young Doo

2013-01-01

The mathematical concept of function has been revisited and further developed with regularity since its introduction in ancient Babylonia (Kleiner, 1989). The difficulty of the concept of a function contributes to complications when students learn of functions and their graphs (Leinhardt, Zaslavsky, & Stein, 1990). To understand the concept of…

The Influence of Toy Design Activities on Middle School Students' Understanding of the Engineering Design Processes

ERIC Educational Resources Information Center

Zhou, Ninger; Pereira, Nielsen L.; Tarun, Thomas George; Alperovich, Jeffrey; Booth, Joran; Chandrasegaran, Senthil; Tew, Jeffrey David; Kulkarni, Devadatta M.; Ramani, Karthik

2017-01-01

The societal demand for inspiring and engaging science, technology, engineering, and mathematics (STEM) students and preparing our workforce for the emerging creative economy has necessitated developing students' self-efficacy and understanding of engineering design processes from as early as elementary school levels. Hands-on engineering design…

Using Dynamic Geometry to Expand Mathematics Teachers' Understanding of Proof

ERIC Educational Resources Information Center

de Villiers, Michael

2004-01-01

This paper gives a broad descriptive account of some activities that the author has designed using Sketchpad to develop teachers' understanding of other functions of proof than just the traditional function of 'verification'. These other functions of proof illustrated here are those of explanation, discovery and systematization (in the context of…

Pre-Service Elementary Teachers' Understanding of Pattern and Function

ERIC Educational Resources Information Center

Sharon, Valerie Vinyard

2010-01-01

Scope and method of study: The purpose of this study was to unpack the understandings pre-service elementary teachers have pertaining to the ideas of pattern and function. The intent was to bring insight into how mathematics teacher educators can use patterning activities to prepare pre-service elementary teachers to support the development of…

Marvels of Math: Fascinating Reads and Awesome Activities.

ERIC Educational Resources Information Center

Haven, Kendall F.

Any topic, math included, becomes more accessible and understandable when human stories are related about the development of the subject. Stories make subjects real and purposeful. They provide a foundation from which students can understand and appreciate mathematics rather than merely memorize a series of rote exercises. This book presents 16…

Preservice Elementary School Teachers' Conceptual Understanding of Place Value within a Constructivist Framework

ERIC Educational Resources Information Center

Murawska, Jaclyn Marie

2013-01-01

This research study examined the development of 43 preservice elementary school teachers' conceptual understanding of place value after participating in a research-based constructivist unit of instruction in place value. The preservice teachers were enrolled in one of three terms of an elementary mathematics methods course in a private midwestern…

A brief historical development of classical mathematics before the Renaissance

NASA Astrophysics Data System (ADS)

Debnath, Lokenath

2011-07-01

'If you wish to foresee the future of mathematics our proper course is to study the history and present condition of the science.' Henri Poincaré 'It is India that gave us the ingenious method of expressing all numbers by ten symbols, each symbol receiving a value of position, as well as an absolute value. We shall appreciate the grandeur of the achievement when we remember that it escaped the genius of Archimedes and Apollonius.' P.S. Laplace 'The Greeks were the first mathematicians who are still 'real' to us today. Oriental mathematics may be an interesting curiosity, but Greek mathematics is the real thing. The Greek first spoke of a language which modern mathematicians can understand.' G.H. Hardy This article deals with a short history of mathematics and mathematical scientists during the ancient and medieval periods. Included are some major developments of the ancient, Indian, Arabic, Egyptian, Greek and medieval mathematics and their significant impact on the Renaissance mathematics. Special attention is given to many results, theorems, generalizations, and new discoveries of arithmetic, algebra, number theory, geometry and astronomy during the above periods. A number of exciting applications of the above areas is discussed in some detail. It also contains a wide variety of important material accessible to college and even high school students and teachers at all levels. Included also is mathematical information that puts the professionals and prospective mathematical scientists at the forefront of current research.

Resilience in mathematics after early brain injury: The roles of parental input and early plasticity.

PubMed

Glenn, Dana E; Demir-Lira, Özlem Ece; Gibson, Dominic J; Congdon, Eliza L; Levine, Susan C

2018-04-01

Children with early focal unilateral brain injury show remarkable plasticity in language development. However, little is known about how early brain injury influences mathematical learning. Here, we examine early number understanding, comparing cardinal number knowledge of typically developing children (TD) and children with pre- and perinatal lesions (BI) between 42 and 50 months of age. We also examine how this knowledge relates to the number words children hear from their primary caregivers early in life. We find that children with BI, are, on average, slightly behind TD children in both cardinal number knowledge and later mathematical performance, and show slightly slower learning rates than TD children in cardinal number knowledge during the preschool years. We also find that parents' "number talk" to their toddlers predicts later mathematical ability for both TD children and children with BI. These findings suggest a relatively optimistic story in which neural plasticity is at play in children's mathematical development following early brain injury. Further, the effects of early number input suggest that intervening to enrich the number talk that children with BI hear during the preschool years could narrow the math achievement gap. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.

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.

Mathematical Modelling as a Tool to Understand Cell Self-renewal and Differentiation.

PubMed

Getto, Philipp; Marciniak-Czochra, Anna

2015-01-01

Mathematical modeling is a powerful technique to address key questions and paradigms in a variety of complex biological systems and can provide quantitative insights into cell kinetics, fate determination and development of cell populations. The chapter is devoted to a review of modeling of the dynamics of stem cell-initiated systems using mathematical methods of ordinary differential equations. Some basic concepts and tools for cell population dynamics are summarized and presented as a gentle introduction to non-mathematicians. The models take into account different plausible mechanisms regulating homeostasis. Two mathematical frameworks are proposed reflecting, respectively, a discrete (punctuated by division events) and a continuous character of transitions between differentiation stages. Advantages and constraints of the mathematical approaches are presented on examples of models of blood systems and compared to patients data on healthy hematopoiesis.

Mathematics teachers' support and retention: using Maslow's hierarchy to understand teachers' needs

NASA Astrophysics Data System (ADS)

Fisher, Molly H.; Royster, David

2016-10-01

As part of a larger study, four mathematics teachers from diverse backgrounds and teaching situations report their ideas on teacher stress, mathematics teacher retention, and their feelings about the needs of mathematics teachers, as well as other information crucial to retaining quality teachers. The responses from the participants were used to develop a hierarchy of teachers' needs that resembles Maslow's hierarchy, which can be used to better support teachers in various stages of their careers. The interviews revealed both non content-specific and content-specific needs within the hierarchy. The responses show that teachers found different schools foster different stress levels and that as teachers they used a number of resources for reducing stress. Other mathematics-specific ideas are also discussed such as the amount of content and pedagogy courses required for certification.

Tutoring Mathematical Word Problems Using Solution Trees: Text Comprehension, Situation Comprehension, and Mathematization in Solving Story Problems. Research Report No. 8.

ERIC Educational Resources Information Center

Reusser, Kurt; And Others

The main concern of this paper is on the psychological processes of how students understand and solve mathematical word problems, and on how this knowledge can be applied to computer-based tutoring. It is argued that only a better understanding of the psychological requirements for understanding and solving those problems will lead to…

Analysis of Undergraduate Students’ Mathematical Understanding Ability of the Limit of Function Based on APOS Theory Perspective

NASA Astrophysics Data System (ADS)

Afgani, M. W.; Suryadi, D.; Dahlan, J. A.

2017-09-01

The aim of this study was to know the level of undergraduate students’ mathematical understanding ability based on APOS theory perspective. The APOS theory provides an evaluation framework to describe the level of students’ understanding and mental structure about their conception to a mathematics concept. The levels of understanding in APOS theory are action, process, object, and schema conception. The subjects were 59 students of mathematics education whom had attended a class of the limit of function at a university in Palembang. The method was qualitative descriptive with 4 test items. The result showed that most of students were still at the level of action conception. They could calculate and use procedure precisely to the mathematics objects that was given, but could not reach the higher conception yet.

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…

Current advances in mathematical modeling of anti-cancer drug penetration into tumor tissues.

PubMed

Kim, Munju; Gillies, Robert J; Rejniak, Katarzyna A

2013-11-18

Delivery of anti-cancer drugs to tumor tissues, including their interstitial transport and cellular uptake, is a complex process involving various biochemical, mechanical, and biophysical factors. Mathematical modeling provides a means through which to understand this complexity better, as well as to examine interactions between contributing components in a systematic way via computational simulations and quantitative analyses. In this review, we present the current state of mathematical modeling approaches that address phenomena related to drug delivery. We describe how various types of models were used to predict spatio-temporal distributions of drugs within the tumor tissue, to simulate different ways to overcome barriers to drug transport, or to optimize treatment schedules. Finally, we discuss how integration of mathematical modeling with experimental or clinical data can provide better tools to understand the drug delivery process, in particular to examine the specific tissue- or compound-related factors that limit drug penetration through tumors. Such tools will be important in designing new chemotherapy targets and optimal treatment strategies, as well as in developing non-invasive diagnosis to monitor treatment response and detect tumor recurrence.

Structural Exclusion through School Mathematics: Using Bourdieu to Understand Mathematics as a Social Practice

ERIC Educational Resources Information Center

Jorgensen, Robyn; Gates, Peter; Roper, Vanessa

2014-01-01

In this paper, we explore a sociological approach to mathematics education and offer a theoretical lens through which we can come to understand mathematics education as part of a wider set of social practices. Many studies of children's experiences in school show that a child's academic success is a product of many factors, some of which…

Chaos Theory for the Practical Military Mind

DTIC Science & Technology

1997-03-01

kept at a conceptual level for the benefit of the novice looking to understand the ‘big picture’ before pursuing the topic further, and for those...individuals who do not need to work at a more mathematical level . Examples of Chaotic systems of military interest are given. This work also addresses...we’ll keep the level conceptual and as non- mathematical as practical. While we will develop definitions throughout this paper, key concepts that are

Description of Student’s Metacognitive Ability in Understanding and Solving Mathematics Problem

NASA Astrophysics Data System (ADS)

Ahmad, Herlina; Febryanti, Fatimah; Febryanti, Fatimah; Muthmainnah

2018-01-01

This research was conducted qualitative which was aim to describe metacognitive ability to understand and solve the problems of mathematics. The subject of the research was the first year students at computer and networking department of SMK Mega Link Majene. The sample was taken by purposive sampling technique. The data obtained used the research instrument based on the form of students achievements were collected by using test of student’s achievement and interview guidance. The technique of collecting data researcher had observation to ascertain the model that used by teacher was teaching model of developing metacognitive. The technique of data analysis in this research was reduction data, presentation and conclusion. Based on the whole findings in this study it was shown that student’s metacognitive ability generally not develops optimally. It was because of limited scope of the materials, and cognitive teaching strategy handled by verbal presentation and trained continuously in facing cognitive tasks, such as understanding and solving problem.

Consequences, Characteristics, and Causes of Mathematical Learning Disabilities and Persistent Low Achievement in Mathematics

PubMed Central

Geary, David C.

2011-01-01

Objective The goals of the review are threefold; a) to highlight the educational and employment consequences of poorly developed mathematical competencies; b) overview the characteristics of the children with persistently low achievement in mathematics; and c) provide a primer on cognitive science research that is aimed at identifying the cognitive mechanisms underlying these learning disabilities and associated cognitive interventions. Method Literatures on the educational and economic consequences of poor mathematics achievement were reviewed and integrated with reviews of epidemiological, behavioral genetic, and cognitive science studies of poor mathematics achievement. Results Poor mathematical competencies are common among adults and result in employment difficulties and difficulties in many common day-to-day activities. Among students, about 7% of children and adolescents have a mathematical learning disability (MLD) and another 10% show persistent low achievement (LA) in mathematics despite average abilities in most other areas. Children with MLD and their LA peers have deficits in understanding and representing numerical magnitude, difficulties retrieving basic arithmetic facts from long-term memory, and delays in learning mathematical procedures. These deficits and delays cannot be attributed to intelligence, but are related to working memory deficits for children with MLD, but not LA children. Interventions that target these cognitive deficits are in development and preliminary results are promising. Conclusion Mathematical learning disabilities and learning difficulties associated with persistent low achievement in mathematics are common and not attributable to intelligence. These individuals have identifiable number and memory delays and deficits that appear to be specific to mathematics learning. The most promising interventions are those that target these specific deficits and, in addition, for children with MLD interventions that target their low working memory capacity. PMID:21285895

Interactions Between Mathematics and Physics: The History of the Concept of Function—Teaching with and About Nature of Mathematics

NASA Astrophysics Data System (ADS)

Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-07-01

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a string (Euler) and heat conduction (Fourier and Dirichlet). The introduction of generalized functions or distributions is shown to stem partly from the development of new theories of physics such as electrical engineering and quantum mechanics that led to the use of improper functions such as the delta function that demanded a proper foundation. We argue that the development of student understanding of mathematics and its nature is enhanced by embedding mathematical concepts and theories, within an explicit-reflective framework, into a rich historical context emphasizing its interaction with other disciplines such as physics. Students recognize and become engaged with meta-discursive rules governing mathematics. Mathematics teachers can thereby teach inquiry in mathematics as it occurs in the sciences, as mathematical practice aimed at obtaining new mathematical knowledge. We illustrate such a historical teaching and learning of mathematics within an explicit and reflective framework by two examples of student-directed, problem-oriented project work following the Roskilde Model, in which the connection to physics is explicit and provides a learning space where the nature of mathematics and mathematical practices are linked to natural science.

Science modelling in pre-calculus: how to make mathematics problems contextually meaningful

NASA Astrophysics Data System (ADS)

Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

2011-04-01

'Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum' (National Council of Teachers of Mathematics (NCTM), Principles and Standards for School Mathematics, NCTM, Reston, VA, 2000). Commonly used pre-calculus textbooks provide a wide range of application problems. However, these problems focus students' attention on evaluating or solving pre-arranged formulas for given values. The role of scientific content is reduced to provide a background for these problems instead of being sources of data gathering for inducing mathematical tools. Students are neither required to construct mathematical models based on the contexts nor are they asked to validate or discuss the limitations of applied formulas. Using these contexts, the instructor may think that he/she is teaching problem solving, where in reality he/she is teaching algorithms of the mathematical operations (G. Kulm (ed.), New directions for mathematics assessment, in Assessing Higher Order Thinking in Mathematics, Erlbaum, Hillsdale, NJ, 1994, pp. 221-240). Without a thorough representation of the physical phenomena and the mathematical modelling processes undertaken, problem solving unintentionally appears as simple algorithmic operations. In this article, we deconstruct the representations of mathematics problems from selected pre-calculus textbooks and explicate their limitations. We argue that the structure and content of those problems limits students' coherent understanding of mathematical modelling, and this could result in weak student problem-solving skills. Simultaneously, we explore the ways to enhance representations of those mathematical problems, which we have characterized as lacking a meaningful physical context and limiting coherent student understanding. In light of our discussion, we recommend an alternative to strengthen the process of teaching mathematical modelling - utilization of computer-based science simulations. Although there are several exceptional computer-based science simulations designed for mathematics classes (see, e.g. Kinetic Book (http://www.kineticbooks.com/) or Gizmos (http://www.explorelearning.com/)), we concentrate mainly on the PhET Interactive Simulations developed at the University of Colorado at Boulder (http://phet.colorado.edu/) in generating our argument that computer simulations more accurately represent the contextual characteristics of scientific phenomena than their textual descriptions.

Understanding Scientific Ideas: An Honors Course.

ERIC Educational Resources Information Center

Capps, Joan; Schueler, Paul

At Raritan Valley Community College (RVCC) in New Jersey, an honors philosophy course was developed which taught mathematics and science concepts independent of computational skill. The course required that students complete a weekly writing assignment designed as a continuous refinement of logical reasoning development. This refinement was…

Anticipation Guides: Reading for Mathematics Understanding

ERIC Educational Resources Information Center

Adams, Anne E.; Pegg, Jerine; Case, Melissa

2015-01-01

With the acceptance by many states of the Common Core State Standards for Mathematics, new emphasis is being placed on students' ability to engage in mathematical practices such as understanding problems (including word problems), reading and critiquing arguments, and making explicit use of definitions (CCSSI 2010). Engaging students in…

Technology Prompts New Understandings: The Case of Equality

ERIC Educational Resources Information Center

Bardini, Caroline; Oldenburg, Reinhard; Stacey, Kaye; Pierce, Robyn

2013-01-01

Changes to students' understanding of mathematical notation may be brought about by using technology within mathematics. Taking equality as a case study, the paper provides brief epistemological, historical, didactical, and computational reviews of its symbolic representation in pen-and-paper and technology-assisted mathematics, most especially in…

Understanding the Complexities of Student Motivations in Mathematics Learning

ERIC Educational Resources Information Center

Walter, Janet G.; Hart, Janelle

2009-01-01

Student motivation has long been a concern of mathematics educators. However, commonly held distinctions between intrinsic and extrinsic motivations may be insufficient to inform our understandings of student motivations in learning mathematics or to appropriately shape pedagogical decisions. Here, motivation is defined, in general, as an…

Mathematical models of cell motility.

PubMed

Flaherty, Brendan; McGarry, J P; McHugh, P E

2007-01-01

Cell motility is an essential biological action in the creation, operation and maintenance of our bodies. Developing mathematical models elucidating cell motility will greatly advance our understanding of this fundamental biological process. With accurate models it is possible to explore many permutations of the same event and concisely investigate their outcome. While great advancements have been made in experimental studies of cell motility, it now has somewhat fallen on mathematical models to taking a leading role in future developments. The obvious reason for this is the complexity of cell motility. Employing the processing power of today's computers will give researches the ability to run complex biophysical and biochemical scenarios, without the inherent difficulty and time associated with in vitro investigations. Before any great advancement can be made, the basics of cell motility will have to be well-defined. Without this, complicated mathematical models will be hindered by their inherent conjecture. This review will look at current mathematical investigations of cell motility, explore the reasoning behind such work and conclude with how best to advance this interesting and challenging research area.

Applications of Functional Near-Infrared Spectroscopy (fNIRS) in Studying Cognitive Development: The Case of Mathematics and Language.

PubMed

Soltanlou, Mojtaba; Sitnikova, Maria A; Nuerk, Hans-Christoph; Dresler, Thomas

2018-01-01

In this review, we aim to highlight the application of functional near-infrared spectroscopy (fNIRS) as a useful neuroimaging technique for the investigation of cognitive development. We focus on brain activation changes during the development of mathematics and language skills in schoolchildren. We discuss how technical limitations of common neuroimaging techniques such as functional magnetic resonance imaging (fMRI) have resulted in our limited understanding of neural changes during development, while fNIRS would be a suitable and child-friendly method to examine cognitive development. Moreover, this technique enables us to go to schools to collect large samples of data from children in ecologically valid settings. Furthermore, we report findings of fNIRS studies in the fields of mathematics and language, followed by a discussion of the outlook of fNIRS in these fields. We suggest fNIRS as an additional technique to track brain activation changes in the field of educational neuroscience.

Applications of Functional Near-Infrared Spectroscopy (fNIRS) in Studying Cognitive Development: The Case of Mathematics and Language

PubMed Central

Soltanlou, Mojtaba; Sitnikova, Maria A.; Nuerk, Hans-Christoph; Dresler, Thomas

2018-01-01

In this review, we aim to highlight the application of functional near-infrared spectroscopy (fNIRS) as a useful neuroimaging technique for the investigation of cognitive development. We focus on brain activation changes during the development of mathematics and language skills in schoolchildren. We discuss how technical limitations of common neuroimaging techniques such as functional magnetic resonance imaging (fMRI) have resulted in our limited understanding of neural changes during development, while fNIRS would be a suitable and child-friendly method to examine cognitive development. Moreover, this technique enables us to go to schools to collect large samples of data from children in ecologically valid settings. Furthermore, we report findings of fNIRS studies in the fields of mathematics and language, followed by a discussion of the outlook of fNIRS in these fields. We suggest fNIRS as an additional technique to track brain activation changes in the field of educational neuroscience. PMID:29666589

Multiple Visions of Teachers' Understandings of Mathematics

ERIC Educational Resources Information Center

Kajander, Ann; Mason, Ralph; Taylor, Peter; Doolittle, Edward; Boland, Tom; Jarvis, Dan; Maciejewski, Wes

2010-01-01

In this dialog, the notion of mathematical understanding as might be needed by classroom teachers is critically examined by mathematics educators, mathematicians, and a classroom teacher, based on the outcomes of recent work with expert classroom teachers. Terminology, assumptions and examples are discussed and analysed from a number of points of…

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…

A Framework for Understanding Whiteness in Mathematics Education

ERIC Educational Resources Information Center

Battey, Dan; Leyva, Luis A.

2016-01-01

In this article, the authors provide a framework for understanding whiteness in mathematics education. While whiteness is receiving more attention in the broader education literature, only a handful of scholars address whiteness in mathematics education in any form. This lack of attention to whiteness leaves it invisible and neutral in documenting…

Understanding Mathematics and Science Matters. Studies in Mathematical Thinking and Learning Series

ERIC Educational Resources Information Center

Romberg, Thomas A., Ed.; Carpenter, Thomas P., Ed.; Dremock, Fae, Ed.

2005-01-01

The research reported in this book provides reliable evidence on and knowledge about mathematics and science instruction that emphasizes student understanding--instruction consistent with the needs of students who will be citizens in an increasingly demanding technological world. The National Center for Improving Student Learning in Mathematics…

Factors That Influence the Understanding of Good Mathematics Teaching

ERIC Educational Resources Information Center

Leong, Kwan Eu

2013-01-01

This study explored the factors that influenced the understanding of good mathematics teaching. A mixed methodology was used investigate the beliefs of beginning secondary teachers on good mathematics teaching. The two research instruments used in this study were the survey questionnaire and an interview. Beginning teachers selected Immediate…

Mathematics Education Graduate Students' Understanding of Trigonometric Ratios

ERIC Educational Resources Information Center

Yigit Koyunkaya, Melike

2016-01-01

This study describes mathematics education graduate students' understanding of relationships between sine and cosine of two base angles in a right triangle. To explore students' understanding of these relationships, an elaboration of Skemp's views of instrumental and relational understanding using Tall and Vinner's concept image and concept…

An Investigation of Secondary Teachers’ Understanding and Belief on Mathematical Problem Solving

NASA Astrophysics Data System (ADS)

Yuli Eko Siswono, Tatag; Wachidul Kohar, Ahmad; Kurniasari, Ika; Puji Astuti, Yuliani

2016-02-01

Weaknesses on problem solving of Indonesian students as reported by recent international surveys give rise to questions on how Indonesian teachers bring out idea of problem solving in mathematics lesson. An explorative study was undertaken to investigate how secondary teachers who teach mathematics at junior high school level understand and show belief toward mathematical problem solving. Participants were teachers from four cities in East Java province comprising 45 state teachers and 25 private teachers. Data was obtained through questionnaires and written test. The results of this study point out that the teachers understand pedagogical problem solving knowledge well as indicated by high score of observed teachers‘ responses showing understanding on problem solving as instruction as well as implementation of problem solving in teaching practice. However, they less understand on problem solving content knowledge such as problem solving strategies and meaning of problem itself. Regarding teacher's difficulties, teachers admitted to most frequently fail in (1) determining a precise mathematical model or strategies when carrying out problem solving steps which is supported by data of test result that revealed transformation error as the most frequently observed errors in teachers’ work and (2) choosing suitable real situation when designing context-based problem solving task. Meanwhile, analysis of teacher's beliefs on problem solving shows that teachers tend to view both mathematics and how students should learn mathematics as body static perspective, while they tend to believe to apply idea of problem solving as dynamic approach when teaching mathematics.

MAESTRO: Mathematics and Earth Science Teachers' Resource Organization

NASA Astrophysics Data System (ADS)

Courtier, A. M.; Pyle, E. J.; Fichter, L.; Lucas, S.; Jackson, A.

2013-12-01

The Mathematics and Earth Science Teachers' Resource Organization (MAESTRO) partnership between James Madison University and Harrisonburg City and Page County Public Schools, funded through NSF-GEO. The partnership aims to transform mathematics and Earth science instruction in middle and high schools by developing an integrated mathematics and Earth systems science approach to instruction. This curricular integration is intended to enhance the mathematical skills and confidence of students through concrete, Earth systems-based examples, while increasing the relevance and rigor of Earth science instruction via quantification and mathematical modeling of Earth system phenomena. MAESTRO draws heavily from the Earth Science Literacy Initiative (2009) and is informed by criterion-level standardized test performance data in both mathematics and Earth science. The project has involved two summer professional development workshops, academic year Lesson Study (structured teacher observation and reflection), and will incorporate site-based case studies with direct student involvement. Participating teachers include Grade 6 Science and Mathematics teachers, and Grade 9 Earth Science and Algebra teachers. It is anticipated that the proposed integration across grade bands will first strengthen students' interests in mathematics and science (a problem in middle school) and subsequently reinforce the relevance of mathematics and other sciences (a problem in high school), both in support of Earth systems literacy. MAESTRO's approach to the integration of math and science focuses on using box models to emphasize the interconnections among the geo-, atmo-, bio-, and hydrospheres, and demonstrates the positive and negative feedback processes that connect their mutual evolution. Within this framework we explore specific relationships that can be described both qualitatively and mathematically, using mathematical operations appropriate for each grade level. Site-based case studies, developed in collaboration between teachers and JMU faculty members, provide a tangible, relevant setting in which students can apply and understand mathematical applications and scientific processes related to evolving Earth systems. Initial results from student questionnaires and teacher focus groups suggest that the anticipated impacts of MAESTRO on students are being realized, including increased valuing of mathematics and Earth science in society and transfer between mathematics and science courses. As a high percentage of students in the MAESTRO schools are of low socio-economic status, they also face the prospect of becoming first-generation college students, hopefully considering STEM academic pathways. MAESTRO will drive the development of challenging and engaging instruction designed to draw a larger pool of students into STEM career pathways.

Firm Foundations: The Effectiveness of an Educational Psychologist Developed Intervention Targeting Early Numeracy Skills

ERIC Educational Resources Information Center

Somerville, Ros; Ayre, Kate; Tunbridge, Daniel; Cole, Katy; Stollery, Richard; Sanders, Mary

2015-01-01

This study evaluates the efficacy of a mathematics intervention devised by Essex Educational Psychology Service (EPS), UK. The intervention was designed to develop understanding and skills across four key domains within arithmetical development, by applying the principles of errorless learning, distributed practice and teaching to mastery. A…

Developing Conceptual Understanding and Procedural Skill in Mathematics: An Iterative Process.

ERIC Educational Resources Information Center

Rittle-Johnson, Bethany; Siegler, Robert S.; Alibali, Martha Wagner

2001-01-01

Proposes that conceptual and procedural knowledge develop in an iterative fashion and improved problem representation is one mechanism underlying the relations between them. Two experiments were conducted with 5th and 6th grade students learning about decimal fractions. Results indicate conceptual and procedural knowledge do develop, iteratively,…

Magnitude knowledge: the common core of numerical development.

PubMed

Siegler, Robert S

2016-05-01

The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: (1) representing increasingly precisely the magnitudes of non-symbolic numbers, (2) connecting small symbolic numbers to their non-symbolic referents, (3) extending understanding from smaller to larger whole numbers, and (4) accurately representing the magnitudes of rational numbers. The present review identifies substantial commonalities, as well as differences, in these four aspects of numerical development. With both whole and rational numbers, numerical magnitude knowledge is concurrently correlated with, longitudinally predictive of, and causally related to multiple aspects of mathematical understanding, including arithmetic and overall math achievement. Moreover, interventions focused on increasing numerical magnitude knowledge often generalize to other aspects of mathematics. The cognitive processes of association and analogy seem to play especially large roles in this development. Thus, acquisition of numerical magnitude knowledge can be seen as the common core of numerical development. © 2016 John Wiley & Sons Ltd.

Bridging the Gap: Fraction Understanding Is Central to Mathematics Achievement in Students from Three Different Continents

ERIC Educational Resources Information Center

Torbeyns, Joke; Schneider, Michael; Xin, Ziqiang; Siegler, Robert S.

2015-01-01

Numerical understanding and arithmetic skills are easier to acquire for whole numbers than fractions. The "integrated theory of numerical development" posits that, in addition to these differences, whole numbers and fractions also have important commonalities. In both, students need to learn how to interpret number symbols in terms of…

Using Data Comparison to Support a Focus on Distribution: Examining Preservice Teachers' Understandings of Distribution when Engaged in Statistical Inquiry

ERIC Educational Resources Information Center

Leavy, Aisling

2006-01-01

This exploratory study, a one group pretest-posttest design, investigated the development of elementary preservice teachers' understandings of distribution as expressed in the measures and representations used to compare data distributions. During a semester-long mathematics methods course, participants worked in small groups on two statistical…

Can Slope Be Negative in 3-Space? Studying Concept Image of Slope through Collective Definition Construction

ERIC Educational Resources Information Center

Moore-Russo, Deborah; Conner, AnnaMarie; Rugg, Kristina I.

2011-01-01

Developing deep conceptual understanding of what Ma (1999) calls fundamental mathematics is a well-accepted goal of teacher education. This paper presents a microanalysis of an intriguing episode within a course designed to encourage such understanding. An adaptation of Krummheuer's (1995) elaboration of Toulmin's (1958/2003) diagrams is used to…

Using Written Work to Investigate Stages in Sixth-Grade Students' Construction and Coordination of Units

ERIC Educational Resources Information Center

Ulrich, Catherine; Wilkins, Jesse L. M.

2017-01-01

Background: Students' ability to construct and coordinate units has been found to have far-reaching implications for their ability to develop sophisticated understandings of key middle-grade mathematical topics such as fractions, ratios, proportions, and algebra, topics that form the base of understanding for most STEM-related fields. Most of the…

The Effects of an Undergraduate Algebra Course on Prospective Middle School Teachers' Understanding of Functions, Especially Quadratic Functions

ERIC Educational Resources Information Center

Duarte, Jonathan T.

2010-01-01

Although current reform movements have stressed the importance of developing prospective middle school mathematics teachers' subject matter knowledge and understandings, there is a dearth of research studies with regard to prospective middle school teachers' confidence and knowledge with respect to quadratic functions. This study was intended to…

Developing a Theoretical Framework for Examining Student Understanding of Fractional Concepts: An Historical Accounting

ERIC Educational Resources Information Center

Cooper, Susan M.; Wilkerson, Trena L.; Montgomery, Mark; Mechell, Sara; Arterbury, Kristin; Moore, Sherrie

2012-01-01

In 2007, a group of mathematics educators and researchers met to examine rational numbers and why children have such an issue with them. An extensive review of the literature on fractional understanding was conducted. The ideas in that literature were then consolidated into a theoretical framework for examining fractions. Once that theoretical…

The Whole Picture (Or a Fraction of It).

ERIC Educational Resources Information Center

Rhine, Steve; Bennett, Tom R.

1998-01-01

Current educational-reform documents recommend that teachers shift from using traditional practices toward practices that foster students' development of mathematical understanding. This article examines a new model of professional development and explains a pizza activity that helps teachers learn more about how children perceive math and develop…

Outsourcing Systems Development for e-Learning Applications

ERIC Educational Resources Information Center

Brodahl, Cornelia; Oftedahl, Heidi

2012-01-01

This study investigated outsourcing of the development of visual, animated and interactive learning objects for mathematics education by a Norwegian university to software vendors in China. It sought to understand the challenges in this outsourcing engagement and competences needed to meet the challenges. The authors tested outsourcing strategies…

Manipulatives Implementation For Supporting Learning Of Mathematics For Prospective Teachers

NASA Astrophysics Data System (ADS)

Sulistyaningsih, D.; Mawarsari, V. D.; Hidayah, I.; Dwijanto

2017-04-01

Manipulatives are needed by teachers to facilitate students understand of mathematics which is abstract. As a prospective mathematics teacher, the student must have good skills in making manipulatives. Aims of this study is to describe the implementation of learning courses of manipulative workshop in mathematics education courses by lecturer at Universitas Muhammadiyah Semarang which includes the preparation of learning, general professional ability, the professional capacity specifically, ability of self-development, development class managing, planning and implementation of learning, a way of delivering the material, and evaluation of learning outcomes. Data collection techniques used were questionnaires, interviews, and observation. The research instrument consisted of a questionnaire sheet, sheet observation and interview guides. Validity is determined using data triangulation and triangulation methods. Data were analyzed using an interactive model. The results showed that the average value of activities in preparation for learning, fosters capabilities of general professional, specialized professional, self-development, manage the classroom, implementing the learning, how to deliver the material, and how to evaluate learning outcomes are 79%, 73%, 67%, 75%, 83%, 72%, 64%, and 54%, respectively

Cognitive analysis as a way to understand students' problem-solving process in BODMAS rule

NASA Astrophysics Data System (ADS)

Ung, Ting Su; Kiong, Paul Lau Ngee; Manaf, Badron bin; Hamdan, Anniza Binti; Khium, Chen Chee

2017-04-01

Students tend to make lots of careless mistake during the process of mathematics solving. To facilitate effective learning, educators have to understand which cognitive processes are used by students and how these processes help them to solve problems. This paper is only aimed to determine the common errors in mathematics by pre-diploma students that took Intensive Mathematics I (MAT037) in UiTM Sarawak. Then, concentrate on the errors did by the students on the topic of BODMAS rule and the mental processes corresponding to these errors that been developed by students. One class of pre-diploma students taking MAT037 taught by the researchers was selected because they performed poorly in SPM mathematics. It is inevitable that they finished secondary education with many misconceptions in mathematics. The solution scripts for all the tutorials of the participants were collected. This study was predominately qualitative and the solution scripts were content analyzed to identify the common errors committed by the participants, and to generate possible mental processes to these errors. Selected students were interviewed by the researchers during the progress. BODMAS rule could be further divided into Numerical Simplification and Powers Simplification. Furthermore, the erroneous processes could be attributed to categories of Basic Arithmetic Rules, Negative Numbers and Powers.

Primary school student teachers’ perception to Pendidikan Matematika Realistik Indonesia (PMRI) instruction

NASA Astrophysics Data System (ADS)

Fauziah, A.; Putri, R. I. I.; Zulkardi; Somakim

2017-12-01

This article aimed to report the perceptions of the students of primary school education to PMRI. PMRI or Realistic Mathematics Education (RME) in Indonesian version is one of the promising mathematics learning innovations developed in Indonesia. The research method consisted of three steps, namely preliminary, teaching experiment, and retrospective Analysis. The participants were six students of the primary school teacher education. In the second phase, the participants took an PMRI lesson. Then, they filled in the perception questionnaire (open and closed). The results of the study showed that the participants agreed that learning by realistic mathematics education principles helped them understand the topic.

Teachers' Explanations of a Key Developmental Understanding of Multiplicative Reasoning

ERIC Educational Resources Information Center

Rhee, Katherine L.

2012-01-01

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

High Five for Mathematics

ERIC Educational Resources Information Center

Looney, Susan; Carr, Kristen

2016-01-01

A first-grade teacher has students use their hands and fingers to engage in and develop understanding of counting, to combine groups to facilitate counting by fives and tens, and to describe their findings using words and equations.

A Case Study of Four Latina/o Pre-Service Teachers in Learning to Teach Mathematics for Understanding and Integrate a Child's Out-of-School Mathematical Knowledge and Experiences

ERIC Educational Resources Information Center

Kalinec-Craig, Crystal

2012-01-01

This dissertation study examines the experiences of four Latina/o pre-service teachers (PSTs) as they learn about teaching mathematics for understanding (TM4U) and integrating a child's out-of-school mathematical knowledge and experiences during instruction. Studying the knowledge and experiences of Latina/o PSTs is necessary because PSTs…

Integrative approaches for modeling regulation and function of the respiratory system.

PubMed

Ben-Tal, Alona; Tawhai, Merryn H

2013-01-01

Mathematical models have been central to understanding the interaction between neural control and breathing. Models of the entire respiratory system-which comprises the lungs and the neural circuitry that controls their ventilation-have been derived using simplifying assumptions to compartmentalize each component of the system and to define the interactions between components. These full system models often rely-through necessity-on empirically derived relationships or parameters, in addition to physiological values. In parallel with the development of whole respiratory system models are mathematical models that focus on furthering a detailed understanding of the neural control network, or of the several functions that contribute to gas exchange within the lung. These models are biophysically based, and rely on physiological parameters. They include single-unit models for a breathing lung or neural circuit, through to spatially distributed models of ventilation and perfusion, or multicircuit models for neural control. The challenge is to bring together these more recent advances in models of neural control with models of lung function, into a full simulation for the respiratory system that builds upon the more detailed models but remains computationally tractable. This requires first understanding the mathematical models that have been developed for the respiratory system at different levels, and which could be used to study how physiological levels of O2 and CO2 in the blood are maintained. Copyright © 2013 Wiley Periodicals, Inc.

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.

Key Understandings in School Mathematics: 1

ERIC Educational Resources Information Center

Watson, Anne

2010-01-01

This article is the first in a series which draws on findings from Nunes, Watson and Bryant (2009): "Key understandings in school mathematics: a report to the Nuffield Foundation." The Nuffield report is soundly based on research about how children learn some of the concepts involved in mathematics. In this series of articles the author takes key…

Reflective Learning and Prospective Teachers' Conceptual Understanding, Critical Thinking, Problem Solving, and Mathematical Communication Skills

ERIC Educational Resources Information Center

Junsay, Merle L.

2016-01-01

This is a quasi-experimental study that explored the effects of reflective learning on prospective teachers' conceptual understanding, critical thinking, problem solving, and mathematical communication skills and the relationship of these variables. It involved 60 prospective teachers from two basic mathematics classes of an institution of higher…

Using Prediction to Promote Mathematical Understanding and Reasoning

ERIC Educational Resources Information Center

Kasmer, Lisa; Kim, Ok-Kyeong

2011-01-01

Research has shown that prediction has the potential to promote the teaching and learning of mathematics because it can be used to enhance students' thinking and reasoning at all grade levels in various topics. This article addresses the effectiveness of using prediction on students' understanding and reasoning of mathematical concepts in a middle…

Comparison of Student Understanding of Line Graph Slope in Physics and Mathematics

ERIC Educational Resources Information Center

Planinic, Maja; Milin-Sipus, Zeljka; Katic, Helena; Susac, Ana; Ivanjek, Lana

2012-01-01

This study gives an insight into the differences between student understanding of line graph slope in the context of physics (kinematics) and mathematics. Two pairs of parallel physics and mathematics questions that involved estimation and interpretation of line graph slope were constructed and administered to 114 Croatian second year high school…

Understanding Mathematics: Some Key Factors

ERIC Educational Resources Information Center

Ali, Asma Amanat; Reid, Norman

2012-01-01

Mathematics is well known as a subject area where there can be problems in terms of understanding as well as retaining positive attitudes. In a large study involving 813 school students (ages approximately 10-12) drawn from two different school systems in Pakistan, the effect of limited working memory capacity on performance in mathematics was…

Promoting the Understanding of Mathematics in Physics at Secondary Level

ERIC Educational Resources Information Center

Thompson, Alaric

2016-01-01

This article explores some of the common mathematical difficulties that 11- to 16-year-old students experience with respect to their learning of physics. The definition of "understanding" expressed in the article is in the sense of transferability of mathematical skills from topic to topic within physics as well as between the separate…

The Mathematics of Global Change

ERIC Educational Resources Information Center

Kreith, Kurt

2011-01-01

This paper is a descriptive and preliminary report on recent efforts to address two questions: 1) Can school mathematics be used to enhance our students' ability to understand their changing world? and 2) What role might computer technology play in this regard? After recounting some of the mathematical tools that led to a better understanding of…

Exploring Positioning as an Analytical Tool for Understanding Becoming Mathematics Teachers' Identities

ERIC Educational Resources Information Center

Skog, Kicki; Andersson, Annica

2015-01-01

The aim of this article is to explore how a sociopolitical analysis can contribute to a deeper understanding of critical aspects for becoming primary mathematics teachers' identities during teacher education. The question we ask is the following: How may power relations in university settings affect becoming mathematics teachers' subject…

Mathematics Program for Grades K-12

ERIC Educational Resources Information Center

Montgomery County Public Schools, 2013

2013-01-01

In the 21st century, a deep understanding of mathematics, and the ability to apply that understanding, is more important than it has ever been. In Montgomery County (Maryland) Public Schools (MCPS), and across the country, mathematics instruction is changing to provide students with the skills and knowledge they need for success in college and the…

A Mixed Methods Analysis of Students' Understanding of Slope and Derivative Concepts and Students' Mathematical Dispositions

ERIC Educational Resources Information Center

Patel, Rita Manubhai

2013-01-01

This dissertation examined understanding of slope and derivative concepts and mathematical dispositions of first-semester college calculus students, who are recent high school graduates, transitioning to university mathematics. The present investigation extends existing research in the following ways. First, based on this investigation, the…

Discrepancies between Students' and Teachers' Perceptions of Homework

ERIC Educational Resources Information Center

Hong, Eunsook; Wan, Min; Peng, Yun

2011-01-01

For homework to help students improve school achievement and develop responsibility and autonomy in academic endeavors in and out of school, the development of teachers' understanding of students' views about homework and their homework behaviors is critical. Whether the subject of the homework is mathematics, reading, or a second language,…

6 Principles for Quantitative Reasoning and Modeling

ERIC Educational Resources Information Center

Weber, Eric; Ellis, Amy; Kulow, Torrey; Ozgur, Zekiye

2014-01-01

Encouraging students to reason with quantitative relationships can help them develop, understand, and explore mathematical models of real-world phenomena. Through two examples--modeling the motion of a speeding car and the growth of a Jactus plant--this article describes how teachers can use six practical tips to help students develop quantitative…

Understanding Proportional Reasoning for Teaching

ERIC Educational Resources Information Center

Kastberg, Signe E.; D'Ambrosio, Beatriz; Lynch-Davis, Kathleen

2012-01-01

Proportional reasoning is an important cornerstone in children's mathematical development. This sort of reasoning has been shown to develop across the early years of schooling (ages 8 to 10) through the middle years (ages 11-14). In the early years, children tend to use additive reasoning to generate solutions to problems, while later comparisons…

Students' Development and Use of Internal Representations When Solving Algebraic Tasks

ERIC Educational Resources Information Center

Cross, Laban J.

2013-01-01

The difficulty in observing, recording, and examining internal representations has been well documented (Goldin & Shteingold, 2001). However, the important role that these internal representations play in the learning and understanding of mathematical concepts has been noted (Yackel, 2000). This study sought to develop a framework for…

Prepare for More Realistic Test Results

ERIC Educational Resources Information Center

Larson, Matthew R.; Leinwand, Steven

2013-01-01

Educators in forty-five states and the District of Columbia are hard at work interpreting and implementing the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010). This work typically involves teacher participation in professional development activities focused on developing an understanding of the content standards as well as the…

The Mathematics of Child Street Vendors.

ERIC Educational Resources Information Center

Saxe, Geoffrey B.

1988-01-01

The influence of cultural practices on the cognitive development of largely unschooled children was investigated among 23 candy sellers and matched non-vendors between 10- and 12-years-old who resided in northeast Brazil. Findings are interpreted as supporting a model of cognitive development in which children construct novel understandings while…

Teacher Identity Work in Mathematics Teacher Education

ERIC Educational Resources Information Center

Neumayer-Depiper, Jill

2013-01-01

Becoming a teacher is not developing an identity, but is developing identity as a continuous process of constructing and deconstructing understandings within the complexities of social practice, beliefs, experiences, and social norms. I take up this stance on identity as articulated in Judith Butler's (1999) work with gender identity and…

Teachers, Tasks, and Tensions: Lessons from a Research-Practice Partnership

ERIC Educational Resources Information Center

Johnson, Raymond; Severance, Samuel; Penuel, William R.; Leary, Heather

2016-01-01

How teachers make sense of new academic standards significantly shapes the implementation of those standards. Professional development organized around the analysis of mathematical tasks has potential to prepare teachers for standards implementation by helping them develop common understandings of standards and how to help students meet ambitious…

Understanding Mathematic Concept in Relation and Function Method through Active Learning Type Group to Group Distributed LKS

NASA Astrophysics Data System (ADS)

Kudri, F.; Rahmi, R.; Haryono, Y.

2018-04-01

This research is motivated by the lack of understanding of mathematical concepts students and teachers have not familiarize students discussed in groups. This researchaims to determine whether an understanding of mathematical concepts junior class VIII SMPN 2 in Ranah Batahan Kabupaten Pasaman Barat by applying active learning strategy group to group types with LKS better than conventional learning. The type of research is experimental the design of randomized trials on the subject. The population in the study were all students VIII SMPN 2 Ranah Batahan Kabupaten Pasaman Barat in year 2012/2013 which consists of our class room experiment to determine the grade and control class with do nerandomly, so that classes VIII1 elected as a experiment class and class VIII4 as a control class. The instruments used in the test empirically understanding mathematical concepts are shaped by the essay with rt=0,82 greater than rt=0,468 means reliable tests used. The data analysis technique used is the test with the help of MINITAB. Based on the results of the data analisis known that both of the sample are normal and homogenity in real rate α = 0,05, so the hypothesis of this research is received. So, it can be concluded students’ understanding mathematical concept applied the active Group to Group learning strategy with LKS is better than the students’ understanding mathematical concept with Conventional Learning.

Yeast for Mathematicians: A Ferment of Discovery and Model Competition to Describe Data.

PubMed

Lewis, Matthew; Powell, James

2017-02-01

In addition to the memorization, algorithmic skills and vocabulary which are the default focus in many mathematics classrooms, professional mathematicians are expected to creatively apply known techniques, construct new mathematical approaches and communicate with and about mathematics. We propose that students can learn these professional, higher-level skills through Laboratory Experiences in Mathematical Biology which put students in the role of mathematics researcher creating mathematics to describe and understand biological data. Here we introduce a laboratory experience centered on yeast (Saccharomyces cerevisiae) growing in a small capped flask with a jar to collect carbon dioxide created during yeast growth and respiration. The lab requires no specialized equipment and can easily be run in the context of a college math class. Students collect data and develop mathematical models to explain the data. To help place instructors in the role of mentor/collaborator (as opposed to jury/judge), we facilitate the lab using model competition judged via Bayesian Information Criterion. This article includes details about the class activity conducted, student examples and pedagogical strategies for success.

Early numerical foundations of young children's mathematical development.

PubMed

Chu, Felicia W; vanMarle, Kristy; Geary, David C

2015-04-01

This study focused on the relative contributions of the acuity of the approximate number system (ANS) and knowledge of quantitative symbols to young children's early mathematical learning. At the beginning of preschool, 191 children (Mage=46 months) were administered tasks that assessed ANS acuity and explicit knowledge of the cardinal values represented by number words, and their mathematics achievement was assessed at the end of the school year. Children's executive functions, intelligence, and preliteracy skills and their parents' educational levels were also assessed and served as covariates. Both the ANS and cardinality tasks were significant predictors of end-of-year mathematics achievement with and without control of the covariates. As simultaneous predictors and with control of the covariates, cardinality remained significantly related to mathematics achievement, but ANS acuity did not. Mediation analyses revealed that the relation between ANS acuity and mathematics achievement was fully mediated by cardinality, suggesting that the ANS may facilitate children's explicit understanding of cardinal value and in this way may indirectly influence early mathematical learning. Copyright © 2015 Elsevier Inc. All rights reserved.

Enhancing Parent Involvement in NC-CCSS for K-2 Mathematics

NASA Astrophysics Data System (ADS)

Johnson, D.

2014-12-01

Key Terms:Parent Involvement, Common Core State Standards, Homework, K - 2 Mathematics In this study, the 2014 REU math team developed and provided a workshop that assisted parents in understanding the North Carolina Common Core State Standards for K-2 Mathematics to assist with student homework assignments. Parent involvement is defined as parent participating in the educational processes and experiences of their children. A chi-square analysis was used to analyze data collected from the pre survey and the post survey administered to participants in the workshop. The study revealed all of the individual components of parent involvement were positively and significantly related to educational goals. The study identified various aspects of parent involvement that yielded statistically significant results in affirming that parent involvement attributed to urban student achievement. These findings were particularly helpful for indicating which kinds of parent involvement influenced academic success. Most notably, parent expectations and styles demonstrated a strong relationship with scholastic outcomes. Parent expectations and styles created an educationally oriented ambience that established an understanding of the certain level of support the child needed to succeed academically. The REU mathematics team focused on three essential questions in this study: (1) What practices will increase parent awareness of K-2 NC-CCSS for mathematics at P. W. Moore Elementary School? (2) What methods can be used to strengthen parent skills in assisting with mathematics homework assignments at P. W. Moore Elementary School? (3) What actions can be taken to motivate parent involvement in the school improvement process focusing on mathematics at P. W. Moore Elementary School?

Bouncing Balls and Graphing Derivatives

ERIC Educational Resources Information Center

Cory, Beth

2010-01-01

National Council of Teachers of Mathematics' (NCTM's) (2000) Connections Standard states that students should "recognize and use connections among mathematical ideas; understand how mathematical ideas interconnect ...; [and] recognize and apply mathematics in contexts outside of mathematics" (p. 354). This article presents an in-depth…

Growth in Mathematical Understanding: How Can We Characterise It and How Can We Represent It?

ERIC Educational Resources Information Center

Pirie, Susan; Kieren, Thomas

1994-01-01

Proposes a model for the growth of mathematical understanding based on the consideration of understanding as a whole, dynamic, leveled but nonlinear process. Illustrates the model using the concept of fractions. How to map the growth of understanding is explained in detail. (Contains 26 references.) (MKR)

Watching Sandy's Understanding Grow.

ERIC Educational Resources Information Center

Pirie, Susan E. B.; Kieren, Thomas E.

1992-01-01

Reviews recent research in the area of mathematical understanding and compares and contrasts it with a model formulated for the growth of understanding. Uses the analysis of a transcript from an interview with an eight-year-old boy to illustrate the power of the model to describe and map the growth of his mathematical understanding. (18…

Undergraduate Students' Perceptions of the Mathematics Courses Included in the Primary School Teacher Education Program

ERIC Educational Resources Information Center

Serin, Mehmet Koray; Incikabi, Semahat

2017-01-01

Mathematics educators have reported on many issues regarding students' mathematical education, particularly students who received mathematics education at different departments such as engineering, science or primary school, including their difficulties with mathematical concepts, their understanding of and preferences for mathematical concepts.…

Forms of Understanding in Mathematical Problem Solving.

DTIC Science & Technology

1982-08-01

mathematical concepts, but more recent studies (e.g., Gelman & Gallistel , 1978) indicate that significant understanding of those concepts should be...Beranek, & Newman, 1980. Gelman, R., & Gallistel , C. R. The child’s understanding of number. Cambridge, Mass.: Harvard University Press, 1978. 43 Greeno

Students' perception and relationship between confidence and anxiety in teaching and learning mathematics: A case study in Sekolah Kebangsaan Bukit Kuda, Klang

NASA Astrophysics Data System (ADS)

Mohd Nordin, Noraimi Azlin; Md Tahir, Herniza; Kamis, Nor Hanimah; Khairul Azmi, Nurul Nisa'

2013-04-01

In general, Mathematics is one of the core subjects need to be learned by students regardless they are in primary and secondary schools. Different students might have different views and interests on Mathematics subjects. This is due to different level of thinking for each student. Students' acceptance and confidence level in learning Mathematics will depend on various factors among them. A program named "Mini Hari Matematik" was conducted in Sekolah Rendah Kebangsaan Bukit Kuda, Klang exclusively for 49 students of standard four, five and six to identify the students' perception and correlation between their confidence and anxiety in learning Mathematics. This program was intended to give exposure to the students on the importance of Mathematics in life and hence, develop their interest in learning Mathematics. We measure the students' perception on teaching and learning Mathematics using statistical approach based on SPSS. The analysis includes mean, variance, observations, correlation and so on. Based on the results obtained, it is found that there is a positive correlation between students' confidence and anxiety in learning Mathematics in their daily life. In addition, students are more attracted to Mathematics if this subject is blended with game elements in their teaching and learning process. As a conclusion, we can see that there are three basic foundations need to be developed in each of the students about Mathematics which are firstly, their early understanding on the subject itself, ability to communicate regarding this subject and how they apply this subject in decision making and problem solving. This program gives high benefit to the students in preparing them towards the science and technology era.

Factors Considered by Elementary Teachers When Developing and Modifying Mathematical Tasks to Support Children's Mathematical Thinking

NASA Astrophysics Data System (ADS)

Fredenberg, Michael Duane

The idea that problems and tasks play a pivotal role in a mathematics lesson has a long standing in mathematics education research. Recent calls for teaching reform appeal for training teachers to better understand how students learn mathematics and to employ students' mathematical thinking as the basis for pedagogy (CCSSM, 2010; NCTM, 2000; NRC 1999). The teaching practices of (a) developing a task for a mathematics lesson and, (b) modifying the task for students while enacting the lesson fit within the scope of supporting students' mathematical thinking. Surprisingly, an extensive search of the literature did not yield any research aimed to identify and refine the constituent parts of the aforementioned teaching practices in the manner called for by Grossman and xiii colleagues (2009). Consequently, my research addresses the two questions: (a) what factors do exemplary elementary teachers consider when developing a task for a mathematics lesson? (b) what factors do they consider when they modify a task for a student when enacting a lesson? I conducted a multiple case study involving three elementary teachers, each with extensive training in the area of Cognitively Guided Instruction (CGI), as well as several years experience teaching mathematics following the principles of CGI (Carpenter et al., 1999). I recorded video of three mathematics lessons with each participant and after each lesson I conducted a semi-structured stimulated recall interview. A subsequent follow-up clinical interview was conducted soon thereafter to further explore the teacher's thoughts (Ginsberg, 1997). In addition, my methodology included interjecting myself at select times during a lesson to ask the teacher to explain her reasoning. Qualitative analysis led to a framework that identified four categories of influencing factors and seven categories of supporting objectives for the development of a task. Subsets of these factors and objectives emerged as particularly relevant when the teachers decided to modify a task. Moreover, relationships between and among the various factors were identified. The emergent framework from this study offers insight into decompositions of the two teaching practices of interest, and, in particular, the utility of the number choices made by the teachers.

Development of Energy Concepts in Introductory Physics Courses.

ERIC Educational Resources Information Center

Arons, Arnold B.

1999-01-01

Believes that a student's understanding of energy concepts can be enhanced by introducing and using the concept of internal energy by articulating the first law of thermodynamics in a simple, phenomenological form without mathematical encumbrances. (Author/CCM)

Building Your Own Regression Model

ERIC Educational Resources Information Center

Horton, Robert, M.; Phillips, Vicki; Kenelly, John

2004-01-01

Spreadsheets to explore regression with an algebra 2 class in a medium-sized rural high school are presented. The use of spreadsheets can help students develop sophisticated understanding of mathematical models and use them to describe real-world phenomena.

Mathematical and Numerical Techniques in Energy and Environmental Modeling

NASA Astrophysics Data System (ADS)

Chen, Z.; Ewing, R. E.

Mathematical models have been widely used to predict, understand, and optimize many complex physical processes, from semiconductor or pharmaceutical design to large-scale applications such as global weather models to astrophysics. In particular, simulation of environmental effects of air pollution is extensive. Here we address the need for using similar models to understand the fate and transport of groundwater contaminants and to design in situ remediation strategies. Three basic problem areas need to be addressed in the modeling and simulation of the flow of groundwater contamination. First, one obtains an effective model to describe the complex fluid/fluid and fluid/rock interactions that control the transport of contaminants in groundwater. This includes the problem of obtaining accurate reservoir descriptions at various length scales and modeling the effects of this heterogeneity in the reservoir simulators. Next, one develops accurate discretization techniques that retain the important physical properties of the continuous models. Finally, one develops efficient numerical solution algorithms that utilize the potential of the emerging computing architectures. We will discuss recent advances and describe the contribution of each of the papers in this book in these three areas. Keywords: reservoir simulation, mathematical models, partial differential equations, numerical algorithms

[For the Introduction of a Conceptual Perspective in Mathematics: Dedekind, Noether, van der Waerden].

PubMed

Koreuber, Mechthild

2015-09-01

,,She [Noether] then appeared as the creator of a new direction in algebra and became the leader, the most consistent and brilliant representative, of a particular mathematical doctrine - of all that is characterized by the term ‚Begriffliche Mathematik‘.“ The aim of this paper is to illuminate this "new direction", which can be characterized as a conceptual [begriffliche] perspective in mathematics, and to comprehend its roots and trace its establishment. Field, ring, ideal, the core concepts of this new direction in mathematical images of knowledge, were conceptualized by Richard Dedekind (1831-1916) within the scope of his number theory research and associated with an understanding of a formation of concepts as a "free creation of the human spirit". They thus stand for an abstract perspective of mathematics in their entirety, described as 'modern algebra' in the 1920s and 1930s, leading to an understanding of mathematics as structural sciences. The establishment of this approach to mathematics, which is based on "general mathematical concepts" [allgemein-mathematische Begriffe], was the success of a cultural movement whose most important protagonists included Emmy Noether (1882-1935) and her pupil Bartel L. van der Waerden (1903-1996). With the use of the term 'conceptual', a perspective is taken in the analysis which allows for developing connections between the thinking of Dedekind, the "working and conceptual methods" [Arbeits- und Auffassungsmethoden] of Noether as well as the methodological approach, represented through the thought space of the Noether School as presented under the term "conceptual world" [Begriffswelt] in the Moderne Algebra of van der Waerden. This essay thus makes a contribution to the history of the introduction of a structural perspective in mathematics, a perspective that is inseparable from the mathematical impact of Noether, her reception of the work of Dedekind and the creative strength of the Noether School.

History of Mathematics: Illuminating Understanding of School Mathematics Concepts for Prospective Mathematics Teachers

ERIC Educational Resources Information Center

Clark, Kathleen Michelle

2012-01-01

The use of the history of mathematics in teaching has long been considered a tool for enriching students' mathematical learning. However, in the USA few, if any, research efforts have investigated how the study of history of mathematics contributes to a person's mathematical knowledge for teaching. In this article, I present the results of…

The Development of Embodied Representations of Numerical Understanding through Gameplay

ERIC Educational Resources Information Center

Clark, Colin Travis

2012-01-01

Young children must develop basic concepts of numeracy--one being that numbers have magnitudes that increase linearly--before they are able to succeed in mathematics. Children from low-income families have been found to be at a greater disadvantage in the development of numeracy, but this disadvantage can be overcome through the use of a simple…

Creating Equitable Classroom Climates: An Investigation of Classroom Strategies in Mathematics and Science Instruction for Developing Preservice Teachers' Use of Democratic Social Values.

ERIC Educational Resources Information Center

Kelly, Catherine A.

2002-01-01

Determined best practices for enhancing preservice teachers' knowledge of gender equity and use of innovative instructional methods for developing classroom democratic social values. Found that development in understanding and application of appropriate, equitable classroom practices emerged over a semester in which preservice teachers were…

Using Cooperative Teams-Game-Tournament in 11 Religious School to Improve Mathematics Understanding and Communication

ERIC Educational Resources Information Center

Veloo, Arsaythamby; Md-Ali, Ruzlan; Chairany, Sitie

2016-01-01

Purpose: This paper was part of a larger study which looked into the effect of implementing Cooperative Teams-Games-Tournament (TGT) on understanding of and communication in mathematics. The study had identified the main and interaction effect of using Cooperative TGT for learning mathematics in religious secondary school classrooms. A…

Modeling Scientific Processes with Mathematics Equations Enhances Student Qualitative Conceptual Understanding and Quantitative Problem Solving

ERIC Educational Resources Information Center

Schuchardt, Anita M.; Schunn, Christian D.

2016-01-01

Amid calls for integrating science, technology, engineering, and mathematics (iSTEM) in K-12 education, there is a pressing need to uncover productive methods of integration. Prior research has shown that increasing contextual linkages between science and mathematics is associated with student problem solving and conceptual understanding. However,…

Teaching with Procedural Variation: A Chinese Way of Promoting Deep Understanding of Mathematics

ERIC Educational Resources Information Center

Lai, Mun Yee; Murray, Sara

2012-01-01

In mathematics education, there has been tension between deep learning and repetitive learning. Western educators often emphasize the need for students to construct a conceptual understanding of mathematical symbols and rules before they practise the rules (Li, 2006). On the other hand, Chinese learners tend to be oriented towards rote learning…

Mathematical Self-Efficacy and Understanding: Using Geographic Information Systems to Mediate Urban High School Students' Real-World Problem Solving

ERIC Educational Resources Information Center

DeBay, Dennis J.

2013-01-01

To explore student mathematical self-efficacy and understanding of graphical data, this dissertation examines students solving real-world problems in their neighborhood, mediated by professional urban planning technologies. As states and schools are working on the alignment of the Common Core State Standards for Mathematics (CCSSM), traditional…

Using Science to Promote Preservice Teacher Understanding of Problem Solving in Mathematics

ERIC Educational Resources Information Center

Tobias, Jennifer M.; Ortiz, Enrique

2007-01-01

Preservice elementary teachers need to be given the experiences of integrating mathematics with other subjects. They need to go into the classroom with the understanding that mathematics is not an isolated topic. This article describes a paper airplane activity that was presented in a class of preservice elementary education teachers to show how…

Developing Conceptual Understanding and Procedural Fluency for Junior High School Students through Model-Facilitated Learning (MFL)

ERIC Educational Resources Information Center

Laswadi; Kusumah, Yaya S.; Darwis, Sutawanir; Afgani, Jarnawi D.

2016-01-01

Conceptual understanding (CU) and procedural fluency (PF) are two important mathematical competencies required by students. CU helps students organizing their knowledge into a coherent whole, and PF helps them to find the right solution of a problem. In order to enhance CU and PF, students need learning experiences in constructing knowledge and…

A Sun-Earth-Moon Activity to Develop Student Understanding of Lunar Phases and Frames of Reference

ERIC Educational Resources Information Center

Ashmann, Scott

2012-01-01

The Moon is an ever-present subject of observation, and it is a recurring topic in the science curriculum from kindergarten's basic observations through graduate courses' mathematical analyses of its orbit. How do students come to comprehend Earth's nearest neighbor? What is needed for them to understand the lunar phases and other phenomena and…