Social Sciences › Education

Mathematics Education and Teaching Techniques

Works Count: 70953

Wikipedia

Description

This cluster of papers explores the concept of Pedagogical Content Knowledge (PCK) in the context of education research, focusing on the knowledge and skills required by teachers to effectively teach specific content areas. The cluster delves into topics such as technological pedagogical content knowledge, teacher professional development, mathematics instruction, classroom discourse, and lesson study.

Keywords

Pedagogical Content Knowledge; Teacher Knowledge; Technological Pedagogical Content Knowledge; Mathematics Instruction; Teacher Professional Development; Educational Technology; Classroom Discourse; Teacher Learning; Lesson Study; Mathematics Education

Knowing and teaching elementary mathematics: teachers' understanding of fundamental mathematics in China and the United States

1999-12-01

Liping Ma

Author's Preface to the Anniversary Edition Series Editor's Introduction to the Anniversary Edition A Note about the Anniversary Edition Foreword Acknowledgments Introduction 1. Subtraction With Regrouping: Approaches To Teaching A … Author's Preface to the Anniversary Edition Series Editor's Introduction to the Anniversary Edition A Note about the Anniversary Edition Foreword Acknowledgments Introduction 1. Subtraction With Regrouping: Approaches To Teaching A Topic 2. Multidigit Number Multiplication: Dealing With Students' Mistakes 3. Generating Representations: Division By Fractions 4. Exploring New Knowledge: The Relationship Between Perimeter And Area 5. Teachers' Subject Matter Knowledge: Profound Understanding Of Fundamental Mathematics 6. Profound Understanding Of Fundamental Mathematics: When And How Is It Attained 7. Conclusion Appendix References New to the Anniversary Edition: Journal Article #1 New to the Anniversary Edition: Journal Article #2 Author Index Subject Index

Mathematica: A system for doing mathematics by computer?

2005-11-23

Bruno Buchberger

Unpacking Pedagogical Content Knowledge: Conceptualizing and Measuring Teachers' Topic-Specific Knowledge of Students

2008-07-01

Heather C. Hill , Deborah Loewenberg Ball , S. Schilling

There is widespread agreement that effective teachers have unique knowledge of students' mathematical ideas and thinking. However, few scholars have focused on conceptualizing this domain, and even fewer have focused … There is widespread agreement that effective teachers have unique knowledge of students' mathematical ideas and thinking. However, few scholars have focused on conceptualizing this domain, and even fewer have focused on measuring this knowledge. In this article, we describe an effort to conceptualize and develop measures of teachers' combined knowledge of content and students by writing, piloting, and analyzing results from multiple-choice items. Our results suggest partial success in measuring this domain among practicing teachers but also identify key areas around which the field must achieve conceptual and empirical clarity. Although this is ongoing work, we believe that the lessons learned from our efforts shed light on teachers' knowledge in this domain and can inform future attempts to develop measures.

Mathematics as an Educational Task

1972-01-01

Hans Freudenthal

Handbook of research on mathematics teaching and learning

1992-12-01

Douglas A. Grouws

Didactical Phenomenology of Mathematical Structures

2002-01-01

Hans Freudenthal

Effects of Video Club Participation on Teachers' Professional Vision

2008-11-26

Miriam Gamoran Sherin , Elizabeth A. van Es

This study investigates mathematics teacher learning in a video-based professional development environment called video clubs. In particular, the authors explore whether teachers develop professional vision, the ability to notice and … This study investigates mathematics teacher learning in a video-based professional development environment called video clubs. In particular, the authors explore whether teachers develop professional vision, the ability to notice and interpret significant features of classroom interactions, as they participate in a video club. Analysis for the study is based on data from two year-long video clubs in which teachers met monthly to watch and discuss video excerpts from each others' classrooms. Participating in a video club was found to influence the teachers' professional vision as exhibited in the video club meetings, in interviews outside of the video club meetings, and in the teachers' instructional practices. These results suggest that professional vision is a productive lens for investigating teacher learning via video. In addition, this article illustrates that video clubs have the potential to support teacher learning in ways that extend beyond the boundaries of the video club meetings themselves.

When the Problem Is Not the Question and the Solution Is Not the Answer: Mathematical Knowing and Teaching

1990-03-01

Magdalene Lampert

This paper describes a research and development project in teaching designed to examine whether and how it might be possible to bring the practice of knowing mathematics in school closer … This paper describes a research and development project in teaching designed to examine whether and how it might be possible to bring the practice of knowing mathematics in school closer too what it means to know mathematics within the discipline by deliberately altering the roles and responsibilities of teacher and students in classroom discourse. The project was carried out as a regular feature of lessons in fifth-grade mathematics in a public school. A case of teaching and learning about exponents derived from lessons taught in the project is described and interpreted from mathematical, pedagogical, and sociolinguistic perspectives. To change the meaning of knowing and learning in school, the teacher initiated and supported social interactions appropriate to making mathematical arguments in response to students’ conjectures. The activities students engaged in as they asserted and examined hypotheses about the mathematical structures that underlie their solutions to problems are contrasted with the conventional activities that characterize school mathematics.

Concept image and concept definition in mathematics with particular reference to limits and continuity

1981-05-01

David Tall , Shlomo Vinner

View PDF Chat

Chapter 6 : Teacher Learning and the Acquisition of Professional Knowledge: An Examination of Research on Contemporary Professlonal Development

1999-01-01

Suzanne M. Wilson , Jennifer Berne

Orchestrating Productive Mathematical Discussions: Five Practices for Helping Teachers Move Beyond Show and Tell

2008-10-21

Mary Kay Stein , Randi A. Engle , Margaret S. Smith +1 more

Teachers who attempt to use inquiry-based, student-centered instructional tasks face challenges that go beyond identifying well-designed tasks and setting them up appropriately in the classroom. Because solution paths are usually … Teachers who attempt to use inquiry-based, student-centered instructional tasks face challenges that go beyond identifying well-designed tasks and setting them up appropriately in the classroom. Because solution paths are usually not specified for these kinds of tasks, students tend to approach them in unique and sometimes unanticipated ways. Teachers must not only strive to understand how students are making sense of the task but also begin to align students' disparate ideas and approaches with canonical understandings about the nature of mathematics. Research suggests that this is difficult for most teachers (Ball, 1993 Ball, D. L. 1993. With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. Elementary School Journal, 94(4): 373–397. [Google Scholar], 2001 Ball, D. L. 2001. "Teaching, with respect to mathematics and students". In Beyond classical pedagogy: Teaching elementary school mathematics, Edited by: Wood, T., Nelson, B. S. and Warfield, J. 11–22. Mahwah, NJ: Erlbaum. [Google Scholar]; Leinhardt & Steele, 2005 Leinhardt, G. and Steele, M. D. 2005. Seeing the complexity of standing to the side: Instructional dialogues. Cognition and Instruction, 23(1): 87–163. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]; Schoenfeld, 1998 Schoenfeld, A. S. 1998. Toward a theory of teaching-in-context. Issues in Education, 4(1): 1–95. [Crossref] , [Google Scholar]; Sherin, 2002 Sherin, M. G. 2002. When teaching becomes learning. Cognition and Instruction, 20(2): 119–150. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). In this article, we present a pedagogical model that specifies five key practices teachers can learn to use student responses to such tasks more effectively in discussions: anticipating, monitoring, selecting, sequencing, and making connections between student responses. We first define each practice, showing how a typical discussion based on a cognitively challenging task could be improved through their use. We then explain how the five practices embody current theory about how to support students' productive disciplinary engagement. Finally, we close by discussing how these practices can make discussion-based pedagogy manageable for more teachers.

Using Knowledge of Children’s Mathematics Thinking in Classroom Teaching: An Experimental Study

1989-01-01

Thomas P. Carpenter , Élizabeth Fennema , Penelope L. Peterson +2 more

This study investigated teachers’ use of knowledge from research on children’s mathematical thinking and how their students’ achievement is influenced as a result. Twenty first grade teachers, assigned randomly to … This study investigated teachers’ use of knowledge from research on children’s mathematical thinking and how their students’ achievement is influenced as a result. Twenty first grade teachers, assigned randomly to an experimental treatment, participated in a month-long workshop in which they studied a research-based analysis of children’s development of problem-solving skills in addition and subtraction. Other first grade teachers (n = 20) were assigned randomly to a control group. Although instructional practices were not prescribed, experimental teachers taught problem solving significantly more and number facts significantly less than did control teachers. Experimental teachers encouraged students to use a variety of problem-solving strategies, and they listened to processes their students used significantly more than did control teachers. Experimental teachers knew more about individual students’ problem-solving processes, and they believed that instruction should build on students’ existing knowledge more than did control teachers. Students in experimental classes exceeded students in control classes in number fact knowledge, problem solving, reported understanding, and reported confidence in their problem-solving abilities.

Mathematics teachers’ “learning to notice” in the context of a video club

2007-01-04

Elizabeth A. van Es , Miriam Gamoran Sherin

Teachers' communication of differential expectations for children's classroom performance: Some behavioral data.

1970-10-01

Jere Brophy , Thomas L. Good

Inquiry as stance: practitioner research for the next generation

2010-12-01

Nicole Mockler

"Inquiry as stance: practitioner research for the next generation." Educational Action Research, 18(4), pp. 571–572 "Inquiry as stance: practitioner research for the next generation." Educational Action Research, 18(4), pp. 571–572

The Mathematical Understandings That Prospective Teachers Bring to Teacher Education

1990-03-01

Deborah Loewenberg Ball

This article focuses on the subject matter knowledge of preservice elementary and secondary mathematics teachers. In order to examine what teacher candidates understand about mathematics as they enter formal teacher … This article focuses on the subject matter knowledge of preservice elementary and secondary mathematics teachers. In order to examine what teacher candidates understand about mathematics as they enter formal teacher education, results from questionnaires and interviews with 252 prospective teachers participating in a large study of teacher education are discussed. The results reveal the mathematical understandings that these elementary and secondary teacher candidates brought with them to teacher education from their precollege and college mathematics experiences, understandings that tended to be rule-bound and thin. Based on these data, the article challenges 3 common assumptions about learning to teach elementary or secondary mathematics: (1) that traditional school mathematics content is not difficult, (2) that precollege education provides teachers with much of what they need to know about mathematics, and (3) that majoring in mathematics ensures subject matter knowledge. These assumptions underlie current teacher education practices as well as proposals to reform the preparation of teachers.

Sociomathematical Norms, Argumentation, and Autonomy in Mathematics

1996-07-01

Erna Yackel , Paul Cobb

This paper sets forth a way of interpreting mathematics classrooms that aims to account for how students develop mathematical beliefs and values and, consequently, how they become intellectually autonomous in … This paper sets forth a way of interpreting mathematics classrooms that aims to account for how students develop mathematical beliefs and values and, consequently, how they become intellectually autonomous in mathematics. To do so, we advance the notion of sociomathematical norms, that is, normative aspects of mathematical discussions that are specific to students' mathematical activity. The explication of sociomathematical norms extends our previous work on general classroom social norms that sustain inquiry-based discussion and argumentation. Episodes from a second-grade classroom where mathematics instruction generally followed an inquiry tradition are used to clarify the processes by which sociomathematical norms are interactively constituted and to illustrate how these norms regulate mathematical argumentation and influence learning opportunities for both the students and the teacher. In doing so, we both clarify how students develop a mathematical disposition and account for students' development of increasing intellectual autonomy in mathematics. In the process, the teacher's role as a representative of the mathematical community is elaborated.

The relationship of teachers' conceptions of mathematics and mathematics teaching to instructional practice

1984-05-01

Alba G. Thompson

Telling Identities: In Search of an Analytic Tool for Investigating Learning as a Culturally Shaped Activity

2005-05-01

Anna Sfard , Anna Prusak

In this article, the authors make an attempt to operationalize the notion of identity to justify the claim about its potential as an analytic tool for investigating learning. They define … In this article, the authors make an attempt to operationalize the notion of identity to justify the claim about its potential as an analytic tool for investigating learning. They define identity as a set of reifying, significant, endorsable stories about a person. These stories, even if individually told, are products of a collective storytelling. The authors’ main claim is that learning may be thought of as closing the gap between actual identity and designated identity, two sets of reifying significant stories about the learner that are also endorsed by the learner. Empirical illustration comes from a study in which the mathematical learning practices of a group of 17-year-old immigrant students from the former Soviet Union, newly arrived in Israel, were compared with those of native Israelis.

Philosophy of Mathematics Education

2024-06-01

Bronisław Czarnocha , María Aparecida Viggiani Bicudo , Paul Ernest

This survey provides a brief and selective overview of research in the philosophy of mathematics education. It asks what makes up the philosophy of mathematics education, what it means, what … This survey provides a brief and selective overview of research in the philosophy of mathematics education. It asks what makes up the philosophy of mathematics education, what it means, what questions it asks and answers, and what is its overall importance and use? It provides overviews of critical mathematics education, and the most relevant modern movements in the philosophy of mathematics. A case study is provided of an emerging research tradition in one country. This is the Hermeneutic strand of research in the philosophy of mathematics education in Brazil. This illustrates one orientation towards research inquiry in the philosophy of mathematics education. It is part of a broader practice of ‘philosophical archaeology’: the uncovering of hidden assumptions and buried ideologies within the concepts and methods of research and practice in mathematics education. An extensive bibliography is also included.

View PDF Chat

Video as a tool for fostering productive discussions in mathematics professional development

2007-01-17

Hilda Borko , Jennifer Jacobs , Eric Eiteljorg +1 more

A Course in Homological Algebra

1971-01-01

P. J. Hilton , U. Stammbach

View PDF Chat

Reconstructing Mathematics Pedagogy from a Constructivist Perspective

1995-03-01

Martin A. Simon

Constructivist theory has been prominent in recent research on mathematics learning and has provided a basis for recent mathematics education reform efforts. Although constructivism has the potential to inform changes … Constructivist theory has been prominent in recent research on mathematics learning and has provided a basis for recent mathematics education reform efforts. Although constructivism has the potential to inform changes in mathematics teaching, it offers no particular vision of how mathematics should be taught; models of teaching based on constructivism are needed. Data are presented from a whole-class, constructivist teaching experiment in which problems of teaching practice required the teacher/researcher to explore the pedagogical implications of his theoretical (constructivist) perspectives. The analysis of the data led to the development of a model of teacher decision making with respect to mathematical tasks. Central to this model is the creative tension between the teacher's goals with regard to student learning and his responsibility to be sensitive and responsive to the mathematical thinking of the students.

What Do New Views of Knowledge and Thinking Have to Say About Research on Teacher Learning?

2000-01-01

Ralph T. Putnam , Hilda Borko

Content Knowledge for Teaching

2008-11-01

Deborah Loewenberg Ball , Mark Hoover , Geoffrey Phelps

This article reports the authors' efforts to develop a practice-based theory of content knowledge for teaching built on Shulman's (1986) notion of pedagogical content knowledge. As the concept of pedagogical … This article reports the authors' efforts to develop a practice-based theory of content knowledge for teaching built on Shulman's (1986) notion of pedagogical content knowledge. As the concept of pedagogical content knowledge caught on, it was in need of theoretical development, analytic clarification, and empirical testing. The purpose of the study was to investigate the nature of professionally oriented subject matter knowledge in mathematics by studying actual mathematics teaching and identifying mathematical knowledge for teaching based on analyses of the mathematical problems that arise in teaching. In conjunction, measures of mathematical knowledge for teaching were developed. These lines of research indicate at least two empirically discernable subdomains within pedagogical content knowledge ( knowledge of content and students and knowledge of content and teaching) and an important subdomain of “pure” content knowledge unique to the work of teaching, specialized content knowledge , which is distinct from the common content knowledge needed by teachers and nonteachers alike. The article concludes with a discussion of the next steps needed to develop a useful theory of content knowledge for teaching.

Mathematical Knowledge for Teaching and the Mathematical Quality of Instruction: An Exploratory Study

2008-09-26

Heather C. Hill , Merrie Blunk , Charalambos Y. Charalambous +4 more

This study illuminates claims that teachers' mathematical knowledge plays an important role in their teaching of this subject matter. In particular, we focus on teachers' mathematical knowledge for teaching (MKT), … This study illuminates claims that teachers' mathematical knowledge plays an important role in their teaching of this subject matter. In particular, we focus on teachers' mathematical knowledge for teaching (MKT), which includes both the mathematical knowledge that is common to individuals working in diverse professions and the mathematical knowledge that is specialized to teaching. We use a series of five case studies and associated quantitative data to detail how MKT is associated with the mathematical quality of instruction. Although there is a significant, strong, and positive association between levels of MKT and the mathematical quality of instruction, we also find that there are a number of important factors that mediate this relationship, either supporting or hindering teachers' use of knowledge in practice.

Building Student Capacity for Mathematical Thinking and Reasoning: An Analysis of Mathematical Tasks Used in Reform Classrooms

1996-06-01

Mary Kay Stein , Barbara W. Grover , Marjorie Henningsen

This article focuses on mathematical tasks as important vehicles for building student capacity for mathematical thinking and reasoning. A stratified random sample of 144 mathematical tasks used during reform-oriented instruction … This article focuses on mathematical tasks as important vehicles for building student capacity for mathematical thinking and reasoning. A stratified random sample of 144 mathematical tasks used during reform-oriented instruction was analyzed in terms of (a) task features (number of solution strategies, number and kind of representations, and communication requirements) and (b) cognitive demands (e.g., memorization, the use of procedures with [and without] connections to concepts, the “doing of mathematics”). The findings suggest that teachers were selecting and setting up the kinds of tasks that reformers argue should lead to the development of students’ thinking capacities. During task implementation, the task features tended to remain consistent with how they were set up, but the cognitive demands of high-level tasks had a tendency to decline. The ways in which high-level tasks declined as well as factors associated with task changes from the set-up to implementation phase were explored.

View PDF Chat

Teachers’ Mathematical Knowledge, Cognitive Activation in the Classroom, and Student Progress

2009-10-20

Jürgen Baumert , Mareike Kunter , Werner Blum +7 more

In both the United States and Europe, concerns have been raised about whether preservice and in-service training succeeds in equipping teachers with the professional knowledge they need to deliver consistently … In both the United States and Europe, concerns have been raised about whether preservice and in-service training succeeds in equipping teachers with the professional knowledge they need to deliver consistently high-quality instruction. This article investigates the significance of teachers’ content knowledge and pedagogical content knowledge for high-quality instruction and student progress in secondary-level mathematics. It reports findings from a 1-year study conducted in Germany with a representative sample of Grade 10 classes and their mathematics teachers. Teachers’ pedagogical content knowledge was theoretically and empirically distinguishable from their content knowledge. Multilevel structural equation models revealed a substantial positive effect of pedagogical content knowledge on students’ learning gains that was mediated by the provision of cognitive activation and individual learning support.

View PDF Chat

Where Is the Mind? Constructivist and Sociocultural Perspectives on Mathematical Development

1994-10-01

Paul Cobb

Currently, considerable debate focuses on whether mind is located in the head or in the individual-in-social-action, and whether development is cognitive self-organization or enculturation into established practices. In this article, … Currently, considerable debate focuses on whether mind is located in the head or in the individual-in-social-action, and whether development is cognitive self-organization or enculturation into established practices. In this article, I question assumptions that initiate this apparent forced choice between constructivist and sociocultural perspectives. I contend that the two perspectives are complementary. Also, claims that either perspective captures the essence of people and communities should be rejected for pragmatic justifications that consider the contextual relevance and usefulness of a perspective. I argue that the sociocultural perspective informs theories of the conditions far the possibility of learning, whereas theories developed from the constructivist perspective focus on what students learn and the processes by which they do so.

Examining Key Concepts in Research on Teachers’ Use of Mathematics Curricula

2005-06-01

Janine Remillard

Studies of teachers’ use of mathematics curriculum materials are particularly timely given the current availability of reform-inspired curriculum materials and the increasingly widespread practice of mandating the use of a … Studies of teachers’ use of mathematics curriculum materials are particularly timely given the current availability of reform-inspired curriculum materials and the increasingly widespread practice of mandating the use of a single curriculum to regulate mathematics teaching. A review of the research on mathematics curriculum use over the last 25 years reveals significant variation in findings and in theoretical foundations. The aim of this review is to examine the ways that central constructs of this body of research—such as curriculum use, teaching, and curriculum materials—are conceptualized and to consider the impact of various conceptualizations on knowledge in the field. Drawing on the literature, the author offers a framework for characterizing and studying teachers’ interactions with curriculum materials.

Developing Measures of Teachers’ Mathematics Knowledge for Teaching

2004-09-01

Heather C. Hill , Stephen Schilling , Deborah Loewenberg Ball

In this article we discuss efforts to design and empirically test measures of teachers’ content knowledge for teaching elementary mathematics. We begin by reviewing the literature on teacher knowledge, noting … In this article we discuss efforts to design and empirically test measures of teachers’ content knowledge for teaching elementary mathematics. We begin by reviewing the literature on teacher knowledge, noting how scholars have organized such knowledge. Next we describe survey items we wrote to represent knowledge for teaching mathematics and results from factor analysis and scaling work with these items. We found that teachers’ knowledge for teaching elementary mathematics was multidimensional and included knowledge of various mathematical topics (e.g., number and operations, algebra) and domains (e.g., knowledge of content, knowledge of students and content). The constructs indicated by factor analysis formed psychometrically acceptable scales.

View PDF Chat

Situated Cognition and the Culture of Learning

1989-01-01

John Seely Brown , Allan Collins , Paul Duguid

Many teaching practices implicitly assume that conceptual knowledge can be abstracted from the situations in which it is learned and used. This article argues that this assumption inevitably limits the … Many teaching practices implicitly assume that conceptual knowledge can be abstracted from the situations in which it is learned and used. This article argues that this assumption inevitably limits the effectiveness of such practices. Drawing on recent research into cognition as it is manifest in everyday activity, the authors argue that knowledge is situated, being in part a product of the activity, context, and culture in which it is developed and used. They discuss how this view of knowledge affects our understanding of learning, and they note that conventional schooling too often ignores the influence of school culture on what is learned in school. As an alternative to conventional practices, they propose cognitive apprenticeship (Collins, Brown, & Newman, in press), which honors the situated nature of knowledge. They examine two examples of mathematics instruction that exhibit certain key features of this approach to teaching.

View PDF Chat

Functions, Graphs, and Graphing: Tasks, Learning, and Teaching

1990-03-01

Gaea Leinhardt , Orit Zaslavsky , Mary Kay Stein

This review of the introductory instructional substance of functions and graphs analyzes research on the interpretation and construction tasks associated with functions and some of their representations: algebraic, tabular, and … This review of the introductory instructional substance of functions and graphs analyzes research on the interpretation and construction tasks associated with functions and some of their representations: algebraic, tabular, and graphical. The review also analyzes the nature of learning in terms of intuitions and misconceptions, and the plausible approaches to teaching through sequences, explanations, and examples. The topic is significant because of (a) the increased recognition of the organizing power of the concept of functions from middle school mathematics through more advanced topics in high school and college, and (b) the symbolic connections that represent potentials for increased understanding between graphical and algebraic worlds. This is a review of a specific part of the mathematics subject mailer and how it is learned and may be taught; this specificity reflects the issues raised by recent theoretical research concerning how specific context and content contribute to learning and meaning.

Professional Noticing of Children's Mathematical Thinking

2010-03-01

Victoria R. Jacobs , Lisa Lamb , Randolph A. Philipp

The construct professional noticing of children's mathematical thinking is introduced as a way to begin to unpack the in-the-moment decision making that is foundational to the complex view of teaching … The construct professional noticing of children's mathematical thinking is introduced as a way to begin to unpack the in-the-moment decision making that is foundational to the complex view of teaching endorsed in national reform documents. We define this expertise as a set of interrelated skills including (a) attending to children's strategies, (b) interpreting children's understandings, and (c) deciding how to respond on the basis of children's understandings. This construct was assessed in a cross-sectional study of 131 prospective and practicing teachers, differing in the amount of experience they had with children's mathematical thinking. The findings help to characterize what this expertise entails; provide snapshots of those with varied levels of expertise; and document that, given time, this expertise can be learned.

What is Technological Pedagogical Content Knowledge (TPACK)?

2013-10-01

Matthew J. Koehler , Punya Mishra , William Cain

This paper describes a teacher knowledge framework for technology integration called technological pedagogical content knowledge (originally TPCK, now known as TPACK, or technology, pedagogy, and content knowledge). This framework builds … This paper describes a teacher knowledge framework for technology integration called technological pedagogical content knowledge (originally TPCK, now known as TPACK, or technology, pedagogy, and content knowledge). This framework builds on Lee Shulman's (1986, 1987) construct of pedagogical content knowledge (PCK) to include technology knowledge. The development of TPACK by teachers is critical to effective teaching with technology. The paper begins with a brief introduction to the complex, ill-structured nature of teaching. The nature of technologies (both analog and digital) is considered, as well as how the inclusion of technology in pedagogy further complicates teaching. The TPACK framework for teacher knowledge is described in detail as a complex interaction among three bodies of knowledge: content, pedagogy, and technology. The interaction of these bodies of knowledge, both theoretically and in practice, produces the types of flexible knowledge needed to successfully integrate technology use into teaching.

View PDF Chat

ANNALS OF MATHEMATICS STUDIES

1961-12-31

Raymond M. Smullyan

The Handbook of Mathematical Cognition

2005-08-15

Jamie I. D. Campbell

Knowing and Teaching Elementary Mathematics

1999-06-12

Liping Ma

Sociomathematical Norms, Argumentation, and Autonomy in Mathematics

1996-07-01

Erna Yackel , Paul Cobb

II encuentros de Educación Matemática. A continuación se mencionan II encuentros de Educación Matemática. A continuación se mencionan

International Handbook of Mathematics Education

1997-01-01

Alan J. Bishop , Ken Clements , Christine Keitel +2 more

Instaurer un débat mathématique en classe de primaire : récit d’une expérimentation autour des transformations géométriques

2025-06-25

Christine Scalisi Neyroud , Jimmy Serment , Valérie Batteau +3 more | Revue de Mathématiques pour l’école

Cet article relate une expérimentation menée sous la forme de lesson study (LS) visant à mettre en œuvre un débat mathématique autour des transformations géométriques en classe de 7-8P. L’équipe … Cet article relate une expérimentation menée sous la forme de lesson study (LS) visant à mettre en œuvre un débat mathématique autour des transformations géométriques en classe de 7-8P. L’équipe a préparé une leçon en commençant par la planification des éléments essentiels à afficher au tableau. Cette expérimentation nous a permis d’identifier des éléments qui favorisent et rendent possible l’émergence de débats en classe de mathématiques.

Middle school students’ views on a children’s book incorporating mathematical concepts

2025-06-25

Rüveyda Karaman Dündar , Sevde Uslu , Rümeysa Çakmak | Nevşehir Hacı Bektaş Veli Üniversitesi SBE Dergisi

Children’s literature integrating mathematical concepts is an effective pedagogical tool for fostering mathematical thinking and enhancing conceptual understanding. By embedding mathematical ideas within narrative structures, such literature can render mathematical … Children’s literature integrating mathematical concepts is an effective pedagogical tool for fostering mathematical thinking and enhancing conceptual understanding. By embedding mathematical ideas within narrative structures, such literature can render mathematical content more accessible and meaningful. This study investigates middle school students’ perceptions of children’s literature incorporating mathematical concepts, examining its perceived benefits and challenges within mathematics instruction. The research was conducted with 14 middle school students from a public school in the Western Black Sea Region, employing a qualitative case study methodology. Content analysis was utilized to examine students’ perspectives. Findings indicate that participants generally held positive attitudes toward such literature, recognizing its potential to facilitate mathematics learning, though certain challenges were identified. Many students recommended these books to peers who struggle with mathematics or demonstrate limited interest in the subject. Participants provided favorable evaluations regarding the book's narrative style, character development, and integration of mathematical concepts, though some critiques were noted. The findings underscore the necessity of a well-structured relationship between textual and visual elements to optimize instructional effectiveness. Future research should explore the integration of children’s literature in mathematics education across diverse educational levels and examine the pedagogical implications of various literary genres in supporting mathematical learning.

Проблема мотивации русскоязычных к изучению языков славянской группы

2025-06-24

P. V. Menshikov | Психолого-педагогический поиск

Исследование посвящено вопросу источников мотивации русскоговорящих к изучению языков славянской группы. Современная славянская культура, включая культуру языковую, активно развивается. Обмен между славянскими культурами обнаруживает важность понимания изучения иных славянских языков, … Исследование посвящено вопросу источников мотивации русскоговорящих к изучению языков славянской группы. Современная славянская культура, включая культуру языковую, активно развивается. Обмен между славянскими культурами обнаруживает важность понимания изучения иных славянских языков, помимо родного. Оценивая текущее состояние изучения славянских языков в России, можно отметить, что оно далеко от идеального, неблагополучно. Цель исследования — выявить психологические детерминанты стимулирования и подавления мотивации русофонов к овладению иными славянскими языками. Выдвинута гипотеза о существовании, с одной стороны, мотивов, которые могут послужить побудителями интереса к славянским языкам и, с другой стороны, ряда антимотивов, блокирующих такой интерес. Основной метод исследования — опрос с помощью авторской методики. Новизна исследования связана с тем, что проблема изучения психологических детерминант мотивации русофонов к овладению неродными для них славянскими языками изучена слабо. Теоретическая значимость связана с решением задач интенсификации культурно-языкового обмена посредством анализа психологических причин, побуждающих и тормозящих освоение иных славянских языков русофонами, а также обогащением теории и практики освоения иных языков в целом. Практическая значимость исследования связана с тем, что основные результаты, полученные автором, могут внести вклад в развитие практик изучения славянских языков русофонами. По итогам исследования, осуществленного на основе авторского опросника, выявлены мотивировки, наиболее часто встречающиеся по выборке респондентов. В качестве ведущих мотивов для изучения языков славянской группы участниками исследования определены «личный интерес к культуре носителей славянских языков» и мотив, обусловленный «деловыми коммуникациями». Основными антимотивами являются «отсутствие временного ресурса» и «отсутствие насущной потребности». Перспективы исследования связаны со сравнительным изучением мотивации, процессов и результатов исследования различных языков в специфических образовательных и учебно-профессиональных ситуациях на всех ступенях освоения новых языков. The research is devoted to the sources of motivation of Russian speakers to learn Slavic group languages. Modern Slavic cultures (including linguistic culture) are actively developing. The exchange between Slavic cultures reveals the importance of understanding the study of Slavic languages other than the native one. Assessing the current state of Slavic language learning in Russia, it can be noted that it is far from ideal, or rather unsatisfactory. The aim of the study is to identify the psychological determinants of stimulating and suppressing the motivation of native Russian speakers to master other Slavic languages. We suggest the hypothesis about the existence, on the one hand, of motives that can serve as motivators of interest in Slavic languages and, on the other hand, a number of anti-motives that block such interest. The main method of the research is a survey using the author’s methodology. The novelty of the research is due to the fact that the problem of studying psychological determinants of Russians to master other Slavic languages is not sufficiently studied. The theoretical significance lies in an attempt to solve the problems of intensifying cultural and linguistic exchange by analyzing the psychological reasons that motivate or inhibit Russophones’ acquisition of Slavic languages, as well as enriching the theory and practice of acquisition of other languages in general. The practical significance of the study is related to the fact that the main results obtained by the author can contribute to the development of practices of learning Slavic languages by Russophones. The results of the study are based on the author’s questionnaire revealed the motivations most frequently encountered in the respondents’ sample. As the leading motives for learning Slavic languages, the participants of the study identified “personal interest in the culture of Slavic language speakers” and “business communication.” The most frequent anti-motives are “lack of time” and “lack of urgent need.” The prospects of the research are connected with comparative study of motivation, processes and results of studying different languages in specific educational and educational-professional situations at all stages of learning new languages.

Design and implementation of a task sequence for teaching homothety

2025-06-24

Yenifer Aguilera Moraga , Paula Verdugo-Hernández , Jessica Gatica | Eurasia Journal of Mathematics Science and Technology Education

The teaching of geometry in Chile faces several challenges, as evidenced by the low performance of students in international assessments. In particular, the concept of homothety is impacted by teaching … The teaching of geometry in Chile faces several challenges, as evidenced by the low performance of students in international assessments. In particular, the concept of homothety is impacted by teaching methodologies that emphasize rote memorization and procedural repetition rather than conceptual understanding. This study explores how a task sequence fosters mathematical work with the concept of homothety among 15- to 16-year-old students in a public high school in the Maule Region of Chile. Grounded in the mathematical working space (MWS) theory, this research provides a framework for analyzing how students engage with mathematical tasks. Employing a qualitative approach, specifically a case study, the findings reveal that the task sequence contributes to progressive mathematical reasoning. The study concludes that the designed activities align with the criteria for “emblematic tasks”, evidencing their fundamental role in supporting students’ conceptual understanding of homothety.

A STUDY ON THE EMOTIONAL TRIGGERS OF TEACHERS IN TRAINING: MATHEMATICAL REDEMPTION

2025-06-23

M Jimenez , José Antonio Juárez López , Gabriel Kantún-Montiel +1 more | Turkish Journal of Computer and Mathematics Education (TURCOMAT).

This article presents an exploratory study on the affective experiences of future teachers. It examines a population of primary school students who recount past negative emotions related to mathematics and … This article presents an exploratory study on the affective experiences of future teachers. It examines a population of primary school students who recount past negative emotions related to mathematics and either continue to experience negative emotions about teaching mathematics (absence of mathematical redemption) or develop positive emotions about teaching mathematics (mathematical redemption). The research aimed to identify the triggering situations that influence the desire for mathematical redemption, either fostering or hindering it. In this study, future teachers' responses to the Teachers’ Attitude Toward Mathematics and Its Teaching (TAMT) test were analyzed using the Theory of Cognitive Structure of Emotions (OCC Theory). The study first identified the presence or absence of mathematical redemption and then explored causal connections between triggering situations and the desire for mathematical redemption.

Instructional design and its implementation: the case of the process of objectification of the rational number through measurement processes

2025-06-23

Walter F. Castro , José Wilde Cisneros , Rodolfo Vergel | Discover Education

Teachers’ Practical Argumentation on the Teaching of the Pythagorean Theorem

2025-06-23

Telesforo Sol , Carlos Ledezma , Alicia Sánchez +1 more | International Journal of Science and Mathematics Education

Investigating the Impact of Real-World Contexts on Geometry Learning and Student Perceptions

2025-06-23

Yasemin Gük , Sibel Somyürek | Research on Education and Psychology

This study aims to examine the change in the self-efficacy beliefs of secondary school students towards geometry after a specific pedagogical practice and investigate their views on the learning process … This study aims to examine the change in the self-efficacy beliefs of secondary school students towards geometry after a specific pedagogical practice and investigate their views on the learning process and learning environment. In this approach, students engaged in activities that helped them connect their theoretical geometry knowledge to real-life situations. The students were required to actively participate in these activities such as taking pictures of geometric shapes they encounter in their daily lives and sharing them in a closed social learning environment with the appropriate tags. The research was carried out using the case study method. Various qualitative and quantitative data were collected through multiple record sources. Quantitative results show that the students' self-efficacy beliefs towards geometry were significantly higher after the pedagogical practice. Qualitative analyses were carried out to reveal students' perceptions of mathematics courses, their perceptions of learning activities, their views on the reflection process, their general evaluations, and the problems they experienced as a result of the learning experience. It was seen that the learning experience and learning environment were generally evaluated positively by the students and various contributions were expressed.

Mathematical practices in the manual of integrative activities: Leveling in comprehensive secondary education

2025-06-21

Ana Dias , André Augusto Deodato | Revemop

This article analyzes the mathematical practices proposed in the mathematics leveling presented in the Manual de Atividades Integradoras [Manual of Integrative Activities] from the perspective of comprehensive education. This qualitative … This article analyzes the mathematical practices proposed in the mathematics leveling presented in the Manual de Atividades Integradoras [Manual of Integrative Activities] from the perspective of comprehensive education. This qualitative and documentary research was conducted between 2023 and 2024, with a focus on the manual mentioned. The study identified that the proposed document presents didactic sequences aligned with the Common National Curriculum Base and activities with open-ended answers, emphasizing the importance of diagnostic assessment, although it does not delve into the concept of assessment and its relationship with leveling, and does not explicitly articulate the intentionality of mathematical practices. As a result, the understanding and implementation of leveling in mathematics revealed a limitation. The research can help mathematics teachers reflect on and reconsider the theoretical and practical aspects of their classes.

Research Bridging Theory and Practice

2025-06-20

Branka Antunović | Metodički obzori

This study explores the potential of the Collaborative Action Research (CAR) model to bridge the gap between research and practice in geometry education. Using the Development of Geometrical Thinking (DGT) … This study explores the potential of the Collaborative Action Research (CAR) model to bridge the gap between research and practice in geometry education. Using the Development of Geometrical Thinking (DGT) program, CAR facilitated a collaborative process among teachers and researchers through iterative cycles of planning, action, observation, and reflection. Conducted with 88 seventh-grade students and four mathematics teachers in Croatia, the study aimed to enhance geometric understanding and problem-solving skills.The CAR model translated theoretical insights into practical teaching strategies, leading to significant improvements in student learning outcomes and teacher attitudes. Teachers became more reflective practitioners, adapting methods to meet students’ needs effectively. These findings affirm CAR’s value as a framework for professional growth and sustained instructional innovation in mathematics education.

A DIDACTIC SOLUTION FOR INTEGERS: A METHODOLOGICAL VARIANT WITH PRACTICAL DEMONSTRATION

2025-06-20

Munkhtaria Khayankhyarvaa | International Journal of Innovative Technologies in Social Science

This study examines the effectiveness of using a symbol counter methodology to teach integer operations within a three-tiered didactic framework: concrete application, visual representation, and symbolic notation. The experimental approach … This study examines the effectiveness of using a symbol counter methodology to teach integer operations within a three-tiered didactic framework: concrete application, visual representation, and symbolic notation. The experimental approach was designed to address common student challenges, such as sign errors, incomplete understanding, and flawed reasoning in mathematical problem-solving. The pilot lesson incorporated student-centered teaching strategies, including hands-on activities, teamwork, discussion, and reflection. The symbol counter, a tool utilizing physical symbols like paper circles with plus or minus signs, helped students grasp concepts such as positive and negative numbers, opposite numbers, and zero through tactile and visual experiences. This method facilitated a deeper understanding of integer properties and operations, including addition, subtraction, multiplication, and division. By transitioning from physical manipulation to mental visualization and symbolic abstraction, students were able to internalize mathematical concepts more effectively. To validate the hypotheses proposed in the study, we explored the feasibility of employing methodological approaches that encourage student engagement in the lesson, critical thinking, self-directed learning, and collaboration. To achieve the established objectives, the following tasks were undertaken: - Identifying the experimental group - Creating the experimental lesson plan - Conducting the experiment - Evaluating the experimental outcomes In high school math classes, we learned the rules for performing operations with integers. The sign calculations were written and formulated as follows: (+) × (+) = (+) (+) × (-) = (-) (-) × (+) = (-) (-) × (-) = (-) These notations can be found in various textbooks and educational materials.

Student Problems

2025-06-20

Agnes Bokanyi-Toth | The Mathematical Gazette

An Experience with Pre-Service Teachers, Using GeoGebra Discovery Automated Reasoning Ttools for Outdoor Mathematics

2025-06-19

Angélica Martínez Zarzuelo , Álvaro Nolla de Celis , Tomás Recio +3 more | Education Sciences

This paper presents an initial output of the project “Augmented Intelligence in Mathematics Education through Modeling, Automatic Reasoning and Artificial Intelligence (IAxEM-CM/PHS-2024/PH-HUM-383)”. The starting hypothesis of this project is that … This paper presents an initial output of the project “Augmented Intelligence in Mathematics Education through Modeling, Automatic Reasoning and Artificial Intelligence (IAxEM-CM/PHS-2024/PH-HUM-383)”. The starting hypothesis of this project is that the use of technological tools, such as mathematical modeling, visualization, automatic reasoning and artificial intelligence, significantly improves the teaching and learning of mathematics, in addition to fostering positive attitudes in students. With this hypothesis in mind, in this article, we describe an investigation that has been developed in initial training courses for mathematics teachers in several universities in Madrid, where students used GeoGebra Discovery automated reasoning tools to explore geometric properties in real objects through mathematical paths. Through these activities, future teachers modeled, conjectured and validated geometric relationships directly on photographs of their environment, with the essential concourse of the automated discovery and verification of geometric properties provided by GeoGebra Discovery. The feedback provided by the students’ answers to a questionnaire concerning this novel approach shows a positive evaluation of the experience, especially in terms of content learning and the practical use of technology. Although technological, pedagogical and disciplinary knowledge is well represented, the full integration of these components (according to the TPACK model) is still incipient. Finally, the formative potential of the approach behind this experience is highlighted in a context where Artificial Intelligence tools have an increasing presence in education, as well as the need to deepen these three kinds of knowledge in similar experiences that articulate them in a more integrated way.

Beşinci Sınıf Öğrencilerinin Ölçmede Uzunluk Kavramına Yönelik Performanslarının İncelenmesi

2025-06-19

Mehmet Hayri Sarı , Neşe Işık Tertemiz | Erzincan Üniversitesi Eğitim Fakültesi Dergisi

Bu araştırmanın amacı, ortaokul 5. sınıf öğrencilerinin uzunluk ölçme konusundaki performanslarını değerlendirmektir. Çalışma, nitel araştırma yaklaşımı çerçevesinde bir durum çalışması olarak tasarlanmıştır. Araştırmanın çalışma grubunu 360 öğrenci oluşturmaktadır. Veri toplama … Bu araştırmanın amacı, ortaokul 5. sınıf öğrencilerinin uzunluk ölçme konusundaki performanslarını değerlendirmektir. Çalışma, nitel araştırma yaklaşımı çerçevesinde bir durum çalışması olarak tasarlanmıştır. Araştırmanın çalışma grubunu 360 öğrenci oluşturmaktadır. Veri toplama aracı olarak, araştırmacılar tarafından geliştirilen “Uzunluk Ölçme Testi” kullanılmıştır. Öğrencilerin teste verdikleri yanıtlar, betimsel analiz yaklaşımıyla değerlendirilmiştir. Çalışmada ele alınan uzunluk ölçme sürecinin yedi boyutunda (karşılaştırma, adlandırma, temsil, tahmin, ölçme, dönüştürme ve problem çözme) elde edilen sonuçlara göre, öğrencilerin alışılmış biçimde verilen sayı ve birimi doğru okuma/yazma, doğrusal uzunluğu tahmin etme ve başlangıç noktası sıfır olan cetvelle uzunluğu belirleme konularında daha yeterli oldukları belirlenmiştir. Ancak, alışılmışın dışında verilen sayı ve birimi adlandırma görevlerinde düşük performans sergiledikleri görülmüştür. Ayrıca öğrencilerin, doğrusal olmayan uzunlukları doğrusal gibi algılama hatasına düştükleri, bu tür uzunluklar üzerinde bir sayının yerini doğru tahmin edemedikleri ve doğrusal olmayan uzunlukları ölçerken hatalar yaptıkları belirlenmiştir. Benzer şekilde, başlangıç noktası sıfırdan farklı olan ölçme araçlarında (örneğin, kırık cetvel) doğrusal uzunlukları doğru belirleme ve istenen uzunluğu verilen birime göre temsil etme (çizme) görevlerinde yetersiz kaldıkları gözlemlenmiştir. Bu nedenle, öğrencilerde uzunluk ölçme anlayışının geliştirilmesinde çalışmada ele alınan yedi boyutun dikkate alınması önerilmektedir.

Senior high school students’ competence in logical operation and logical reasoning

2025-06-18

Kodirun , Kadir Kadir , Busnawir +1 more | Frontiers in Education

The research suggests that the framework of logical operations and inference patterns remains unfinished even in adulthood. While various logical models exist beyond the classical true-or-false reasoning model, secondary school … The research suggests that the framework of logical operations and inference patterns remains unfinished even in adulthood. While various logical models exist beyond the classical true-or-false reasoning model, secondary school students must primarily understand and apply classical reasoning rules. In mathematics, proof, reasoning, and refutation are essential due to the frequent use of logical operations in the subject. This study assessed general logical knowledge and operations within mathematical contexts through classroom tests involving 448 students from 10 public schools and four vocational schools. The students performed best on tasks requiring correct conclusions (69.02%), followed by interpreting “at most”/”at least” (63.41%), with the lowest success rate in negation tasks (29.91%), including negating “at least,” “exists,” and “for every”. The results reveal that accurate interpretation was not dominant across all logical operations for these students. Students performed best on geometric problems (70.05%), followed by algebra, statistics, and calculus problems, with the lowest success rate in calculus-related logical problems (28.04%). Statistical tests showed no significant gender differences in performance; however, according to human capital theory, students with teachers as parents performed significantly better.

Matematik Öğretmen Adaylarının Matematiksel İspata Yönelik Görüşleri ve Matematiksel Muhakeme Öz Yeterlik İnançları

2025-06-18

İrem Gizem Acar , Gülcan Öztürk , Filiz Tuba Dikkartın Övez | Afyon Kocatepe Üniversitesi Sosyal Bilimler Dergisi

Bu çalışmada matematik öğretmen adaylarının matematiksel ispata yönelik görüşleri ile matematiksel muhakeme öz yeterlik inançlarını belirlemek ve aralarında bir ilişki olup olmadığını ortaya koymak amaçlanmıştır. Çalışma keşfedici korelasyonel model kullanılarak … Bu çalışmada matematik öğretmen adaylarının matematiksel ispata yönelik görüşleri ile matematiksel muhakeme öz yeterlik inançlarını belirlemek ve aralarında bir ilişki olup olmadığını ortaya koymak amaçlanmıştır. Çalışma keşfedici korelasyonel model kullanılarak gerçekleştirilmiştir. Çalışma grubunu Türkiye’nin batısındaki bir üniversitede uygun örnekleme yöntemi ile belirlenen ilköğretim matematik öğretmenliği ve ortaöğretim matematik öğretmenliği programlarında öğrenim gören 455 matematik öğretmen adayı oluşturmuştur. Çalışmanın verileri; kişisel bilgi formu, “matematiksel ispata yönelik görüş ölçeği” ve “matematiksel muhakeme öz yeterlik ölçeği” kullanılarak çevrim içi form aracılığı ile toplanmıştır. Çalışma sonucunda öğretmen adaylarının matematiksel muhakeme öz yeterlik inanç puanlarının öğrenim görülen sınıf düzeyi ve cinsiyet değişkenlerine göre istatistiksel olarak anlamlı farklılık olduğu bulunmuştur. Ayrıca matematiksel ispata yönelik görüş puanları ile matematiksel muhakeme öz yeterlik inanç puanlarının orta düzeyde anlamlı olarak ilişkili olduğu görülmüştür.

Unraveling Discourse Entwined in Mathematics Standards

2025-06-18

Ashley Schmidt , Daniel Edelen | School Science and Mathematics

ABSTRACT Standards dictate what is taught daily in mathematics classrooms, impacting students, educators, and families. Those in positions of power not only influence the policies that oversee the standards revision … ABSTRACT Standards dictate what is taught daily in mathematics classrooms, impacting students, educators, and families. Those in positions of power not only influence the policies that oversee the standards revision process, but also shape public perception on the necessity and outcome of the standards. In this paper, we present a discursive framework for studying how mathematics standards have been languaged into discourses. We use microethnographic principles and critical discourse analysis to present multiple perspectives of standards through collected speeches, government websites, and policy documents. Our discursive analysis revealed that political and social contexts are intricately woven into the language surrounding these standards. There remains a dearth of literature on how these discourses are collectively understood by educational stakeholders including families, students, and educators.

A comparative analysis of whole number multiplication and division in syllabi and textbooks: insights from Zambia, South Africa and Japan

2025-06-18

Arthur Mungalu , Takuya Baba | International journal of comparative education and development

Purpose This paper compared the treatment of whole number multiplication and division in syllabi and textbooks from Zambia, South Africa and Japan. Design/methodology/approach In-depth topic trace mapping was applied to … Purpose This paper compared the treatment of whole number multiplication and division in syllabi and textbooks from Zambia, South Africa and Japan. Design/methodology/approach In-depth topic trace mapping was applied to determine when whole number multiplication and division were taught in the syllabi and textbooks. Vertical analysis involved applying structure analysis to the proportions of Greer’s (1992) multiplication and division problem situations in textbooks. Further, the study used descriptive analysis to examine similarities and differences in the cognitive expectations of the textbook problems. Findings The study found cross-national similarities and differences in educational opportunities that the intended curricula present. Multiplication and division were taught from Grade 2 to Grade 4, except in South Africa and Japan, where division was introduced in Grade 3. At the same time, the South African syllabus presented the two concepts up to Grade 6. Further, equal group and rectangular array situations were prevalent in all three countries’ documents. The study also found that procedural knowledge and problem-solving problems were popularly applied in all three countries’ textbooks. In contrast, the mathematical reasoning and problem-solving activities were only found in South African and Japanese textbooks to varying degrees. Research limitations/implications The study is limited to textbook comparison; there is a need to examine the actual usage of syllabi and textbooks by teachers in the classroom setting. Further, the representation dimension of cognitive expectation was limited to “drawings”. A broader view of this dimension (to include symbolic and linguistic representation modes) is needed. Practical implications The study’s findings have the potential to significantly impact curriculum reform on multiplication and division, particularly in Zambia and other countries facing similar challenges. By revealing the similarities and differences in the treatment of multiplication and division, the study offers actionable insights for curriculum developers, textbook writers and teachers. Social implications Inclusive curricula and textbooks have implications for learner achievement. Originality/value Most studies have analysed multiplication and division independently. The present study could offer a broad understanding of the two related concepts by analysing the two units simultaneously. Furthermore, analysing the two units and the subtopics presents an in-depth understanding of their development. The study reduces the dearth of literature on comparative studies in Africa and between developed and developing countries. Moreover, the study findings offer actionable information for the analysed countries, including those with similar experiences.

Comparing pedagogical content knowledge on-action and in-action in physics teaching in Lesotho secondary schools

2025-06-18

Nthoesele Hlaela , Loyiso C. Jita | Eurasia Journal of Mathematics Science and Technology Education

Effective teaching requires both pedagogical content knowledge (PCK) on-action and PCK in-action. However, the interplay of knowledge on-action and in-action is unclear in classroom practice. Therefore, studies are required to … Effective teaching requires both pedagogical content knowledge (PCK) on-action and PCK in-action. However, the interplay of knowledge on-action and in-action is unclear in classroom practice. Therefore, studies are required to investigate the interplay of the two types of knowledge. This paper presents an explanatory sequential mixed method design to investigate physics teachers’ pedagogical content knowledge on-action through a sample of 87 physics teachers who responded to a paper-and-pencil test. The study also involved a subsample of two physics teachers as case studies engaging a qualitative investigation entailing interviews and video recorded classroom observations. Data were quantitatively analyzed using the extended Rasch model and qualitatively analyzed using the narratives. The findings revealed significant gaps in teachers’ knowledge on-action, suggesting challenges in applying this knowledge effectively in classrooms. This study recommends the involvement of teachers in continuous professional development meant to stimulate reflection in teacher knowledge, focusing on different PCK components.

Math meets life: bridging middle school students’ lived experiences and social justice mathematical modelling tasks

2025-06-17

Kayla Sutcliffe , Hong Zhang , Hyunyi Jung +1 more | Research in Mathematics Education

THE KLR MODEL: MASTERING INTEGER ADDITION AND SUBTRACTION IN GRADE 7

2025-06-17

Kian M. Chatto , Liezyl Mae G. Aldave , Romar S. Baoy | EPRA International Journal of Multidisciplinary Research (IJMR)

This study aimed to determine the effectiveness of the KLR Model as an intervention in mastering integer addition and subtraction among Grade 7 students. The purpose of this experimental-qualitative study … This study aimed to determine the effectiveness of the KLR Model as an intervention in mastering integer addition and subtraction among Grade 7 students. The purpose of this experimental-qualitative study was to address difficulties in mastering these operations. The participants were 15 Grade 7 students from Asuncion National High School. The study introduced an intervention called the KLR Model (Keep it Simple, Learn the Rules, Reach Mastery), a tutorial approach aimed at enhancing students' arithmetic skills through engaging learning strategies. The pre-test and post-test results showed a significant improvement: the pre-test had a mean score of 7.39, while the post-test showed a mean score of 12.61. A paired-samples t-test revealed a statistically significant difference between the two scores, t(14) = 9.35, p < .001, indicating a highly significant improvement in integer mastery following the intervention. These findings suggest that the KLR Model effectively improved students’ performance in integer operations. To provide a comprehensive understanding of the students' experiences, the researchers conducted in-depth interviews with selected participants. From their responses, nine themes emerged: Active Participation Enhances Understanding, Visual Tools Support Concept Formation, Student-Constructed Rules Deepen Understanding, Solving Independently Builds Confidence, Peer Interaction Encourages Collaboration, Conflicting Ideas Within Groups Pose a Challenge, Need for Immediate Feedback, Learning Process Improves Self-Esteem, and Self-Discovery Boosts Interest. Keywords: KLR, Mastering İnteger, Addition, Subtraction, Philippines

Digging deeper to unpack the current trends of teachers’ morphology content and pedagogical knowledge

2025-06-17

Cortney Dilgard , Tracey S. Hodges | Reading and Writing

Mathematical Definitions: A Key to Conceptual Clarity and Theoretical Rigor

2025-06-17

Maryam Al-Kandari | IntechOpen eBooks

This chapter presents the Conceptual Definition Model (CDM) as a comprehensive and structured framework for enhancing the teaching and learning of mathematics through a focus on definitional clarity. The model … This chapter presents the Conceptual Definition Model (CDM) as a comprehensive and structured framework for enhancing the teaching and learning of mathematics through a focus on definitional clarity. The model underscores the pivotal role of precise, logically grounded definitions in cultivating conceptual understanding and theoretical coherence. CDM integrates elements such as logical structure, illustrative examples, counterexamples, and the articulation of necessary and sufficient conditions to help students navigate mathematical meanings more deeply. Rather than treating definitions as static or memorized statements, this model promotes their use as dynamic cognitive instruments that guide reasoning and inquiry. By engaging students in activities such as dissecting definitions, testing edge cases, and constructing definitions in reverse, CDM fosters analytical thinking and ownership of knowledge. The chapter argues for a paradigm shift in mathematical pedagogy—from passive assimilation to active construction of meaning—thereby empowering learners to participate meaningfully in the logical architecture of mathematics. The educational value of this model is further emphasized through its potential to stimulate reflective questioning and resolve cognitive conflict, ultimately improving proof comprehension and logical reasoning.

Praxeological analysis of linear algebra content presentation: A case study of Indonesian mathematics textbooks

2025-06-17

Denik Agustito , Krida Singgih Kuncoro , Betty Kusumaningrum +3 more | Eurasia Journal of Mathematics Science and Technology Education

Textbooks serve as a crucial medium in enhancing students' comprehension of mathematical concepts, particularly in algebra. This research aims to evaluate the representation of algebra in grade 8 mathematics textbooks … Textbooks serve as a crucial medium in enhancing students' comprehension of mathematical concepts, particularly in algebra. This research aims to evaluate the representation of algebra in grade 8 mathematics textbooks using a practical approach, with a specific focus on the topic of two-variable linear equation systems. The study employs praxeological analysis, grounded in the theoretical framework of the Anthropological Theory of the Didactic (ATD). This analysis examines tasks (T ), techniques (τ ), technology (θ ), and theory (Θ ) as presented in the textbooks. The findings indicate that while the textbooks are effective in introducing linear algebra concepts and facilitating problem-solving, they fall short in fostering a deeper understanding of two-variable linear equations. The study concludes that material presentation should go beyond procedural techniques by integrating the supporting technology (θ ) and theory (Θ ) associated with the techniques (τ ). Without this comprehensive approach, students risk relying solely on procedural methods without grasping the underlying rationale and theories, particularly in more advanced algebraic contexts. Moreover, the presentation of selected textbook materials may contribute to the emergence of epistemological and didactic learning obstacles. To address these challenges, the study recommends a more holistic and conceptually driven presentation of algebraic content to promote meaningful and effective learning.

‘Things haven’t gone the way I thought they’d go’: secondary mathematics teachers talk about trialling a problem-solving pedagogy

2025-06-16

Karina J. Wilkie | Journal of Mathematics Teacher Education

Ethnomathematics in Pre-Service Mathematics Teacher Education: A Glance through Culturally Responsive Pedagogy

2025-06-16

Koena Mabotja | IntechOpen eBooks

Over the past year, research on ethnomathematics has been on an upward trajectory. Literature provides evidence that ethnomathematics can improve learners’ understanding and achievement in mathematics. Equally important, South Africa’s … Over the past year, research on ethnomathematics has been on an upward trajectory. Literature provides evidence that ethnomathematics can improve learners’ understanding and achievement in mathematics. Equally important, South Africa’s mathematics curriculum offers opportunities for integrating ethnomathematics by promoting using various sociocultural contexts in teaching mathematics. Nevertheless, research highlights the inadequacy of existing ethnomathematics research, particularly in pre-service mathematics teacher education in South Africa. As a result, this chapter uses Culturally Responsive Pedagogy theory to foreground teacher educators’ and student teachers’ views about ethnomathematics in pre-service mathematics teacher education. Purposive sampling was used as the sampling procedure to select teacher educators and student teachers. Focus group discussions and semi-structured interviews were used for collecting data collection. Data were analysed through thematic analysis. Three main findings were revealed in the study: mathematics is viewed as a product of diverse cultural contributions; ethnomathematics is perceived as a pedagogy that can enhance learners’ access to mathematical understanding; and ethnomathematics provides opportunities for learners to explore mathematics in everyday contexts. It is concluded that pre-service mathematics education should effectively equip student teachers with pedagogical knowledge and skills to integrate ethnomathematics into their prospective classrooms.

The equal sign and equivalence: interplay between textbook research and curriculum development

2025-06-16

Pang Jeongsuk , Yujin Lee | ZDM

Mathematics Education & Some Methodological Considerations

2025-06-16

Alifasi Phiri , Jason Mwanza , Pamela Buhere | Jumuga Journal of Education Oral Studies and Human Sciences (JJEOSHS)

The research article seeks to determine the casual difference in performance in Circle Theorems when in concert with Concrete-Representational-Abstract (CRA) Instructional Approach. As a conventional method of instruction on Grade … The research article seeks to determine the casual difference in performance in Circle Theorems when in concert with Concrete-Representational-Abstract (CRA) Instructional Approach. As a conventional method of instruction on Grade 11 pupils, the latter is compared with the traditional method of instruction in Mathematics education. In turn, Circle Theorems (CT) are viewed as properties that display relationships between angles within the geometry of a circle; and includes: Chord circle theorem, Tangent circle theorem, Cyclic quadrilateral circle theorem, Angle in a semi-circle theorem, Alternate segment circle theorem, Angle at the centre circle theorem and Angles in the segment circle theorem. The latter is not the main concern of this treatise. It conceptualises education as the process which does an all-round harmonious development of the individual to modify behaviour, attitude and thinking – all in its endeavour to investigate the effect of using Concrete– Representation–Abstract (CRA) Instructional Approach on Grade 11 pupils’ performance in circle theorems in the Katete District, Eastern province, Zambia. It its methodology and design, it utilises descriptive statistics design; as the researchers used the difference-in-differences methods to assess the impact of the interventions on pupil performance. Overall, it establishes that there was a significant difference in scores between the pupils who were taught circle geometry using Concrete–Representational–Abstract (CRA) Instructional Approach and the pupils who were taught the same topic using the traditional approach for both post-test and delayed post-test (for post- test: Value= 65.667; sig= .004 < 0.05, for delayed post- test: Value = 78.333, sig= .000<0.05) according to means.

Variability in the use of ambitious mathematics instructional practices in the context of a national-scale professional development program

2025-06-15

Jannika Lindvall | Scandinavian Journal of Educational Research

Grammar

2025-06-15

S. Susan Marandi | Cambridge University Press eBooks

Many paths, one unknown: Uncovering the diverse minds behind algebraic thinking

2025-06-13

Septiani Yugni Maudy | UNION Jurnal Ilmiah Pendidikan Matematika

This qualitative study examines the diversity in algebraic thinking among high school students (Grades VII-IX) by considering algebraic activity models, reasoning types, and generalization layers. We used clinical interviews along … This qualitative study examines the diversity in algebraic thinking among high school students (Grades VII-IX) by considering algebraic activity models, reasoning types, and generalization layers. We used clinical interviews along with task-based assessments so that we could investigate students' problem-solving processes with just a hermeneutic phenomenological approach. Participants solved contextualized algebra problems using several solution strategies. These strategies included visual representations, arithmetic generalizations, proportional reasoning, and symbolic parameterization. The findings reveal three key conclusions: (1) students think algebraically and develop along a continuum from concrete representations to abstract symbolic reasoning; (2) cultural and instructional contexts influence their ability to transition between factual, contextual, and symbolic generalization layers quite greatly; and (3) multimodal approaches understand algebra better via accommodating diverse cognitive styles. This study contributes in two primary ways for mathematics education research: First, it analyzes semiotic progression within non-Western educational contexts through such culturally-situated framework, which then addresses a gap for current algebra research. Second, it offers design principles validated empirically for creating inclusive algebraic tasks. These tasks do support multiple entry points as well as solution pathways. The results do show that it is important for us to teach in an adaptive manner by both recognizing and then nurturing diverse mathematical styles of thinking in algebra education.

Concept images of the notion of asymptote: a study with prospective teachers

2025-06-13

Mónica Arnal-Palacián , Andrés Pérez-Montilla | Research Square (Research Square)

<title>Abstract</title> This study aims to characterize how prospective teachers (PSTs) interpret students’ thinking through a professional task dialogue focused on asymptotes. Drawing on the theory of concept images, we conducted … <title>Abstract</title> This study aims to characterize how prospective teachers (PSTs) interpret students’ thinking through a professional task dialogue focused on asymptotes. Drawing on the theory of concept images, we conducted a descriptive and interpretative analysis of the discourse of 38 PSTs. The findings reveal a predominant use of descriptive discourse, evaluations of the teacher's interventions, a focus on task solutions and reliance on their prior experiences as mathematics learners. In terms of concept images, the horizontal asymptote is frequently interpreted as a limit, while the vertical and slant asymptotes are often perceived as linear entities.

Female undergraduates’ perception of mathematics: a mixed-methods study

2025-06-13

Tara Paudel , Niroj Dahal , Md. Kamrul Hasan | Frontiers in Education

Mathematics is essential in daily life and career development, yet gender disparities persist, particularly in contexts such as Nepal, where socio-cultural norms influence educational access. This study examines the perceptions … Mathematics is essential in daily life and career development, yet gender disparities persist, particularly in contexts such as Nepal, where socio-cultural norms influence educational access. This study examines the perceptions of female undergraduate mathematics students at Tribhuvan University, Nepal, exploring factors affecting their attitudes, self-efficacy, and motivation. A mixed-methods QUAN-QUAL research design integrated quantitative surveys ( n = 75) and qualitative interviews ( n = 4). Quantitative findings revealed that 72% of participants held negative attitudes toward mathematics, perceiving it as stressful (66%) and male-dominated (65%), with low self-efficacy (37% negative) and ambivalent motivation (49% uncertain). Caste/ethnicity significantly influenced perceptions of mathematics as male-dominated (χ 2 = 23.923, p = 0.021). Qualitative insights highlighted socio-cultural barriers, including familial pressures prioritizing marriage over education, gendered stereotypes, and limited parental education. Female undergraduate students reported balancing household duties with academic demands, exacerbating stress and self-doubt. Despite recognizing mathematics use, systemic inequities hindered engagement. The study underlines the need for gender-sensitive curricula, confidence-building pedagogies, and community awareness to challenge stereotypes and enhance support. Recommendations include policy reforms, scholarships for marginalized groups, and teacher training to foster inclusive learning environments. Addressing these barriers is critical to transforming mathematics education into an equitable and empowering space for Nepali female students.

Students’ motivation as a mediator between extra-mathematical knowledge and word problem-solving

2025-06-13

Hardi Sigus , Kaja Mädamürk | Discover Education

Comparison of Accounting Expert Teacher’s Cognitive Skill Model Versus Average Student for Solving Introductory Accounting Equations

2025-06-13

Mahadhir Mohamed , Sheerad Sahid , Nor Aishah Buang | International Journal of Academic Research in Accounting Finance and Management Sciences

Transformations Throw Down: Extending Mathematics Knowledge with Assemblr

2025-06-13

Brian T. Johnson , Rebecca Bramwell , Josef Stamps +2 more | Journal of Technology-Integrated Lessons and Teaching

The purpose of these 8th grade math lessons was to extend students’ knowledge of sequences of mathematical transformations by providing students with a digital experience of transformations in a three- … The purpose of these 8th grade math lessons was to extend students’ knowledge of sequences of mathematical transformations by providing students with a digital experience of transformations in a three- dimensional environment. Assemblr, an augmented reality app was used to create these experiences for students after they learned these concepts in 2D. Past studies noted that augmented reality activities and gamification promote active learning and increase academic performance (Lampropoulus, et al., 2022; Sukriadi et al,. 2023; Kurniawan, et al., 2024). Students used Assemblr to extend their knowledge in a 3D environment. Their learning was expressed in a game where correct answers to Assemblr challenge questions related to transformations initiated a turn for a team to connect dots and create a square.

Transforming equations into equivalent equations—an empirical study of the equation transformation capability as a multidimensional construct

2025-06-13

Norbert Noster , Hans-Stefan Siller | Educational Studies in Mathematics

NUMERACY SKILLS OF BEGINNING LEARNERS: BASIS FOR A CONTEXTUALIZED MATHEMATICS PROGRAM OF GRADE TWO LEARNERS

2025-06-12

Riche Lyn T. Guevarra | EPRA International Journal of Environmental Economics Commerce and Educational Management

This research determined the numeracy skills of Grade Two learners in Sta. Cruz South District, Division of Davao del Sur, to support the formulation of a contextualized mathematics program. Using … This research determined the numeracy skills of Grade Two learners in Sta. Cruz South District, Division of Davao del Sur, to support the formulation of a contextualized mathematics program. Using a non-experimental descriptive survey design, the study involved 400 learners who completed a mathematics test developed by the researcher. The assessment focused on three core skill areas: verbal counting, numerical operations, and problem-solving. Post-test results showed significant improvement from pre-test scores, with learners reaching a “Satisfactory” level in verbal counting and numerical skills, and a “Very Satisfactory” level in problem-solving. Analysis also revealed statistically significant differences in numeracy performance based on gender and school classification (urban vs. rural), highlighting the role of contextual variables in early mathematics learning. The study was anchored on Piaget’s Cognitive Development Theory and Constructivist Learning Theory, emphasizing hands-on and meaningful learning experiences. Based on the findings, a contextualized mathematics program was designed to better address the learners’ needs. The study recommended that educational leaders prioritize teacher training, inclusive instructional practices, and parent engagement to strengthen early numeracy foundations. Keywords: Numeracy Skills, Beginning Learners, Basis for a Contextualized Mathematics Program, Grade Two Learners

Chemistry teachers’ pedagogical content knowledge: A review of empirical research published in SSCI Journals from 1986 to 2024

2025-06-12

Feng Deng , Lifan Zhang , Junhao Zhu +2 more | Teaching and Teacher Education