Theory Of Mathematics Education Research Articles

Highlighting Theory to Connect Research and Practice

What role should educational research play in practice and vice versa? What is the role of theory in connecting research and practice? These are some of the questions that readers are invited to consider in Research for Educational Change: Transforming Researchers' Insights Into Improvement in Mathematics Teaching and Learning. Using a novel approach, this book brings these questions to the foreground and examines the links among research, practice, and theory in mathematics education.

Tracing conceptual development in mathematics: epistemology of webs of reasons

The purpose of this article is to show how the philosophical theory of inferentialism can be used to understand students’ conceptual development in the field of mathematics. Based on the works of philosophers such as Robert Brandom, an epistemological theory in mathematics education is presented that offers the opportunity to trace students’ conceptual development in both its individual and social facets through analyzing patterns of reasoning. A design experiment on decimal numbers serves as a paradigmatic example. The overall goal is to illustrate the relationship between mathematical standard and individual ways of reasoning in conceptual development processes.

The Influence of Culture on Students’ Mathematics Achievement Across 51 Countries

The results of international large-scale assessments have shown that countries vary considerably in their mathematics performance. Culture has been suggested as a possible cause for the national difference, but insufficient empirical research has been conducted to investigate the effect of culture on mathematics achievement. Based on Hofstede’s conceptualization of culture, the present study examined the relationship between national culture and students’ mathematics achievement by analyzing data from 51 countries using two-level hierarchical linear modeling. The results showed that national culture played an important role in shaping mathematic achievement. It accounted for 23.89% of the country differences in mathematics performance after controlling for student gender, family socioeconomic status, and national GDP per capita. One cultural dimension “long-term orientation” had a strong positive association with mathematics achievement. The implication of the findings is discussed, followed by a discussion of issues regarding employing culture dimensions theory in mathematics education.

Psychological Theories in Mathematics Education

Psychological Theories in Mathematics Education

French and English theoretical perspectives in Mathematics Education Research: an overview and discussion of key issues

In this article we focus on issues related to theories in mathematics education as used in both French and English settings. As the final article in this special issue, we review the earlier articles and focus on the key ideas and issues which stand out for us. As with the other articles, we seek to address both common and contrasting perspectives, drawing on the examples which illustrate uses of theory. We end by pointing to issues of validation, scale and policy which challenge both groups and look towards facing such challenges jointly.

MATHEMATICS TEXTBOOK ANALYSIS IN TERMS OF SUPPORT TO CONTEXTUALIZED TEACHING

In the process of teaching mathematics in the primary school cycle in the Republic of Srpska , the textbook has a very important role, considering its focusing effect on the learning and teaching, that is to say, on the structure of students’ mathematical knowledge. In this sense, the use of textbooks in initial teaching of mathematics, particularly in the design and implementation of the process of teaching, is one of the important indicators of the mode of work and the place of students and teachers in the educational process. This paper research points out the necessity of aligning the textbook concept with modern theories of mathematics education, including the creation and writing of textbooks that will serve the realization of achieving goals of modern mathematics teaching. Among other things, the textbook model that will meet set requirements will feature the representation methods, procedures, and teaching approaches that promote active and interactive learning, as well as, creative and critical thinking. The paper also points out the contemporary tendencies that new models of textbooks should be primarily based on contextualization, which implies a problem solving approach to teaching and the development of higher forms of learning and thought processes. This context is the starting point for empirical analysis with the aim to test the support for standard math textbooks for junior grades of elementary school approved for use in the Republic of Srpska in school year 2016/2017, and the process of contextualization of learning and teaching mathematics in elementary school teaching. In the first part of the paper, the theoretical aspects of the fundamental concepts of contextual teaching and learning in mathematics teaching in junior grades of elementary school, as well as the importance of the textbooks in acquiring knowledge are shown. The first part of the paper also deals with the analysis of current textbooks focusing especially on the elements of the contextual approach to the process of teaching. The second part of the paper deals with explaining numeric indicators, which indicate that in the textbooks of mathematics from the first to the fifth grade different modes of contextual problems are identified primarily with regard to different forms of expression and presentation (illustrated, textual, combined - picture, text). The results of their number indicate the unsatisfactory support of standard textbooks to the process of contextualization of learning and teaching mathematics in junior grades of elementary school teaching, since textbook context, both in terms of sources of information, and methodical scenarios have dominant transmissive role in teaching mathematics.

Reflective abstraction in computational thinking

Computational thinking has become an increasingly popular notion in K-12 and college level education. Although researchers have accepted that abstraction is a central concept in computational thinking, they are quick to disagree on the meaning of it. A focus on reflective abstraction has led to the development of APOS Theory in Mathematics education. This has resulted in many cases of improved student learning in Mathematics (Arnon et al., 2013). Our main aim in this paper is to construct a theoretical bridge between computational thinking and APOS Theory and show that reflective abstraction can be used in the context of computational thinking.

History of mathematics in secondary school teachers’ training: towards a nonviolent mathematics education

In the context of mathematics teachers’ training, the concept of depaysement epistemologique (epistemological disorientation) emphasizes that the contact with the history of mathematics, particularly with the use of original sources, pushes aside commonplace students’ perspectives about the discipline and offers them a critical look towards mathematics’s historical, social and cultural aspects. Conceptually supported by the theory of objectivation, an emergent sociocultural theory in mathematics education, this study describes the depaysement epistemologique lived by future mathematics teachers engaged in the reading of historical texts. A phenomenological approach allowed us to clarify various meanings associated with students’ lived experiences and a dialogical perspective provides a way to get these meanings in tension through a polyphonic narration. Our reading of this polyphonic narration suggests that depaysement epistemologique associated with the reading of historical texts encouraged empathy from students towards the authors and their future learners, opening up the possibility for a nonviolent mathematics education.

Working With Cultural-Historical Activity Theory

This article focuses on the experiences of two researchers, Wolff-Michael ROTH and Luis RADFORD, using cultural-historical activity theory in mathematics education. The aim is to provide insights into the ways these researchers see and engage with activity theory, how they have come to adopt and expand it, and some of the challenges and concerns that they have had using it. These questions are not usually addressed within typical scientific papers. Yet, they are important for understanding both the dynamics of research and the practical use of cultural- historical activity theory. Since the format of research report papers is not necessarily well suited to convey personal experiences and thinking, the present article takes the form of a conversation, which provides an effective vehicle for exploring and articulating these matters. This provides a basis for understanding more deeply the underlying assumptions of this theory; its dynamics and how it is applied in research of mathematics practice, thinking, and learning; and insights into the manner in which experienced researchers grapple with the theoretical dimensions of their research.

Advancements in research on creativity and giftedness in mathematics education: introduction to the special issue

Creativity and giftedness in mathematics education research are topics of an increased interest in the education community during recent years. This introductory paper to the special issue on Mathematical Creativity and Giftedness in Mathematics Education has a twofold purpose: to offer a brief historical perspective on the study of creativity and giftedness, and to place an emphasis on the added value of the present volume to the research in the field. The historical overview addresses the development of research and practice in creativity and giftedness with specific attention to creativity and giftedness in mathematics. We argue that this special issue makes a significant contribution to bridging domain-general theories of creativity and giftedness with theories in mathematics education with special attention given to nurturing these phenomena in the process of mathematics teaching and learning.

Eliciting Mathematics Interest: New Directions for Context Personalization and Example Choice

ABSTRACTBuilding on common assumptions in theories of interest and mathematics education, this experimental study examined the effect of context personalization based on individual preferences, group personalization, and example choice with preselected popular examples on middle school students' situational interest and performance in mathematics. Participants (N = 713) learned a principle in probability calculus in one of four instructional conditions. Individual interest and perceived competence were examined as moderators on triggered and maintained situational interest, perceived value, task effort, and performance. Results showed that example choice triggered situational interest in the learning activity and that context personalization influenced perceived value and effort, contingent on students' perceived competence and individual interest in mathematics. We discuss results in relation to previous findings on interest-based interventions and the theoretical and practical implications.

Theories of mathematics education of Yoshinobu Wada in early postwar Japan

Theories of mathematics education of Yoshinobu Wada in early postwar Japan

Dialogue between theories interpreted as research praxeologies: the case of APOS and the ATD

The notion of “praxeology” from the anthropological theory of the didactic (ATD) can be used as a framework to approach what has recently been called the networking of theories in mathematics education. Theories are interpreted as research praxeologies, and different modalities of “dialogues” between research praxeologies are proposed, based on alternatively considering the main features and proposals of one theory from the perspective of the other. To illustrate this networking methodology, we initiate a dialogue between APOS (action-process-object-schema) and the ATD itself. It starts from the theoretical component of both research praxeologies followed by the technological and technical ones. Both dialogue modalities and the resulting insights are illustrated, and the elements of APOS and the ATD that the dialogue can promote and develop are underlined. The results found indicate that a complete dialogue taking into account all components of research praxeologies appears as an unavoidable step in the networking of research praxeologies.

Theoretical Framework of Researcher Knowledge Development in Mathematics Education

The goal of this paper is to present a framework of researcher knowledge development in conducting a study in mathematics education. The key components of the framework are: knowledge germane to conducting a particular study, processes of knowledge accumulation, and catalyzing filters that influence a researcher decision making. The components of the framework originated from a confluence between constructs and theories in Mathematics Education, Higher Education and Sociology. Previously published interviews with professor Jeremy Kilpatrick and professor Michele Artigue are used for illustrating how the framework can be utilized in data analysis. Criteria for framework evaluation are discussed.

Transitioning from “It Looks Like” to “It Has To Be” in Geometrical Workspaces: affect and near-to-me attention

Abstract Within a practitioner researcher framework, this paper draws on a particular mathematics education theory and aspects of neuroscience to show that, from a learner’s perspective, moving to a deductive reasoning style appropriate to basic Euclidean geometry, can be facilitated, or impeded, by emotion and/or directed attention. This shows that the issue of a person’s deductive reasoning is not a merely cognitive one, but can involve affective aspects related to perception – particularly perception of nearby sense data – and emotion. The mathematics education theory that has been used is that of the Espace de Travail Mathématique, the English translation of which is known as Mathematical Working Spaces (MWS). The aspects of neuroscience that have been used pertain to the distinct processing streams known as top-down and bottom-up attention. The practitioner research perspective is aligned with Mason’s teaching-practice-based ‘noticing’; qualitative data analysed in this report include individual interviews with school teachers on in-service courses and reflective notes from teaching. Basic Euclidean geometry is used as the medium for investigating transition from ‘it looks like’ to a reasoned ‘it has to be’.

Schooling novice mathematics teachers on structures and strategies: a Bourdieuian perspective on the role of “others” in classroom practices

School discursive practices produce and reproduce acceptable notions of the good mathematics teacher, thereby shaping identity and agency in becoming a teacher. In this paper, I draw on key aspects of Bourdieu’s social field theory—his conceptual “thinking tools” and his reflexive sociology—to explore the relations and discourses of school mathematics classrooms as experienced by two novice secondary mathematics teachers. Presentation and analysis of interview transcript data, juxtaposed with fictional “dear novice teacher” letters from the field, reveal the ways in which the two novice mathematics teachers carefully negotiate space for enacting agency amid institutional school “others.” The reflections in this paper are made relevant for mathematics teacher education through a better understanding of novice mathematics teacher agency, including an account of how these two teachers are being “schooled” on the structures and strategies of classroom practices. An additional contribution of this paper to theory in mathematics education lies in the approach to analysis that draws on Bourdieu’s reflexive sociology, specifically the concept of a field of opinion, to introduce competing discourses offered by novice teachers in mathematics classrooms and by teacher educators/researchers in teacher education programs.

Insubordinação Criativa: um convite à reinvenção do educador matemático

Neste artigo apresenta-se o conceito de insubordinação criativa com o objetivo de analisar as contribuições que atitudes decorrentes dessa perspectiva podem trazer aos fazeres dos educadores matemáticos. Para isso, colocam-seem pauta discussões a respeito da complexidade educativa, da autonomia profissional, da prática reflexiva e do trabalho colaborativo. Pretende-se suscitar reflexões sobre a questão: Por que considerar a insubordinação criativa para redimensionar as práticas dos educadores matemáticos? Diante desta intenção, busca-se dialogar com teóricos da Educação e da Educação Matemática que se expressam de forma crítica e comprometida com a democracia, a justiça social, a ética e a solidariedade. Assim, justifica-sea necessidade de a comunidade reinventar as práticas da Educação Matemática.

The Inquiry of Students' Attitude towards Group Discussion and Presentation in a Course of Mathematics Education

This research is a survey study on students' attitude toward a class employing small group discussion and presentation by the method of free-listing. Participants in this study were students who registered in the course of Mathematical Logics and Writing during 2011 and 2014. Senior students who took the course of theory of mathematics education previously usually registered the course. The class for this course used to be designed as a class adopting group discussion and presentation. Main theme of this research is not to demonstrate some theories or hypothesis on teaching and learning, but rather to inquire students' attitude toward a class employing the constituents first and then through analyzing the results of this study to find practical ideas and strategy for design and implementation of a class which brings cultivation of students' understanding, communication and moreover writing in mathematics. Since the survey was given in the <TEX>$8^{th}$</TEX> week of this class, participants of this research could be expected to have more concrete idea for positive or negative aspects of the classes employing these constituents. We compared both research results of 2011 and 2014 to view any changes in students' attitude. Research results are follows. Students began to think that group discussions and presentation bring out better learning to them. Not to give students psychological burden of discussion and presentation, instructors need to provide comfortable atmosphere through arranging suitable grouping and enough time for discussion. Moreover, simple evaluations criteria for group discussions and presentation should be well structured and more concrete guides for them are required to make students to feel comfortable and to concentrate on the given subject for discussion.

Adapting the academic motivation scale for use in pre-tertiary mathematics classrooms

The Academic Motivation Scale (ams) is a comprehensive and widely used instrument for assessing motivation based on the self-determination theory. Currently, no such comprehensive instrument exists to assess the different domains of motivation (stipulated by the self-determination theory) in mathematics education at the pre-tertiary level (grades 11 and 12) in Asia. This study adapted the ams for this use and assessed the properties of the adapted instrument with 1610 students from Singapore. Exploratory and confirmatory factor analyses indicated a five-factor structure for the modified instrument (the three original ams intrinsic subscales collapsed into a single factor). Additionally, the modified instrument exhibited good internal consistency (mean α = .88), and satisfactory test-retest reliability over a 1-month interval (mean r xx = .73). The validity of the modified ams was further demonstrated through correlational analyses among scores on its subscales, and with scores on other instruments measuring mathematics attitudes, anxiety and achievement.

Social theory in mathematics education: Guest editorial

The articles in this Special Issue arose originally from the work of the Research Forum on Sociological Frameworks in Mathematics Education Research at the conference of the International Group for the Psychology of Mathematics Education (PME) in 2009. The acceptance of this Research Forum at PME was indicative of the shift within mathematics education research during the last two decades involving what has been called the “social turn” (Lerman, 2000). Researchers concerned with a wide variety of issues within mathematics education have come increasingly to see the inseparability of culture, context and cognition. Even within research that focuses primarily on cognitive aspects of learning and knowledge, notions of situated learning and distributed knowledge (Lave & Wenger, 1991) are widely used, as well as other theoretical perspectives that emphasise social aspects of learning, drawing in particular on Vygotskian psychology (Vygotsky, 1978). Moving beyond seeing mathematics learning solely as the endeavour of individual students and teachers has been reflected in a broader conceptualization of the subject matter of the field of mathematics education research. Valero (2010) has drawn our attention to the complexity of the networks of communities, interest groups and practices relevant to mathematics education and to the need for research to address this multiplicity of social practices and the connections between them. We are thus aware of the importance of studying the various communities and practices in which students and teachers participate, both within the classroom and beyond. We recognise the influence of policy and institutional structures and constraints at local, national and international levels. We appreciate the impact of the various discourses available inside and outside the school—discourses in the sense written with a capital D by Gee (1996 )a nd defined as incorporating “theories” about what is normal and right and structuring the kinds of identities available to participants. This increasing attention to social aspects of learning has been accompanied by a growth in research foregrounding issues of social justice. Differing levels of achievement in mathematics in particular as well as in education as a whole have been associated with membership of various social groups and the effects of such factors as gender, ethnicity, class and linguistic background on the achievement of students in school mathematics have long been a focus of study. However, our ways of understanding the phenomenon of school failure have developed. In particular, there has been a move from locating the reasons for failure in the characteristics of the individuals concerned or of their communities towards seeking to understand how the