Theories of mathematics education: European perspectives, commentaries and viable research directions

We briefly comment on different perspectives on (1) the role of mathematics education theories, (2) the issue of plurality and healthy heterogeneity versus consolidation; (3) underlying inquiry systems or the implicit role of philosophy in theories of mathematics education. This paper also outlines developments within the European research scene on theory usage in mathematics education research, which complement the discussion at the 29th PME research forum in Melbourne.     

Textbook research in mathematics education: development status and directions

This paper presents a survey study aiming to systematically examine, analyse and review relevant research focusing on mathematics textbooks and hence identify future directions in this field of research. The literature surveyed is selected from different data sources, including mainly journal articles, research theses and conference proceedings. The survey revealed that important progress has been made over the last few decades in mathematics textbook research, though the major achievement has been concentrated in the areas of textbook analysis (including textbook comparison), and the use of textbooks in teaching and learning. It is overall no longer true that the textbook research in mathematics is “scattered, inconclusive, and often trivial” as described six decades ago; however, the development of research on mathematics textbooks has been unbalanced in different areas. Following the review and discussion, the paper proposes five needed directions for advancing the research in this field.     

Problem solving in Chinese mathematics education: research and practice

This paper is an attempt to paint a picture of problem solving in Chinese mathematics education, where problem solving has been viewed both as an instructional goal and as an instructional approach. In discussing problem-solving research from four perspectives, it is found that the research in China has been much more content and experience-based than cognitive and empirical-based. We also describe several problem-solving activities in the Chinese classroom, including “one problem multiple solutions,” “multiple problems one solution,” and “one problem multiple changes.” Unfortunately, there are no empirical investigations that document the actual effectiveness and reasons for the effectiveness of those problem-solving activities. Nevertheless, these problem-solving activities should be useful references for helping students make sense of mathematics.     

Interviewing in mathematics education research: Choosing the questions

With the development of qualitative methodologies, interviewing has become one of the main tools in mathematics education research. As the first step in analyzing interviewing in mathematics education we focus here on the stage of planning, specifically, on designing the interview questions. We attempt to outline several features of interview questions and understand what guides researchers in choosing the interview questions. Our observations and conclusions are based on examining research in mathematics education that uses interviews as a data-collection tool and on interviews with practicing researchers reflecting on their practice.     

Game and decision theory in mathematics education: epistemological, cognitive and didactical perspectives

In the 1950s, game and decision theoretic modeling emerged—based on applications in the social sciences—both as a domain of mathematics and interdisciplinary fields. Mathematics educators, such as Hans Georg Steiner, utilized game theoretical modeling to demonstrate processes of mathematization of real world situations that required only elementary intuitive understanding of sets and operations. When dealing with n-person games or voting bodies, even students of the 11th and 12th grade became involved in what Steiner called the evolution of mathematics from situations, building of mathematical models of given realities, mathematization, local organization and axiomatization. Thus, the students could participate in processes of epistemological evolutions in the small scale. This paper introduces and discusses the epistemological, cognitive and didactical aspects of the process and the roles these activities can play in the learning and understanding of mathematics and mathematical modeling. It is suggested that a project oriented study of game and decision theory can develop situational literacy, which can be of interest for both mathematics education and general education.     

Exploring MLD in mathematics education: Ten years of research

Mathematical learning disabilities or difficulties (MLD) are an increasing source of educational inequalities. This article explores research about MLD in Mathematics Education over the past ten years. The methodology focuses on specific, validated keywords. These keywords are used to identify articles in leading journals in mathematics education. Our work makes several new contributions to the field of mathematics education, notably: a reusable methodology and keywords for a literature review; an exhaustive list of articles about MLD in leading mathematics education journals; a discussion of the definitions and features of MLD used in these articles; and a tool to classify research dealing with MLD (categories that characterize students with MLD). We also highlight some unexplored dimensions regarding MLD in Mathematics Education research.     

Connecting social perspectives on mathematics teacher education in online environments

This article explores theoretical issues underpinning the design and use of online learning environments in mathematics teacher education. It considers the contribution of social theories of learning to conceptualising technology-mediated interaction, focusing specifically on community of practice models and the notion of digital mathematics performance. The article begins by introducing social perspectives on collaboration. Because of the diversity of theories within this broad research paradigm, the next section outlines networking strategies that have been proposed for connecting theoretical approaches. There follows a discussion of studies that illustrate the community of practice and performance-based approaches to research into online mathematics teacher education. The main purpose of the article is to show how these approaches could be connected by examining the same teaching and learning scenarios through different theoretical lenses. The final section identifies implications of this exploration for the design of online learning environments in mathematics teacher education to capitalise on the affordances of Web-based technologies.     

Combining theories in research in mathematics teacher education

In this paper, we describe how the combination of two theories, each embedded in a different realm, may contribute to evaluating teachers’ knowledge. One is Shulman’s theory, embedded in general, teacher education, and the other is Fischbein’s theory, addressing learners’ mathematical conceptions and misconceptions. We first briefly describe each of the two theories and our suggestions for combining them, formulating the Shulman–Fischbein framework. Then, we present two research segments that illustrate the potential of the implementation of the Shulman–Fischbein framework to the study of mathematics teachers’ ways of thinking. We conclude with general comments on possible contributions of combining theories that were developed in mathematics education and in other domains to mathematics teacher education.     

A global survey of international perspectives on modelling in mathematics education

In this article we survey the current debate on modelling and, describe different perspectives on this debate. We relate these perspectives with earlier perspectives and show similarities and differences between these different approaches.     

Sociocultural perspectives in research on and with mathematics teachers: a zone theory approach

Sociocultural theories view teacher learning as changing participation in social practices that develop their professional identities rather than as acquisition of new knowledge or beliefs that are internal to the individual. Although sociocultural research on mathematics teacher education has tended to focus on understanding teachers’ learning, this article argues that sociocultural perspectives can also guide more interventionist research involving changing classroom practice. The approach illustrated here uses an adaptation of Valsiner’s zone theory to analyse teacher learning and development in two separate research studies. In one study the aim was to understand how teachers incorporated digital technologies into their practice, while the other study helped teachers implement an investigative approach to working mathematically consistent with a new syllabus. In both studies, productive tensions between teachers’ beliefs, contexts, and goals were a trigger for learning and development.     

An analysis of history of mathematics research literature in Turkey: the mathematics education perspective1

Research in history of mathematics gained momentum in the past two decades in Turkey. The present paper aims to describe the patterns in the history of mathematics research in Turkey and to analyse the research in Turkey using a mathematics education framework. The qualitative paradigm and a case study design are used in the study. The obtained data were analysed by using the document analysis technique with the help of a content analysis. The study group which is comprised of twenty-two postgraduate theses at master's or doctoral level were purposefully selected from the higher education council postgraduate theses database. Findings indicate a dearth of research in the area and that most of the theses are done in the area of mathematics education. Moreover, the focus, in general, was on attitudinal variables, and cognitive aspects seemed to be ignored.     

The onto-semiotic approach to research in mathematics education

In this paper we synthesize the theoretical model about mathematical cognition and instruction that we have been developing in the past years, which provides conceptual and methodological tools to pose and deal with research problems in mathematics education. Following Steiner’s Theory of Mathematics Education Programme, this theoretical framework is based on elements taken from diverse disciplines such as anthropology, semiotics and ecology. We also assume complementary elements from different theoretical models used in mathematics education to develop a unified approach to didactic phenomena that takes into account their epistemological, cognitive, socio cultural and instructional dimensions.     

Balancing mathematics education research and the NCTM standards

The release of the Principles and Standards for School Mathematics in the United States by the National Council of Teachers of Mathematics (NCTM) brought to the forefront the debate of whether research should determine the validity of the espoused Standards? Or conversely whether the Standards should influence the research agenda of the mathematics education community? How should university teacher educators address this issue? Should pre-service and practicing teachers blindly, accept the Standards as well as the research, or do we cultivate the critical thinking skills that will allow preparing teachers to resolve this dilemma? In this article a university mathematics educator and an idealistic pre-service elementary teacher try to resolve the dilemma of balancing the Standards with research and personal beliefs about the teaching and learning of mathematics.     

Online distance mathematics education in Brazil: research, practice and policy

In this article, we address online distance mathematics education research and practice in Brazil, which are relative newcomers to the educational scene. We present the national context of education in Brazil, highlighting the organization of the educational system, and also a summary of national legislation on distance education and an overview of digital inclusion in the country. We outline the potential and relevance of distance education for the Brazilian educational system and show how it could intervene in the system. With respect to research and practice in online mathematics education, we present support for research, examples of studies and highlight different aspects being addressed, including its essential components. In addition, we discuss the synergy between distance education and teacher education, and mathematics distance education and modeling, as well as other initiatives in the national scenario.