The Mathematics Education and Neurosciences project is an interdisciplinary research program that bridges mathematics education research with neuroscientific research. The bidirectional collaboration will provide greater insight into young children's (aged four to six years) mathematical abilities. Specifically, by combining qualitative ‘design research’ with quantitative ‘experimental research’, we aim to come to a more thorough understanding of prerequisites that are involved in the development of early spatial and number sense. The mathematics education researchers are concerned (...) with kindergartner's spatial structuring ability, while the neuroscientists are studying kindergartner's automatic quantity processing and its effect on mathematical development. The outcomes of these investigations should contribute to practical ways of fostering and supporting young children's mathematical thinking and learning. (shrink)

The article examines the current state of the mathematical education of the students-philosophers that depends on language of the humanitarian mathematics, evidence of its statements and methodological problem of the cognition of the mathematical facts. One of important tasks of philosophy of mathematical education consists in motivation of the need for training mathematics of students-philosophers. The main criterion of the usefulness of mathematics for philosophers is revealed in the ways of justification of its truth and (...) completeness of reasoning of mathematical statements. This reflects the attractiveness of mathematical knowledge for philosophers that is characterized by the fact that the truth is revealed along with a proof in mathematics. One of the main so-called ‘acupuncture points‘ of mathematical education of philosophers, as the author believes, is the language of modern mathematics. In General, the linguistic aspect is very important in modern science. The second ‘acupuncture point‘ of mathematical education of philosophers is the level of evidence claims. Third, according to the author, is responsible for knowledge of mathematical truths, is involved in not only our existence, but also transcendental knowledge. In the context of philosophy of the future of modern civilization, mathematics is indispensable as a necessary element of scientific and philosophical picture of the world. To support the conclusions the author draws a broad philosophical and scientific context. (shrink)

The fifteenth Journal for Research in Mathematics Education monograph had its origins in a conference titled An Interdisciplinary Conference on Assessment in K--12 Mathematics: Collaborations Between Mathematics Education and Psychometrics, which was held in 2011 in Atlanta, Georgia. The basis for the conference was the renaissance in the field of psychometrics in which an increasing variety of psychometric models are becoming available through advances in computer hardware and software. This is opening new avenues for studying (...) the mathematical knowledge of teachers and students. The overarching purpose of the monograph is to guide further interdisciplinary collaborations between mathematics education researchers and psychometricians by examining theoretical and conceptual issues that have arisen in recent efforts to apply contemporary psychometric models to mathematics education research. Specifically, its chapters are intended to (a) illustrate for mathematics education researchers the two main categories of psychometric models-models that locate individuals along continua and models that place individuals into discrete groups, as well as hybrids of these approaches; (b) provide examples that apply these different categories of psychometric models to mathematics education research; (c) illustrate how researchers have selected different psychometric models on the basis of the researchers' goals and (d) demonstrate issues related to item development. With these goals in mind, the monograph will enhance an awareness among mathematics education researchers that it is increasingly possible to select from a variety of model options when pursuing particular research goals and that choosing among models involves trade-offs. (shrink)

In this article, modern standards of early years mathematics education are criticized and a proposal for change is presented. Today's early years mathematics education standards rest on a view of mathematics that became obsolete already at the end of the 19th century while the spirit of children's mathematics is precisely the spirit of modern mathematics. The proposal for change is not a return to the “new mathematics” movement, but something different.

Research In Mathematics Education In Australasia 2016–2019 (sometimes shortened to RiMEA 2016–2019) is a timely and important edited collection where contributors provide critical reviews on mathem...

Although many agree that all teaching rests on a theory of knowledge, this is an in-depth exploration of the philosophy of mathematics for education, building on the work of Lakatos and Wittgenstein.

This volume provides new sources of knowledge based on Michael Otte’s fundamental insight that understanding the problems of mathematics education – how to teach, how to learn, how to communicate, how to do, and how to represent ...

In the mathematics education research literature, there is a growing body of scholarship on how mathematicians practice their craft. The purpose of this chapter is to survey some of this literature and explain how it can contribute to the philosophy of mathematical practice. We first describe how mathematics educators use empirical methodologies to investigate the behaviors of mathematicians and argue that findings from these studies can inform the philosophy of mathematical practice. We then illustrate this by summarizing (...) research on mathematicians’ understandings and mathematicians’ proof reading. (shrink)

I articulate Charles S. Peirce’s philosophy of mathematical education as related to his conception of mathematics, the nature of its method of inquiry, and especially, the reasoning abilities required for mathematical inquiry. The main thesis is that Peirce’s philosophy of mathematical education primarily aims at fostering the development of the students’ semeiotic abilities of imagination, concentration, and generalization required for conducting mathematical inquiry by way of experimentation upon diagrams. This involves an emphasis on the relation between theory (...) and practice and between mathematics and other fields including the arts and sciences. For achieving its goals, the article is divided in three sections. First, I expound Peirce’s philosophical account of mathematical reasoning. Second, I illustrate this account by way of a geometrical example, placing special emphasis on its relation to mathematical education. Finally, I put forth some Peircean philosophical principles for mathematical education. (shrink)

In recent years, philosophical work directly concerned with the practice of mathematics has intensified, giving rise to a movement known as the philosophy of mathematical practice . In this paper we offer a survey of this movement aimed at mathematics educators. We first describe the core questions philosophers of mathematical practice investigate as well as the philosophical methods they use to tackle them. We then provide a selective overview of work in the philosophy of mathematical practice covering topics (...) including the distinction between formal and informal proofs, visualization and artefacts, mathematical explanation and understanding, value judgments, and mathematical design. We conclude with some remarks on the potential connections between the philosophy of mathematical practice and mathematics education. (shrink)

This paper surveys central justifications and approaches adopted by educators interested in incorporating history of mathematics into mathematics teaching and learning. This interest itself has historical roots and different historical manifestations; these roots are examined as well in the paper. The paper also asks what it means for history of mathematics to be treated as genuine historical knowledge rather than a tool for teaching other kinds of mathematical knowledge. If, however, history of mathematics is not subordinated (...) to the ideas and methods at the heart of the usual mathematical curriculum – algebraic equations, functions, derivatives, analytic geometry – if it becomes an essential subject for mathematics, then the attempt to find a place for history of mathematics requires refining our understanding of the nature of mathematics education itself. Thus, the paper asks not only how can history of mathematics be incorporated into mathematics education but also how the idea of mathematics education may need to be adjusted to accommodate history. (shrink)

Most scientific domains have guidelines concerning ethics in research. These guidelines are designed to enable researchers to conduct good research while avoiding potential harm to research participants. This paper examines the bases for ethical codes in research and discusses how these codes are operationalized in research conducted in the field of mathematics education.

It is a rather safe statement to claim that the social dimensions of the scientific process are accepted in a fair share of studies in the philosophy of science. It is a somewhat safe statement to claim that the social dimensions are now seen as an essential element in the understanding of what human cognition is and how it functions. But it would be a rather unsafe statement to claim that the social is fully accepted in the philosophy of (...) class='Hi'>mathematics. And we are not quite sure what kind of statement it is to claim that the social dimensions in theories of mathematics education are becoming more prominent, compared to the psychological dimensions. In our contribution we will focus, after a brief presentation of the above claims, on this particular domain to understand the successes and failures of the development of theories of mathematics education that focus on the social and not primarily on the psychological. (shrink)

O mundo está em dificuldades e a matemática está envolvida. Somos educadores de matemática - professores, pesquisadores, ativistas. Qual é a nossa resposta? Qual é a nossa responsabilidade? Na primeira parte deste texto, sintetizo as características da educação matemática de que podemos precisar: responsabilidade, crítica, imaginação, incerteza, conduzida em um espírito de relacionamento ético, humildade, liberdade de aprendizado e reconhecimento do valor fundamental de cada ser humano, criatura não humana, idioma, cultura e ecossistema, e nossa dependência deles para nossa própria (...) existência e sobrevivência. Na segunda parte, proponho o dialogismo como uma postura epistemológica para a educação matemática da qual essas características decorrem. Desenvolvo alguns dos fundamentos epistemológicos do dialogismo, baseando-me particularmente no trabalho de Bakhtin sobre a linguagem e sua filosofia do ato. Essas ideias incluem significado, resposta, capacidade de resposta, interdependência e não-finalidade. Ilustro essas ideias em relação a duas situações: linguagem e diversidade cultural nas salas de aula de matemática; e o papel da matemática no contexto da biodiversidade. Concluo enfatizando que pensar dialogicamente sobre a matemática em uma época de problemas aponta para a importância de nossa responsabilidade uns com os outros em cada momento de nossa existência. (shrink)

This book offers an up-to-date overview of the research on philosophy of mathematics education, one of the most important and relevant areas of theory. The contributions analyse, question, challenge, and critique the claims of mathematics education practice, policy, theory and research, offering ways forward for new and better solutions. The book poses basic questions, including: What are our aims of teaching and learning mathematics? What is mathematics anyway? How is mathematics related to society (...) in the 21st century? How do students learn mathematics? What have we learnt about mathematics teaching? Applied philosophy can help to answer these and other fundamental questions, and only through an in-depth analysis can the practice of the teaching and learning of mathematics be improved. The book addresses important themes, such as critical mathematics education, the traditional role of mathematics in schools during the current unprecedented political, social, and environmental crises, and the way in which the teaching and learning of mathematics can better serve social justice and make the world a better place for the future. (shrink)

In this article we contend that attempts to foster democratic education in the United States' public schools rarely include mathematics class in meaningful ways. We begin with Dewey's conception of democracy and then argue that current ways of thinking about mathematics do not provide adequate foundations for democratic mathematics education. Our reconceptualization of mathematics draws on Dewey's uniquely humanistic philosophy of mathematics. We conclude with some implications of democratic mathematics education for (...) school and society. Thus, this project seeks to blur the theory-practice dualism, developing a theoretical argument which draws sustenance from and seeks to contribute back to educational practice. (shrink)

Current formal mathematics, being divorced from the empirical, is entirely a social construct, so that mathematical theorems are no more secure than the cultural belief in two-valued logic, incorrectly regarded as universal. Computer technology, by enhancing the ability to calculate, has put pressure on this social construct, since proof-oriented formal mathematics is awkward for computation, while computational mathematics is regarded as epistemo-logically insecure. Historically, a similar epistemological fissure between computational/practical Indian mathematics and formal/spiritual Western mathematics (...) persisted for centuries, during a dialogue of civilizations, when texts on "algorismus" and "infinitesimal" calculus were imported into Europe, enhancing the ability to calculate. It is argued here that this epistemological tension should be resolved by accepting mathematics as empirically based and fallible, and by revising accordingly the mathematics syllabus outlined by Plato. (shrink)

An international group of distinguished scholars brings a variety of resources to bear on the major issues in the study and teaching of mathematics, and on the problem of understanding mathematics as a cultural and social phenomenon. All are guided by the notion that our understanding of mathematical knowledge must be grounded in and reflect the realities of mathematical practice. Chapters on the philosophy of mathematics illustrate the growing influence of a pragmatic view in a field traditionally (...) dominated by platonic perspectives. In a section on mathematics, politics, and pedagogy, the emphasis is on politics and values in mathematics education. Issues addressed include gender and mathematics, applied mathematics and social concerns, and the reflective and dialogical nature of mathematical knowledge. The concluding section deals with the history and sociology of mathematics, and with mathematics and social change. Contributors include Philip J. Davis, Helga Jungwirth, Nel Noddings, Yehuda Rav, Michael D. Resnik, Ole Skovsmose, and Thomas Tymoczko. (shrink)

How can we deal with the diversity of theories in mathematics education? This was the main question that led the authors of this book to found the Networking Theories Group. Starting from the shared assumption that the existence of different theories is a resource for mathematics education research, the authors have explored the possibilities of interactions between theories, such as contrasting, coordinating, and locally integrating them. The book explains and illustrates what it means to network theories; (...) it presents networking as a challenging but fruitful research practice and shows how the Group dealt with this challenge considering five theoretical approaches, namely the approach of Action, Production, and Communication (APC), the Theory of Didactical Situations (TDS), the Anthropological Theory of the Didactic (ATD), the approach of Abstraction in Context (AiC), and the Theory of Interest-Dense Situations (IDS). A synthetic presentation of each theory and their connections shows how the activity of networking generates questions at the theoretical, methodological and practical levels and how the work on these questions leads to both theoretical and practical progress. The core of the book consists of four new networking case studies which illustrate what exactly can be gained by this approach and what kind of difficulties might arise. (shrink)

The traditional way of presenting mathematical knowledge is logical deduction, which implies a monolithic structure with topics in a strict hierarchical relationship. Despite many recent developments and methodical inventions in mathematics education, many curricula are still close in spirit to this hierarchical structure. However, this organisation of mathematical ideas may not be the most conducive way for learning mathematics. In this paper, we suggest that flattening curricula by developing self-contained micro topics and by providing multiple entry points (...) to knowledge by making the dependency graph of notions and subfields as sparse as possible could improve the effectiveness of teaching mathematics. We argue that a less strictly hierarchical schedule in mathematics education can decrease mathematics anxiety and can prevent students from ‘losing the thread’ somewhere in the process. This proposal implies a radical re-evaluation of standard teaching methods. As such, it parallels philosophical deconstruction. We provide two examples of how the micro topics can be implemented and consider some possible criticisms of the method. A full-scale and instantaneous change in curricula is neither feasible nor desirable. Here, we aim to change the prevalent attitude of educators by starting a conversation about the flat curriculum alternative. (shrink)

A Volume in Cognition, Equity & Society: International Perspectives formally known as International Perspectives on Mathematics Education - Cognition, Equity & Society Series Editor Bharath Sriraman, The University of Montana and Lyn English, Queensland University of Technology The diversity of research in mathematics education has been addressed as both, a problem and a strength. When manifested through adherence to different intellectual roots and theoretical orientations, diversions constitute 'refractions' of mathematics education. The collection and analysis (...) of empirical data in a study are by necessity refracted through the specific analytical lens employed, as well as the aim of the study itself. Refractions can also refer to looking at old phenomena through new lenses. The chapters in this book are refracted through philosophical, political, mathematical and personal lenses by distinguished authors in the field, addressing issues about the elusive experience of doing mathematics, purification of texts, refractions, mathematics and ethnomathematics, political messages in textbook tasks, mathematics education policy debate, the political in mathematics education research, philosophy and mathematics, meanings and representations, identity of mathematical modeling, and dilemmas in the teaching of calculus. An ancient Sanskrit adage states that Knowledge is something that grows when shared, but shrinks when hoarded. Academics engaged in the generation of new Knowledge are blessed with both the time and the freedom to engage in pursuits that allow for intellectual pleasure. As a phenomenon of the Zeitgeist many have succumbed to the increased corporatization of academic work, engaging in activities for monetary and self advancement purposes. Are there any real intellectuals left in academia, a l Adorno, Bourdieu, Chomsky, Foucault, among others? This Festschrift is dedicated to academics that don't bother with self promotion or aggrandizement of themselves or their ideas in simplistic terms. (shrink)

The field of mathematics education has been fashioned by a diversity of theoretical and philosophical perspectives. The purpose of this study is to add to this field an analysis of the philosophical position of critical realism. To achieve this objective, the study addresses the following questions: what does critical realism have to offer mathematics education? How may critical realism underlabour for this discipline? In addressing these questions, the study provides an overview of the basic theories and (...) the possible weak points of and arguments against critical realism and realism in general. It then draws upon the notion of a dialectical phenomenology to provide a sequence of Achilles' heel critiques of some of the perspectives that constitute broadly the theoretical landscape of mathematics education research. This critique proceeds with an analysis of didactically oriented empiricism, hermeneutics, pragmatism, postmodernism, traditionally recognized forms of constructivism, traditionally recognized theories of activity, and ethnomathematics. The last section summarizes the implications of philosophical underlabouring for a more beneficial science of mathematics education. (shrink)

Indonesia has recently faced problems in various aspects of life. The results of a social media survey in Indonesia in early 2021 that the biggest threat to the Pancasila ideology is communism and other western ideologies. Communism has a dark history in the life of the Indonesian people. It shows the problem of thinking and philosophical views of the Indonesian people. This research is textbook research that aims to analyze philosophy books, namely mathematics education philosophy textbooks written with (...) a Western cultural background by Paul Ernest. This book was chosen as the object of analysis because this book is the essential reference textbook for the philosophy of mathematics education in universities providing prospective mathematics teachers in Indonesia. The research results show that this book contributes to developing Western thoughts that are contrary to Pancasila. It needs to eliminate the most critical thing in this book. It is the atheistic and individualistic philosophy underlying the ideology of mathematics education because this is not in line with the theistic collectivistic Pancasila. Therefore, this research recommends developing a textbook on the philosophy of mathematics education. It should be under the Pancasila ideology or written based on the Pancasila ideology. (shrink)

In this paper I present a picture of the social status of the Antwerp arithmetic teachers. This requires first a closer look at the Antwerp schoolmaster in general. Because no fewer than two-thirds of them were also reckoning masters most of the conclusions about teachers are also valid for reckoning masters. The consequences of the sack of Antwerp in 1585 provides us with a wealth of information about the social position of its inhabitants. The material about reckoning teachers is presented. (...) Especially important, in this period of religious turmoil and civil war, is the information concerning the religious convictions of reckoning masters. Finally, a closer look is given to the contents of the arithmetic books and the introduction of arabic numerals. (shrink)

It is a rather safe statement to claim that the social dimensions of the scientific process are accepted in a fair share of studies in the philosophy of science. It is a somewhat safe statement to claim that the social dimensions are now seen as an essential element in the understanding of what human cognition is and how it functions. But it would be a rather unsafe statement to claim that the social is fully accepted in the philosophy of (...) class='Hi'>mathematics. And we are not quite sure what kind of statement it is to claim that the social dimensions in theories of mathematics education are becoming more prominent, compared to the psychological dimensions. In our contribution we will focus, after a brief presentation of the above claims, on this particular domain to understand the successes and failures of the development of theories of mathematics education that focus on the social and not primarily on the psychological. (shrink)

This book discusses both the philosophy of mathematics and of mathematics education. The first part is a critique of existing approaches and a new philosophy of mathematics. Chapters include: (1) "A Critique of Absolutist Philosophies of Mathematics," (2) "The Philosophy of Mathematics Reconceptualized," (3) "Social Constructivism as a Philosophy of Mathematics," (4) "Social Constructivism and Subjective Knowledge," and (5) "The Parallels of Social Constructivism." The second part of the book explores the philosophy of (...) mathematics education and shows that many aspects of mathematics education rest on underlying, usually implicit, philosophical assumptions. Making these assumptions explicit puts a critical tool into the hands of teachers and researchers. Chapters in this section are: (6) "Aims and Ideologies of Mathematics Education," (7) "Groups with Utilitarian Ideologies," (8) "Groups with Purist Ideologies," (9) "The Social Change Ideology of the Public Educators," (10) "Critical Review of Cockcroft and the National Curriculum," (11) "Hierarchy in Mathematics, Learning, Ability and Society," (12) "Mathematics, Values and Equal Opportunities," and (13) "Investigation, Problem Solving and Pedagogy." Each chapter contains notes. (Contains 654 references.) (MKR). (shrink)

The purpose of this paper is the influence of Science- Technology- Engineering- Art- Mathematics education on the Olympic education of primary and middle school students. The research object is the Beijing Olympic model school. The frame structure and educational concept of STEAM education are studied, and a questionnaire survey on the current situation of Olympic education is conducted. Finally, improvement measures based on the survey results are provided combined with STEAM education, and the teaching (...) effect is analyzed. The results show that after the improvement of the educational model, the student’s mastery of the Olympic knowledge has been greatly improved. The proportion of students who can master all knowledge increases from 5.78 to 8.45%, by 2.67%. The proportion of students with knowledge of most Olympic sports increases from 48.6 to 55.67%, by 7.07%. The proportion of students with little or no knowledge drops to 1.54%. Meanwhile, students are increasingly interested in Olympic events, especially after being inspired by the STEAM education model. The proportion of students who are very concerned about Olympic events has increased by 6.45%. The proportion of students who are more concerned about Olympic events has increased by 5.11%. Thus, the Olympic education work has achieved some results. Students gradually become interested in the Olympic events. They begin to actively pay attention to the Olympic events and learn the Olympic spirit. Then, their physical literacy is improved. (shrink)

Le but de cet article est d’étudier l’enseignement des mathématiques au Collège d’Artillerie espagnol de 1764 à 1842, et de repérer les influences étrangères sur elle. Après quelques hésitations, un programme standard est adopté commençant par l’arithmétique et finissant par le calcul différentiel et intégral et la mécanique. L’unique changement important fut en 1819 quand la mécanique devint une matière indépendante. Pendant les premières décennies, avec Giannini comme premier professeur, l’emprise italienne était importante, néanmoins il existait une influence française et (...) anglaise. Avec le temps l’inspiration française augmenta. Les manuels employés pendant la plupart du temps étaient ceux de Giannini ou Odriozola, professeurs du Collège; mais ils ont utilisé aussi des livres de mathématiciens français comme Lacroix, Legendre ou Monge. The present article studies the impact of foreign influence on mathematics education at the Spanish Royal College of Artillery from 1764 to 1842. After some vacillation, the academy’s standard teaching program included from arithmetic to calculus and mechanics. The most noteworthy change occurred in 1819 when mechanics would be considered as an independent subject. During the first decades during which time Giannini was first professor, the academy’s approach to teaching mathematics was mostly influenced by methods being used in Italy and, to a certain degree, in England and France. French influence increased considerably with time. While most of the textbooks used at the academy were authored by two of its professors, Giannini and Odriozola, the curriculum would be expanded to include works by French mathematicians such as Lacroix, Monge and Legendre. (shrink)

Open peer commentary on the article “Examining the Role of Re-Presentation in Mathematical Problem Solving: An Application of Ernst von Glasersfeld’s Conceptual Analysis” by Victor V. Cifarelli & Volkan Sevim. Upshot: Cifarelli and Sevim’s analysis of Marie’s problem solving activity raises two questions for me. The first regards what Marie is reflectively abstracting: the use of the generic phrase her solution activity finesses a largely unarticulated disagreement in the mathematics education community about what the nature of actions are (...) in Piaget’s theory. The second question involves the implications that radical constructivist research in mathematics has for day-to-day mathematics instruction. (shrink)

Mathematics achievement in different education systems around the world is assessed periodically in the Programme for International Student Assessment. PISA is deemed to yield robust...

This editorial, introducing the Journal for Theoretical & Marginal Mathematics Education, is historically situated in a moment when the field of mathematics education research is on the precipice of acknowledging that the old world is dying. That is to say, the way research has been done before is no longer adequate for operating within the White, Colonial, cis-hetero Patriarchal, Abled Capitalist dystopia we find ourselves. This inadequacy is, however, not a reason for despair but instead for (...) celebration. Instead of directing our resources towards reifying existing norms and structures, towards adopting exhausted methods and theories—as is the way of the old world—we can instead foster a ‘new aesthetics’ of mathematics education research, wherein we remake the very material that constitutes mathematics education research itself. In doing so, we engage with the politics of the margins of mathematics education research. We discuss the critical, philosophical, and psychoanalytic as three potential, but non-exhaustive, departures from mathematics education research as it has been. Each of these marginal approaches, in their own way, points to the ways that presuming a fixed mathematics education research enacts exclusionary politics and precludes change. Let this be our manifesto, written from the margins, for a more root-grasping, more self-reflective, and freer mathematics education research. (shrink)

There are different narratives on mathematics as part of our world, some of which are more appropriate than others. Such narratives might be of the form ‘Mathematics is useful’, ‘Mathematics is beautiful’, or ‘Mathematicians aim at theorem-credit’. These narratives play a crucial role in mathematics education and in society as they are influencing people’s willingness to engage with the subject or the way they interpret mathematical results in relation to real-world questions; the latter yielding important (...) normative considerations. Our strategy is to frame current narratives of mathematics from a virtue-theoretic perspective. We identify the practice of mathematizing, put forward by Freudenthal’s ‘Realistic mathematics education’, as virtuous and use it to evaluate different narratives. We show that this can help to render the narratives more adequately, and to provide implications for societal organization. (shrink)