The Philosophy of Mathematics Education Today

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Springer Verlag (2018)
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Abstract

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.

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ISBN(s)

9783319777597   9783319777603   3030085325   3319777599

DOI

10.1007/978-3-319-77760-3
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Chapters

Developing Rules Due to the Use of Family Resemblances in Classroom Communication

In mathematics education research the recognition and utilization of similarities is highlighted in various ways, for example in the context of learning by analogies or metaphors. In this article Wittgenstein’s concept of “family resemblances” will be presented and illustrated by empirical examples.... see more

Hades—The Invisible Side of Mathematical Thinking

The chapter presents a philosophical approach to teaching and learning mathematics in which five philosophical methods are translated into methods of reading and writing mathematical texts. The philosophical approaches are Hermeneutics, Analytical philosophy, Dialectics, Experience based and Specula... see more

Time for Work: Finding Worth-While-Ness in Making Mathematics

In this chapter we are concerned to understand the connection that can occur for primary school children between relevant practical, “hands-on” engagement with the material world in partnership with others and the development of mathematical commitment, enthusiasm and understanding. We draw on our p... see more

Teaching of Velocity in Mathematics Classes—Chances for Philosophical Ideas

The way the concept of velocity is presented in elementary mathematics textbooks builds on text problems and nowadays also on the use of tables. However the genesis of the velocity concept refers to a centuries-old search within the context of motion underlined with philosophical ideas. The concept ... see more

Creativity Research in Mathematics Education Simplified: Using the Concept of Bisociation as Ockham’s Razor

This chapter proposes that bisociation, the Koestler theory of the creativity of the “Aha!” Moment, is the Ockham Razor for creativity research in mathematics education. It shows the power of bisociation in simplifying unnecessary components and in the synthesis of the fragmented ones. The discussio... see more

Towards a Wider Perspective: Opening a Philosophical Space in the Mathematics Curriculum

The chapter argues that philosophical inquiry may have a place in the math classroom, helping to facilitate understandings that serve to complement and critically judge the inferences acquired in and with mathematics. In other words, philosophical inquiry may aid in the opening of a “wider horizon o... see more

Using Rules for Elaborating Mathematical Concepts

This chapter focuses on an inferential view on elaborating concepts in mathematics classrooms. A framework is going to be presented and used, which helps to analyse and to reflect on the processes of teaching and learning mathematical concepts. The framework is based on Wittgenstein’s theory of lang... see more

Making Distinctions: A Phenomenological Exploration in Mathematics Education

After a brief remark about methods, readers are invited to consider two related phenomena, and then to connect their experience with my comments about them. Two mathematical tasks follow, both intended to highlight particular features of attention and how it shifts. After a brief commentary about at... see more

Mathematics Education Actualized in the Cyberspace: A Philosophical Essay

In this article it is assumed that the role of the Philosophy of Mathematics Education is to analyze and ponder about reality, or a vision of the world, a conception of knowledge and of the human being, shedding light on the meanings and senses that emerge in the works by Mathematics Education autho... see more

The Separation of Mathematics from Reality in Scientific and Educational Discourse

This contribution aims to illustrate that the separation between mathematics and reality is an outcome of several shifts in historic mathematics discourse. Therefore, Foucault’s method of problematisation and Deleuze’s distinction between axiomatic and problematic formalisation in mathematics are us... see more

On the Roles of Language in Mathematics Education

The language of mathematics attracted recently the attention of philosophers, historians of mathematics, and researchers in mathematics education . There exist a considerable number of approaches, each of which studies one particular aspect of the language of mathematics that is relevant in the part... see more

On the Need for Theory of Mathematics Learning and the Promise of ‘Commognition’

In this chapter, research in mathematics education is defined as a special type of discourse in which potentially useful stories about learning and teaching mathematics are being told. A consistent collection of stories coming from a given discourse is known as a theory. A commognitive version of th... see more

Some Thoughts on a Mathematics Education for Environmental Sustainability

Planet Earth is beset by myriad environmental problems attributable to the unsustainable nature of human activities. These problems include climate change, species loss, pervasive pollution, and ecosystem degradation, all of which are examples of ‘post-normal situations’: they generate urgent, compl... see more

The Struggle Is Pedagogical: Learning to Teach Critical Mathematics

Paulo Freire’s and Amílcar Cabral’s orientation of social struggles as pedagogical suggests that when teachers are involved in community issues and struggles, they develop some of the necessary political-pedagogical knowledge to teach critical mathematics . One does not learn to swim in a library, w... see more

Students’ Foregrounds and Politics of Meaning in Mathematics Education

Beginning with the presentation of two fictitious South African children, Nthabiseng and Pieter, I outline the idea of a politics of meaning in mathematics education. Such a politics refers to the social, economic, cultural and religious conditions for experiencing meaning. It refers as well to the ... see more

The Ethics of Mathematics: Is Mathematics Harmful?

In this chapter I challenge the idea that mathematics is an unqualified force for good. Instead I show the harm that learning mathematics can inadvertently cause unless it is taught and applied carefully. I acknowledge that mathematics is a widespread force for good but make the novel case that ther... see more

The Concept of Culture in Critical Mathematics Education

A well-known critique in the research literature of critical mathematics education suggests that framing educational questions in cultural terms can encourage ethnic-cultural essentialism, obscure conflicts within cultures and promote an ethnographic or anthropological stance towards learners. Never... see more

Epistemological Questions About School Mathematics

In proposing that mathematics pedagogy limits and regulates epistemological legitimacy, the chapter raises thorny questions about the assumption that mathematical knowledge is co-constructed and shared through respectful exchanges between a teacher and her students. In the proposal, questions of dif... see more

The Amalgam of Faith and Reason: Euclid’s Elements and the Scientific Thinker

Problematizing the truths of mathematics education is one of the roles of the philosophy of mathematics education. That mathematics education is a matter of reason and science—not of faith and religion—and that mathematics is timeless, universal and immutable, objective knowledge that is independent... see more

A Dialogical Conception of Explanation in Mathematical Proofs

In this chapter, I argue that the issue of explanatoriness in mathematical proofs can be fruitfully addressed within the dialogical conceptualization of proofs that I have been developing in recent years. The key idea is to emphasize the observation that a proof is a piece of discourse aimed at an i... see more

The Philosophy of Mathematical Education Between Platonism and the Computer

Mathematics causes some specific epistemological and educational difficulties. On the one hand, it must accept the merely representational character of all knowledge. On the other hand, mathematical knowledge claims a special truth status, compared to other knowledge. The difference between a symbol... see more

The Who and What of the Philosophy of Mathematical Practices

In the first part an outline is presented of the emergent new field of the study and the philosophy of mathematical practices, including mathematics education. In the second part the focus is on particular themes within this field that correspond more or less to my personal contributions over a thir... see more

The Philosophy of Mathematics Education: An Overview

This chapter offers an overview of the philosophy of mathematics education. This sub-field is characterised in both narrow and broad terms, concerning the aims of mathematics education and all philosophical aspects of research in mathematics education, respectively. The sub-field is also explored in... see more

A Plea for a Critical Transformative Philosophy of Mathematics Education

A disciplinary educational research field cannot, I think, avoid tackling general questions about the educational aims it pursues, as well as more specific questions concerning the teaching and learning of its contents, the nature of these contents and its methodology and theoretical foundations.

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The Interest of Philosophy of Mathematics (Education).Karen François - 2024 - Philosophia Mathematica 32 (1):137-142.

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