Mathematical Practice as Sculpture of Utopia: Models, Ignorance, and the Emancipated Spectator (original) (raw)
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In this work I look at mathematics education from a Derridean perspective. The foundation stone for my analysis is the debate between mathematicians and mathematics educators. In the first part I delineate some theoretical elements, which I claim limit mathematics educators" critiques of mathematicians. The principal one is the notion of mathematics education as a research domain fashioned by empiricism and science. However, this constraint also precludes us from introducing Derrida as a theoretical reference. From this standpoint, the thesis begins to articulate a notion of research compatible with Derrida"s notion of writing and, simultaneously, allows us to incorporate Derrida as such a theoretical reference. Subsequently, I progress towards a critique which would overcome the limits already suggested in the first part of the thesis. I suggest that Derrida provides us with theoretical elements, which allow us to take mathematics educators" critiques of mathematicians further than currently projected. To further develop my analysis, and at this point, I bring to the forefront the following question: "What is the meaning of mathematics in mathematics education?" I am, however, not interested in just an abstract discussion of this question. Rather, I attempt to illustrate how this question appears to be essentially and constantly present in the very history and literature of mathematics education. Revisiting Derrida, I lay bare the elements of the debate relating to the meaning of the word "mathematics". I confront that question using Derrida"s famous passage that "there is nothing beyond the text". In my final chapter and before my conclusion I sketch the history of mathematics education in the Twentieth Century and I explore the idea of how the phenomenon of the internationalization of the English language is closely linked to the inauguration of the term "mathematics education". A significant moment in this history is when the "Commission Internationale de l"Enseignement Mathématique" transforms into the "International Commission on Mathematical Instruction". I conclude my thesis by arguing that a critique of mathematicians" notions of mathematics may endanger the very foundation and status of mathematics education as a research entity in its own right.
Critical Issues in Mathematics Education
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Pedagogical Research, 2020
Of all the arguments directed against presenting mathematical topics within a cultural and historical context, the most serious ones are those that we will refer to as the time and the content arguments. In this paper, after briefly describing these stances, we will endeavor to evaluate and refute their rationales using a social constructivist line of reasoning. To this end, we will first discuss the basic tenets of radical and social constructivism and then, through some simple concrete examples, show how social constructivism organically heralds the pedagogical methodology that imparts mathematical concepts in conjunction with their historical and cultural contexts.
The Philosophy of Mathematics Education: An Overview
ICME-13 Monographs
This paper focuses on the sub-field of study the philosophy of mathematics education from one perspective. The field is characterised in both narrow and broad terms, and from both bottom-up (questions and practices) and top-down perspectives (in terms of philosophy and its branches). From the bottom-up one can characterize the area in terms of questions, and I have asked: What are the aims and purposes of teaching and learning mathematics? What is mathematics? How does mathematics relate to society? What is learning mathematics? What is mathematics teaching? What is the status of mathematics education as knowledge field? I have characterized the sub-field using a "top down" perspective using the branches of philosophy. Looking briefly into the contributions of ontology and metaphysics, aesthetics, epistemology and learning theory, social philosophy, ethics, and the research methodology of mathematics education reveals both how rich and deep the contributions of philosophy are to the theoretical foundations of our field of study. But even these two approaches leave many questions unanswered. For example: what are the responsibilities of mathematics and what is the responsibility of our own subfield, the philosophy of mathematics education? I conclude that the role of the philosophy of mathematics education is to analyse, question, challenge, and critique the claims of mathematics education practice, policy and research.
The Philosophy of Mathematics Education
ICME-13 Topical Surveys, 2016
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