This paper discusses the problem of social exclusion, reported to be intrinsically connected to mathematical teaching, from the perspective of Hegel's philosophy and Lacan's psychoanalysis. It provides a characterization of mathematics from a language viewpoint discusses the perennial demand for more mathematical achieving from the perspective of hysterics and obsessive symptoms and shows how desire is linked with the choice of values in assessment.KEY WORDS: Hegel, Lacan and Zizek, inclusion and diversity, language and communication, mathematics education and psychoanalysis
We criticize the polysemy of the signifier “mathematics”. Its commonsense meaning should not be considered enough to ground mathematics education. We describe a form of speech emerging in Ancient Greece, originated from the social necessity to avoid intra-family clashes by means of precise agreements, written laws, and democratic dialog in a singular historical situation. This form of speech emerged together with coinage, was made numerically precise with the Pythagorean movement, and logically precise after the crisis unleashed by Russell’s paradox in the beginning of the last century. We show how this form of speech has developed in history together with communities that came to be known as “exact sciences”, among which is Mathematics, a distinguished community of speech. We end the paper suggesting a political agenda for mathematics education.
A idéia de descobrir a matemática dentro do cérebro humano tem fascinado educadores. Qual neurônio será responsável pelas operações e abstrações matemáticas? Uma vez descoberto o gene que garante a formação desse neurônio, os problemas de ensino da matemática recebem impulso notável. As questões do “talento” para matemática, a orientação profissional, a seleção dos futuros matemáticos e a escolha de métodos de ensino encontrarão novas soluções. Ao menos, essa é a vontade de verdade de que fala Michel Foucault.
Starting from a proof of the fundamental theorem of calculus accessible to K-12 students, we apply Hegel’s Science of Logic to Barrow’s theorem. This article may also be considered as an introduction to speculative philosophy, adequate for mathematics educators. We focus on the subsection Barrier and Ought, where Hegel twists Kant’s aphorism you can because you ought and obtains a precept of action aimed at infirming conservative political positions. We direct Hegel’s Ought to criticize the pedagogical conservatism of the twentieth century mathematics (M20) community and its consequences to mathematics education. From the development of the article we elicit the concept of speculative mathematics as a political agenda for mathematics education.
Keywors: Fundamental theorem of calculus; Barrow’s theorem; Hegel’s Logic; Speculative philosophy; Mathematics community.
Hegel e a comunidade matemática: uma história pela esquerda
Resumo: A parir de uma demonstração do teorema fundamental do cálculo, acessível ao ensino médio, aplicamos a Ciência da Lógica de Hegel ao teorema de Barrow. O artigo também pode ser considerado como introdução à filosofia especulativa, adequada a educadores matemáticos. Focalizamos a subseção Barrier and Ought (Barreira e Dever), onde Hegel altera o aforismo kantiano podes porque deves e obtém um preceito para ação dirigido a abalar posições políticas conservadoras. Valemo-nos do Dever em Hegel para criticar o conservadorismo da comunidade de matemática do século vinte (M20) e suas consequências para a educação matemática. A partir do desenvolvimento do artigo, inferimos o conceito de matemática especulativa como agenda política para a educação matemática.
Palavras-chave: Teorema fundamental do cálculo; Teorema de Barrow; Lógica de Hegel; Filosofia especulativa; Comunidade matemática
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