An important characteristic ofcontemporary reflections in mathematicseducation is the attention given tolanguage and discourse. No longer viewed asonly a more or less useful tool to expressthought, language today appears to beinvested with unprecedented cognitive andepistemological possibilities. One wouldsay that the wall between language andthought has crumbled to the point that nowwe no longer know where one ends and theother begins. At any rate, the thesis thatthere is independence between theelaboration of a thought and itscodification is no longer acceptable. Theattention given to language cannot ignore,nevertheless, the question of itsepistemological limits. More precisely,can we ascribe to language and to thediscursive activity the force of creatingthe theoretical objects of the world ofindividuals? In this article, I suggestthat all efforts to understand theconceptual reality and the production ofknowledge cannot restrict themselves tolanguage and the discursive activity, butthat they equally need to include thesocial practices that underlie them. Thispoint is illustrated through the analysisof the relationship between mathematicalknowledge and the social practice of theRenaissance.

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On the epistemological limits of language: Mathematical knowledge and social practice during the renaissance

Māl, enunciations, and the prehistory of Arabic algebra

Simplifying equations in Arabic algebra

Arabic algebra derives its epistemic value not from proofs but from correctly performing calculations using coequal polynomials. This idea of ‘mathematics as calculation’ had an important influence on the epistemological status of European mathematics until the seventeenth century. We analyze the basic concepts of early Arabic algebra such as the unknown and the equation and their subsequent changes within the Italian abacus tradition. We demonstrate that the use of these concepts has been problematic in several aspects. Early Arabic algebra reveals anomalies which can be attributed to the diversity of influences in which the al-jabr practice flourished. We argue that the concept of a symbolic equation as it emerges in algebra textbooks around 1550 is fundamentally different from the ‘equation’ as known in Arabic algebra.

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A Conceptual Analysis of Early Arabic Algebra

This paper utilizes poststructural theory to analyze student artifacts that were collected from a history of mathematics course. The course was designed to counter three types of mathematical narratives, relating to: 1) race, 2) intelligence, and 3) innateness. To address these narratives, the course highlighted the contributions of communities of color and other minoritized populations in the historical development of mathematics. It also explicitly challenged dominant constructions of mathematical history and problematized their use to further the power and privilege of particular groups. Analyses of student artifacts showed that this course provided space for students to defy innate intelligence racial narratives and strengthen their own counter-stories.

Interrogating Innate Intelligence Racial Narratives: Students’ Construction of Counter-Stories within the History of Mathematics

(1926). The Origin of the Term “Algebra”. The American Mathematical Monthly: Vol. 33, No. 9, pp. 437-440.

Solomon Gandz

Papers

The Origin of the Term “Algebra”

On the Origin of the Term “Root”

On Three Interesting Terms Relating to Area

Did the Arabs Know the Abacus

On The Origin of The Term “Root.” Second Article