Didactics and History of Mathematics: Knowledge and Self-Knowledge |
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| Authors: | Michael N Fried |
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| Institution: | (1) Program for Science and Technology Education, The Institutes for Applied Research, Ben-Gurion University of the Negev, P.O.B. 653, Beer-Sheva, 84105, Israel |
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| Abstract: | The basic assumption of this paper is that mathematics and history of mathematics are both forms of knowledge and, therefore,
represent different ways of knowing. This was also the basic assumption of Fried (2001) who maintained that these ways of
knowing imply different conceptual and methodological commitments, which, in turn, lead to a conflict between the commitments
of mathematics education and history of mathematics. But that conclusion was far too peremptory. The present paper, by contrast,
takes the position, relying in part on Saussurean semiotics, that the historian's and working mathematician's ways of knowing
are complementary. Recognizing this fact, it is argued, brings us to a deeper understanding of ourselves as creatures that
do mathematics. This understanding, which is a kind of mathematical self-knowledge, is then proposed as an alternative commitment
for mathematics education. In light of that commitment, history of mathematics assumes an essential role in mathematics education
both as a subject and as a mediator between the aforementioned ways of knowing. |
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| Keywords: | conflicting and complementary epistemologies diachrony synchrony mathematical self-knowledge |
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