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| Title: | How Do You Know that You Know? Making Believe in Mathematics |
| Authors: | Bass, Hyman |
| Keywords: | mathematics education
mathematicians |
| Issue Date: | 31-Oct-2009 |
| Abstract: | Knowing in a discipline means not only knowing its products, and their uses, but also
about the genesis of its knowledge, how that knowledge is warranted, and how contrary
views are reconciled. This shapes the entailments of teaching and learning of that
discipline whether at age 8, 18, or 80. This lecture will focus on the discipline of
mathematics, illustrating what mathematicians do when they seek to “prove” a claim,
taking note of the challenges presented by the advent of computer-based proofs. Proving
is a fundamental mathematical practice, learned by few students, and then only late in
their education. I will consider how proving could shape the early learning of
mathematics, including the use of “generic” proofs. Examples from elementary
classrooms will illustrate why the warrants for shared knowledge in a field matters for the
curriculum at any point. |
| Appears in Collections: | Education, School of
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Files in This Item:
| File |
Description |
Size | Format | |
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| Bass-2009.pdf | Text of lecture | 128Kb | Adobe PDF | View/Open |
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