Using instructor error-intentional or not-to extend mathematical understanding and change students' epistemic beliefs
Harbaugh, A.G. (2010) Using instructor error-intentional or not-to extend mathematical understanding and change students' epistemic beliefs. In: Annual Meeting of the Pacific Northwest Section of the Mathematical Association of America, 9 - 10 April 2010, Seattle University, Seattle, WA
The nature of mathematical research is often hidden from our students by well written text- books, error-free classroom lectures, and single-strategy homework exercises. What students do not see is the many errors that lead to fruitful discoveries, the dead-end strategies pursued along the way, or the spark of creativity which illuminates the correct direction to obtain the desired solution. This presentation will discuss how errors be they intentional or not on the part of the instructor can lead to rich classroom discussions, a deeper mathematical understanding of the problems (often via clarification of assumptions), and changes in students epistemic beliefs regarding the nature of mathematical knowledge. Three problems will be presented, one each from trigonometry, statistics and differential equations. The error and origination of each problem will be discussed in light of the pedagogic benefits serendipitously made avail- able to the students. In addition to the pedagogic benefits, this presentation will also examine the epistemic beliefs held by math students and how exploration of mathematical errors can illuminate the nature and ramifications of such beliefs. A brief introduction to the theory of personal epistemology and mathematical epistemic beliefs will be incorporated into the presentation.
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