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Building on “Misconceptions” and Students’ Intuitions in Advanced Mathematics

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Toward Equity and Social Justice in Mathematics Education

Part of the book series: Research in Mathematics Education ((RME))

Abstract

The goal of this chapter is to challenge deficit perspectives about students and their knowledge. I argue that predominant reliance on formal procedural knowledge in most undergraduate mathematics curricula and the oftentimes focus on students’ misconceptions contribute to the racialized and gendered inequities in mathematics education. I discuss my design of an instructional tool to learn the formal limit definition in calculus called the Pancake Story. The story builds on a misconception and student’s everyday intuitions. A successful sensemaking episode by a Chicana student illustrates the utility of everyday intuitions leveraged in the story and the inaccuracy and harm of the notion of “misconceptions.” Recognizing misconceptions as students’ attempts to make sense of mathematics, solidifying such knowledge by finding an appropriate context for it, and leveraging other knowledge resources are explicit ways to challenge dominant power structures in our practice.

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Notes

  1. 1.

    A search for “students’ misconceptions in mathematics” on Google scholar resulted in 31,900 publications since 2000. Since 2016, there were about 13,100 results.

  2. 2.

    This defining property is usually written as for every number ε > 0, there exists a number δ > 0 such that if 0 < | x – a |< δ then | f (x) – L |< ε.

  3. 3.

    The story is not to be solved mathematically because it lacks sufficient information (e.g., constraint on the thickness of the pancakes). The numbers were selected to connect with the limit of a linear function, f (x)= 3x+2 at x= 1. I fully recognize that a function involved in the story is not linear and that one cup of batter makes an extremely thick 5 inch pancake!

  4. 4.

    This inequality is incorrect. The inequality should have been 4.5 < f (x) <5.5, but Adriana arrived at this inequality in using the | f (x) − L |< ε from the statement of the definition.

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Authors and Affiliations

  1. The University of Arizona, Tucson, AZ, USA

    Aditya P. Adiredja

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  1. Aditya P. Adiredja
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Correspondence to Aditya P. Adiredja .

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  1. Teacher Education, Michigan State University, East Lansing, Michigan, USA

    Tonya Gau Bartell

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Adiredja, A.P. (2018). Building on “Misconceptions” and Students’ Intuitions in Advanced Mathematics. In: Bartell, T. (eds) Toward Equity and Social Justice in Mathematics Education. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-92907-1_4

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  • DOI: https://doi.org/10.1007/978-3-319-92907-1_4

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