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San Diego State University


Obstacles and Affordances for Integer Reasoning:
An Analysis of Children’s Thinking and the History of Mathematics

Jessica Pierson Bishop
The University of Georgia

Lisa L. Lamb and Randolph A. Philipp
San Diego State University

Ian Whitacre
Florida State University

Bonnie P. Schappelle and Melinda L. Lewis
San Diego State University

Abstract: We identify and document 3 cognitive obstacles, 3 cognitive affordances, and 1 type of integer understanding that can function as either an obstacle or affordance for earners while they extend their numeric domains from whole numbers to include negative integers. In particular, we highlight 2 key subsets of integer reasoning: understanding or knowledge that may, initially, interfere with one’s learning integers (which we call cognitive obstacles) and understanding or knowledge that may afford progress in understanding and operating with integers (which we call cognitive affordances). We analyzed historical mathematical writings related to integers as well as clinical interviews with children ages 6–10 to identify critical, persistent cognitive obstacles and powerful ways of thinking that may help learners to overcome obstacles.

in Journal for Research in Mathematics Education, January 2014, Vol. 45, No. 1, pp. 19–61.

Lisa Lamb, Randolph Philipp, and Bonnie Schappelle are CRMSE Members. Ian Whitacre is a graduate of the MSED program. Jessica Pierson Bishop is a former CRMSE Member.