A Cross-Sectional Investigation of Students' Reasoning About Integer Addition and Subtraction: Ways of Reasoning, Problem Types, and Flexibility

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  • 1 San Diego State University
  • 2 Texas State University
  • 3 San Diego State University
  • 4 Florida State University
  • 5 San Diego State University

In a cross-sectional study, 160 students in Grades 2, 4, 7, and 11 were interviewed about their reasoning when solving integer addition and subtraction open-numbersentence problems. We applied our previously developed framework for 5 Ways of Reasoning (WoRs) to our data set to describe patterns within and across participant groups. Our analysis of the WoRs also led to the identification of 3 problem types: change-positive, all-negatives, and counterintuitive. We found that problem type influenced student performance and tended to evoke a different way of reasoning. We showed that those with more experience with negative numbers use WoRs more flexibly than those with less experience and that flexibility is correlated with accuracy. We provide 3 types of resources for educators: (a) WoRs and problem-types frameworks, (b) characterization of flexibility with integer addition and subtraction, and (c) development of a trajectory of learning about integers.

Contributor Notes

Lisa L. Lamb, School of Teacher Education and Center for Research in Mathematics and Science Education, San Diego State University, CRMSE, 6475 Alvarado Road, Suite 206, San Diego, CA 92120; lisa.lamb@sdsu.edu

Jessica Pierson Bishop, Department of Mathematics, Texas State University, 601 University Drive, San Marcos, TX 78666; jbishop01@txstate.edu

Randolph A. Philipp, School of Teacher Education and Center for Research in Mathematics and Science Education, San Diego State University, CRMSE, 6475 Alvarado Road, Suite 206, San Diego, CA 92120; rphilipp@sdsu.edu

Ian Whitacre, School of Teacher Education, Florida State University, 1114 West Call Street, G123 Stone Building, Tallahassee, FL 32306; iwhitacre@fsu.edu

Bonnie P. Schappelle, Center for Research in Mathematics and Science Education, San Diego State University, CRMSE, 6475 Alvarado Road, Suite 206, San Diego, CA 92120; bschappelle@sdsu.edu

(Corresponding author is Lamb lisa.lamb@sdsu.edu)(Corresponding author is Bishop jbishop01@txstate.edu)(Corresponding author is Philipp rphilipp@sdsu.edu)(Corresponding author is Whitacre iwhitacre@fsu.edu)(Corresponding author is Schappelle bschappelle@sdsu.edu)
Journal for Research in Mathematics Education

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