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Title

Integer comparisons across the grades: Students' justifications and ways of reasoning.

Creator

Whitacre, Ian, Azuz, Beti, Lamb, Lisa L.C., Bishop, Jessica Pierson, Schappelle, Bonnie P., Philipp, Randolph A.

Abstract/Description

This study is an investigation of students’ reasoning about integer comparisons—a topic that is often counterintuitive for students because negative numbers of smaller absolute value are considered greater (e.g., −5 > − 6). We posed integercomparison tasks to 40 students each in Grades 2, 4, and 7, as well as to 11th graders on a successful mathematics track. We coded for correctness and for students’ justifications, which we categorized in terms of 3 ways of reasoning: magnitudebased,...
Show moreThis study is an investigation of students’ reasoning about integer comparisons—a topic that is often counterintuitive for students because negative numbers of smaller absolute value are considered greater (e.g., −5 > − 6). We posed integercomparison tasks to 40 students each in Grades 2, 4, and 7, as well as to 11th graders on a successful mathematics track. We coded for correctness and for students’ justifications, which we categorized in terms of 3 ways of reasoning: magnitudebased, orderbased, and developmental/other. The 7th graders used orderbased reasoning more often than did the younger students, and it more often led to correct answers; however, the collegetrack 11th graders, who responded correctly to almost every problem, used a more balanced distribution of orderand magnitudebased reasoning. We present a framework for students’ ways of reasoning about integer comparisons, report performance trends, rank integercomparison tasks by relative difficulty, and discuss implications for integer instruction.
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Date Issued

20170301

Identifier

FSU_libsubv1_scholarship_submission_1533933513_1f7fc6a8, 10.1016/j.jmathb.2016.11.001

Format

Citation