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Integer comparisons across the grades

Title: Integer comparisons across the grades: Students' justifications and ways of reasoning.
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Inaccessible until Mar 1, 2020 due to copyright restrictions.

Name(s): Whitacre, Ian, author
Azuz, Beti, author
Lamb, Lisa L.C., author
Bishop, Jessica Pierson, author
Schappelle, Bonnie P., author
Philipp, Randolph A., author
Type of Resource: text
Genre: Text
Journal Article
Date Issued: 2017-03-01
Physical Form: computer
online resource
Extent: 1 online resource
Language(s): English
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 integer-comparison 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: magnitude-based, order-based, and developmental/other. The 7th graders used order-based reasoning more often than did the younger students, and it more often led to correct answers; however, the college-track 11th graders, who responded correctly to almost every problem, used a more balanced distribution of order-and magnitude-based reasoning. We present a framework for students’ ways of reasoning about integer comparisons, report performance trends, rank integer-comparison tasks by relative difficulty, and discuss implications for integer instruction.
Identifier: FSU_libsubv1_scholarship_submission_1533933513_1f7fc6a8 (IID), 10.1016/j.jmathb.2016.11.001 (DOI)
Keywords: Integers, Negative numbers, Children’s mathematical thinking, Order, Magnitude
Publication Note: https://doi.org/10.1016/j.jmathb.2016.11.001
Preferred Citation: Whitacre, I., Azuz, B., Lamb, L. L., Bishop, J. P., Schappelle, B. P., & Philipp, R. A. (2017). Integer comparisons across the grades: Students' justifications and ways of reasoning. Journal of Mathematical Behavior, 45, 47-62. [Teacher Ed]
Persistent Link to This Record: http://purl.flvc.org/fsu/fd/FSU_libsubv1_scholarship_submission_1533933513_1f7fc6a8
Owner Institution: FSU
Is Part Of: The Journal of Mathematical Behavior.
Issue: vol. 45

Choose the citation style.
Whitacre, I., Azuz, B., Lamb, L. L. C., Bishop, J. P., Schappelle, B. P., & Philipp, R. A. (2017). Integer comparisons across the grades: Students' justifications and ways of reasoning. The Journal Of Mathematical Behavior. Retrieved from http://purl.flvc.org/fsu/fd/FSU_libsubv1_scholarship_submission_1533933513_1f7fc6a8