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Happy and sad thoughts

Title: Happy and sad thoughts: An exploration of children's integer reasoning.
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Name(s): Whitacre, Ian, author
Bishop, Jessica, author
Lamb, Lisa, author
Phillipp, Randolph, author
Schappelle, Bonnie P., author
Lewis, Melinda, author
Type of Resource: text
Genre: Text
Issuance: serial
Date Issued: 2012
Physical Form: computer
online resource
Extent: 1 online resource
Language(s): English
Abstract/Description: The purpose of this study was to investigate elementary children's conceptions that might serve as foundations for integer reasoning. Working from an abstract algebraic perspective and using an opposite-magnitudes context that is relevant to children, we analyzed the reasoning of 33 children in grades K-5. We focus our report on three prominent ways of reasoning. We do this by describing and analyzing the responses of three particular children (in Grades 1, 3, and 5) who exemplify these ways of reasoning. We view each of the three ways of reasoning as rich and interesting, and we see relationships of each to formal integer reasoning. At the same time, we view these ways of reasoning in terms of increasing levels of sophistication, potentially belonging to a single learning trajectory. Thus, we see the roots of more sophisticated integer reasoning in children's early intuitions about opposite magnitudes.
Identifier: FSU_migr_ste_faculty_publications-0010-P (IID)
Keywords: Integers, Negative numbers, Opposite magnitudes, Children's reasoning
Note: This is the author's version of a work that was accepted for publication in The Journal of Mathematical Behavior. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in The Journal of Mathematical Behavior, Volume 31, Issue 3, September 2012, Pages 356–365http://dx.doi.org/10.1016/j.jmathb.2012.03.001'>http://dx.doi.org/10.1016/j.jmathb.2012.03.001">http://dx.doi.org/10.1016/j.jmathb.2012.03.001
Citation: Ian Whitacre, Jessica Pierson Bishop, Lisa L.C. Lamb, Randolph A. Philipp, Bonnie P. Schappelle, Melinda L. Lewis. Happy and sad thoughts: An exploration of children's integer reasoning. The Journal of Mathematical Behavior, Volume 31, Issue 3, September 2012, Pages 356–365 http://dx.doi.org/10.1016/j.jmathb.2012.03.001
Subject(s): Education
Links: http://dx.doi.org/10.1016/j.jmathb.2012.03.001
Persistent Link to This Record: http://purl.flvc.org/fsu/fd/FSU_migr_ste_faculty_publications-0010-P
Host Institution: FSU
Is Part of Series: School of Teacher Education Faculty Publications.
Is Part Of: The Journal of Mathematical Behavior.
Issue: 3, 31

Choose the citation style.
Whitacre, I., Bishop, J., Lamb, L., Phillipp, R., Schappelle, B. P., & Lewis, M. (2012). Happy and sad thoughts: An exploration of children's integer reasoning. Journal Of Mathematical Behavior. Retrieved from http://dx.doi.org/10.1016/j.jmathb.2012.03.001

Title: Happy and sad thoughts: An exploration of children's integer reasoning.
Name(s): Whitacre, Ian, author
Bishop, Jessica, author
Lamb, Lisa, author
Phillipp, Randolph, author
Schappelle, Bonnie P., author
Lewis, Melinda, author
Type of Resource: text
Genre: Text
Issuance: serial
Date Issued: 2012
Physical Form: computer
online resource
Extent: 1 online resource
Language(s): English
Abstract/Description: The purpose of this study was to investigate elementary children's conceptions that might serve as foundations for integer reasoning. Working from an abstract algebraic perspective and using an opposite-magnitudes context that is relevant to children, we analyzed the reasoning of 33 children in grades K-5. We focus our report on three prominent ways of reasoning. We do this by describing and analyzing the responses of three particular children (in Grades 1, 3, and 5) who exemplify these ways of reasoning. We view each of the three ways of reasoning as rich and interesting, and we see relationships of each to formal integer reasoning. At the same time, we view these ways of reasoning in terms of increasing levels of sophistication, potentially belonging to a single learning trajectory. Thus, we see the roots of more sophisticated integer reasoning in children's early intuitions about opposite magnitudes.
Identifier: FSU_migr_ste_faculty_publications-0010 (IID), 10.1016/j.jmathb.2012.03.001 (DOI)
Keywords: Integers, Negative numbers, Opposite magnitudes, Children's reasoning
Note: This is the author's version of a work that was accepted for publication in The Journal of Mathematical Behavior. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in The Journal of Mathematical Behavior, Volume 31, Issue 3, September 2012, Pages 356–365http://dx.doi.org/10.1016/j.jmathb.2012.03.001'>http://dx.doi.org/10.1016/j.jmathb.2012.03.001">http://dx.doi.org/10.1016/j.jmathb.2012.03.001
Citation: Ian Whitacre, Jessica Pierson Bishop, Lisa L.C. Lamb, Randolph A. Philipp, Bonnie P. Schappelle, Melinda L. Lewis. Happy and sad thoughts: An exploration of children's integer reasoning. The Journal of Mathematical Behavior, Volume 31, Issue 3, September 2012, Pages 356–365 http://dx.doi.org/10.1016/j.jmathb.2012.03.001
Subject(s): Education
Links: http://dx.doi.org/10.1016/j.jmathb.2012.03.001
Persistent Link to This Record: http://purl.flvc.org/fsu/fd/FSU_migr_ste_faculty_publications-0010
Host Institution: FSU
Is Part of Series: School of Teacher Education Faculty Publications.
Is Part Of: The Journal of Mathematical Behavior.
Issue: 3, 31