Sorting to Develop Definitional Reasoning

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All too often, definitions of mathematical ideas and objects are presented as facts to memorize in mathematics classrooms (de Villiers 1998; Keiser 2000). This is unfortunate, as it means that students are not provided opportunities to engage in a form of reasoning that is arguably at the heart of mathematics—definitional reasoning. Making sense of, constructing, and using definitions to determine what counts as an object (e.g., an odd number, a triangle) develop students' ability to communicate about mathematical ideas and their conceptual understanding of properties and relations (Keiser 2000).

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Contributor Notes

Marta Kobiela, marta.kobiela@mcgill.ca, is an assistant professor of mathematics education at McGill University in Montreal, Canada. Her research investigates the learning of disciplinary and professional practices.

Kara J. Jackson, karajack@uw.edu, is an associate professor of mathematics education at the University of Washington–Seattle. Her research focuses on how to support system-wide instructional improvement that enables all students to participate in rigorous mathematical activity.

Annie Savard, annie.savard@mcgill.ca, is an associate professor in mathematics education at McGill University in Montreal. She is interested in the contribution of school mathematics to the development of citizenship competencies such as decision making or critical thinking toward gambling or other financial activities.

Emily Shahan, eshahan@uw.edu, teaches mathematics methods courses in the University of Washington's elementary and secondary teacher education programs.

(Corresponding author is Kobiela marta.kobiela@mcgill.ca)(Corresponding author is Jackson karajack@uw.edu)(Corresponding author is Savard annie.savard@mcgill.ca)(Corresponding author is Shahan eshahan@uw.edu)
Teaching Children Mathematics

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