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Richardson, Janessa; Bachman, Rachel M. – Mathematics Teacher, 2017
This article describes a preservice teacher's imaginative exploration of completing the square through a process of reasoning and sense making. She recounts historical perspectives and her own discoveries in the process of completing the square. Through this process of sense making, she engaged with the content standard of completing the square to…
Descriptors: Preservice Teachers, Mathematics Instruction, Mathematical Concepts, Mathematical Logic
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Johnson, Gwendolyn J.; Thompson, Denisse R.; Senk, Sharon L. – Mathematics Teacher, 2010
Recognizing that textbooks play a prominent role in fostering students' understanding of reasoning and proof, the authors conducted a study to examine the extent to which textbooks used in U.S. high schools provide opportunities for students to encounter proof-related reasoning and how the nature of proof-related reasoning in textbooks varies by…
Descriptors: High Schools, Textbooks, Mathematical Logic, Validity