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Making Sense of Extraneous Solutions

Mathematics Teacher Volume 106, Number 6, ISSN 0025-5769


Principles and Standards for School Mathematics (NCTM 2000) states, "Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning." The focus on reasoning and sense making with technology in the lesson presented in this article will enable students to do more than just carry out procedures; they will be able to understand the procedures and know how the procedures might be used in different situations while interpreting the results (NCTM 2009). The lesson includes three key elements of reasoning and sense making with functions: (1) using multiple representations of functions as a means of demonstrating mathematical flexibility in problem solving; (2) modeling by using families of functions; and (3) analyzing the effects of parameters (NCTM 2010). According to the Programme for International Student Assessment (PISA 2007), American students lag behind international students in their ability to analyze, reason, communicate, solve, and interpret a variety of mathematical problems. This lesson allows teachers to use a pedagogical approach to teaching mathematics through problem solving (see Schoen 2003) and also address these PISA areas of concern.


Zelkowski, J.S. (2013). Making Sense of Extraneous Solutions. Mathematics Teacher, 106(6), 452-458. Retrieved May 19, 2019 from .

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