Are We Meeting Pedagogic Requirements? – The Quadratic Equation

Russell Jay Hendel

Hendel [8] recently proposed four pillars of good pedagogy: executive function, goal-setting, attribution theory and self-efficacy. These pillars are consistent with and supplement the pedagogical hierarchies [1,4,5,16,29,30,31]. These pillars also supplement the National Council of Teachers of Mathematics [NCTM] Process Standards [13,23] as well as the Standards of Mathematical Practice (SMP) of the Common Core State Standards of Mathematics(CCSSM) [11]. A natural follow-up question is whether, and how, current and past textbooks are meeting these requirements. This paper addresses this follow-up question by studying five pre-2000 textbooks [2,6,10,26,27] and three post-2000 books [12,17,28]. For purposes of specificity, the paper exclusively focuses on the treatment of the quadratic function/equation. Using the four pillars, the following questions are asked: What would executive function require for teaching the quadratic function/equation? What does the theory of goal-setting tell us about teaching the quadratic function/equation? What does attribution theory require? The paper’s main conclusions are that: i) some pre-2000 textbooks are already meeting the new standards; ii) no single textbook meets all requirements; iii) the requirements of pedagogic excellence—of Hendel, the Process Standards or the SMP—should be met by placing a primary focus on verbal problems. The paper also addresses operational concerns and shows how both operational and pedagogic concerns can be met simultaneously.

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