How Students Think When Doing Algebra
Steve Rhine ยท Rachel Harrington ยท Colin Starr
แแแ. 2018 ยท IAP
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Algebra is the gateway to college and careers, yet it functions as the eye of the needle because of low pass rates for the middle school/high school course and studentsโ struggles to understand. We have forty years of research that discusses the ways students think and their cognitive challenges as they engage with algebra. This book is a response to the National Council of Teachers of Mathematicsโ (NCTM) call to better link research and practice by capturing what we have learned about studentsโ algebraic thinking in a way that is usable by teachers as they prepare lessons or reflect on their experiences in the classroom. Through a Fund for the Improvement of Post-Secondary Education (FIPSE) grant, 17 teachers and mathematics educators read through the past 40 years of research on studentsโ algebraic thinking to capture what might be useful information for teachers to knowโover 1000 articles altogether. The resulting five domains addressed in the book (Variables & Expressions, Algebraic Relations, Analysis of Change, Patterns & Functions, and Modeling & Word Problems) are closely tied to CCSS topics. Over time, veteran math teachers develop extensive knowledge of how students engage with algebraic conceptsโtheir misconceptions, ways of thinking, and when and how they are challenged to understandโand use that knowledge to anticipate studentsโ struggles with particular lessons and plan accordingly. Veteran teachers learn to evaluate whether an incorrect response is a simple error or the symptom of a faulty or naรฏve understanding of a concept. Novice teachers, on the other hand, lack the experience to anticipate important moments in the learning of their students. They often struggle to make sense of what students say in the classroom and determine whether the response is useful or can further discussion (Leatham, Stockero, Peterson, & Van Zoest 2011; Peterson & Leatham, 2009). The purpose of this book is to accelerate early career teachersโ โexperienceโ with how students think when doing algebra in middle or high school as well as to supplement veteran teachersโ knowledge of content and students. The research that this book is based upon can provide teachers with insight into the nature of a studentโs struggles with particular algebraic ideasโto help teachers identify patterns that imply underlying thinking. Our book, How Students Think When Doing Algebra, is not intended to be a โhow toโ book for teachers. Instead, it is intended to orient new teachers to the ways students think and be a book that teachers at all points in their career continually pull of the shelf when they wonder, โhow might my students struggle with this algebraic concept I am about to teach?โ The primary audience for this book is early career mathematics teachers who donโt have extensive experience working with students engaged in mathematics. However, the book can also be useful to veteran teachers to supplement their knowledge and is an ideal resource for mathematics educators who are preparing preservice teachers.
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