Teaching the Strand of CCSS Slope through Metacognition in Middle School, High School, and Advanced Placement Mathematics

Abstract

The strand of slope presents every year from 7th grade through Advanced Placement Calculus. The Common Core Learning Standards require and encourage a thorough understanding of slope and slope-related concepts such as unit rate, parallel and perpendicular lines, and the derivative. Unfortunately, many secondary mathematics teachers struggle to teach students to monitor their process and conceptualize an overall strategy for solving complex and fundamental problems. This thesis examines the role of metacognition-focused instruction on achievement, and offers research-supported teaching methods in the context of slope and unit rate that support metacognition. These methods are then presented in a series of lessons, one each from 7th grade through calculus, examining slope through a metacognitive lens. Lessons are tied together enabling teachers to solidify their own understanding of the big picture role of slope in secondary mathematics: earlier lessons foreshadow calculus concepts, and later lessons look back to the earlier foundation of unit rate and basic uses of slope. By examining slope within a metacognitive context, teachers can strengthen standards-based curriculum, solidify understanding of slope, and incorporate teaching tools to support achievement.