Building Conceptual Understanding and Algebraic Reasoning in Algebra

Abstract

Algebra is a mechanism through which students build necessary and applicable skills for our technologically driven society and workforce, consequently success in algebra is considered the key to increased academic achievement in mathematics in high school and upper level mathematics. This thesis project is a comprehensive study which examines algebra from a number of perspectives - cognitive science, historical development, type of knowledge, teacher beliefs, and the impact of instructional materials - in order to gain greater understanding in the concept of learning and teaching algebra. The literature review examines the merits of symbolic versus rhetoric algebraic notation, educator’s approach to teaching math concepts and procedures, and teacher’s attitudes and expectations for student achievement in algebra. The project offers three lessons focused on building abstract reasoning, and conceptual and procedural fluency. Student worksheets for each lesson are included.