ABSTRACT

This chapter addresses the content strand F and development of algebraic reasoning, from patterns and properties of numbers in elementary school, through expressions and equations in middle school, to the extended functions and modeling in high-school mathematics. The most common difficulty with algebraic reasoning cited in literature is the attempt by many students to maintain arithmetic thinking when moving into algebraic situations. The chapter focuses on first type, the algebra studied in school that includes the solution of polynomial equations with one or more variables and basic properties of functions and graphs in the secondary grades, as well as algebraic thinking and pre-algebra topics developed in earlier grades. Algebra requires abstract thinking about relationships that is developed across the grade levels. The chapter explores some of the most critical foundational work for algebra concepts—algebraic notation and variables, simplifying expressions and solving one-variable equations, coordinate plane graphing, and linear functions—along with teaching strategies for these concepts across the PreK–12 curriculum.