Equation solving, students’ mathematical strategies, big data, diagnostic assessment, student errors, student’s mathematical thinking

Abstract

Recent research shows that young students can engage in algebraic reasoning before their first course in algebra.
 However, the extent to which elementary school children can develop proficiency with algebraic notation and procedures is still unclear. We analyzed fifth grade students’ ability to represent and solve verbal problems using equations with variables on both sides of the equal sign, interrelate algebraic and graphical representations of the problem, and realize that values other than the solution would lead to inequalities. From third to fifth grade, students from a Boston, MA, USA public school participated in weekly lessons based on a functional approach to arithmetic and algebra. Lessons involved verbal, algebraic, tabular, and graphical representations of functions. In grade four, they solved word problems using variables, data tables, and Cartesian graphs to compare functions. By grade five they were introduced to standard procedures to solve equations. In written assessments in fifth grade, approximately two-thirds of participating students (a) compared the graphs of two functions in an equation; (b) identified the point in the Cartesian plane where the two functions were equal, (c) represented a word problem as an equation with a variable on both sides of the equal sign. Approximately half of the students solved the equation and noted that values other than the solution would lead to inequalities. In a follow up interview, more students found the correct solution to the equation and nearly half of those gave valid explanations about the meaning of the solution.