A categorization of equations from expert students

Abstract

Secondary school students have difficulties in solving equations, even when they have learned the standard procedures and how to manipulate algebraic expressions. They do not seem to recognize when to use these procedures, because they do not see the structure of equations: they lack symbol sense. Experts categorize problems according to fundamental problem characteristics. Landa suggested analyzing expert knowledge, looking for crucial thinking steps, and teaching these with explicit attention to algorithmization of identification. In our study, four expert students were asked to think aloud when categorizing a set of equations according to the methods for solving equations. Using these results, the author formulated six categories of equations. These categories can be used in teaching the solving of equations. We suggest teachers start early with formulating categories of equations and with recognizing the different categories. Categories formulated in lower secondary school (grades 8 and 9) will form a basis for the categories used in grades 11 and 12.