Fourth graders’ expression of the general case

Abstract

This study forms part of a classroom teaching experiment on the development of a group of 25 9–10 years old students’ algebraic thinking. More specifcally, it explored their reasoning while solving word problems built around functional relationships to determine how they generalized through questions posed using natural language, drawn fgures or the keyword ‘many’. Their written and oral answers to those questions were analyzed qualitatively to determine which approach most efectively supported the expression of their generalization. The results reveal the benefts of posing questions about the general case in diferent ways while teaching students to use conventional algebraic representations. According to these fndings, representing indeterminate quantities with the keyword ‘many’ induces generalization more successfully than representing them with letters. The use of letters prompts students to seek meaning for the letters, either conventionally, as an unknown or variable quantity, or otherwise, as a label or specifc values assigned according to their own criteria. Identifying the most efective procedures may help teachers and curriculum designers formulate mathematical tasks that encourage students to express the generality they perceive in particular cases. Determining the communication demands of each approach is likewise highly useful.