Fourth graders’ expression of the general case

Abstract

This study forms part of a classroom teaching experiment (CTE) on the development of a group of 25 9 10 years old students’ algebraic thinking. More specifically, it explores their reasoning while solving word problems built around functional relationships to determine how they generalize through questions posed using natural language, drawn figures or the keyword “many”. Their written and oral answers to those questions are qualitatively analyzed to determine which approach most effectively supports the expression of their generalization. The results reveal the benefits of posing questions about the general case in different ways while teaching students to use conventional algebraic representations. According to these findings, 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 specific values assigned according to their own criteria. Identifying the most effective 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.