The transition from arithmetic to algebra : to reason, explain, argue, generalize and justify

This paper considers year eleven students' solutions of a specific task, which includes both a numerical part and a generalization of the task context that needs a transition from arithmetic to algebra. We investigate if students can solve the given problem, explain a solution and justify why the generalized problem always can be solved. Students prefer to explain in rhetoric rather than in symbolic algebra. Seven different ways of explaining are traced among the written answers. Few students are able to give an acceptable justification for the solution of the generalized problem, even after a course including work with this kind of problem. There are signs of students being unfamiliar with meta-cognitive activity.Godkänd; 2006; 20070507 (ysko)