Invited Paper



Students benefit from learning multiple procedures for solving the same or related problems. However, past research on comparison instruction has focused on comparing multiple formal procedures. This study investigated whether the benefits of comparing procedures extend to comparisons that involve informal and formal procedures. We also examined how learner characteristics, including prior knowledge and attitudes toward mathematics, affect learning from comparing procedures. We addressed these issues in college students' learning procedures for solving systems of equations problems in algebra. Learners who liked mathematics learned equally well whether they received comparison or sequential instruction. However, among learners who did not like mathematics, instruction that included support for comparisons between the formal and informal procedures led to greater gains in conceptual knowledge than did sequential instruction of the procedures.