Does comparing informal and formal procedures promote mathematics learning? The benefits of bridging depend on attitudes toward mathematics

Students benefit from learning multiple procedures for solving the same or related problems.However, past research on comparison instruction has focused on comparing multipleformal procedures. This study investigated whether the benefits of comparing proceduresextend to comparisons that involve informal and formal procedures. We also examinedhow 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 likedmathematics learned equally well whether they received comparison or sequential instruction.However, among learners who did not like mathematics, instruction that included supportfor comparisons between the formal and informal procedures led to greater gains inconceptual knowledge than did sequential instruction of the procedures.