Asymmetry in student achievement on multiple-choice and constructed-response items in reversible mathematics processes

In this paper we report the results of an experiment designed to test the hypothesis that when faced with a question involving the inverse direction of a reversible mathematical process, students solve a multiple-choice version by verifying the answers presented to them by the direct method, not by undertaking the actual inverse calculation. Participants responded to an online test containing equivalent multiple-choice and constructed-response items in two reversible algebraic techniques: factor/expand and solve/verify. The findings supported this hypothesis: Overall scores were higher in the multiple-choice condition compared to the constructed-response condition, but this advantage was significantly greater for items concerning the inverse direction of reversible processes compared to those involving direct processes.