Using refutational text to address the multiplication makes bigger misconception

Abstract

Understanding rational numbers is a source of difficulty with mathematics for students across ages and nationalities. This intervention study focuses on the misconception on the part of the students to think that multiplication makes the operand numbers bigger and division makes them smaller, independently of the numbers involved. In this study, a refutational text was administered to 6^th grade students to help them disengage from these misconceptions. Refutational texts directly state the erroneous beliefs and immediately overturn them by presenting the alternative correct ideas in a comprehensive and persuasive way. From the 87 6^th grade students that participated in the Pre/Post/Retention-test intervention study, 51 students (experimental group) received the refutational text. The results showed that the refutational text helped the students partly overcome the multiplication makes bigger misconception, and the results had a long-term effect. Not only the high, but also the low prior knowledge students were profited from the intervention. In addition, students managed to transfer the acquired knowledge about multiplication also to division items: the results showed statistically significantly less mistakes of the kind division makes smaller after the intervention. Theoretical and educational implications are discussed.