Why Sense-Making through Magnitude May Be Harder for Fractions than for Whole Numbers

Abstract

What is the role of fraction magnitude knowledge in learning fraction addition? An experiment with 71 6th and 7th grade students compared fraction addition instruction and practice with a magnitude representation to a tightly controlled non-magnitude condition. In the magnitude condition, students with better fraction magnitude estimation skills benefitted more from the conceptual instruction and this relationship was moderated by students’ knowledge of how magnitude relates to fraction addition and equivalence. However, students with better fraction magnitude estimation skills benefitted less from the practice problems with magnitude. In the non-magnitude condition, fraction magnitude estimation was not predictive of learning. This study indicates that students with magnitude knowledge can leverage it to learn fraction addition concepts from magnitude representations, but, for those students, magnitude representations may be a distraction from practicing the procedure.


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