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

- Eliane Wiese,
*University of California, Berkeley, Berkeley, CA, USA*
- Rony Patel,
*Carnegie Mellon University*
- Kenneth Koedinger,
*Carnegie Mellon University*

## 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.

Back to Table of Contents