The Concept of Magnitude and What It Tells Us About How Struggling Students Learn Fractions

Abstract

This commentary summarizes emerging research into fractions instruction for students who are at risk for failure. Each of the three articles emphasizes a measure conception of fractions. Teaching fractions as measurement helps students learn the magnitude of rational numbers. However, measurement is only part of the way that students should conceptualize fractions. Instruction also needs to emphasize fractions as division. The article also draws attention to the teaching qualifications of those who typically instruct at-risk students in Tier 2 and 3 settings. More often than not, these individuals lack the pedagogical content knowledge needed to adapt instruction and address student misconceptions. This is a critical issue going forward as the field attempts to balance procedural understanding with key underlying fractional ideas such a measurement and division.