Fractions are a difficult concept that most children (and even adults) struggle with, despite the substantial time that is devoted to teaching it in school. Researchers at Florida State University propose a new framework to make the topic easier for children to understand.

Currently, children struggle with understanding individual fractions, as well as math involving fractions. This is because they tend to think of a fraction as two whole numbers, rather than a single number, causing them to incorrectly conceptualize the magnitude of fractions.

Dr. David Braithwaite and Robert Siegler propose a new framework for conceptualizing fractions called Putting Fractions Together (PFT).

PFT emphasizes that fractions and fraction sums, like whole numbers, are made up by combining smaller units. For example, the whole number 3 is made up of 1, 1, 1. Along the same lines, ⅗ is made of up ⅕, ⅕, ⅕.

Previous work has looked at the role of units in children's understanding of fractions, but PFT stands out due to its emphasis on these ideas in fraction addition as well.

Florida State researchers also tested PFT in relation to fraction arithmetic to see if it would improve children's knowledge of individual fractions and fraction sums and found that there was a large improvement in children's general understanding of fractions and fraction addition with the intervention. They state that the success of the intervention was likely caused, at least in part, by the PFT framework, due to its prominence in the instructions provided, the procedures used, and the feedback given.

These findings extend the integrated theory of numerical development created by Siegler and Braithwaite (2017).

The most relevant aspect of this theory in relation to PFT is that it predicts that understanding the magnitude of numbers is closely tied to understanding arithmetic as a whole. This study extends this aspect of the theory to fractions and fraction arithmetic - combining unit fractions to understand the magnitude of fractions and therefore understanding plausible fraction sums.

Furthermore, these findings also have implications for math education. In order to effectively teach fractions and fraction arithmetic to children, they need to be able to conceptualize the magnitude of individual fractions.

This study showed that asking children to conceptualize the magnitudes of fractions through number lines was an effective approach to teaching this complicated aspect of math. By creating a visual and physical representation, the study provided a process by which children could learn how to mentally represent fractions and fraction addition.

This study and proposed conceptual framework suggest that children do have the ability to make sense of fraction arithmetic. PFT provides a framework that helps children understand that fractions consist of units, which helps them understand their magnitude, and therefore, how they work in arithmetic.

By Ashley Pieper