An Alternative Route to Fractions Knowledge

• In Event: 35.069 - Fractions Learning: One Subject, Multiple Perspectives

Abstract

Objective. This research presents evidence that the human perceptual system provides access to fraction magnitudes and advances an argument that leveraging this sensitivity may prove fruitful for improving education on fraction symbols.
There is a widely-held assumption that any sound conception of fractions must be built upon foundational ideas of equal sharing or partitioning (e.g., Pitkethly & Hunting, 1996; Steffe, 2001). However, a growing body of evidence suggests that a perceptually based system for processing nonsymbolically instantiated fractions may provide a more intuitive foundation (Duffy, Huttenlocher, & Levine, 2005; Jacob, Vallentin, & Nieder, 2012; McCrink & Wynn, 2007). This system processes magnitudes of nonsymbolic ratios in several representational formats, such as fractions formed by the relative lengths of two lines. It may be that this ratio perception ability can be leveraged to improve fractions knowledge without appealing to partitive reasoning.
I will present two key findings that demonstrate the potential for using perceptual learning modules to teach about the magnitudes of symbolic fractions: 1) that nonsymbolic ratio sensitivity automatically affects processing of symbolic fractions among adults; and 2) that this ratio sensitivity is present even among primary school aged children with little fractions training.
Experiment 1 used a modified number Stroop paradigm to explore the interface between nonsymbolic ratio perception and symbolic fraction processing among 40 undergraduate students. Participants selected the larger of two symbolic fractions that varied along three dimensions: the values of the symbolic fractions being compared, the congruity of the absolute physical sizes of the fractions relative to the symbolic fraction decision, and the congruity of the nonsymbolic ratios formed by the sizes of the fonts used to print the numerators and denominators of each fraction relative to the symbolic fraction decision. Participants were instructed to select the larger fraction in each pair while ignoring differences in font size. Results indicated that participants were slower and less accurate when symbolic fractions were printed in rational font magnitudes that were incongruent with symbolic fraction comparison decisions (Figure 1).
Experiment 2 used a match-to-sample task to explore nonsymbolic ratio sensitivity among a small initial sample of young children (n = 7; Grades pre K to 3rd grade). Using a tablet computer, children chose which of two nonsymbolic ratios matched a nonsymbolic target ratio of a given magnitude. Results indicated that young children’s accuracy was distance-dependent: They were quite accurate when the distance between target and distractor magnitudes was large, and accuracy fell as the distance between target and distractor magnitudes decreased (Figure 2). These patterns are consistent with young children having an intuitive understanding of actual fraction magnitudes similar to their intuitive understanding of the relative sizes of different collections of objects.
Together, these findings show that nonsymbolic ratio magnitudes interface with symbolic processing and that the potential for this interaction exists even for primary school aged children. Given this symbolic-to-nonsymbolic interface, there may be untapped potential for using perceptual training modules to help make fractions symbols semantically meaningful for learners.

Author

• Percival Grant Matthews, University of Wisconsin - Madison