#### Abstract

Both children and adults find fractions challenging. Understanding how adults cognitively process fractions is important for making beneficial changes to math education in the future. We investigated whether the size of a fraction's denominator plays a significant role in the speed and accuracy with which adults compare the magnitude, or values, of two fractions (e.g., which is bigger ¾ or 3/19?). Should adults find fractions with large denominators more difficult to differentiate based on magnitude, it would suggest that participants are deconstructing the fractions into their component parts (e.g., focusing on the denominator), rather than thinking about the magnitude of the fractions in terms of the value of the fractions as a whole (e.g., ¾ = 0.75 or 75%). If participants are focusing on the components of fractions, then they may make slower and more error prone decisions when the comparison involves fractions with larger denominators, because these are fractions that actually possess smaller magnitudes (e.g., ¾ = 0.75 vs. 3/19 = 0.16). As hypothesized, adults in our study made significantly more mistakes when comparing fractions with larger denominators (11-20) as compared to fractions with smaller denominators (1-10). Adults focus on the denominators of fractions and treat them as whole number indicators of the fractions' magnitude, and this can lead to decreased accuracy on a magnitude comparison task.

#### Modified Abstract

Children and adults find fractions challenging We investigated whether the size of a fraction's denominator plays a role in the speed and accuracy with which adults compare the magnitudes of two fractions (e.g., which is bigger ¾ or 3/19?). Should adults find fractions with large denominators more difficult to differentiate based on magnitude, it would suggest that participants are deconstructing the fractions into their component parts, rather than thinking about the magnitude of the fractions (e.g., ¾ = 0.75 vs. 3/19 = 0.16). As hypothesized, participants made significantly more mistakes when comparing fractions with larger denominators (11-20) relative to fractions with smaller denominators (1-10). Adults treat the denominators of fractions as whole numbers, and this can lead to decreased accuracy on a magnitude comparison task.

#### Research Category

Psychology

#### Mentor #1 Information

Dr. Clarissa A Thompson

#### Presentation Format

Poster

#### Start Date

March 2016

#### Research Area

Cognitive Psychology

The Effect of Denominator Size on a Magnitude Comparison Task

Both children and adults find fractions challenging. Understanding how adults cognitively process fractions is important for making beneficial changes to math education in the future. We investigated whether the size of a fraction's denominator plays a significant role in the speed and accuracy with which adults compare the magnitude, or values, of two fractions (e.g., which is bigger ¾ or 3/19?). Should adults find fractions with large denominators more difficult to differentiate based on magnitude, it would suggest that participants are deconstructing the fractions into their component parts (e.g., focusing on the denominator), rather than thinking about the magnitude of the fractions in terms of the value of the fractions as a whole (e.g., ¾ = 0.75 or 75%). If participants are focusing on the components of fractions, then they may make slower and more error prone decisions when the comparison involves fractions with larger denominators, because these are fractions that actually possess smaller magnitudes (e.g., ¾ = 0.75 vs. 3/19 = 0.16). As hypothesized, adults in our study made significantly more mistakes when comparing fractions with larger denominators (11-20) as compared to fractions with smaller denominators (1-10). Adults focus on the denominators of fractions and treat them as whole number indicators of the fractions' magnitude, and this can lead to decreased accuracy on a magnitude comparison task.