Title: Relating to Fractions
Legend: Red = 2nd graders, Blue = 5th graders. Each dot represents one child, and shows his/her performance on the relational reasoning (TORR Jr.) and fractions understanding (FKA). Overall better relational reasoning skill is indicated by higher scores (more rightward) and better fractions skills indicated by higher scores. Overall, we see that children who perform better on the TORR Jr. also perform better on the FKA. Additional analyses (not shown here) demonstrate that this is not due to better general cognitive skills or general math skills.
Citation: Kalra, P.B., Hubbard, E.M., Matthews, P.G. (2020). Taking the relational structure of fractions seriously: Relational reasoning predicts fraction knowledge in elementary school children. Contemporary Educational Psychology, 62, 101896 https://doi.org/10.1016/j.cedpsych.2020.101896
Abstract: Understanding and using symbolic fractions in mathematics is critical for access to advanced STEM concepts. However, children and adults consistently struggle with fractions. Here, we take a novel perspective on symbolic fractions, considering them within the framework of relational structures in cognitive psychology, such as those studied in analogy research. We tested the hypothesis that relational reasoning ability is important for reasoning about fractions by examining the relation between scores on a domain-general test of relational reasoning (TORR Jr.) and a test of fraction knowledge consisting of various types of fraction problems in 194 second grade and 145 fifth grade students. We found that relational reasoning was a significant predictor of fractions knowledge, even when controlling for non-verbal IQ and fractions magnitude processing for both grades. The effects of relational reasoning also remained significant when controlling for overall mathematics knowledge and skill for second graders but was attenuated for fifth graders. These findings suggest that this important subdomain of mathematical cognition is integrally tied to relational reasoning and opens the possibility that instruction targeting relational reasoning may prove to be a viable avenue for improving children’s fractions skills.
About the Lab: The Educational Neuroscience Lab explores questions at the intersection of education and neuroscience, in the emerging field of Educational Neuroscience. Our research examines the neural underpinnings of cognitive processes that are relevant for education, and the role of educational experiences and enculturation as primary drivers of brain plasticity to create the neural circuits that underlie human specific abilities. Our research combines the latest technological advances in understanding the human brain as a “learning organ” with insights from cognitive psychology and education to help build the emerging field of educational neuroscience.