Lower Math Gains are Associated With Lack of Automaticity of Multiplication Facts in Long-Term Memory

• In Event: 2-159 - Applications of Cognitive Science Research: Contributions to Education Across Levels of Analysis

Integrative Statement

One of the crucial milestones in elementary school math is to learn and become fluent in retrieving multiplication facts. Models of the neural basis of arithmetic argue that left inferior frontal cortex is involved in cognitive control of verbal representations of math facts in left lateral temporal cortex, whereas bilateral intra-parietal cortex is involved in numerical calculation. Lower levels of math competence for multiplications is associated with greater effortful retrieval because of less robust verbal representations and the engagement of numerical operations as a back-up strategy.
Previous studies on multiplication have focused on brain activation in isolated nodes of the network and have not used longitudinal designs, so we do not know how changes in functional connectivity between these nodes is related to gains in multiplication over time. The objective of this study was to investigate how changes in multiplication task performance is associated with changes in functional connectivity of temporal cortex with frontal and parietal cortices. Longitudinal data were collected from 45 children, with an average 2.2-year interval between the two sessions, when they were about 11 years old at time 1 (T1) and 13 years old at time 2 (T2). At the two time points, children solved a single-digit multiplication task inside the scanner, as well as verbal and numerosity localizer tasks. A Psychophysiological Interaction (PPI) analysis was carried out by defining the seed in the temporal cortex (i.e. posterior superior and middle temporal gyri) and examining changes in connectivity with frontal cortex (i.e. left inferior frontal gyrus; IFG) as well as parietal cortex (i.e. left and right inferior and superior parietal lobules; IPL/SPL). We calculated changes in response times over time as the measure of longitudinal improvement in the task. We found that Non-improvers showed greater levels of functional connectivity of left temporal cortex with left IFG and left IPS at T2, as compared to Improvers. The left IFG overlapped a cluster independently identified by a verbal localizer task and the left IPS cluster overlapped a cluster independently identified by a numerosity localizer task.
These results suggest that lack of improvement in multiplications are associated with greater cognitive control of verbal representations and greater engagement of numerical operations. These findings are interpreted as Non-improvers reverting from retrieval to less efficient numerical operations to solve the multiplication task over time, which can be attributed to the decay of memory traces of multiplication facts in long-term memory. These results have educational implications suggesting the importance of encouraging the construction of a strong and reliable storage of multiplication facts in long-term memory and highlighting the importance of developing and maintaining automaticity in their retrieval. Only by gaining this automaticity would cognitive resources be available to be invested in the acquisition of more advanced math concepts and the solving of complex problems. Our findings suggest that automaticity in older children should not be taken for granted and recommends continued practice on simple multiplication facts throughout middle elementary school to make sure that this building block is solid to support successful math development.

Authors

• Macarena Suarez-Pellicioni, Vanderbilt University
  Presenting Author

• Jérôme Prado, Institut des Sciences Cognitives, Centre National de la Recherche Scientifique (CNRS); Université de Lyon
  Non-Presenting Author

• James Booth, Vanderbilt University
  Non-Presenting Author