Early Engagement of Parietal Cortex for Subtraction Solving Predicts Longitudinal Gains in Behavioral Fluency in Children

Abstract

There is debate in the literature regarding how single-digit arithmetic fluency is achieved over development. While the Fact-retrieval hypothesis suggests that with practice, children shift from quantity-based procedures to verbally retrieving arithmetic problems from long-term memory, the Schema-based hypothesis claims that problems are solved through quantity-based procedures and that practice leads to these procedures becoming more automatic. To test these hypotheses, a sample of 46 typically developing children underwent functional magnetic resonance imaging (fMRI) when they were 11 years old (time 1), and 2 years later (time 2). We independently defined regions of interest (ROIs) involved in verbal and quantity processing using rhyming and numerosity judgment localizer tasks, respectively. The verbal ROIs consisted of left middle/superior temporal gyri (MTG/STG) and left inferior frontal gyrus (IFG), whereas the quantity ROIs consisted of bilateral inferior/superior parietal lobules (IPL/SPL) and bilateral middle frontal gyri (MFG)/right IFG. Participants also solved a single-digit subtraction task in the scanner. We defined the extent to which children relied on verbal vs. quantity mechanisms by selecting the 100 voxels showing maximal activation at time 1 from each ROI, separately for small and large subtractions. We studied the brain mechanisms at time 1 that predicted gains in subtraction fluency and how these mechanisms changed over time with improvement. When looking at brain activation at time 1, we found that improvers showed a larger neural problem size effect in bilateral parietal cortex, whereas no effects were found in verbal regions. Results also revealed that children who showed improvement in behavioral fluency for large subtraction problems showed decreased activation over time for large subtractions in both parietal and frontal regions implicated in quantity, whereas non-improvers maintained similar levels of activation. All children, regardless of improvement, showed decreased activation over time for large subtraction problems in verbal regions. The greater parietal problem size effect at time 1 and the reduction in activation over time for the improvers in parietal and frontal regions implicated in quantity processing is consistent with the Schema-based hypothesis arguing for more automatic procedures with increasing skill. The lack of a problem size effect at time 1 and the overall decrease in verbal regions, regardless of improvement, is inconsistent with the Fact-retrieval hypothesis.

Gray matter volume in left intraparietal sulcus predicts longitudinal gains in subtraction skill in elementary school

“…The finding of this association only for younger children may suggest that brain structure of the left IPS is important early on because children rely more on quantity-based calculation strategies, whereas older children tend to retrieve the solution from long-term memory. Using fMRI, a previous study showed no evidence for such a shift, with no involvement of retrieval-related brain regions predicting subtraction gains ( Suárez-Pellicioni et al, 2020 ). Our results are more likely due to the younger group relying on quantity mechanisms to compute the calculations required to solve the subtraction test, while older children may have automatized these procedures ( Fayol and Thevenot, 2012 ; LeFevre et al, 2006 ).…”

“…Whereas the higher the GMV in left IPS at T1 the more they gained in subtraction skill, the higher the GMV in the left MTG/STG at T1 the less they gained in this operation. This finding suggests that structural integrity of quantity representation regions in the brain is what explains improvement in this operation, whereas the structural integrity of verbal representation regions, which potentially could have facilitated the use of the retrieval strategy, seems to be detrimental to improvement in this operation ( Suárez-Pellicioni et al, 2020 ).…”

“…Time-point 1 of this dataset is the basis of other publications including Berteletti and Booth (2015 , 2015 ), Berteletti et al (2014) , Demir-Lira et al (2019) , Demir et al (2014 , 2015 ) and Prado et al (2014) . The longitudinal data of this dataset is the basis of other publications including Demir-Lira et al (2016) , Suárez-Pellicioni and Booth (2018) , and Suárez-Pellicioni et al (2018 , 2019 , 2020 ). None of these studies have looked at the role of gray matter volume in predicting gains in subtraction or multiplication skill, which constitutes the objective of this study.…”

“…Previous brain structure studies focusing on arithmetic performance have not taken into account the evidence from fMRI studies suggesting that different mechanisms are involved in solving different operations ( Arsalidou and Taylor, 2011 ; Rosenberg-Lee et al, 2011 ) depending on the degree of retrieval or calculation they require ( Polspoel et al, 2017 ). Probably the clearest difference between operations is shown between subtraction and multiplication, with subtraction relying on calculation and activating quantity mechanisms in the parietal cortex (particularly the intraparietal sulcus (IPS); Prado et al, 2011 , 2014 ; Suárez-Pellicioni et al, 2020 ) and multiplication relying on retrieval of solutions from long-term memory and considered not to involve quantity mechanisms in IPS ( Prado et al, 2011 , 2014 ; Suárez-Pellicioni et al, 2018 , 2019 ).…”

“…The main objective of this study is to fill these gaps in the literature by studying the association of GMV in regions of the brain important for representing quantity and for the storage of arithmetic facts in long-term memory with gains in two operations known to have a different engagement of these mechanisms: subtraction and multiplication. To this aim, we used an ROI approach, focusing on the brain regions that have been reported to be functionally related to children’s subtraction gains ( Suárez-Pellicioni et al, 2020 ) and that are considered to be crucial for quantity representation ( Dehaene et al, 2003 ): the bilateral IPS ( Arsalidou et al, 2018 ; Arsalidou and Taylor, 2011 ; Battista et al, 2018 ) and regions that are considered to store the representation of arithmetic facts in a verbal code in long-term memory, the left MTG/STG ( Prado et al, 2011 , 2014 ; Suárez-Pellicioni et al, 2018 , 2019 ) Given that most of the cross-sectional and longitudinal studies described above found the effects in the left IPS, we studied hemispheric differences by using separate ROIs for the left and right IPS.…”