Developmental dissociation in the neural responses to simple multiplication and subtraction problems.
ABSTRACT: Mastering single-digit arithmetic during school years is commonly thought to depend upon an increasing reliance on verbally memorized facts. An alternative model, however, posits that fluency in single-digit arithmetic might also be achieved via the increasing use of efficient calculation procedures. To test between these hypotheses, we used a cross-sectional design to measure the neural activity associated with single-digit subtraction and multiplication in 34 children from 2nd to 7th grade. The neural correlates of language and numerical processing were also identified in each child via localizer scans. Although multiplication and subtraction were undistinguishable in terms of behavior, we found a striking developmental dissociation in their neural correlates. First, we observed grade-related increases of activity for multiplication, but not for subtraction, in a language-related region of the left temporal cortex. Second, we found grade-related increases of activity for subtraction, but not for multiplication, in a region of the right parietal cortex involved in the procedural manipulation of numerical quantities. The present results suggest that fluency in simple arithmetic in children may be achieved by both increasing reliance on verbal retrieval and by greater use of efficient quantity-based procedures, depending on the operation.
Project description:Different specific mechanisms have been suggested for solving single-digit arithmetic operations. However, the neural correlates underlying basic arithmetic (multiplication, addition, subtraction) are still under debate. In the present study, we systematically assessed single-digit arithmetic in a group of acute stroke patients (n = 45) with circumscribed left- or right-hemispheric brain lesions. Lesion sites significantly related to impaired performance were found only in the left-hemisphere damaged (LHD) group. Deficits in multiplication and addition were related to subcortical/white matter brain regions differing from those for subtraction tasks, corroborating the notion of distinct processing pathways for different arithmetic tasks. Additionally, our results further point to the importance of investigating fiber pathways in numerical cognition.
Project description:It has been proposed that recent cultural inventions such as symbolic arithmetic recycle evolutionary older neural mechanisms. A central assumption of this hypothesis is that the degree to which a preexisting mechanism is recycled depends on the degree of similarity between its initial function and the novel task. To test this assumption, we investigated whether the brain region involved in magnitude comparison in the intraparietal sulcus (IPS), localized by a numerosity comparison task, is recruited to a greater degree by arithmetic problems that involve number comparison (single-digit subtractions) than by problems that involve retrieving number facts from memory (single-digit multiplications). Our results confirmed that subtractions are associated with greater activity in the IPS than multiplications, whereas multiplications elicit greater activity than subtractions in regions involved in verbal processing including the middle temporal gyrus (MTG) and inferior frontal gyrus (IFG) that were localized by a phonological processing task. Pattern analyses further indicated that the neural mechanisms more active for subtraction than multiplication in the IPS overlap with those involved in numerosity comparison and that the strength of this overlap predicts interindividual performance in the subtraction task. These findings provide novel evidence that elementary arithmetic relies on the cooption of evolutionary older neural circuits.
Project description:Arithmetic facts, in particular multiplication tables, are thought to be stored in long-term memory and to be interference prone. At least two representations underpinning these arithmetic facts have been suggested: a physical representation of the digits and a numerical magnitude representation. We hypothesized that both representations are possible sources of interference that could explain individual differences in multiplication fact performance and/or in strategy use. We investigated the specificity of these interferences on arithmetic fact retrieval and explored the relation between interference and performance on the different arithmetic operations and on general mathematics achievement. Participants were 79 fourth-grade children (Mage=9.6 years) who completed a products comparison and a multiplication production task with verbal strategy reports. Performances on a speeded calculation test including the four operations and on a general mathematics achievement test were also collected. Only the interference coming from physical representations was a significant predictor of the performance across multiplications. However, both the magnitude and physical representations were unique predictors of individual differences in multiplication. The frequency of the retrieval strategy across multiplication problems and across individuals was determined only by the physical representation, which therefore is suggested as being responsible for memory storage issues. Interestingly, this impact of physical representation was not observed when predicting performance on subtraction or on general mathematical achievement. In contrast, the impact of the numerical magnitude representation was more general in that it was observed across all arithmetic operations and in general mathematics achievement.
Project description: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.
Project description:Some individuals experience more difficulties with math than others, in particular when arithmetic problems get more complex. Math ability, on one hand, and arithmetic complexity, on the other hand, seem to partly share neural underpinnings. This study addresses the question of whether this leads to an interaction of math ability and arithmetic complexity for multiplication and division on behavioral and neural levels. Previously screened individuals with high and low math ability solved multiplication and division problems in a written production paradigm while brain activation was assessed by combined functional near-infrared spectroscopy (fNIRS) and electroencephalography (EEG). Arithmetic complexity was manipulated by using single-digit operands for simple multiplication problems and operands between 2 and 19 for complex multiplication problems and the corresponding division problems. On the behavioral level, individuals with low math ability needed more time for calculation, especially for complex arithmetic. On the neural level, fNIRS results revealed that these individuals showed less activation in the left supramarginal gyrus (SMG), superior temporal gyrus (STG) and inferior frontal gyrus (IFG) than individuals with high math ability when solving complex compared to simple arithmetic. This reflects the greater use of arithmetic fact retrieval and also the more efficient processing of arithmetic complexity by individuals with high math ability. Oscillatory EEG analysis generally revealed theta and alpha desynchronization with increasing arithmetic complexity but showed no interaction with math ability. Because of the discovered interaction for behavior and brain activation, we conclude that the consideration of individual differences is essential when investigating the neurocognitive processing of arithmetic.
Project description:We describe functional and structural data acquired using a 3T scanner in a sample of 132 typically developing children, who were scanned when they were approximately 11 years old (i.e. Time 1). Sixty-three of them were scanned again approximately 2 years later (i.e. Time 2). Children performed four tasks inside the scanner: two arithmetic tasks and two localizer tasks. The arithmetic tasks were a single-digit multiplication and a single-digit subtraction task. The localizer tasks, a written rhyming judgment task and a numerosity judgment task, were used to independently identify verbal and quantity brain areas, respectively. Additionally, we provide data on behavioral performance on the tasks inside the scanner, participants' scores on standardized tests, including reading and math skill, and a developmental history questionnaire completed by parents. This dataset could be useful to answer questions regarding the neural bases of the development of math in children and its relation to individual differences in skill. The data, entitled "Brain Correlates of Math Development", are freely available from OpenNeuro (https://openneuro.org).
Project description:The triple-code model (TCM) of number processing suggests the involvement of distinct parietal cortex areas in arithmetic operations: the bilateral horizontal segment of the intraparietal sulcus (hIPS) for arithmetic operations that require the manipulation of numerical quantities (e.g., subtraction) and the left angular gyrus (AG) for arithmetic operations that require the retrieval of answers from long-term memory (e.g., multiplication). Although neuropsychological, neuroimaging, and brain stimulation studies suggest the dissociation of these operations into distinct parietal cortex areas, the role of strategy (online calculation vs. retrieval) is not yet fully established. In the present study, we further explored the causal involvement of the left AG for multiplication and left hIPS for subtraction using a neuronavigated repetitive transcranial magnetic stimulation (rTMS) paradigm. Stimulation sites were determined based on an fMRI experiment using the same tasks. To account for the effect of strategy, participants were asked whether they used retrieval or calculation for each individual problem. We predicted that the stimulation of the left AG would selectively disrupt the retrieval of the solution to multiplication problems. On the other hand, stimulation of the left hIPS should selectively disrupt subtraction. Our results revealed that left AG stimulation was detrimental to the retrieval and online calculation of solutions for multiplication problems, as well as, the retrieval (but not online calculation) of the solutions to subtraction problems. In contrast, left hIPS stimulation had no detrimental effect on both operations regardless of strategy.
Project description:Neuroimaging studies suggest segregated neuronal systems underlying number magnitude processing (e.g. subtraction) and arithmetic fact retrieval (e.g. multiplication). While number magnitude processing is thought to rely on the intraparietal sulcus (IPS) bilaterally, arithmetic fact retrieval is thought to rely on the left angular gyrus (AG). However, evidence from brain damaged patients and brain stimulation challenges this view and suggests considerable overlap between the systems underlying number magnitude processing and arithmetic fact retrieval. This study investigates, whether sex differences in number processing can account for these conflicting findings. A subtraction and a multiplication task were administered to 40 men and 34 women in their luteal phase during functional MRI. Replicating previous studies in men, we found the IPS to be more strongly activated during subtraction than multiplication, and the AG to be more strongly activated during multiplication than subtraction. However, no differences between the two tasks were observed in women.
Project description:Many studies have shown that solving addition and subtraction problems can induce overt shifts of spatial attention. In particular, right-side targets are detected faster than left-side targets when preceded by an addition operation, while left-side targets are detected faster than right-side targets when preceded by a subtraction operation. However, the interaction between space and arithmetic in multiplication or division is hardly studied and remains controversial. In order to make a strong case for the interaction between space and mental arithmetic, we attempted to replicate the spatial-arithmetic association in addition and subtraction (Experiment 1), and at the same time investigated whether shift of spatial attention would also be induced by multiplication or division operations (Experiment 2). We found that solving addition problems facilitated the detection of right-side targets, whereas left-side targets were detected faster after solving subtraction problems. However, no interaction between space and arithmetic operation was observed in multiplication or division. The implication of these findings is discussed.
Project description:Although lesion studies over the past several decades have focused on functional dissociations in posterior parietal cortex (PPC) during arithmetic, no consistent view has emerged of its differential involvement in addition, subtraction, multiplication, and division. To circumvent problems with poor anatomical localization, we examined functional overlap and dissociations in cytoarchitectonically defined subdivisions of the intraparietal sulcus (IPS), superior parietal lobule (SPL) and angular gyrus (AG), across these four operations. Compared to a number identification control task, all operations except addition, showed a consistent profile of left posterior IPS activation and deactivation in the right posterior AG. Multiplication and subtraction differed significantly in right, but not left, IPS and AG activity, challenging the view that the left AG differentially subserves retrieval during multiplication. Although addition and multiplication both rely on retrieval, multiplication evoked significantly greater activation in right posterior IPS, as well as the prefrontal cortex, lingual and fusiform gyri, demonstrating that addition and multiplication engage different brain processes. Comparison of PPC responses to the two pairs of inverse operations: division versus multiplication and subtraction versus addition revealed greater activation of left lateral SPL during division, suggesting that processing inverse relations is operation specific. Our findings demonstrate that individual IPS, SPL and AG subdivisions are differentially modulated by the four arithmetic operations and they point to significant functional heterogeneity and individual differences in activation and deactivation within the PPC. Critically, these effects are related to retrieval, calculation and inversion, the three key cognitive processes that are differentially engaged by arithmetic operations. Our findings point to distribute representation of these processes in the human PPC and also help explain why lesion and previous imaging studies have yielded inconsistent findings.