Multiple skills underlie arithmetic performance: A large-scale structural equation modeling analysis

Current theoretical approaches point to the importance of several cognitive skills not specific to mathematics for the etiology of mathematics disorders (MD). In the current study, we examined the role of many of these skills, specifically: rapid automatized naming, attention, reading, and visual perception, on mathematics performance among a large group of college students (N = 1,322) with a wide range of arithmetic proficiency. Using factor analysis, we discovered that our data clustered to four latent variables 1) mathematics, 2) perception speed, 3) attention and 4) reading. In subsequent structural equation modeling, we found that the latent variable perception speed had a strong and meaningful effect on mathematics performance. Moreover, sustained attention, independent from the effect of the latent variable perception speed, had a meaningful, direct effect on arithmetic fact retrieval and procedural knowledge. The latent variable reading had a modest effect on mathematics performance. Specifically, reading comprehension, independent from the effect of the latent variable reading, had a meaningful direct effect on mathematics, and particularly on number line knowledge. Attention, tested by the attention network test, had no effect on mathematics, reading or perception speed. These results indicate that multiple factors can affect mathematics performance supporting a heterogeneous approach to mathematics. These results have meaningful implications for the diagnosis and intervention of pure and comorbid learning disorders

The Unique Role of Spatial Working Memory for Mathematics Performance

We explored the multi-dimensionality of mathematics and working memory (WM) by examining the differential relationships between different areas of mathematics with visual, spatial, and verbal WM. Previous research proposed that visuospatial WM is a unique predictor of mathematics, but neuroimaging and cognitive research suggest divisions within visuospatial WM. We created a new WM task to isolate visuospatial WM’s visual and spatial components and maintained consistent design across tasks and found that spatial WM predicted mathematics and visual WM did not. We also found that verbal WM predicted all mathematics areas included, while spatial WM was a unique predictor of numerical understanding and geometry, not arithmetic and estimation. These findings integrate previous neuroimaging, cognitive and educational psychology research and further our understanding of the relationship between WM and mathematics

Multiple Skills Underlie Arithmetic Performance: A Large-Scale Structural Equation Modeling Analysis

Current theoretical approaches point to the importance of several cognitive skills not specific to mathematics for the etiology of mathematics disorders (MD). In the current study, we examined the role of many of these skills, specifically: rapid automatized naming, attention, reading, and visual perception, on mathematics performance among a large group of college students (N = 1,322) with a wide range of arithmetic proficiency. Using factor analysis, we discovered that our data clustered to four latent variables 1) mathematics, 2) perception speed, 3) attention and 4) reading. In subsequent structural equation modeling, we found that the latent variable perception speed had a strong and meaningful effect on mathematics performance. Moreover, sustained attention, independent from the effect of the latent variable perception speed, had a meaningful, direct effect on arithmetic fact retrieval and procedural knowledge. The latent variable reading had a modest effect on mathematics performance. Specifically, reading comprehension, independent from the effect of the latent variable reading, had a meaningful direct effect on mathematics, and particularly on number line knowledge. Attention, tested by the attention network test, had no effect on mathematics, reading or perception speed. These results indicate that multiple factors can affect mathematics performance supporting a heterogeneous approach to mathematics. These results have meaningful implications for the diagnosis and intervention of pure and comorbid learning disorders

Neural Correlates of Numerical Estimation: The Role of Strategy Use

Introduction: Computation estimation is the ability to provide an approximate answer to a complex arithmetic problem without calculating it exactly. Despite its importance in daily life, the neuronal network underlying computation estimation is largely unknown. Methods: We looked at the neuronal correlates of two computational estimation strategies: approximated calculation and sense of magnitude (SOM)–intuitive representation of magnitude, without calculation. During an fMRI scan, thirty-one college students judged whether the result of a two-digit multiplication problem was larger or smaller than a given reference number. In two different blocks, they were asked to use a specific strategy (AC or SOM). Results: The two strategies activated brain regions related to calculation, numerical cognition, decision-making, and working memory. AC more than SOM elicited activations in multiple, domain-specific brain regions in the parietal lobule, including the left SMG (BA 40), the bilateral superior parietal lobule (BA 7), and the right inferior parietal lobule (BA 7). The activation level of the IFG was positively correlated to individual accuracy, indicating that the IFG has an essential role in both strategies. Conclusions: These finding suggest that the analogic code of magnitude is more involved in the AC than the SOM strategy

The Cognitive Estimation Task Is Nonunitary: Evidence for Multiple Magnitude Representation Mechanisms Among Normative and ADHD College Students

There is a current debate on whether the cognitive system has a shared representation for all magnitudes or whether there are unique representations. To investigate this question, we used the Biber cognitive estimation task. In this task, participants were asked to provide estimates for questions such as, “How many sticks of spaghetti are in a package?” The task uses different estimation categories (e.g., time, numerical quantity, distance, and weight) to look at real-life magnitude representations. Experiment 1 assessed (N = 95) a Hebrew version of the Biber Cognitive Estimation Task and found that different estimation categories had different relations, for example, weight, time, and distance shared variance, but numerical estimation did not. We suggest that numerical estimation does not require the use of measurement in units, hence, it represents a more “pure” numerical estimation. Experiment 2 found that different factors explain individual abilities in different estimation categories. For example, numerical estimation was predicted by preverbal innate quantity understanding (approximate number sense) and working memory, whereas time estimations were supported by IQ. These results demonstrate that cognitive estimation is not a unified construct

The Cognitive Estimation Task is nonunitary: Evidence for multiple magnitude representation mechanisms among normative and ADHD college students

There is a current debate on whether the cognitive system has a shared representation for all magnitudes or whether there are unique representations. To investigate this question, we used the Biber cognitive estimation task. In this task, participants were asked to provide estimates for questions such as, “How many sticks of spaghetti are in a package?” The task uses different estimation categories (e.g., time, numerical quantity, distance, and weight) to look at real-life magnitude representations. Experiment 1 assessed (N = 95) a Hebrew version of the Biber Cognitive Estimation Task and found that different estimation categories had different relations, for example, weight, time, and distance shared variance, but numerical estimation did not. We suggest that numerical estimation does not require the use of measurement in units, hence, it represents a more “pure” numerical estimation. Experiment 2 found that different factors explain individual abilities in different estimation categories. For example, numerical estimation was predicted by preverbal innate quantity understanding (approximate number sense) and working memory, whereas time estimations were supported by IQ. These results demonstrate that cognitive estimation is not a unified construct

Understanding Estimations of Magnitudes: An fMRI Investigation

The current study examined whether discrete numerical estimation is based on the same cognitive process as estimation of continuous magnitudes such as weight and time. While the verbal estimation of numerical quantities has a contingent unit of measurement (e.g., how many cookies fit in a cookie jar? _X_ cookies), estimation of time and weight does not (e.g., how much time does it take to fill a bath with water? _X_ minutes/hours/seconds). Therefore, estimation of the latter categories has another level of difficulty, requiring extensive involvement of cognitive control. During a functional magnetic resonance imaging (fMRI) scan, 18 students performed estimations with three estimation categories: number, time, and weight. Estimations elicited activity in multiple brain regions, mainly: (1) visual regions including bilateral lingual gyrus), (2) parietal regions including the left angular gyrus and right supramarginal gyrus, and (3) the frontal regions (cingulate gyrus and the inferior frontal cortex). Continuous magnitude estimations (mostly time) produced different frontal activity than discrete numerical estimations did, demonstrating different profiles of brain activations between discrete numerical estimations and estimations of continuous magnitudes. The activity level in the right middle and inferior frontal gyrus correlated with the tendency to give extreme responses, signifying the importance of the right prefrontal lobe in estimations