Defective number module or impaired access? Numerical magnitude processing in first graders with mathematical difficulties

This study examined numerical magnitude processing in first graders with severe and mild forms of mathematical difficulties, children with mathematics learning disabilities (MLD) and children with low achievement (LA) in mathematics, respectively. In total, 20 children with MLD, 21 children with LA, and 41 regular achievers completed a numerical magnitude comparison task and an approximate addition task, which were presented in a symbolic and a nonsymbolic (dot arrays) format. Children with MLD and LA were impaired on tasks that involved the access of numerical magnitude information from symbolic representations, with the LA children showing a less severe performance pattern than children with MLD. They showed no deficits in accessing magnitude from underlying nonsymbolic magnitude representations. Our findings indicate that this performance pattern occurs in children from first grade onward and generalizes beyond numerical magnitude comparison tasks. These findings shed light on the types of intervention that may help children who struggle with learning mathematics

Challenges in mathematical cognition: a collaboratively-derived research agenda

This paper reports on a collaborative exercise designed to generate a coherent agenda for research on mathematical cognition. Following an established method, the exercise brought together 16 mathematical cognition researchers from across the fields of mathematics education, psychology and neuroscience. These participants engaged in a process in which they generated an initial list of research questions with the potential to significantly advance understanding of mathematical cognition, winnowed this list to a smaller set of priority questions, and refined the eventual questions to meet criteria related to clarity, specificity and practicability. The resulting list comprises 26 questions divided into six broad topic areas: elucidating the nature of mathematical thinking, mapping predictors and processes of competence development, charting developmental trajectories and their interactions, fostering conceptual understanding and procedural skill, designing effective interventions, and developing valid and reliable measures. In presenting these questions in this paper, we intend to support greater coherence in both investigation and reporting, to build a stronger base of information for consideration by policymakers, and to encourage researchers to take a consilient approach to addressing important challenges in mathematical cognition

Mean accuracy on the numerical magnitude comparison tasks as a function of grade and distance.

<p>Solid lines indicate data on the symbolic magnitude comparison task (<i>M</i>_{Grade 1} = .89; <i>M</i>_{Grade 3} = .92), and dashed lines indicate data on the non-symbolic magnitude comparison task (<i>M</i>_{Grade 1} = .88; <i>M</i>_{Grade 3} = .92).</p

Scatterplots showing the significant associations between the numerical magnitude processing tasks and timed (top panels) and untimed (bottom panels) mathematics achievement in Grade 1.

<p>Scatterplots showing the significant associations between the numerical magnitude processing tasks and timed (top panels) and untimed (bottom panels) mathematics achievement in Grade 1.</p

Partial correlations between the mapping and numerical magnitude comparison tasks controlling for grade.

<p>Motor reaction time was additionally included as a covariate in the reaction time analyses. NS = non-symbolic; S = symbolic. *<i>p<</i>.05; **<i>p<</i>.01.</p

Correlations between the experimental tasks and mathematics achievement.

<p>Timed = timed mathematics achievement; Untimed = untimed mathematics achievement; NS = non-symbolic; S = symbolic. *<i>p<</i>.05; **<i>p<</i>.01.</p

Scatterplots showing the significant associations between the numerical magnitude processing tasks and timed mathematics achievement in Grade 3.

<p>Scatterplots showing the significant associations between the numerical magnitude processing tasks and timed mathematics achievement in Grade 3.</p

Mean reaction time (based on correct responses only) on the numerical magnitude comparison tasks as a function of grade and distance.

<p>Solid lines indicate data on the symbolic magnitude comparison task (<i>M</i>_{Grade 1} = 1199.71 ms; <i>M</i>_{Grade 3} = 698.65 ms), and dashed lines indicate data on the non-symbolic magnitude comparison task (<i>M</i>_{Grade 1} = 1013.28 ms; <i>M</i>_{Grade 3} = 799.62 ms).</p

Counting many as one: Young children can understand sets as units except when counting

Young children frequently make a peculiar counting mistake. When asked to count units that are sets of multiple items, such as the number of families at a party, they often count discrete items (i.e., individual people) rather than the number of sets (i.e., families). One explanation concerns children’s incomplete understanding of what constitutes a unit, resulting in a preference for discrete items. Here, we demonstrate that children’s incomplete understanding of counting also plays a role. In an experiment with 4- to 5-year-old children (N = 43), we found that even if children are able to name sets, group items into sets, and create one-to-one correspondences with sets, many children are nevertheless unable to count sets as units. We conclude that a nascent understanding of the abstraction principle of counting is also a cause of some children’s counting errors.</p

Regression analyses and Bayes factors explaining cross-sectional variance in arithmetic and reading at Time 1 (<i>n =</i> 74).

<p>Regression analyses and Bayes factors explaining cross-sectional variance in arithmetic and reading at Time 1 (<i>n =</i> 74).</p