Nonsymbolic and symbolic magnitude comparison skills as longitudinal predictors of mathematical achievement

What developmental roles do nonsymbolic (e.g., dot arrays) and symbolic (i.e., Arabic numerals) magnitude comparison skills play in children’s mathematics? In the literature, one notices several gaps and contradictory findings. We assessed a large sample in kindergarten, grade 1 and 2 on two well-known nonsymbolic and symbolic magnitude comparison measures. We also assessed children’s initial IQ and developing Working Memory (WM) capacities. Results demonstrated that symbolic and nonsymbolic comparison had different developmental trajectories; the first underwent larger developmental improvements. Both skills were important longitudinal predictors of children’s future mathematical achievement above and beyond IQ and WM. Nonsymbolic comparison was predictive in kindergarten. Symbolic comparison, however, was consistently a stronger predictor of future mathematics compared to nonsymbolic, and its predictive power at the early stages was even comparable to that of IQ. Furthermore, results bring forth methodological implications regarding the role of different types of magnitude comparison measures

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

The development of symbolic and nonsymbolic skills in Grade 1.

<p>The development of symbolic and nonsymbolic skills in Grade 1.</p

Linear regression analysis predicting nonsymbolic scores at Time 2 with symbolic and nonsymbolic scores at Time 1 as predictors.

<p>Linear regression analysis predicting nonsymbolic scores at Time 2 with symbolic and nonsymbolic scores at Time 1 as predictors.</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

Descriptive statistics and reliabilities of the measures collected at Time 1 (<i>n =</i> 74) and Time 2 (<i>n =</i> 67).

<p>Descriptive statistics and reliabilities of the measures collected at Time 1 (<i>n =</i> 74) and Time 2 (<i>n =</i> 67).</p

Longitudinal regression analyses and Bayes factors predicting children’s arithmetic and reading at time 2 (<i>n</i> = 67).

<p>Longitudinal regression analyses and Bayes factors predicting children’s arithmetic and reading at time 2 (<i>n</i> = 67).</p

Symbolic Numerical Magnitude Processing Is as Important to Arithmetic as Phonological Awareness Is to Reading

<div><p>In this article, we tested, using a 1-year longitudinal design, whether symbolic numerical magnitude processing or children’s numerical representation of Arabic digits, is as important to arithmetic as phonological awareness is to reading. Children completed measures of symbolic comparison, phonological awareness, arithmetic, reading at the start of third grade and the latter two were retested at the start of fourth grade. Cross-sectional and longitudinal correlations indicated that symbolic comparison was a powerful domain-specific predictor of arithmetic and that phonological awareness was a unique predictor of reading. Crucially, the strength of these independent associations was not significantly different. This indicates that symbolic numerical magnitude processing is as important to arithmetic development as phonological awareness is to reading and suggests that symbolic numerical magnitude processing is a good candidate for screening children at risk for developing mathematical difficulties.</p></div

Associations between all measures under study.

<p>Associations between all measures under study.</p

Correlation between Math Fluency scores and magnitude comparison scores.

<p>Scatterplot showing significant correlation between standard scores on the Math Fluency subtest of the Woodcock-Johnson III battery and overall mean score of the magnitude comparison task (symbolic and nonsymbolic combined) for all participants. The solid line represents the linear regression line for this relationship.</p