A Diffusion Model Analysis of Magnitude Comparison in Children with and without Dyscalculia: Care of Response and Ability Are Related to Both Mathematical Achievement and Stimuli

Abstract

The respective roles of the approximate number system (ANS) and an access deficit (AD) in developmental dyscalculia (DD) are not well-known. Most studies rely on response times (RTs) or accuracy (error rates) separately. We analyzed the results of two samples of elementary school children in symbolic magnitude comparison (MC) and non-symbolic MC using a diffusion model. This approach uses the joint distribution of both RTs and accuracy in order to synthesize measures closer to ability and response caution or response conservatism. The latter can be understood in the context of the speed-accuracy tradeoff: It expresses how much a subject trades in speed for improved accuracy. We found significant effects of DD on both ability (negative) and response caution (positive) in MC tasks and a negative interaction of DD with symbolic task material on ability. These results support that DD subjects suffer from both an impaired ANS and an AD and in particular support that slower RTs of children with DD are indeed related to impaired processing of numerical information. An interaction effect of symbolic task material and DD (low mathematical ability) on response caution could not be refuted. However, in a sample more representative of the general population we found a negative association of mathematical ability and response caution in symbolic but not in non-symbolic task material. The observed differences in response behavior highlight the importance of accounting for response caution in the analysis of MC tasks. The results as a whole present a good example of the benefits of a diffusion model analysis.

Validation of an Early Numeracy Screener for First Graders

“…retrieving arithmetic facts) and domain-general skills (e.g., working memory) discussed in the previous section. There are studies indicating that children with mathematical difficulties have poorer ANS than their peers without such difficulties (Mazzocco et al, 2011;Szardenings, Kuhn, Ranger, & Holling 2018). Difficulties with basic arithmetic fact retrievals are considered a trademark for children with mathematical difficulties at an early school age, and consequently children with mathematical difficulties commit more procedural errors and use developmentally immature and error prone procedures.…”

Παραγοντική Διερεύνηση του MathPro, ενός Ψυχομετρικού Εργαλείου Εντοπισμού Μαθησιακών Δυνατοτήτων και Δυσκολιών στα Μαθηματικά

“…Γενικά, ο όρος μαθηματική μαθησιακή δυσκολία χρησιμοποιείται για να περιγράψει μαθηματικούς τομείς στους οποίους παρατηρούνται ελλείμματα στις αριθμητικές ικανότητες (Karagiannakis et al, 2017). Επιπροσθέτως, οι ερευνητές συγκλίνουν στην άποψη πως οι μαθηματικές μαθησιακές δυσκολίες είναι ουσιαστικά ένα εγγενές ελάττωμα, το οποίο προκαλεί δυσκολίες στην εκμάθηση των μαθηματικών (Butterworth & Laurillard, 2010) και δεν οφείλονται και ούτε μπορούν να εξηγηθούν από τη χαμηλή νοημοσύνη, την απουσία επαρκών ευκαιριών μάθησης, την ανεπαρκή εκπαίδευση ή την ηλικία (Szardenings, Kuhn, Ranger & Holling, 2018).…”

Las Habilidades Lingüísticas Y El Sistema Numérico Aproximado en La Eficacia Del Cálculo Aritmético

“…No obstante, el valor predictivo del SNA en cálculo resulta ser muy pequeño, y solo considerando la velocidad de este y no el coeficiente de weber. Este aspecto resulta sugerente ya que se ha propuesto el SNA como el núcleo cognitivo que sustenta el procesamiento numérico y la causa primaria de la Discalculia del Desarrollo (DD) y de las Dificultades de Aprendizaje en Matemáticas (DAM) (Butterworth, 2018;Szardenings, Kuhn, Ranger y Holling, 2017).…”