Mathematical and cognitive predictors of the development of mathematics

Explanatory model of emotional-cognitive variables in school mathematics performance: a longitudinal study in primary school

This study tested a structural model of cognitive-emotional explanatory variables to explain performance in mathematics. The predictor variables assessed were related to students' level of development of early mathematical competencies (EMCs), specifically, relational and numerical competencies, predisposition toward mathematics, and the level of logical intelligence in a population of primary school Chilean students (n = 634). This longitudinal study also included the academic performance of the students during a period of 4 years as a variable. The sampled students were initially assessed by means of an Early Numeracy Test, and, subsequently, they were administered a Likert-type scale to measure their predisposition toward mathematics (EPMAT) and a basic test of logical intelligence. The results of these tests were used to analyse the interaction of all the aforementioned variables by means of a structural equations model. This combined interaction model was able to predict 64.3% of the variability of observed performance. Preschool students' performance in EMCs was a strong predictor for achievement in mathematics for students between 8 and 11 years of age. Therefore, this paper highlights the importance of EMCs and the modulating role of predisposition toward mathematics. Also, this paper discusses the educational role of these findings, as well as possible ways to improve negative predispositions toward mathematical tasks in the school domain.

Preschool predictors of mathematics in first grade children with autism spectrum disorder

Up till now, research evidence on the mathematical abilities of children with autism spectrum disorder (ASD) has been scarce and provided mixed results. The current study examined the predictive value of five early numerical competencies for four domains of mathematics in first grade. Thirty-three high-functioning children with ASD were followed up from preschool to first grade and compared with 54 typically developing children, as well as with normed samples in first grade. Five early numerical competencies were tested in preschool (5-6 years): verbal subitizing, counting, magnitude comparison, estimation, and arithmetic operations. Four domains of mathematics were used as outcome variables in first grade (6-7 years): procedural calculation, number fact retrieval, word/language problems, and time-related competences. Children with ASD showed similar early numerical competencies at preschool age as typically developing children. Moreover, they scored average on number fact retrieval and time-related competences and higher on procedural calculation and word/language problems compared to the normed population in first grade. When predicting first grade mathematics performance in children with ASD, both verbal subitizing and counting seemed to be important to evaluate at preschool age. Verbal subitizing had a higher predictive value in children with ASD than in typically developing children. Whereas verbal subitizing was predictive for procedural calculation, number fact retrieval, and word/language problems, counting was predictive for procedural calculation and, to a lesser extent, number fact retrieval. Implications and directions for future research are discussed.

Rechenschwäche im Grundschulalter: Reduzierte Verfügbarkeit basalen arithmetischen Faktenwissens und Belastung des Arbeitsgedächtnisses bei Drittklässlern

Nachteile im Aufbau und Abruf basalen arithmetischen Faktenwissens (zum Beispiel der Summe zweier Ziffern) bilden ein zentrales Merkmal bei Kindern mit Rechenschwäche. Die vorliegende Studie verfolgt das Ziel, die reduzierte Verfügbarkeit basalen arithmetischen Wissens und dadurch bedingte besondere Belastungen des Arbeitsgedächtnisses bei Kindern mit Rechenschwäche genauer zu untersuchen. Drittklässler mit und ohne Rechenschwäche bearbeiteten Verifikationsaufgaben zur Addition im Zahlenraum bis 20 mit und ohne Zehnerübergang, einerseits unter Standardbedingungen, andererseits unter kontinuierlicher Ausführung einfacher Zweitaufgaben (verbal und motorisch). In getrennten Varianzanalysen (VA) zur Lösungsgüte und zur Lösungszeit erwiesen sich alle drei Haupteffekte zu den Faktoren Rechenleistung, Zehnerübergang und Durchführungsbedingung (in beiden VA) und alle Zweifachinteraktionen (in der VA zur Lösungsgüte) als signifikant. Kinder mit Rechenschwäche haben demnach grundlegende Nachteile beim Abruf basaler arithmetischer Fakten und besonders ausgeprägte Nachteile bei Aufgaben mit Zehnerübergang und unter Belastung des Arbeitsgedächtnisses durch Zweitaufgaben. Die Befunde untermauern die Annahme, dass die Rechenschwäche eng mit Defiziten im basalen arithmetischen Faktenwissen assoziiert ist. Darüber hinaus legen sie nahe, dass sich diese Defizite umso gravierender auswirken, je größer die aktuelle Belastung des Arbeitsgedächtnisses ausfällt. Die Relevanz des frühen Aufbaus von arithmetischem Faktenwissen und die Notwendigkeit des Einsatzes geeigneter diagnostischer Maßnahmen zur frühzeitigen Erkennung von entsprechenden Defiziten werden hervorgehoben.