Arithmetical difficulties and low arithmetic achievement: analysis of the underlying cognitive functioning

This study analyzed the cognitive functioning underlying arithmetical difficulties and explored the predictors of arithmetic achievement in the last three grades of Spanish Primary Education. For this purpose, a group of 165 students was selected and divided into three groups of arithmetic competence: Mathematical Learning Disability group (MLD, n = 27), Low Achieving group (LA, n = 39), and Typical Achieving group (TA, n = 99). Students were assessed in domain-general abilities (working memory and PASS cognitive processes), and numerical competence (counting and number processing) during the last two months of the academic year. Performance of children from the MLD group was significantly poorer than that of the LA group in writing dictated Arabic numbers (d = –0.88), reading written verbal numbers (d = –0.84), transcoding written verbal numbers to Arabic numbers (–0.75) and comprehension of place value (d = –0.69), as well as in simultaneous (d = –0.62) and successive (d = –0.59) coding. In addition, a specific developmental sequence was observed in both groups, the implications of which are discussed. Hierarchical regression analysis revealed simultaneous coding (β = .47, t(155) = 6.18, p < .001) and number processing (β = .23, t(155) = 3.07, p < .01) as specific predictors of arithmetical performance.Universidade de Vigo | Ref. INOU201

Cognitive processing and mathematical achievement: a study with schoolchildren between fourth and sixth grade of primary education

This investigation analyzed the relation between cognitive functioning and mathematical achievement in 114 students in fourth, fifth, and sixth grades. Differences in cognitive performance were studied concurrently in three selected achievement groups: mathematical learning disability group (MLD), low achieving group (LA), and typically achieving group (TA). For this purpose, performance in verbal memory and in the PASS cognitive processes of planning, attention, and simultaneous and successive processing was assessed at the end of the academic course. Correlational analyses showed that phonological loop and successive and simultaneous processing were related to mathematical achievement at all three grades. Regression analysis revealed simultaneous processing as a cognitive predictor of mathematical performance, although phonological loop was also associated with higher achievement. Simultaneous and successive processing were the elements that differentiated the MLD group from the LA group. These results show that, of all the variables analyzed in this study, simultaneous processing was the best predictor of mathematical performance

La función ejecutiva de actualización y el rendimiento en comprensión lectora y resolución de problemas

In this investigation, the capacity of the working memory (WM) updating executive function to predict individual differences in reading comprehension and problem solving was analyzed in 5th-graders of Primary Education. In addition, we examined whether this relation is direct or mediated by domain-general or domain-specific variables. For this purpose, a series of tasks was administered to assess fluid intelligence, WM information updating, arithmetic abilities, arithmetic problem solving, lexical processing, and reading comprehension in 49 students aged between 10 and 11 years. The results support the idea that updating is an important predictor of reading comprehension, beyond the influence of domainspecific skills and fluid intelligence. In the case of problem solving, our findings confirm that updating plays an important role although, perhaps due to task content, the relation seems to be mediated by fluid intelligence at this developmental stageEsta investigación analizó, en niños de 5º curso de Educación Primaria, la capacidad predictora de la función ejecutiva de actualización de la Memoria Operativa (MO) en las diferencias individuales en comprensión lectora y resolución de problemas aritméticos. Además, se estudió si esta relación es directa o está mediada por variables de dominio general o específico. Con este fin se administró un conjunto de pruebas que evalúan la inteligencia fluida, la actualización de la información en la MO, la competencia aritmética, la resolución de problemas aritméticos, el procesamiento léxico y la comprensión lectora a 49 alumnos con edades comprendidas entre los 10 y 11 años. Los resultados apoyan la idea que la actualización de la MO es un importante predictor de la comprensión lectora, más allá de la influencia de las habilidades de dominio específico y de la inteligencia fluida. En el caso de la resolución de problemas, nuestros hallazgos confirman que la actualización juega un papel importante aunque, en este momento evolutivo, quizá por el propio contenido de la tarea, la relación parece mediada por la inteligencia fluid

Executive functioning skills and (low) math achievement in primary and secondary school

Schoolchildren with better executive functioning skills achieve better mathematics results. It is less clear how inhibition, cognitive flexibility, and working memory combine to predict mathematics achievement and difficulty throughout primary and secondary school. This study aimed to find the best combination of executive function measures for predicting mathematical achievement in Grades 2, 6, and 10 and to test whether this combination predicts the probability of having mathematical difficulties across school grades even when fluid intelligence and processing speed were included in the models. A total of 426 students—141 2nd graders (72 girls), 143 6th graders (72 girls), and 142 10th graders (79 girls)—were cross-sectionally assessed with 12 executive tasks, one standardized mathematical task, and a standardized test of intelligence. Bayesian regression analyses found various combinations of executive predictors of mathematical achievement for each school grade spanning Grade 2 to measures of cognitive inhibition (negative priming) and cognitive flexibility (verbal fluency); Grade 6 to measures of inhibition: resistance to distractor interference (receptive attention), cognitive flexibility (local–global), and working memory (counting span); and Grade 10 to measures of inhibition: resistance to distractor interference (receptive attention) and prepotent response inhibition (stop signal) and working memory (reading span). Logistic regression showed that the executive models derived from the Bayesian analyses had a similar ability to classify students with mathematical difficulty and their peers with typical achievement to broader cognitive models that included fluid intelligence and processing speed. Measures of processing speed, cognitive flexibility (local–global), and prepotent response inhibition (stop signal) were the main risk factors in Grades 2, 6, and 10, respectively. Cognitive flexibility (verbal fluency) in Grade 2 and fluid intelligence, which was more stable in all three grades, acted as protective factors against mathematical difficulty. These findings inform practical considerations for establishing preventive and intervention proposals.Ministerio de Ciencia e Innovación | Ref. EDU2011-2269

Cognitive processing and arithmetic achievement

Esta investigación analizó la relación entre el funcionamiento cognitivo y el logro aritmético de 114 alumnos españoles de 4º, 5º y 6º curso. Con este fin se evaluó, a finales del curso escolar, el logro aritmético, el rendimiento en la memoria verbal y en los procesos cognitivos PASS planificación, atención, procesamiento simultáneo y sucesivo. Los análisis correlacionales mostraron que el lazo fonológico, el procesamiento sucesivo y el simultáneo se relacionaron con el logro aritmético en los tres niveles educativos. El análisis de regresión señaló al simultáneo como predictor cognitivo del rendimiento aritmético, aunque el lazo fonológico también se asoció a un mayor logro. Estos resultados demostraron que, de entre todas las variables analizadas en este estudio, el procesamiento simultáneo fue el mejor predictor del rendimiento aritmético.This research examined the relationship between cognitive functioning and arithmetic achievement of 114 Spanish students of 4 th, 5 th and 6 th grade. For this purpose was evaluated at the end of the school, arithmetic achievement, performance on verbal memory and PASS cognitive processes, planning, attention, simultaneous and successive processing. Correlational analyzes showed that the phonological loop, the successive and simultaneous processing related to arithmetic achievement in three educational levels. Regression analysis indicated the simultaneous as a cognitive predictor of performance arithmetic, although the phonological loop was also associated with higher achievement. These results showed that among all the variables analyzed in this study, simultaneous processing was the best predictor of arithmetical performance

Mathematical learning disabilities and attention deficit and/or hyperactivity disorder: A study of the cognitive processes involved in arithmetic problem solving

Background: The purpose of this study was to examine the contribution of cognitive functioning to arithmetic problem solving and to explore the cognitive profiles of children with attention deficit and/or hyperactivity disorder (ADHD) and with mathematical learning disabilities (MLD). Methods: The sample was made up of a total of 90 students of 4th, 5th, and 6th grade organized in three: ADHD (n = 30), MLD (n = 30) and typically achieving control (TA; n = 30) group. Assessment was conducted in two sessions in which the PASS processes and arithmetic problem solving were evaluated. Results: The ADHD group’s performance in planning and attention was worse than that of the control group. Children with MLD obtained poorer results than the control group in planning and simultaneous and successive processing. Executive processes predicted arithmetic problem solving in the ADHD group whereas simultaneous processing was the unique predictor in the MLD sample. Conclusions: Children with ADHD and with MLD showed characteristic cognitive profiles. Groups’ problem-solving performance can be predicted from their cognitive functioning

La comprensión conceptual aritmética en la escuela elemental

This study analyzed the arithmetic conceptual comprehension from a dual perspective (conceptual and strategic) of students in 4th, 5th and 6th grades of Elementary school, selected based on three achievement groups: mathematical learning disabilities (MLD; n=51), typical achievement (TA; n=60) and high achievement (HA; n=21). Specifically, it aimed to (1) characterize students based on their arithmetic conceptual knowledge and (2) analyze how the different achievement groups cope with more complex tasks based on their previous conceptual skills. The BANEVHAR battery was applied to assess conceptual understanding and the full scale of the CAS battery was used as a reliable estimator of intelligence. The results pointed out the conceptual deficits of students with MLD with respect to their peers with TA and HA, who seem to reach these educational levels with acquired conceptual skills. In addition, it was observed that there are differences between the groups not only in conceptual knowledge but also in the strategic coping of tasks when these are novel or complex. In this context, students with HA can solve tasks more efficiently. These findings highlight the importance of conceptual and strategic teaching of arithmetic and suggest its practical implementation at school.Este estudio analizó la comprensión conceptual aritmética desde una doble vía, (conceptual y estratégica) del alumnado escolarizado en 4º, 5º y 6º de Educación Primaria, seleccionado en base a tres grupos de logro: dificultades de aprendizaje en matemáticas (DAM; n=51), competencia normal (CN; n=60) y alto rendimiento (AR; n=21). Concretamente, pretendió (1) caracterizar al alumnado en base a su conocimiento conceptual aritmético y (2) analizar cómo los distintos grupos de logro afrontan tareas más complejas en base a sus habilidades conceptuales previas. Se utilizó la batería BANEVHAR para evaluar la comprensión conceptual y la escala completa de la batería CAS como estimador fiable de inteligencia. Los resultados señalaron los déficits conceptuales del alumnado con DAM respecto a sus iguales de CN y AR que parecen llegar a estos niveles educativos con las habilidades conceptuales adquiridas. Además, se observó que existen diferencias entre los tres grupos en el afrontamiento estratégico de las tareas cuando estas son novedosas o complejas. En este contexto, el alumnado con AR es capaz de resolver las tareas de forma más eficiente. Estos hallazgos resaltan la importancia de la enseñanza conceptual y estratégica de la aritmética y sugieren su implementación práctica en la escuela

Math modules training improves math achievement & associated cognitive processing

Background: Previous research point to a correlation between mathematical skills and cognitive processes involved in planning and simultaneous processing. Consistent with multicomponent models of mathematical achievement (domain-general and domain-specific skills), PASS theory appears to be very useful as a multifactorial framework that provides specific tests to monitor the development of mathematical competence and to direct intervention procedures and improve mathematical skills. Objective: This study was conducted to assess the impact of the Math Modules Cognitive Training Program on the mathematical competence of typical 2nd-grade students in calculation, problem-solving, and underlying mental functions, compared to a control group. The program was designed to optimize the Planning/FE, Attention, Simultaneous, and Successive cognitive processes through a series of tasks. Participants: The study involved 60 students aged between 6 and 8 years (Mdn = 7 years and 7 months), who were in the second grade of two urban public schools. Method: The program focused on mathematical skill tasks related to fluent calculation and mathematical problem solving that requires PASS cognitive processes for successful completion. The intervention group received the Math Modules program, and the control group followed their usual classroom program. Students were evaluated in calculation, problem-solving, and PASS cognitive processes. Results: Our results showed that the Math Modules Cognitive Training Program focused on calculation and problem solving skills were effective in improving children’s mathematical performance and their PASS cognitive processes, generating gains not achieved by the control group. Conclusions: Our study suggests that fluid calculation and problem-solving math tasks, based on planning and simultaneous processing, could foster curricular math competency

Mathematical difficulties vs. High achievement: an analysis of arithmetical cognition in elementary school

This study analyzed the contribution of cognitive processes (planning, attention, simultaneous and successive processing) and domain-specific skills (counting, number processing and conceptual comprehension) to the arithmetic performance achieved in the last three grades (4th, 5th, and 6th) of elementary school. Three groups of students with a different arithmetic achievement level were characterized. The predictive value of the cognitive processes and the math specific skills are explored through diverse covariance and discriminant analyses. Participants were 110 students (M = 10.5 years, SD = 1.17) classified in three groups: mathematical difficulties (MD; n = 26), high achieving (HA; n = 26), and typical achieving (TA; n = 58). Cognitive processes and domain-specific skills were evaluated in two individual sessions at the end of the school year. Nonverbal intelligence was assessed in a final collective session with each class. The mathematical difficulties group’s achievement was deficient in simultaneous and successive processing, number processing, and conceptual comprehension compared to the typical achievement group. High achievement children obtained significantly better results than the typical achievement children in simultaneous processing, counting, number processing, and conceptual comprehension. Number processing and conceptual comprehension were the most consistent classifiers, although successive and simultaneous processing, respectively, also contributed to identifying students with mathematical difficulties and high achievement. These findings have practical implications for preventive and intervention proposals linked to the observed profiles

Predictors of arithmetical achievement in Primary Education 4th-graders

Esta investigación analizó los mecanismos cognitivos subyacentes al rendimiento aritmético en el 4º curso de Educación Primaria. Con este fin se evaluó, a través de las pruebas de dígitos del WISC-R, y de las escalas correspondientes de las baterías D.N:CAS y BANEVHAR, el rendimiento en memoria verbal, velocidad de procesamiento, planificación, atención, procesamiento simultáneo y sucesivo y competencia numérica de 74 alumnos. Los análisis correlacionales mostraron que todas las variables seleccionadas, salvo la planificación, se relacionaron significativamente con el rendimiento aritmético. El simultáneo y el procesamiento numérico emergieron, en el análisis de regresión jerárquico realizado, como predictores del rendimiento aritmético.In this investigation, the cognitive mechanisms underlying arithmetical achievement in Primary Education 4th-graders were analyzed. For this purpose, using the Digit Span test of the WISC-R and the scales from the batteries D.N:CAS and BANEVHAR, the performance in verbal memory, processing speed, planning, simultaneous and successive processing, attention, and numeric competence was assessed in 74 students. The correlational analyses showed that, except for planning, all the variables selected were significantly related to arithmetical achievement. Simultaneous and number processing emerged as predictors of arithmetical performance in the hierarchical regression analysis carried out.peerReviewe