Maria Chiara Passolunghi

Domain-Specific and Domain-General Precursors of Mathematical Achievement: A Longitudinal Study from Kindergarten to First Grade.

BACKGROUND Many contributing factors, both domain specific and domain general, influence childrens performance in school achievement. AIMS This research aims to verify the importance of kindergarten measures of cognitive abilities and numerical competence in the role of predicting mathematical school achievement at the end of first grade. SAMPLE AND METHODS A total of 70 children (38 females and 32 males) took part in the study. We tested the children at the beginning of their last year of kindergarten (time 1) on the following cognitive abilities: IQ, phonology, counting skills, verbal short-term memory, visuo-spatial short-term memory, working memory, and processing speed. Then, we tested the same children at end of their last year of kindergarten (time 2) on a measure of numerical competence and at the end of their first year of primary school (time 3) on a test of math achievement. RESULTS Path analysis models revealed the direct influence of working memory and processing speed on predicting numerical competence in pre-schoolers and the influence of processing speed and verbal IQ on predicting math achievement in first graders. Moreover, this study found a direct link between numerical competence and math achievement. CONCLUSIONS Both domain-specific and domain-general factors contribute to determining math achievement at the end of first grade.

Working Memory Failures in Children with Arithmetical Difficulties

A large body of literature has examined the relationship between working memory and arithmetic achievement, but results are still ambiguous. To examine this relationship, we compared the performance of third and fifth graders with arithmetic difficulties (AD) and controls of the same age, grade, and verbal intelligence on a battery of working memory tasks, differentiating between different aspects of working memory. Children with AD scored significantly lower on active working memory tasks requiring manipulation of the to-be-recalled information (Listening Completion task, Corsi Span Backwards, Digit Backwards), but not in passive working memory tasks, requiring the recall of information in the same format in which it had been presented (Digit, Word, and Corsi Forwards Span tasks), nor in tasks involving word processing (word articulation rate, forwards and backwards word spans). A regression analysis showed that the best predictors of differences between AD children and the control group were the Corsi Span Backwards, the Listening Completion task, and the rate of articulation of pseudowords. The analysis of strategies used by children in mental calculation revealed the greater tendency of children with AD to rely on more primitive strategies: finger use never appeared as the most frequent strategy in skilled children, whereas it was the most used strategy in children with AD. Verbal and visual strategies appeared associated with successful performance in third graders, but in fifth grade, the most successful strategy was verbalization.

Selective Spatial Working Memory Impairment in a Group of Children With Mathematics Learning Disabilities and Poor Problem-Solving Skills

This study examines visual and spatial working memory skills in 35 third to fifth graders with both mathematics learning disabilities (MLD) and poor problem-solving skills and 35 of their peers with typical development (TD) on tasks involving both low and high attentional control. Results revealed that children with MLD, relative to TD children, failed spatial working memory tasks that had either low or high attentional demands but did not fail the visual tasks. In addition, children with MLD made more intrusion errors in the spatial working memory tasks requiring high attentional control than did their TD peers. Finally, as a post hoc analysis the sample of MLD was divided in two: children with severe MLD and children with low mathematical achievement. Results showed that only children with severe MLD failed in spatial working memory (WM) tasks if compared with children with low mathematical achievement and TD. The findings are discussed on the basis of their theoretical and clinical implications, in particular considering that children with MLD can benefit from spatial WM processes to solve arithmetic word problems, which involves the ability to both maintain and manipulate relevant information.

Spatial and visual working memory ability in children with difficulties in arithmetic word problem solving

Although various studies support the multicomponent nature of visuospatial working memory, to date there is no general consensus on the distinction of its components. A difference is usually proposed between visual and spatial components of working memory, but the individual roles of these components in mathematical learning disabilities remains unclear. The present study aimed to examine the involvement of visual and spatial working memory in poor problem-solvers compared with children with normal level of achievement. Fourth-grade participants were presented with tasks measuring phonological loop, central executive, and visual versus spatial memory. In two separate experiments, both designed to distinguish visual and spatial component involvement, poor problem-solvers specifically failed on spatial—but not visual or phonological—working memory tasks. Results are discussed in the light of possible working memory models, and specifically demonstrate that problem-solving ability can benefit from analysis of spatial processes, which involves ability to manipulate and transform relevant information; instead, no benefit is gained from the analysis of visual pictorial detail.

Working memory and early numeracy training in preschool children.

Many factors influence children’s performance in mathematical achievement, including both domain-specific and domain-general factors. This study aimed to verify and compare the effects of two types of training on early numerical skills. One type of training focused on the enhancement of working memory, a domain-general precursor, while the other focused on the enhancement of early numeracy, a domain-specific precursor. The participants were 48 five-year-old preschool children. Both the working memory and early numeracy training programs were implemented for 5 weeks. The results showed that the early numeracy intervention specifically improved early numeracy abilities in preschool children, whereas working memory intervention improved not only working memory abilities but also early numeracy abilities. These findings stress the importance of performing activities designed to train working memory abilities, in addition to activities aimed to enhance more specific skills, in the early prevention of learning difficulties during preschool years.

The contribution of general cognitive abilities and approximate number system to early mathematics

BACKGROUND Math learning is a complex process that entails a wide range of cognitive abilities to be fulfilled. There is sufficient evidence that both general and specific cognitive skills assume a fundamental role, despite the absence of shared consensus about the relative extent of their involvement. Moreover, regarding general abilities, there is no agreement about the recruitment of the different memory components or of intelligence. In relation to specific factors, great debate subsists regarding the role of the approximate number system (ANS). AIMS Starting from these considerations, we wanted to conduct a wide assessment of memory components and ANS, by controlling for the effects associated with intelligence and also exploring possible relationships between all precursors. SAMPLE AND METHOD To achieve this purpose, a sample of 157 children was tested at both beginning and end of their Grade 1. Both general (memory and intelligence) and specific (ANS) precursors were evaluated by a wide battery of tests and put in relation to concurrent and subsequent math skills. Memory was explored in passive and active aspects involving both verbal and visuo-spatial components. RESULTS Path analysis results demonstrated that memory, and especially the more active processes, and intelligence were the strongest precursors in both assessment times. ANS had a milder role which lost significance by the end of the school year. Memory and ANS seemed to influence early mathematics almost independently. CONCLUSION Both general and specific precursors seemed to have a crucial role in early math competences, despite the lower involvement of ANS.

Cognitive and Emotional Factors in Children with Mathematical Learning Disabilities

Emotional and cognitive factors were examined in 18 children with mathematical learning disabilities (MLD), compared with 18 normally achieving children, matched for chronological age, school level, gender and verbal IQ. Working memory, short‐term memory, inhibitory processes, speed of processing and level of anxiety in mathematics were assessed in the two groups. The results corroborated the hypothesis that children with MLD are impaired in working memory capacity, inhibitory ability, and speed of processing. However, no impairment was found in short‐term memory tasks requiring passive storage of verbal and numerical information. Moreover, while the children with MLD showed higher levels of anxiety in mathematics, their anxiety levels in other school subjects were similar to those of normal achievers. Implications for identifying underlying emotional and cognitive deficits in children with MLD are discussed, along with possible approaches to treatment.

Early numerical abilities and cognitive skills in kindergarten children

In this study, a unitary path analysis model was developed to investigate the relationship between cognitive variables (derived from published studies) and early numerical abilities in children attending the last year of kindergarten. We tested 100 children starting their last year of kindergarten on the following cognitive abilities: intelligence, phonological abilities, counting, verbal and visuospatial short-term memory and working memory, processing speed, and early numerical abilities. The same children were tested again on early numerical abilities at the end of the same year. The childrens early numerical abilities at the beginning of the final year of kindergarten were found to be directly related to their verbal intelligence, phonological abilities, processing speed, and working memory and to be indirectly related to their nonverbal intelligence. Early numerical abilities at the end of the same year are directly related not only to early numerical abilities assessed at the beginning of the year but also to working memory and phonological abilities as well as have an indirect relationship with verbal and nonverbal intelligence. Overall, our results showed that both general and specific abilities are related to early mathematic learning in kindergarten-age children.

Approximate additions and working memory in individuals with Down syndrome.

There is some evidence that individuals with Down syndrome (DS) may have a poorer mathematical performance and a poorer working memory (WM) than typically developing (TD) children of the same mental age. In both typical and atypical individuals, different aspects of arithmetic and their relationships with WM have been largely studied, but the specific contribution of WM to the representation and elaboration of non-symbolic quantities has received little attention. The present study examined whether individuals with DS are as capable as TD children matched for fluid intelligence of estimating numerosity both of single sets and of added sets resulting when two sequentially presented sets are added together, also considering how these tasks related to verbal and visuospatial WM. Results showed that the DS groups performance was significantly worse than the TD groups in numerosity estimation involving one set, but not when estimating the numerosity resulting from the addition. Success in the addition task was related to success in the working memory tasks, but only for the group with DS; this applied especially to the visuospatial component, which (unlike the verbal component) was not impaired in the group with DS. It is concluded that the two numerosity tasks involve different processes. It is concluded that the arithmetical and working memory difficulties of individuals with DS are not general, and they can draw on their WM resources when estimating the numerosity of additions.

Mathematics anxiety, working memory, and mathematics performance in secondary-school children

Mathematics anxiety (MA) has been defined as “a feeling of tension and anxiety that interferes with the manipulation of numbers and the solving of math problems in a wide variety of ordinary life and academic situations.” Previous studies have suggested that a notable proportion of children in primary and secondary school suffer from MA, which is negatively correlated with calculation skills. The processing efficiency and attentional control theories suggest that working memory (WM) also plays an important part in such anxious feelings. The present study aimed to analyze the academic achievement and cognitive profiles of students with high math anxiety (HMA) and low math anxiety (LMA). Specifically, 32 students with HMA and 34 with LMA matched for age, gender, generalized anxiety, and vocabulary attending sixth to eighth grades were selected from a larger sample. The two groups were tested on reading decoding, reading comprehension, mathematics achievement, and on verbal short-term memory and WM. Our findings showed that HMA students were weak in several measures of mathematics achievement, but not in reading and writing skills, and that students with HMA reported lower scores on short-term memory and WM performances (with associated difficulties in inhibiting irrelevant information) than children with LMA. In addition, a logistic regression showed that weaknesses in inhibitory control and fact retrieval were the strongest variables for classifying children as having HMA or LMA.