Strategy use, the development of automaticity, and working memory involvement in complex multiplication

Maths performance of adults with and without developmental coordination disorder (DCD): The role of working memory and maths anxiety

Previous studies have shown that children with Developmental Coordination Disorder (DCD)/Dyspraxia have poorer maths performance compared to their neurotypical (NT) counterparts. However, no studies have explored the cognitive and emotional factors affecting the maths performance of adults with DCD. This study, therefore, investigated the role of working memory (WM), maths anxiety (MAS), and maths self-efficacy on the maths performance of adults with DCD. We found that adults with DCD had lower WM and maths performance and were more maths anxious than their NT peers. However, there were no significant differences in maths self-efficacy. When looking at the predictors of maths performance, we found a positive relationship between WM resources and the DCD maths performance, possibly indicating that they relied more on WM resources to perform simple mental arithmetic tasks than NTs. On the other hand, MAS had an inverse relationship with the NT maths performance but not with the DCD performance. The reasons and implications of these findings will be discussed.

The impact of anxiety and life quality on the mathematical performance of dyscalculic middle school children

Dyscalculia is a specific difficulty in learning mathematics that strongly influences activities of daily living that require skills such as counting and simple mathematical operations. The aim of this study is to investigate the effect of negative emotions on mathematical performance in children with and without developmental dyscalculia using psychosocial tests, a quality of life test, an anxiety test and the Zareki-R mathematical performance test. This pilot study was realized on a sample of 20 children in the first year of secondary school (a group of 10 dyscalculic children and another group of 10 control children with an average age of 12.65 years). Descriptive statistics showed that dyscalculic children had low scores on all Zareki-R subtests. The Mann Whitney analysis revealed a significant difference between dyscalculic children and typically developing children on the Zareki-R subtests and the quality of life test, but no significance was found for the anxiety test. Analysis of the ANOVA by gender revealed no significant differences for the three tests, and the opposite for the ANOVA by age (F = 3.86, dll = 2, p ˂ 0.05). Using multiple linear regression, the subtests of physical quality of life, emotional quality of life and academic quality of life were significantly different for the two groups. In conclusion, the psychosocial quality of life and the high level of anxiety in dyscalculic children strongly influence their performance in mathematics.

Positive impact of sleep on recall of multiplication facts

This study tested the hypothesis that learning complex multiplication problems (e.g. 8 × 23 = 184) prior to sleep would benefit recall in adult participants compared with learning the problems prior to a period of wakefulness. This study used a within-participant design where all participants learnt complex multiplication problems in two conditions separated by one week. In one condition, learning was before bed (sleep learning condition) and in the other condition learning was in the morning (wake learning condition). In each condition, recall was tested approximately 10.5 h later. Data were collected online from 77 participants. In the subset of the sample with greater than or equal to 60% accuracy at the initial learning session (n = 37), the sleep learning condition participants had better recall compared with the wake learning condition. This equated to a moderate effect size, Cohen's d = 0.51. Regardless of initial levels of learning (n = 70) the same beneficial effect of sleep on recall was found with a small effect size, Cohen's d = 0.33. This study has identified a beneficial effect of learning prior to sleep on recall of complex multiplication problems compared with learning these problems during the daytime. Future research should explore whether similar effects are observed with children learning simple multiplication facts.

The Cognitive Ability of Chinese Students with Dyslexia and Mathematical Learning Disabilities

This study aims to investigate the core cognitive factors that affect reading and math performance of children of the grades 1-6 in Xi'an, Shaanxi Province, China, as well as the differences between children with dyslexia and mathematical disabilities (MD). Therefore, this study mainly evaluated the Cattell Horn Carroll (CHC) cognitive factors for 427 Chinese children and explored the core cognitive factors that affect Chinese children's reading and math performance. Students with dyslexia (n = 34), students with mathematics learning disabilities (n = 34), and 34 normal children were randomly selected as the control group. In order to explore the differences in cognitive development, we analyzed the differences among the three groups (Dyslexia, mathematical learning disabilities (MD), and normal children). The results revealed the following: (1) almost all cognitive ability factors in this study are significantly related to students' reading and mathematical achievements. (2) the core cognitive factors for predicting Chinese dyslexia students are crystallized intelligence, auditory processing and working memory. Executive function, spatial relationship and working memory are the core cognitive factors to predict Chinese children's mathematical achievements. (3) in addition, there are differences in cognitive deficits between disabled Chinese children in reading and math, among which those with reading deficits have extensive auditory processing deficits; while children with mathematic deficits have worse executive function. Recommendations were made based on these findings.

Mapping components of verbal and visuospatial working memory to mathematical topics in seven- to fifteen-year-olds

BACKGROUND

Developmental research provides considerable evidence of a strong relationship between verbal and visuospatial working memory (WM) and mathematics ability across age groups. However, little is known about how components of WM (i.e., short-term storage, processing speed, the central executive) might relate to mathematics sub-categories and how these change as children develop.

AIMS

This study aimed to identify developmental changes in relationships between components of verbal and visuospatial WM and specific mathematics abilities.

SAMPLE

Children (n = 117) were recruited from four UK schools across three age groups (7-8 years; 9-10 years; and 14-15 years).

METHODS

Children's verbal and visuospatial short-term storage, processing speed, and central executive abilities were assessed. Age-based changes in the contributions from these abilities to performance on mathematics sub-categories were examined.

RESULTS

When WM was examined both as an amalgamation of its component parts, and individually, relationships with mathematics were more evident in younger children compared to the middle and older age groups. However, when unique variance was examined for each WM predictor (controlling for the other components), many of those relationships disappeared. Relationships with processing speed and the central executive were found to be more evident in the older age groups.

CONCLUSIONS

The WM-mathematics relationship changes dependent on age and mathematical sub-component. Overlap in individual WM abilities in younger children, compared to reliance on the central executive and processing speed in older children, suggests a set of fluid resources important in mathematics learning in younger children but separating out as children grow older.

Replicating five pupillometry studies of Eckhard Hess

Several papers by Eckhard Hess from the 1960s and 1970s report that the pupils dilate or constrict according to the interest value, arousing content, or mental demands of visual stimuli. However, Hess mostly used small sample sizes and undocumented luminance control. In a first experiment (N = 182) and a second preregistered experiment (N = 147), we replicated five studies of Hess using modern equipment. Our experiments (1) did not support the hypothesis of gender differences in pupil diameter change with respect to baseline (PC) when viewing stimuli of different interest value, (2) showed that solving more difficult multiplications yields a larger PC in the seconds before providing an answer and a larger maximum PC, but a smaller PC at a fixed time after the onset of the multiplication, (3) did not support the hypothesis that participants' PC mimics the pupil diameter in a pair of schematic eyes but not in single-eyed or three-eyed stimuli, (4) did not support the hypothesis of gender differences in PC when watching a video of a male trying to escape a mob, and (5) supported the hypothesis that arousing words yield a higher PC than non-arousing words. Although we did not observe consistent gender differences in PC, additional analyses showed gender differences in eye movements towards erogenous zones. Furthermore, PC strongly correlated with the luminance of the locations where participants looked. Overall, our replications confirm Hess's findings that pupils dilate in response to mental demands and stimuli of an arousing nature. Hess's hypotheses regarding pupil mimicry and gender differences in pupil dilation did not replicate.

The mathematical flexibility of college students: The role of cognitive and affective factors

BACKGROUND

Traditional math instruction that emphasizes procedures and rote memorization is common in math classes, particularly within the United States. Students may be able to perform steps and recite information, but flexible thinking in math is also an important ability. Lay theories assume that extensive experience in math would lead to increased flexibility, but some research has posited a change-resistant account, which argues that experience with traditional instruction may make it difficult to think flexibly about even simple concepts.

AIMS

The current study explored the mathematical flexibility of college students who completed their K-12 education in the United States, and investigated how affective and cognitive factors contributed to flexible thinking.

SAMPLE

Participants were 128 undergraduate students at a competitive U.S. public university.

METHOD

Mathematical flexibility was measured through a novel task that asked participants to generate as many strategies as they could for a simple arithmetic problem. These strategies were coded to create scores of fluency (number of strategies) and flexibility (number of unique strategies).

RESULTS AND CONCLUSIONS

On average, participants were only able to provide little more than three unique strategies beyond the primary strategy taught in K-12 classrooms. Measures of math anxiety, math identity, need for cognition, and working memory were all unrelated to flexibility. However, student perceptions of how many possible solutions exist were significantly related to flexibility. These results provide evidence for a change-resistance account and provide further evidence that math flexibility is a unique construct.

Individual Differences in Math Ability Determine Neurocognitive Processing of Arithmetic Complexity: A Combined fNIRS-EEG Study

Some individuals experience more difficulties with math than others, in particular when arithmetic problems get more complex. Math ability, on one hand, and arithmetic complexity, on the other hand, seem to partly share neural underpinnings. This study addresses the question of whether this leads to an interaction of math ability and arithmetic complexity for multiplication and division on behavioral and neural levels. Previously screened individuals with high and low math ability solved multiplication and division problems in a written production paradigm while brain activation was assessed by combined functional near-infrared spectroscopy (fNIRS) and electroencephalography (EEG). Arithmetic complexity was manipulated by using single-digit operands for simple multiplication problems and operands between 2 and 19 for complex multiplication problems and the corresponding division problems. On the behavioral level, individuals with low math ability needed more time for calculation, especially for complex arithmetic. On the neural level, fNIRS results revealed that these individuals showed less activation in the left supramarginal gyrus (SMG), superior temporal gyrus (STG) and inferior frontal gyrus (IFG) than individuals with high math ability when solving complex compared to simple arithmetic. This reflects the greater use of arithmetic fact retrieval and also the more efficient processing of arithmetic complexity by individuals with high math ability. Oscillatory EEG analysis generally revealed theta and alpha desynchronization with increasing arithmetic complexity but showed no interaction with math ability. Because of the discovered interaction for behavior and brain activation, we conclude that the consideration of individual differences is essential when investigating the neurocognitive processing of arithmetic.

Effects of Working Memory, Strategy Use, and Single-Step Mental Addition on Multi-Step Mental Addition in Chinese Elementary Students

The aim of this paper was to examine the roles of working memory, single-step mental addition skills, and strategy use in multi-step mental addition in two independent samples of Chinese elementary students through different approaches to manipulate two dimensions of task characteristics (the primary task). In Study 1, we manipulated strategy types through the dimension of schema automaticity (whether intermediate sums were 10s) and the dimension of working memory load (WML, two steps versus four steps). A hierarchical linear model (HLM) analysis was conducted at case level, strategy level, and individual level. In Study 2, we manipulated task characteristics through schema automaticity (one-time versus two-time regrouping) and the WML (partial versus complete decomposition). A three-level HLM analysis was applied. The general findings of Study 1 and Study 2 suggested that shorter response time on single-step mental addition corresponded to shorter response time on multi-step mental addition. The use of strategies (from easier to more difficult strategies) negatively predicted response time on multi-step mental addition. Easier strategy was associated with shorter response time on multi-step mental addition. Better phonological loop was associated with shorter response time on multi-step mental addition. The findings in both studies highlighted the important role of phonological loop in mental addition in Chinese children, suggesting that the involvement of a specific subcomponent of working memory in mental arithmetic might be subject to linguistic, instructional, and contextual factors.

ADHD and math - The differential effect on calculation and estimation

Adults with ADHD were compared to controls when solving multiplication problems exactly and when estimating the results of multidigit multiplication problems relative to reference numbers. The ADHD participants were slower than controls in the exact calculation and in the estimation tasks, but not less accurate. The ADHD participants were similar to controls in showing enhanced accuracy and speed for smaller problem sizes, for trials in which the reference numbers were smaller (vs. larger) than the exact answers and for reference numbers that were far (vs. close) from the exact answer. The two groups similarly used the approximated calculation and the sense of magnitude strategies. They differed however in strategy execution, mainly of the approximated calculation strategy, which requires working memory resources. The increase in reaction time associated with using the approximated calculation strategy was larger for the ADHD compared to the control participants. Thus, ADHD seems to selectively impair calculation processes in estimation tasks that rely on working memory, but it does not hamper estimation skills that are based on sense of magnitude. The educational implications of these findings are discussed.

Arithmetic learning in advanced age

Acquisition of numerical knowledge and understanding of numerical information are crucial for coping with the changing demands of our digital society. In this study, we assessed arithmetic learning in older and younger individuals in a training experiment including brain imaging. In particular, we assessed age-related effects of training intensity, prior arithmetic competence, and neuropsychological variables on the acquisition of new arithmetic knowledge and on the transfer to new, unknown problems. Effects were assessed immediately after training and after 3 months. Behavioural results showed higher training effects for younger individuals than for older individuals and significantly better performance after 90 problem repetitions than after 30 repetitions in both age groups. A correlation analysis indicated that older adults with lower memory and executive functions at baseline could profit more from intensive training. Similarly, training effects in the younger group were higher for those individuals who had lower arithmetic competence and executive functions prior to intervention. In younger adults, successful transfer was associated with higher executive functions. Memory and set-shifting emerged as significant predictors of training effects in the older group. For the younger group, prior arithmetic competence was a significant predictor of training effects, while cognitive flexibility was a predictor of transfer effects. After training, a subgroup of participants underwent an MRI assessment. A voxel-based morphometry analysis showed a significant interaction between training effects and grey matter volume of the right middle temporal gyrus extending to the angular gyrus for the younger group relative to the older group. The reverse contrast (older group vs. younger group) did not yield any significant results. These results suggest that improvements in arithmetic competence are supported by temporo-parietal areas in the right hemisphere in younger participants, while learning in older people might be more widespread. Overall, our study indicates that arithmetic learning depends on the training intensity as well as on person-related factors including individual age, arithmetic competence before training, memory, and executive functions. In conclusion, we suggest that major progress can be also achieved by older participants, but that interventions have to take into account individual variables in order to provide maximal benefit.

Effectiveness of working memory training among children with dyscalculia: evidence for transfer effects on mathematical achievement-a pilot study

We examined whether the working memory (WM) capacity of developmentally dyscalculic children can be improved by a WM training program and whether outcomes relate to mathematical performance. The experimental design comprised two groups with developmental dyscalculia with grade 4 schooling: an experimental group (n = 14; mean age = 115.29 months) and a control group (n = 14; mean age = 116.07 months). All participants were assessed on measures of WM, mathematic attainment, and nonverbal mental ability (Raven test) before and after training. The WM training program focused on manipulating and maintaining arithmetic information. The results show that both WM and mathematical performances improved significantly after intervention, indicating a strong relationship between these two constructs. The control group improved slightly in Raven's progressive matrices and a reading number task. These findings are discussed in terms of near and far transfer toward trained and untrained skills and stress the positive impact of WM training on learning mathematics in children with dyscalculia.

Verbal and visual-spatial working memory and mathematical ability in different domains throughout primary school

The relative importance of visual-spatial and verbal working memory for mathematics performance and learning seems to vary with age, the novelty of the material, and the specific math domain that is investigated. In this study, the relations between verbal and visual-spatial working memory and performance in four math domains (i.e., addition, subtraction, multiplication, and division) at different ages during primary school are investigated. Children (N = 4337) from grades 2 through 6 participated. Visual-spatial and verbal working memory were assessed using online computerized tasks. Math performance was assessed at the start, middle, and end of the school year using a speeded arithmetic test. Multilevel Multigroup Latent Growth Modeling was used to model individual differences in level and growth in math performance, and examine the predictive value of working memory per grade, while controlling for effects of classroom membership. The results showed that as grade level progressed, the predictive value of visual-spatial working memory for individual differences in level of mathematics performance waned, while the predictive value of verbal working memory increased. Working memory did not predict individual differences between children in their rate of performance growth throughout the school year. These findings are discussed in relation to three, not mutually exclusive, explanations for such age-related findings.

Adults' and children's monitoring of story events in the service of comprehension

When reading narratives, adults monitor shifts in time, space, characters, goals, and causation. Shifts in any of these dimensions affect both moment-by-moment reading and memory organization. The extant developmental literature suggests that middle school children have relatively sophisticated understandings of each of these dimensions but does not indicate whether they spontaneously monitor these dimensions during reading experiences. In four experiments, we examined the processing of event shifts by adults and children, using both an explicit verb-clustering task and a reading time task. The results indicate that middle school children's and adults' post-reading memory is organized using these dimensions but that children do not monitor dimensions during moment-by-moment reading in the same manner as adults. These differences were not a function of differentially difficult texts for children and adults, or between-group differences. The findings have implications for models of adult and child text processing and for understanding children's developing narrative comprehension.

Working memory, math performance, and math anxiety

The cognitive literature now shows how critically math performance depends on working memory, for any form of arithmetic and math that involves processes beyond simple memory retrieval. The psychometric literature is also very clear on the global consequences of mathematics anxiety. People who are highly math anxious avoid math: They avoid elective coursework in math, both in high school and college, they avoid college majors that emphasize math, and they avoid career paths that involve math. We go beyond these psychometric relationships to examine the cognitive consequences of math anxiety. We show how performance on a standardized math achievement test varies as a function of math anxiety, and that math anxiety compromises the functioning of working memory. High math anxiety works much like a dual task setting: Preoccupation with one's math fears and anxieties functions like a resource-demanding secondary task. We comment on developmental and educational factors related to math and working memory, and on factors that may contribute to the development of math anxiety.