Ernest C. D. M. van Lieshout

The developmental onset of symbolic approximation: beyond nonsymbolic representations, the language of numbers matters

Symbolic (i.e., with Arabic numerals) approximate arithmetic with large numerosities is an important predictor of mathematics. It was previously evidenced to onset before formal schooling at the kindergarten age (Gilmore et al., 2007) and was assumed to map onto pre-existing nonsymbolic (i.e., abstract magnitudes) representations. With a longitudinal study (Experiment 1), we show, for the first time, that nonsymbolic and symbolic arithmetic demonstrate different developmental trajectories. In contrast to Gilmore et al.’s (2007) findings, Experiment 1 showed that symbolic arithmetic onsets in grade 1, with the start of formal schooling, not earlier. Gilmore et al. (2007) had examined English-speaking children, whereas we assessed a large Dutch-speaking sample. The Dutch language for numbers can be cognitively more demanding, for example, due to the inversion property in numbers above 20. Thus, for instance, the number 48 is named in Dutch “achtenveertig” (eight and forty) instead of “forty eight.” To examine the effect of the language of numbers, we conducted a cross-cultural study with English- and Dutch-speaking children that had similar SES and math achievement skills (Experiment 2). Results demonstrated that Dutch-speaking kindergarteners lagged behind English-speaking children in symbolic arithmetic, not nonsymbolic and demonstrated a working memory overload in symbolic arithmetic, not nonsymbolic. Also, we show for the first time that the ability to name two-digit numbers highly correlates with symbolic approximate arithmetic not nonsymbolic. Our experiments empirically demonstrate that the symbolic number system is modulated more by development and education than the nonsymbolic system. Also, in contrast to the nonsymbolic system, the symbolic system is modulated by language.

Arithmetic difficulties in children with cerebral palsy are related to executive function and working memory

BACKGROUND Although it is believed that children with cerebral palsy are at high risk for learning difficulties and arithmetic difficulties in particular, few studies have investigated this issue. METHODS Arithmetic ability was longitudinally assessed in children with cerebral palsy in special (n = 41) and mainstream education (n = 16) and controls in mainstream education (n = 16). Second grade executive function and working memory scores were used to predict third grade arithmetic accuracy and response time. RESULTS Children with cerebral palsy in special education were less accurate and slower than their peers on all arithmetic tests, even after controlling for IQ, whereas children with cerebral palsy in mainstream education performed as well as controls. Although the performance gap became smaller over time, it did not disappear. Children with cerebral palsy in special education showed evidence of executive function and working memory deficits in shifting, updating, visuospatial sketchpad and phonological loop (for digits, not words) whereas children with cerebral palsy in mainstream education only had a deficit in visuospatial sketchpad. Hierarchical regression revealed that, after controlling for intelligence, components of executive function and working memory explained large proportions of unique variance in arithmetic accuracy and response time and these variables were sufficient to explain group differences in simple, but not complex, arithmetic. CONCLUSIONS Children with cerebral palsy are at risk for specific executive function and working memory deficits that, when present, increase the risk for arithmetic difficulties in these children.

The Effect of Cerebral Palsy on Arithmetic Accuracy is Mediated by Working Memory, Intelligence, Early Numeracy, and Instruction Time

The development of addition and subtraction accuracy was assessed in first graders with cerebral palsy (CP) in both mainstream (16) and special education (41) and a control group of first graders in mainstream education (16). The control group out-performed the CP groups in addition and subtraction accuracy and this difference could not be fully explained by differences in intelligence. Both CP groups showed evidence of working memory deficits. The three groups exhibited different developmental patterns in the area of early numeracy skills. Children with CP in special education were found to receive less arithmetic instruction and instruction time was positively related to arithmetic accuracy. Structural equation modeling revealed that the effect of CP on arithmetic accuracy is mediated by intelligence, working memory, early numeracy, and instruction time.

Working memory in nonsymbolic approximate arithmetic processing: a dual-task study with preschoolers

Preschool children have been proven to possess nonsymbolic approximate arithmetic skills before learning how to manipulate symbolic math and thus before any formal math instruction. It has been assumed that nonsymbolic approximate math tasks necessitate the allocation of Working Memory (WM) resources. WM has been consistently shown to be an important predictor of childrens math development and achievement. The aim of our study was to uncover the specific role of WM in nonsymbolic approximate math. For this purpose, we conducted a dual-task study with preschoolers with active phonological, visual, spatial, and central executive interference during the completion of a nonsymbolic approximate addition dot task. With regard to the role of WM, we found a clear performance breakdown in the central executive interference condition. Our findings provide insight into the underlying cognitive processes involved in storing and manipulating nonsymbolic approximate numerosities during early arithmetic.

Cognitive correlates of mathematical achievement in children with cerebral palsy and typically developing children.

BACKGROUND Remarkably few studies have investigated the nature and origin of learning difficulties in children with cerebral palsy (CP). AIMS To investigate math achievement in terms of word-problem solving ability in children with CP and controls. Because of the potential importance of reading for word-problem solving, we investigated reading as well. SAMPLE Children with CP attending either special (n= 41) or mainstream schools (n= 16) and a control group of typically developing children in mainstream schools (n= 16). METHOD Group differences in third grade math and reading, controlled for IQ, were tested with analyses of co-variance (ANCOVAs). Hierarchical regression was used to investigate cognitive correlates of third grade math and reading. Predictors included verbal and non-verbal IQ measured in first grade, components of working memory (WM) and executive function (EF) measured in second grade, and arithmetic fact fluency and reading measured in third grade. RESULTS Children with CP in special schools performed significantly worse than their peers on word-problem solving and reading. There was a trend towards worse performance in children with CP in mainstream schools compared to typically developing children. CONCLUSIONS Impairments of non-verbal IQ and WM updating predicted future difficulties in both word-problem solving and reading. Impairments of visuospatial sketchpad and inhibition predicted future word-problem, but not reading difficulty. Conversely, deficits of phonological loop predicted reading but not word-problem difficulty. Concurrent arithmetic fact fluency and reading ability were both important for word-problem solving ability. These results could potentially help to predict which children are likely to develop specific learning difficulties, facilitating early intervention.

The relationship between medical impairments and arithmetic development in children with cerebral palsy.

Arithmetic ability was tested in children with cerebral palsy without severe intellectual impairment (verbal IQ ≥ 70) attending special (n = 41) or mainstream education (n = 16) as well as control children in mainstream education (n = 16) throughout first and second grade. Children with cerebral palsy in special education did not appear to have fully automatized arithmetic facts by the end of second grade. Their lower accuracy and consistently slower (verbal) response times raise important concerns for their future arithmetic development. Differences in arithmetic performance between children with cerebral palsy in special or mainstream education were not related to localization of cerebral palsy or to gross motor impairment. Rather, lower accuracy and slower verbal responses were related to differences in nonverbal intelligence and the presence of epilepsy. Left-hand impairment was related to slower verbal responses but not to lower accuracy.

The effects of instruction on situation model construction: an eye fixation study on text comprehension in primary school children

This study examined whether the formation of a situation model can be encouraged by a situation‐focused instruction in primary school children. To achieve this, the standard reading‐for‐comprehension instruction was adapted so that it would emphasise the importance of imagination in narrative text comprehension. The results showed that the situational instruction enhanced the situation model construction abilities in good comprehenders in such a way that it improved not only their memory for the situation model but also the ease with which they filled in the gaps in time and space that appeared in the narratives. In poor comprehenders, the situational instruction led to a redistribution of attentional resources allocated to textbase‐ and situation‐level processing. It was suggested that this caused them to go beyond encoding the explicit text and instead construct a situation model from it, and that they did so without enriching the model with general‐knowledge inferences as much as good comprehenders.

Working memory and number line representations in single-digit addition: Approximate versus exact, nonsymbolic versus symbolic.

How do kindergarteners solve different single-digit addition problem formats? We administered problems that differed solely on the basis of two dimensions: response type (approximate or exact), and stimulus type (nonsymbolic, i.e., dots, or symbolic, i.e., Arabic numbers). We examined how performance differs across these dimensions, and which cognitive mechanism (mental model, transcoding, or phonological storage) underlies performance in each problem format with respect to working memory (WM) resources and mental number line representations. As expected, nonsymbolic problem formats were easier than symbolic ones. The visuospatial sketchpad was the primary predictor of nonsymbolic addition. Symbolic problem formats were harder because they either required the storage and manipulation of quantitative symbols phonologically or taxed more WM resources than their nonsymbolic counterparts. In symbolic addition, WM and mental number line results showed that when an approximate response was needed, children transcoded the information to the nonsymbolic code. When an exact response was needed, however, they phonologically stored numerical information in the symbolic code. Lastly, we found that more accurate symbolic mental number line representations were related to better performance in exact addition problem formats, not the approximate ones. This study extends our understanding of the cognitive processes underlying childrens simple addition skills.

Cognitive predictors of children's development in mathematics achievement: A latent growth modeling approach

Research has identified various domain-general and domain-specific cognitive abilities as predictors of childrens individual differences in mathematics achievement. However, research into the predictors of childrens individual growth rates, namely between-person differences in within-person change in mathematics achievement is scarce. We assessed 334 childrens domain-general and mathematics-specific early cognitive abilities and their general mathematics achievement longitudinally across four time-points within the first and second grades of primary school. As expected, a constellation of multiple cognitive abilities contributed to the childrens starting level of mathematical success. Specifically, latent growth modeling revealed that WM abilities, IQ, counting skills, nonsymbolic and symbolic approximate arithmetic and comparison skills explained individual differences in the childrens initial status on a curriculum-based general mathematics achievement test. Surprisingly, however, only one out of all the assessed cognitive abilities was a unique predictor of the childrens individual growth rates in mathematics achievement: their performance in the symbolic approximate addition task. In this task, children were asked to estimate the sum of two large numbers and decide if this estimated sum was smaller or larger compared to a third number. Our findings demonstrate the importance of multiple domain-general and mathematics-specific cognitive skills for identifying children at risk of struggling with mathematics and highlight the significance of early approximate arithmetic skills for the development of ones mathematical success. We argue the need for more research focus on explaining childrens individual growth rates in mathematics achievement.