Language-specific effects on number computation in toddlers

Spontaneous quantitative processing in Chinese singular and plural picture naming: An event-related potentials analysis

Chinese nouns lack inflection and cannot reflect the quantitative relationship between singular and plural numbers. However, neural processes of picture naming are different from those of words. We assume that Chinese single and plural picture naming is different, and they may involve quantitative processing. Therefore, Experiment 1 was designed by picking picture naming as the task and Chinese as the target language and compared the accuracy, reaction time, and event-related potentials (ERPs) between single and plural picture naming, where two types of pictures were mixed. Although the T-test showed no significant differences in behavioral data, there were differences in ERPs. ERP differences involved two effects: P1 of 160-180 ms and P2 of 220-260 ms in the parietal-occipital lobe. These differences are suggested to reflect the neural differences in quantitative processing. Therefore, Chinese singular and plural picture naming consists of word production and implicit quantitative processing simultaneously. To explore the relationship between the two processings, we added a semantic factor (inanimate vs. animate items) to the quantity factor of Experiment 1 and carried out Experiment 2, with the observation indexes unchanged. There were no significant differences in behavioral data among the four conditions. After variance analysis, ERPs results indicated an interaction between semantic and quantitative factors in the central area at 180-280 ms. In summary, we suggest that Chinese singular and plural picture naming includes two simultaneous neural processing tasks: word production and quantitative processing, which interact in the central area at 180-280 ms.

Language and Math: What If We Have Two Separate Naming Systems?

The role of language in numerical processing has traditionally been restricted to counting and exact arithmetic. Nevertheless, the impact that each of a bilinguals’ languages may have in core numerical representations has not been questioned until recently. What if the language in which math has been first acquired (LLmath) had a bigger impact in our math processing? Based on previous studies on language switching we hypothesize that balanced bilinguals would behave like unbalanced bilinguals when switching between the two codes for math. In order to address this question, we measured the brain activity with magneto encephalography (MEG) and source estimation analyses of 12 balanced Basque-Spanish speakers performing a task in which participants were unconscious of the switches between the two codes. The results show an asymmetric switch cost between the two codes for math, and that the brain areas responsible for these switches are similar to those thought to belong to a general task switching mechanism. This implies that the dominances for math and language could run separately from the general language dominance.

Predictive model for early math skills based on structural equations

Early math skills are determined by higher cognitive processes that are particularly important for acquiring and developing skills during a child's early education. Such processes could be a critical target for identifying students at risk for math learning difficulties. Few studies have considered the use of a structural equation method to rationalize these relations. Participating in this study were 207 preschool students ages 59 to 72 months, 108 boys and 99 girls. Performance with respect to early math skills, early literacy, general intelligence, working memory, and short-term memory was assessed. A structural equation model explaining 64.3% of the variance in early math skills was applied. Early literacy exhibited the highest statistical significance (β = 0.443, p < 0.05), followed by intelligence (β = 0.286, p < 0.05), working memory (β = 0.220, p < 0.05), and short-term memory (β = 0.213, p < 0.05). Correlations between the independent variables were also significant (p < 0.05). According to the results, cognitive variables should be included in remedial intervention programs.

Young Natural-Number Arithmeticians

When preschoolers count to check their arithmetic predictions, their counts are better than when they simply count a set of items on count-only tasks. This is so even for 2 1/2- and 3-year-olds dealing with small values. Such results lend support to the view that learning about verbal counting benefits from a nonverbal count-arithmetic system and challenge theories that place understanding of verbal counting at 4 1/2 or 5 years. That preschoolers readily engage in predicting-and-checking number tasks has implications for educational programs.

The Cognitive Predictors of Computational Skill with Whole versus Rational Numbers: An Exploratory Study

The purpose of the present study was to explore the 3(rd)-grade cognitive predictors of 5th-grade computational skill with rational numbers and how those are similar to and different from the cognitive predictors of whole-number computational skill. Students (n = 688) were assessed on incoming whole-number calculation skill, language, nonverbal reasoning, concept formation, processing speed, and working memory in the fall of 3(rd) grade. Students were followed longitudinally and assessed on calculation skill with whole numbers and with rational numbers in the spring of 5(th) grade. The unique predictors of skill with whole-number computation were incoming whole-number calculation skill, nonverbal reasoning, concept formation, and working memory (numerical executive control). In addition to these cognitive abilities, language emerged as a unique predictor of rational-number computational skill.

Mathematical skills in 3- and 5-year-olds with spina bifida and their typically developing peers: a longitudinal approach

Preschoolers with spina bifida (SB) were compared to typically developing (TD) children on tasks tapping mathematical knowledge at 36 months (n = 102) and 60 months of age (n = 98). The group with SB had difficulty compared to TD peers on all mathematical tasks except for transformation on quantities in the subitizable range. At 36 months, vocabulary knowledge, visual-spatial, and fine motor abilities predicted achievement on a measure of informal math knowledge in both groups. At 60 months of age, phonological awareness, visual-spatial ability, and fine motor skill were uniquely and differentially related to counting knowledge, oral counting, object-based arithmetic skills, and quantitative concepts. Importantly, the patterns of association between these predictors and mathematical performance were similar across the groups. A novel finding is that fine motor skill uniquely predicted object-based arithmetic abilities in both groups, suggesting developmental continuity in the neurocognitive correlates of early object-based and later symbolic arithmetic problem solving. Models combining 36-month mathematical ability and these language-based, visual-spatial, and fine motor abilities at 60 months accounted for considerable variance on 60-month informal mathematical outcomes. Results are discussed with reference to models of mathematical development and early identification of risk in preschoolers with neurodevelopmental disorder.

Pedagogical Effect of Action on Arithmetic Performances in Wynn-Like Tasks Solved by 2-Year-Olds

Previous studies have provided evidence of interference due to a language-default mode (i.e., the singular/plural opposition) in 2-year-old children when solving arithmetic problems using a traditional onlooker method. However, an action-based method could help to bypass this language bias. In particular, when an arithmetic problem is presented to the children by the experimenter (onlooker mode) or realized by the children themselves (actor mode), performances are better with the latter. Thus, an experimental procedure based on “math in action” allows a brain-and-mind shift from a global language-bias (singular/plural) strategy to an exact numerical strategy. In this framework, we examined whether the exact numerical strategy induced by the actor method remains operational when children had to subsequently solve the same arithmetic problem using the traditional onlooker method. Results from 112 children suggest that this pedagogical effect of action bypasses the interference from language in onlooker mode after an initial confrontation of the problem in actor mode. This enduring embodiment effect has important implications for cognitive and preschool assessment in toddlers.

How verbal and spatial manipulation networks contribute to calculation: an fMRI study

The manipulation of numbers required during calculation is known to rely on working memory (WM) resources. Here, we investigated the respective contributions of verbal and/or spatial WM manipulation brain networks during the addition of four numbers performed by adults, using functional magnetic resonance imaging (fMRI). Both manipulation and maintenance tasks were proposed with syllables, locations, or two-digit numbers. As compared to their maintenance, numbers manipulation (addition) elicited increased activation within a widespread cortical network including inferior temporal, parietal, and prefrontal regions. Our results demonstrate that mastery of arithmetic calculation requires the cooperation of three WM manipulation systems: an executive manipulation system conjointly recruited by the three manipulation tasks, including the anterior cingulate cortex (ACC), the orbital part of the inferior frontal gyrus, and the caudate nuclei; a left-lateralized, language-related, inferior fronto-temporal system elicited by numbers and syllables manipulation tasks required for retrieval, selection, and association of symbolic information; and a right superior and posterior fronto-parietal system elicited by numbers and locations manipulation tasks for spatial WM and attentional processes. Our results provide new information that the anterior intraparietal sulcus (IPS) is involved in tasks requiring a magnitude processing with symbolic (numbers) and nonsymbolic (locations) stimuli. Furthermore, the specificity of arithmetic processing is mediated by a left-hemispheric specialization of the anterior and posterior parts of the IPS as compared to a spatial task involving magnitude processing with nonsymbolic material.

The role of language in mathematical development: evidence from children with specific language impairments

A sample (n=48) of eight-year-olds with specific language impairments is compared with age-matched (n=55) and language matched controls (n=55) on a range of tasks designed to test the interdependence of language and mathematical development. Performance across tasks varies substantially in the SLI group, showing profound deficits in production of the count word sequence and basic calculation and significant deficits in understanding of the place-value principle in Hindu-Arabic notation. Only in understanding of arithmetic principles does SLI performance approximate that of age-matched-controls, indicating that principled understanding can develop even where number sequence production and other aspects of number processing are severely compromised.