The role of inhibition in overcoming arithmetic natural number bias in the Chinese context: Evidence from behavioral and ERP experiments

The natural number bias (NNB) in arithmetic operations refers to the application of natural number properties to reasoning about rational numbers. Previous studies found the NNB interferes with students’ problem-solving. However, few studies have examined it in the Chinese context or the underlying mechanism by which it can be overcome. Addressing these gaps, in Experiments 1a (n = 31) and 1b (n = 30), we found that Chinese students demonstrate the NNB despite linguistic differences between Chinese and western languages. Experiment 2 (n = 38) adopted a negative priming paradigm and found that inhibitory control was necessary to overcome the NNB. Experiment 3 (n = 34) employed the event-related potential technique; we observed increased P2 amplitude when students solved congruent problems, and increased N2 and decreased P3 amplitude when they solved incongruent problems. These results indicated that the NNB is rooted in intuitive thinking, and overcoming this bias relies on inhibition.     

Early non-parental care and toddler behaviour problems: Links with temperamental negative affectivity and inhibitory control

This longitudinal study examined the link between multiple aspects of early non-parental care and internalizing and externalizing behaviour at 30 months of age. We also examined whether this link was mediated by children's inhibitory control and moderated by early temperamental negative affectivity. Participants were 193 mothers and their infants (91 girls; 79 firstborn). Negative affectivity was measured with a temperament questionnaire at 3 months of age. Information on non-parental care (i.e. centre-based care, number of hours, number of concurrent arrangements, long-term instability of care and age of entry) was obtained through monthly maternal interviews across the first year of life. At 30 months of age, toddlers’ inhibitory control was measured with observational tasks, and behaviour problem questionnaires were completed by the mothers and the caregivers. The mediation model was not supported. Greater observed inhibitory control, however, was related to less caregiver-reported internalizing and externalizing behaviour. Furthermore, negative affectivity moderated the effect of early non-parental care on behaviour problems. Non-parental care was unrelated to behaviour problems in toddlers who displayed low or mean levels of negative affectivity as infants. For infants high in negativity, however, centre-based care was associated with higher mother-rated internalizing and externalizing problems. In sum, the link between aspects of non-parental care during the first year of life and toddlers’ behaviour problems was not mediated through inhibitory control. Instead, inhibitory control and non-parental care, in conjunction with negative affectivity, appear to be two independent predictors of toddlers’ internalizing and externalizing behaviour.     

Performance in solving arithmetic problems: a comparison of children with different levels of achievement in mathematics and reading

The aim of the present study was to investigate the performance in arithmetic related to achievement levels in reading and mathematics. Basic arithmetical facts and multi‐step calculations were examined. The participants were 941 pupils aged 8 (N = 415), 10 (N = 274) and 13 (N = 252) years. The pupils were divided into four groups by standardized achievement tests. One group showed low achievement in both mathematics and reading (MLRL), a second group showed low achievement in mathematics only (ML‐only), a third group in reading only (RL‐only) and a fourth group showed normal achievement in both mathematics and reading (NA). The ML‐only and the MLRL groups did not differ significantly in basic arithmetical facts at any age level, but both groups performed below the RL‐only and NA groups. The two latter groups also performed similarly at all year levels. In multi‐step calculation all groups differed significantly at the lowest age level, with the NA as the group with the best achievement, followed by RL‐only, ML‐only and the MLRL group. At the two highest age levels the relations between the groups, in multi‐step calculation, were in accordance with the results regarding basic facts. The findings indicate, for both normal and low general mathematical ability, that low achievement in reading to a small extent interferes with the pupils’ development of arithmetic performance     

Lexical-semantic processing and reading: relations between semantic priming,visual word recognition and reading comprehension

The aim of this study was to investigate relations between lexical-semantic processing and two components of reading: visual word recognition and reading comprehension. Sixty-eight children from private schools in Porto Alegre, Brazil, from 7 to 12 years, were evaluated. Reading was assessed with a word/nonword reading task and a reading comprehension task. Lexical-semantic processing was evaluated with a semantic priming experiment. Correlations were conducted in order to examine the relations between semantic priming effects (SPEs) and performance in reading tasks. Regression analyses were performed to test the hypothesis that word reading mediates the relation between semantic priming and reading comprehension. The results showed that SPEs correlated with both word reading and reading comprehension measures. Additionally, partial mediation by word reading was found for the prediction of reading comprehension by SPEs. The results are discussed in the context of reading models and other studies relating semantic priming and reading measures.     

Maternal childhood emotional abuse predicts Chinese infant behavior problems: Examining mediating and moderating processes

The current study examined the mediating effect of maternal negative expressiveness as well as the moderating effects of infant inhibitory control (IC) in the association between maternal childhood emotional abuse (CEA) and infant behavior problems. Drawing from 207 families from mainland China, 2-wave data were reported in this study when the infants were 6 months (T1) and 14 (T2) months. Mothers (Mean age = 32.85 years, SD = 4.04) reported their CEA on the Childhood Trauma Questionnaire-Short Form (CTQ-SF) at T1, and their negative expressiveness on the Self-Expressiveness in the Family Questionnaire (SEFQ) at T2. The Infant-Toddler Social and Emotional Assessment (ITSEA) and a reverse categorization task were used to measure infant behavior problems and IC at T2, respectively. The results showed that T1 maternal CEA, rather than physical and sexual abuse, uniquely predicted T2 negative expressiveness. Maternal negative expressiveness significantly mediated the positive relations of maternal CEA and infant externalizing, internalizing and dysregulation problems. In addition, the moderated mediation model showed that the association between maternal negative expressiveness and infant dysregulation problems was moderated by infant IC. Specifically, the mediating pathway from maternal CEA to dysregulation problems through maternal negative expressiveness was significant, only for infants with poor IC. The results were robust even after controlling for family socio-economic status (SES), maternal childhood physical and sexual abuse. The importance of mediating and moderating processes in understanding the effect of maternal emotional abuse during childhood on infant behavior problems is discussed.     

Language-related longitudinal predictors of arithmetic word problem solving: A structural equation modeling approach

We investigated the longitudinal relations between cognitive skills, specifically language-related skills, and word-problem solving in 340 children (6.10–9.02 years). We used structural equation modeling to examine whether word-problem solving, computation skill, working memory, nonverbal reasoning, oral language, and word reading fluency measured at second grade were associated with performance on measures of word-problem solving in fourth grade. Results indicated that prior word-problem solving, computation skill, nonverbal reasoning, and oral language were significantly associated with children’s later word-problem solving. Multi-group modeling suggested that these relations were not significantly different for boys versus girls. Implications of these findings are discussed.     

Pathways to arithmetic: The role of visual-spatial and language skills in written arithmetic,arithmetic word problems,and nonsymbolic arithmetic

This study set out to develop and test a pathway model of the relations between general cognitive skills, specifically visual-spatial and spoken and written language skills, and competence in three forms of arithmetic that vary in modes of number representation. A total of 88 Chinese 4-year-olds participated and were tested first in kindergarten second grade (K2) and then in kindergarten third grade (K3). Language skills, including phonological, morphological, and visual-orthographic skills, and visual-spatial skills were measured at K2, and arithmetic outcomes, including written arithmetic, word problems, and nonsymbolic arithmetic, at K3. The results generally supported our model. Specifically, visual-spatial skills contributed to the prediction of all three types of arithmetic outcomes. Morphological skills predicted word problems, whereas phonological skills predicted written arithmetic. Finally, visual-orthographic skills contributed to both written and nonsymbolic arithmetic. These findings underscore the importance of delineating the specificity of cognitive processes in learning diverse forms of arithmetic.     

The relationship between performance on mathematical word problems and language proficiency for students learning through the medium of Irish

Ireland has two official languages—Gaeilge (Irish) and English. Similarly, primary- and second-level education can be mediated through the medium of Gaeilge or through the medium of English. This research is primarily focused on students (Gaeilgeoirí) in the transition from Gaeilge-medium mathematics education to English-medium mathematics education. Language is an essential element of learning, of thinking, of understanding and of communicating and is essential for mathematics learning. The content of mathematics is not taught without language and educational objectives advocate the development of fluency in the mathematics register. The theoretical framework underpinning the research design is Cummins’ (1976). Thresholds Hypothesis. This hypothesis infers that there might be a threshold level of language proficiency that bilingual students must achieve both in order to avoid cognitive deficits and to allow the potential benefits of being bilingual to come to the fore. The findings emerging from this study provide strong support for Cummins’ Thresholds Hypothesis at the key transitions—primary- to second-level and second-level to third-level mathematics education—in Ireland. Some implications and applications for mathematics teaching and learning are presented.

Linguistic and pedagogical factors affecting children's understanding of arithmetic word problems: A comparative study

2493 children aged from 5 to 15 years in 114 classes in 25 primary schools were asked to do a similar set of 22 arithmetic word problems. 1195 of the children were in Grades K through 6 in Victorian schools (Australia) and 1298 were in Grades 4 through 6 in Papua New Guinea (PNG) schools. For both samples the questions were posed in English. This was the first language for most children in the Victorian sample but, for the PNG sample, English was usually the second, third, or even fourth language (even though it is the language of instruction in PNG schools). While the test instrument was based on widely accepted information processing models of how children solve arithmetic word problems, the data obtained were not so much in accord with these models as with psycholinguistic theories on children's acquisition of polarised comparative pairs (like more and less). The data also indicate that children from the two samples used similar strategies and made similar errors, with the order of relative difficulty being the same for both samples, the main factor determining difficulty being the semantic structure of the questions. Differences in performance between corresponding grades from the two samples can be attributed to differences in the degree of English language competence rather than to numerical facility.     

The relations among young children's peer-reported trustworthiness, inhibitory control, and preschool adjustment

Sixty-five (38 male and 27 female) preschool children (mean age = 5 years 1 month) completed measures of peers’ trustworthiness (promise keeping and secret keeping). Teachers rated the preschool children's inhibitory control, trustworthiness, and preschool adjustment. Structural Equation Modeling (SEM) yielded support for the hypothesized model. The expected positive paths were found from (1) gender to preschool adjustment and inhibitory control, (2) age to peer-reported trustworthiness, (3) peer-reported trustworthiness to preschool adjustment, (4) inhibitory control to peer-reported trustworthiness, and (5) inhibitory control to preschool adjustment. The findings confirmed the hypothesized development of trustworthiness with age and girls’ advantage over boys in inhibitory control and preschool adjustment. The findings supported the hypotheses that trustworthiness is associated with preschool adjustment and mediates, in part, the relation between inhibitory control and preschool adjustment.     

Conditions for linking school mathematics and moral education: A case study

In recent years the mathematics education research community has undergone a social turn towards a greater interest in the values and broader educational purposes of mathematics education, including issues of social justice and citizenship education. Building on these developing interests, this paper presents a conceptual framework that links the teaching of school mathematics with moral education. Then, in a case study involving two countries, England and Canada, this framework is used to explore the affordances and constraints faced by mathematics teachers in those countries if they want to intentionally practice moral education in the classroom.     

Sources of self-efficacy in mathematics: A validation study

The purpose of this study was to develop and validate items with which to assess A. Bandura’s (1997) theorized sources of self-efficacy among middle school mathematics students. Results from Phase 1 (N = 1111) were used to develop and refine items for subsequent use. In Phase 2 of the study (N = 824), a 39-item, four-factor exploratory model fit best. Items were revised to strengthen psychometric properties. In Phase 3 (N = 803), a 24-item, four-factor confirmatory factor model fit best. This final model was invariant across gender and ethnicity. Subscales correlated with self-efficacy, self-concept, mastery goals, and optimism. Results suggest that the sources scale is psychometrically sound and could be adapted for use in other domains.     

A comparative study of variations in arithmetic fluency between Norwegian and Finnish third graders

ABSTRACT

The study aimed to investigate variations in addition and subtraction fluency by observing grade three students in Norway (n = 253, M_age = 8.38 y.) and Finland (n = 209, M_age = 9.35 y.) while controlling for their age and non-verbal reasoning. Gender differences were also examined. The focus of the study was on the performance of the low-achieving (LA) students in comparison to the typically achieving (TA) group, not neglecting differences in how early educational support was organised across the two countries. Two-minute speed tests in both addition and subtraction within the 1–20 number range were used to assess fluency. The Finnish students outperformed students in the Norwegian sample both in addition and subtraction fluency. There were more Norwegian students in the LA group (i.e. performance at or below the 25th percentile) in both addition (37.9% vs. 20.1%) and subtraction (39.1% vs. 15.8%). In comparison to the TA students, the LA students made more errors and skipped over more arithmetic tasks in an attempt to solve them. Observed differences are discussed in relation to both country characteristics concerning early mathematics education and early educational support.     

Teacher,classroom, and student growth orientation in mathematics: A multilevel examination of growth goals,growth mindset,engagement, and achievement

This study examined associations between student- (N = 1414), classroom-, and teacher (N = 91) growth orientation and mathematics engagement and achievement using a multilevel model. Results demonstrated positive associations between student growth orientation and mathematics outcomes and positive associations between classroom and teacher growth orientation and mathematics achievement. There was also a marginally significant interaction effect between classroom and teacher growth orientation on classroom engagement. Findings hold relevance for educational interventions surrounding growth constructs and teachers’ personal growth orientation.     

Working memory and mathematics in primary school children: A meta-analysis

Working memory, including central executive functions (inhibition, shifting and updating) are factors thought to play a central role in mathematical skill development. However, results reported with regard to the associations between mathematics and working memory components are inconsistent. The aim of this meta-analysis is twofold: to investigate the strength of this relation, and to establish whether the variation in the association is caused by tests, sample characteristics and study and other methodological characteristics. Results indicate that all working memory components are associated with mathematical performance, with the highest correlation between mathematics and verbal updating. Variation in the strength of the associations can consistently be explained by the type of mathematics measure used: general tests yield stronger correlations than more specific tests. Furthermore, characteristics of working memory measures, age and sample explain variance in correlations in some analyses. Interpretations of the contribution of moderator variables to various models are discussed.     

Riding the bumps in mathematics learning: Relations between academic buoyancy,engagement, and achievement

Academic buoyancy is conceptualised as the capacity to successfully navigate the typical adversities experienced during the course of schooling. Studies have shown positive relations between academic buoyancy and beneficial achievement-related beliefs, emotions, and behaviours. Relations with achievement are often small and studies of reciprocal relations are lacking. In a sample of 1,242 primary school students, we examined reciprocal relations between academic buoyancy, engagement, and achievement. Baseline levels of academic buoyancy and engagement positively predicted subsequent achievement. Achievement predicted gain in academic buoyancy but not engagement. Engagement, but not academic buoyancy, predicted gain in achievement. However, academic buoyancy predicted achievement gain indirectly, mediated through concurrent engagement. Building engagement, academic buoyancy, and foundational mathematics skills, could work synergistically to show downstream benefits for students’ achievement.     

Examining the dynamics of mathematics anxiety,perceived cost,and achievement: A control-value theory approach

Concerns about the influence of students’ perceived negative consequences of engagement in a task (i.e., cost) on their emotions, motivation, and cognition have increased in the last decade. The use of longitudinal models is needed to provide new insights into the role of perceived cost in mathematics learning. Grounded in the control-value theory, this study examined cross-lagged relations of mathematics anxiety, perceived cost, and mathematics achievement. The participants (N = 335) reported their mathematics anxiety and perceived cost four times during Grades 7 and 8, and their mathematics grades were attained from their school records. Cross-lagged panel model analysis revealed evidence of a long-term positive reciprocal relationship between mathematics anxiety and effort/emotional cost, a gradually diminished relationship between effort/emotional cost and mathematics performance, and a positive achievement to anxiety link during the transition between grade levels. Moreover, mathematics performance is a distal predictor of mathematics anxiety through effort/emotional cost rather than a proximal predictor or an outcome of anxiety. This study also clarified the distinction in the central role of effort/emotional versus opportunity cost in the interrelatedness of mathematics anxiety and performance, where the latter failed to demonstrate significant paths. Specific timing for interventions was discerned. Early cost prevention interventions along with considerations of academic achievement to alleviate both anxiety and perceived effort/emotional are highlighted as crucial for a positive high school mathematics experience.     

PISA and policy-borrowing: A philosophical perspective on their interplay in mathematics education

Mathematics achievement in different education systems around the world is assessed periodically in the Programme for International Student Assessment (PISA). PISA is deemed to yield robust international comparisons of mathematical attainment that enable individual countries and regions to monitor the performance of their education systems relative to standards being achieved internationally, with a view to informing their mathematics education policy decisions. Initially, the role of PISA in instigating mathematics education policy borrowing is outlined using England as a case study, and some existing technical critiques of PISA are then reviewed. Following this, aspects of Ludwig Wittgenstein’s later philosophy of mind are used to reason that an over-reliance on the use of PISA to inform policy decisions in mathematics education may be problematic. It is suggested that, when PISA is viewed through a later Wittgensteinian lens, a potential deficiency in the underpinning psychometric model, pertaining to the inherent indeterminism in unmeasured mathematical abilities, may weaken PISA’s utility in guiding mathematics education policy decisions. It is concluded that, whilst PISA mathematics scores may give some indication of the mathematical proficiency of a nation’s students, caution is required before mathematics education policies are borrowed from other jurisdictions on the basis of PISA performance. Implications for the other PISA domains are also outlined.