Math Competence Research Articles

Representations of numerical and non-numerical magnitude both contribute to mathematical competence in children.

A growing body of evidence suggests that non-symbolic representations of number, which humans share with nonhuman animals, are functionally related to uniquely human mathematical thought. Other research suggesting that numerical and non-numerical magnitudes not only share analog format but also form part of a general magnitude system raises questions about whether the non-symbolic basis of mathematical thinking is unique to numerical magnitude. Here we examined this issue in 5- and 6-year-old children using comparison tasks of non-symbolic number arrays and cumulative area as well as standardized tests of math competence. One set of findings revealed that scores on both magnitude comparison tasks were modulated by ratio, consistent with shared analog format. Moreover, scores on these tasks were moderately correlated, suggesting overlap in the precision of numerical and non-numerical magnitudes, as expected under a general magnitude system. Another set of findings revealed that the precision of both types of magnitude contributed shared and unique variance to the same math measures (e.g. calculation and geometry), after accounting for age and verbal competence. These findings argue against an exclusive role for non-symbolic number in supporting early mathematical understanding. Moreover, they suggest that mathematical understanding may be rooted in a general system of magnitude representation that is not specific to numerical magnitude but that also encompasses non-numerical magnitude.

Adult Perceptions of In-Class Collaborative Problem Solving as Mitigation for Statistics Anxiety

Two purposes existed for initiating this qualitative case study involving adults who had completed a college-level business statistics course. The first purpose was to explore adult challenges with stress and anxiety during the course: a phenomenon labeled statistics anxiety in the literature. The second purpose was to gain insight into adult perceptions of an instructional methodology that employed collaborative problem solving as an intervention to reduce student anxiety levels. Findings from this research provided valuable insights regarding adult perceptions of statistics and statistics courses. First, 75% of the participants recalled their performance in the course as being challenged by elevated levels of stress and anxiety. We also found a distinct inverse correlation between adult self-perception of math competency and statistics anxiety levels. Also notable were findings that a majority of the adult participants perceived working collaboratively markedly reduced anxiety levels, resulting in improved performance on tasks and assessments.

Affective and Motivational Factors Mediate the Relation between Math Skills and Use of Math in Everyday Life.

This study focused on the use of math in everyday life (the propensity to recognize and solve quantitative issues in real life situations). Data from a Dutch nation-wide research on math among adults (N = 521) were used to investigate the question whether math anxiety and perceived math competence mediated the relationship between math skills and use of math in everyday life, taken gender differences into account. Results showed that women reported higher math anxiety, lower perceived math competence, and lower use of math in everyday life, compared to men. Women's skills were estimated at a lower level than men's. For both women and men, higher skills were associated with higher perceived math competence, which in turn was associated with more use of math in everyday life. Only for women, math anxiety also mediated the relation between math skills and use of math in everyday life.

Intervention integrating physical activity with math: Math performance, perceived competence, and need satisfaction

Integrating physical activity (PA) with academics in the classroom is a newly explored approach, promising to improve both PA and academic achievement. The purposes of this study were to examine (a) the effect of lessons integrating PA with math, compared to traditional lessons, on math performance and perceived competence in math over an 8-week period, and (b) whether perceived competence in math and need satisfaction associated with the integrated lessons could predict math performance at the end of the intervention. Fourteen 4th and 5th grade classes were assigned to an integrated PA group (N = 106; using the “Move for Thought” kit), or a control group (N = 118; traditional lessons). A measure of perceived competence in math and a comprehensive, timed math test were completed before and after the intervention by both groups. Perceived need satisfaction associated with the integrated lessons was measured at the end of the intervention. The improvement in math performance in the integrated PA group was significantly larger compared to that of the control group. Perceived competence for math remained high and stable over time in both groups. Hierarchical regression analysis, controlling for gender and pretest math performance, showed that both perceived competence in math and satisfaction of the need for competence associated with the integrated lessons significantly predicted posttest math performance. This study makes a unique contribution to the literature on Self-Determination Theory-based interventions for enhancing academic performance by examining the effects of integrating PA with an academic subject.

Attitudes towards math in primary school students: Differences depending on the grade and gender

The main aim of this study is to check whether there are differences in some variables related to attitudes towards math in primary school students according to the course and gender. The sample consists of 897 students of the fifth and sixth year of primary education (50.2% boys and 49.8% girls). The results indicate that the boys, compared to girls, have a higher perceived competence in math, they are more intrinsically motivated extrinsic and exhibit lower levels of anxiety. As for the differences in terms of this variable, the results indicate that students in grade 5 have a higher perceived competence for math, perceive most useful, are more intrinsically motivated to this subject and show anxiety levels and some negative feelings toward the lower than grade 6. Therefore, girls show a "profile" of less adaptive than men conditions, both in terms of their perceived competition as their motivation towards math and also in terms of the emotions associated with this matter. As for the differences depending on the course, students from grade 5 are those with a much more positive attitudinal and motivational conditions than grade 6.

Attitudes towards math in primary school students: Differences depending on the grade and gender

The main aim of this study is to check whether there are differences in some variables related to attitudes towards math in primary school students according to the course and gender. The sample consists of 897 students of the fifth and sixth year of primary education (50.2% boys and 49.8% girls). The results indicate that the boys, compared to girls, have a higher perceived competence in math, they are more intrinsically motivated extrinsic and exhibit lower levels of anxiety. As for the differences in terms of this variable, the results indicate that students in grade 5 have a higher perceived competence for math, perceive most useful, are more intrinsically motivated to this subject and show anxiety levels and some negative feelings toward the lower than grade 6. Therefore, girls show a "profile" of less adaptive than men conditions, both in terms of their perceived competition as their motivation towards math and also in terms of the emotions associated with this matter. As for the differences depending on the course, students from grade 5 are those with a much more positive attitudinal and motivational conditions than grade 6.

The Mediating Relation between Symbolic and Nonsymbolic Foundations of Math Competence.

This study investigated the relation between symbolic and nonsymbolic magnitude processing abilities with 2 standardized measures of math competence (WRAT Arithmetic and KeyMath Numeration) in 150 3rd- grade children (mean age 9.01 years). Participants compared sets of dots and pairs of Arabic digits with numerosities 1–9 for relative numerical magnitude. In line with previous studies, performance on both symbolic and nonsymbolic magnitude processing was related to math ability. Performance metrics combining reaction and accuracy, as well as weber fractions, were entered into mediation models with standardized math test scores. Results showed that symbolic magnitude processing ability fully mediates the relation between nonsymbolic magnitude processing and math ability, regardless of the performance metric or standardized test.

Mathematical Anxiety influences the cortical connectivity profiles in lower alpha band during working memory tasks

Introduction Highly math-anxious (HMA) individuals are characterized by a strong tendency to avoid math, which ultimately undercuts their math competence and forecloses important career paths (Ashcraft, 2002). It is hypothesized that worries and intrusive thoughts associated with math anxiety (MA) reduce working memory resources needed for cognitively demanding math tasks (Chang & Beilock, 2016). However, mental processes that access the memory representations of mathematical knowledge has not been fully uncovered (Ashcraft, 2001). Previous studies indicate that the frontal cortex is dominantly involved in working memory (WM) and more specifically while updating the working memory representations (Smith & Jonides, 1997). Additionally, Klados et. al. 2015 show that higher event-related potential (ERP) measures of HMA subjects are predominantly located at frontocentral sites at cortex, while performing WM tasks. Here, we aim to explore the changes in cortical connectivity profile induced by MA during WM tasks. Methods EEG recordings were measured from 32 adults during performance of WM tasks with two levels of difficulty, 1-back (BT1) and 2-back (BT2) (Klados et al., 2015). According to the Abbreviated Math Anxiety Scale (AMAS), half of the participants were selected among the highly math anxious (HMA) students, whereas the other half had low math anxiety (LMA) (Hopko et al., 2003). ERPs were recorded via a Neurofax EEG-1200 system from 57 electrode sites according to a modified international 10/10 system using an Electrocap. Epoch length was 1200 ms including 200 ms prestimulus baseline. Signals were filtered offline between 0.5 and 45 Hz and submitted to an ICA procedure to identify ocular artifact components (Bell & Sejnowski, 1995). These artifact components were filtered with REGICA (Schlogl et al., 2007, Klados et al., 2009, 2011). Resulting waveforms were inspected visually and epochs containing visible artifacts in the first 500 ms post-stimulus were removed. To overcome the impact of varying electrical conductivity among head compartments on functional connectivity analyses (Nolte et. al., 200), the cortical activity was estimated from 28 EEG signals by adopting a cortical dipole model (He & Wu, 1999, Mattia et. al., 2009). Here, we referenced MNI152 template as an average head model. Scalp, cortex, outer- and inner-skull were extracted by implementing the Boundary Element Method (BEM) with 302 nodes (Uscedu, 2016). Finally, a column-norm normalization was used to prevent the linear inverse problem. This way, we obtained a transition kernel from 57 scalp signals to 302 cortical signals. We constructed connectivity matrices based on 302 cortical signals by using Magnitude Squared Coherence (MSC) in upper alpha band (8-10 Hz) (Lithari et. al., 2012, Klados et. al., 2013). Then, we embed these connectivity networks to the “connectivity components” by employing a nonlinear dimensional reduction technique (Coifman & Lafon, 2016). The first component captures the highest variance, i.e. the similarity/dissimilarity of the connectivity patterns of source regions. We used 2-way ANOVA with factors MA (HMA & LMA) and task difficulty (BT1 & BT2) along the first connectivity component. The p-values were adapted by the FDR correction (Benjamini & Hochberg, 1995). Results Fig.1 demonstrates the mixed effect of group by task interaction on the connectivity profiles. There is a significant interaction between MA and task difficulty, that is prominent in dorsolateral prefrontal cortex (DLPFC), temporal lobe, left ventromedial PFC, right inferior-parietal lobule (IPL), somatosensory and right motor areas. For each significant region (p(G x T)

Oportunidades académicas de calidad para jóvenes en desventaja: tres años de evaluación de impacto de un centro educativo autogestionado en un barrio de Montevideo de contexto crítico.

ABSTRACT. We study the three-year impact of a private tuition-free middle school on the academic outcomes of poor students. Several features of the treatment school fit with innovative paradigms that have delivered successful outcomes in poor urban areas. Our research design exploits the excess of applicants over the school capacity and the fact that participants were selected randomly. Specifically, we follow a cohort of students that entered middle school in 2010 and that were randomly assigned to attend the treatment school or public school as usual. We find that the treatment school impacted favorably on students’ academic advancement and math competencies. Also, the treatment school had a positive —and quite robust over time— impact on students’ and their parents’ academic expectations. This culture of high expectations has been previously identified in the literature as a key input for school success.

Computer software data analysis skills required for capacity building of university lecturers for effective educational research

The study was carried out to identify the computer software data analysis skills required for capacity building of university lecturers for effective educational research. Three research questions and one null hypothesis were formulated, to guide the study. The survey research design was adopted for the study and a structured questionnaire was used for data collection. Data obtained from 220 Lectures of the faculties of education in University of Nigeria, Nsukka and Nnamdi Azikiwe University, Awka were studied and analyzed. The study revealed computer, communication and math competency skill needs of the lecturers for effective data analysis in educational research using computer software. It was therefore recommended that administrators of the universities should organize regular training and retraining sessions for their lecturers on the identified areas of need to build up their capacity in the use of computer software for efficient educational research especially in the 21st century. Key words: Computer software, data analysis, educational research, capacity building, skills.

The relation between 1st grade grey matter volume and 2nd grade math competence

Mathematical and numerical competence is a critical foundation for individual success in modern society yet the neurobiological sources of individual differences in math competence are poorly understood. Neuroimaging research over the last decade suggests that neural mechanisms in the parietal lobe, particularly the intraparietal sulcus (IPS) are structurally aberrant in individuals with mathematical learning disabilities. However, whether those same brain regions underlie individual differences in math performance across the full range of math abilities is unknown. Furthermore, previous studies have been exclusively cross-sectional, making it unclear whether variations in the structure of the IPS are caused by or consequences of the development of math skills. The present study investigates the relation between grey matter volume across the whole brain and math competence longitudinally in a representative sample of 50 elementary school children. Results show that grey matter volume in the left IPS at the end of 1st grade relates to math competence a year later at the end of 2nd grade. Grey matter volume in this region did not change over that year, and was still correlated with math competence at the end of 2nd grade. These findings support the hypothesis that the IPS and its associated functions represent a critical foundation for the acquisition of mathematical competence.

An investigation of boys’ and girls’ emotional experience of math, their math performance, and the relation between these variables

Gender differences in children’s emotional experience of math, their math performance, and the relation between these variables were investigated in two studies. In Study 1, test anxiety, math anxiety, and math performance (whole-number computation) were measured in 134 children in grades 3–8 (ages 7–15 years). In Study 2, perceived math competence, math anxiety, and math performance (whole-number computation) were measured in 208 children in grades 3–6 (ages 8–13 years) using data from the study of Jansen et al. (Learning and Individual Differences, 24, 190–197, 2013). Gender differences occurred only in test anxiety (boys had lower test anxiety than girls). Concerning the relationship between emotional experience of math and math performance, math anxiety and math performance were negatively related, but only for girls, even when controlled for test anxiety (Study 1). However, only the relation between perceived math competence and math performance was significant in Study 2, for both boys and girls. The relation between math anxiety and math performance was not significant in this study after controlling for perceived math competence. Therefore, we might conclude that perceived math competence is a crucial variable when investigating children’s emotional experience concerning math.

Validating the Interpretations of PISA and TIMSS Tasks: A Rating Study

Scholastic tests regard cognitive abilities to be domain-specific competences. However, high correlations between competences indicate either high task similarity or a dependence on common factors. The present rating study examined the validity of 12 Programme for International Student Assessment (PISA) and Third or Trends in International Mathematics and Science Study (TIMSS) tasks. Two tasks per competence (reading, mathematics, science, problem solving) from PISA and TIMSS were assessed by 34 teachers and 33 psychology students on 11 scales: difficulty, curriculum reference, knowledge versus thinking, reading competence, verbal ability, math competence, science competence, problem solving, reasoning, general knowledge, and intelligence. Intraclass correlation between two randomly chosen raters was ric =.59. None of the tasks represented the intended target competence concisely. In five PISA tasks, competences other than those intended were seen as being more relevant. TIMSS tasks were seen as more curriculum-related and requiring more school knowledge than PISA tasks. For solving PISA tasks, thinking/reasoning ability and general intelligence were rated as being more important (d = 0.36). Only small differences were found between students’ and teachers’ ratings.

Preschoolers' Dot Enumeration Abilities Are Markers of Their Arithmetic Competence

The abilities to enumerate small sets of items (e.g., dots) and to compare magnitudes are claimed to be indexes of core numerical competences that scaffold early math development. Insofar as this is correct, these abilities may be diagnostic markers of math competence in preschoolers. However, unlike magnitude comparison abilities, little research has examined preschoolers' ability to enumerate small sets, or its significance for emerging math abilities; which is surprising since dot enumeration is a marker of school-aged children's math competence. It is nevertheless possible that general cognitive functions (working memory, response inhibition in particular) are associated with preschoolers' math abilities and underlie nascent dot enumeration abilities. We investigated whether preschoolers' dot enumeration abilities predict their non-verbal arithmetic ability, over and above the influence of working memory and response inhibition. Two measures of dot enumeration ability were examined—inverse efficiency and paradigm specific (response time profiles) measures—to determine which has the better diagnostic utility as a marker of math competence. Seventy-eight 42-to-57 month-olds completed dot enumeration, working memory, response inhibition, and non-verbal addition and subtraction tasks. Dot enumeration efficiency predicted arithmetic ability over and above the influence of general cognitive functions. While dot enumeration efficiency was a better predictor of arithmetic ability than paradigm specific response time profiles; the response time profile displaying the smallest subitizing range and steepest subitizing slope, also displayed poor addition abilities, suggesting a weak subitizing profile may have diagnostic significance in preschoolers. Overall, the findings support the claim that dot enumeration abilities and general cognitive functions are markers of preschoolers' math ability.

Self-concept of Indigenous and non-Indigenous Australian students: Competence and affect components and relations to achievement

Previous research on differences and similarities in self-concept of Indigenous and non-Indigenous Australian students did not consider the possible differentiation between competence and affect components. As a result, it is unknown whether previously found differences between Indigenous and non-Indigenous students' self-concepts are the result of their beliefs about their abilities or their feelings about specific domains. Thus, the present study aims to examine and compare the structure, the mean levels, and the relations to achievement measures of Indigenous and non-Indigenous Australian students' self-concepts in academic and non-academic domains when taking the competence–affect separation into account. Self-concepts in math, English, school, physical ability, and art were measured with 1809 secondary school students including 343 Indigenous students. For Indigenous and non-Indigenous students, confirmatory factor analyses demonstrated that all self-concept facets measured could be separated into competence and affect components although the correlations between competence and affect components were high, particularly for art and physical ability self-concepts. Non-Indigenous students demonstrated higher levels of school competence, English competence, English affect, and math competence self-concepts. Indigenous students displayed higher levels of physical ability competence self-concept while no group differences could be found for school affect, math affect, physical ability affect, and art competence and art affect self-concepts. Invariance tests revealed an invariant factor structure and invariant relations between the multiple self-concept facets and achievement factors across Indigenous and non-Indigenous students. Hence, the present study adds to our understanding of the similarities and differences regarding Indigenous and non-Indigenous Australian students' self-concepts.

Individual differences in kindergarten math achievement: The integrative roles of approximation skills and working memory

Kindergarteners can conduct basic computations with large nonsymbolic (e.g. dots, objects) and symbolic (i.e. Arabic numbers) numerosities in an approximate manner. These abilities are related to individual differences in mathematics achievement. At the same time, these individual differences are also determined by Working Memory (WM). The interrelationship between approximation, WM and math achievement has been largely unexplored. Also, the differential role of nonsymbolic and symbolic approximation in explaining math competencies is yet unclear. We examined an integrative theoretical model on the association between approximation (addition and comparison) and WM in 444 kindergarteners. As expected, approximation entailed two distinct abilities (nonsymbolic and symbolic). Both abilities correlated with mathematics achievement (i.e. counting and exact arithmetic), even when WM was taken into account. The association between nonsymbolic approximation and math achievement was completely mediated by symbolic approximation skills. These findings add to our understanding of the cognitive architecture underlying kindergarten math achievement.

Classroom context, teacher expectations, and cognitive level: Predicting children's math ability judgments

Classroom practices that make ability differences salient communicate differential teacher expectations for students. This study reports on a new observational tool for measuring Classroom Ability-based Practices (CAP) and explores how young children's self-perceptions of ability in mathematics are related to their teachers' expectations for them and to their cognitive reasoning skills in classrooms that vary in usage of such ability-differentiated practices. The sample consisted of 193 children and their teachers in 15 first grade classrooms. The CAP was a reliable measure of ability-based differential teacher treatment and showed criterion validity as a moderator variable in predicting children's ability perceptions. In highly ability-differentiating classrooms, children's self-ratings were more congruent with teachers' expectations of students' mathematics ability. Also in highly ability-differentiating classrooms, higher cognitive levels predicted lower self-ability ratings in math. These findings extend our understanding of the social and cognitive factors that shape young children's self-judgments of math competence.

Enjoying mathematics or feeling competent in mathematics? Reciprocal effects on mathematics achievement and perceived math effort expenditure

The multidimensionality of the academic self-concept in terms of domain specificity has been well established in previous studies, whereas its multidimensionality in terms of motivational functions (the so-called affect-competence separation) needs further examination. This study aims at exploring differential effects of enjoyment and competence beliefs on two external validity criteria in the field of mathematics. Data analysed in this study were part of a large-scale longitudinal research project. Following a five-wave design, math enjoyment, math competence beliefs, math achievement, and perceived math effort expenditure measures were repeatedly collected from a cohort of 4,724 pupils in Grades 3-7. Confirmatory factor analysis (CFA) was used to test the internal factor structure of the math self-concept. Additionally, a series of nested models was tested using structural equation modelling to examine longitudinal reciprocal interrelations between math competence beliefs and math enjoyment on the one hand and math achievement and perceived math effort expenditure on the other. Our results showed that CFA models with separate factors for math enjoyment and math competence beliefs fit the data substantially better than models without it. Furthermore, differential relationships between both constructs and the two educational outcomes were observed. Math competence beliefs had positive effects on math achievement and negative effects on perceived math effort expenditure. Math enjoyment had (mild) positive effects on subsequent perceived effort expenditure and math competence beliefs. This study provides further support for the affect-competence separation. Theoretical issues regarding adequate conceptualization and practical consequences for practitioners are discussed.

Teachers' and students' perceptions of self-regulated learning and math competence: Differentiation and agreement

Teachers' diagnostic competence is a crucial determinant of their teaching quality. However, prior research has indicated only a moderate association between teachers' and students' assessments of students' competence/self-concept and motivation. Furthermore, it is unclear how well teachers are able to differentiate between students' overall competence and other competence-relevant characteristics. The present article therefore investigated teachers' and students' perceptions of math competence/self-concept and two aspects of self-regulated learning (preactional and actional strategies), using a sample of 73 teachers and their fifth-grade students (N=1289). Exploratory structural equation modeling revealed three-factor solutions, indicating that both teachers and students differentiated between the assumed self-regulated learning factors and math competence/self-concept. Latent correlations between teachers' and students' perceptions were small to moderate; their assessments of students' math competence/self-concept showed the highest agreement. The findings are discussed with respect to their implications for assessing and improving teachers' diagnostic competence of students' learning.

Development of social‐emotional competence in boys of color: A cross‐sectional cohort analysis from pre‐K to second grade.

This article explores the development of psychosocial competence in boys of color (BOC; 226 African Americans and 109 Latinos). Changes in competence were assessed over 2 years in cohorts of low-income BOC beginning in pre-K, kindergarten, or first grade. Psycho-social competence was assessed in terms of self-regulation, interpersonal skills, and positive relationships with peers and teachers. Psycho-social and academic competence in literacy and math were assessed in prekindergarten through second grade using teacher reports, child reports, and normed measures. One-year follow-up data were available on measures of psycho-social competence. BOC evidenced high levels of psycho-social competence, especially on self-regulation, which was related to both math and reading achievement. Teachers and children held similarly favorable views of their relationships, but teacher ratings of peer relationships of BOC were less positive. Although emotional self-regulation was stable, declines were observed in self-regulation of attention, quality of peer relationships, teacher-rated closeness, and satisfaction with life at school, especially over the transition from pre-K to primary school.