Memories of math: Narrative predictors of math affect,math motivation,and future math plans

This mixed-methods study focuses on narratives that undergraduates tell about pivotal moments (i.e., turning points) in their prior history with math. A key objective was to examine whether these turning points would be associated with participants’ current math affect, math motivation, and future plans with math. Undergraduate participants (N = 210) completed quantitative measures assessing math anxiety, math self-expectancy, and math value, and also wrote narratives about a turning point with math and their future math plans. Thematic analysis revealed four themes in the math turning point narratives: (1) redemption, (2) contamination, (3) consistently positive, and (4) consistently negative. Quantitative analyses indicated that participants who wrote consistently positive narratives reported significantly lower math anxiety and higher math self-expectancy and math value relative to participants who wrote other types of narratives. Further, participants who wrote consistently negative turning point narratives were more likely to indicate that they would avoid math in the future. These results suggest that an individual’s memory of their early math experiences can color their math affect, math motivation, and plans for pursuing math in the future, even years after the experience has occurred. Implications for math education are discussed.     

Co-development of math anxiety,math self-concept,and math value in adolescence: The roles of parents and math teachers

Despite the well-documented negative implications of math anxiety on math learning, a scarcity of theory-guided, long-term longitudinal research limits knowledge about how math anxiety develops over time. Guided by the Control-Value Theory of Achievement Emotions (Pekrun, 2006), the present study addresses this gap by examining (1) how math anxiety develops in tandem with the development of control and value appraisals across secondary schooling, and (2) how these three constructs co-develop in relation to characteristics of home and school contexts. We used growth mixture modeling to investigate how math anxiety, math self-concept (a frequently examined indicator of control appraisal), and math utility value (one dimension of math value) develop in parallel in a sample of 3116 adolescents, who were assessed annually across middle and high school. We identified three trajectory classes: a stable class, characterized by stably modest math anxiety, high math self-concept, and high math utility value, a linear change class, characterized by increasing math anxiety and decreasing math self-concept and utility value, and a fluctuating class, characterized by curvilinear changes in math anxiety, math self-concept, and math utility value. Parental academic support and teacher bias differentiated the stable class from the fluctuating class at the transition to middle school, and from the linear change class at the transition to high school. Our findings point to the heterogeneous contributions of control and value appraisals towards the development of math anxiety and highlight the importance of investigating multiple dimensions of the socio-ecological context at different stages of math anxiety development.     

Math achievement,stereotypes, and math self-concepts among elementary-school students in Singapore

Singaporean elementary-school students (N = 299) completed Child Implicit Association Tests (Child IAT) as well as explicit measures of gender identity, math–gender stereotypes, and math self-concepts. Students also completed a standardized math achievement test. Three new findings emerged. First, implicit, but not explicit, math self-concepts (math = me) were positively related to math achievement on a standardized test. Second, as expected, stronger math–gender stereotypes (math = boys) significantly correlated with stronger math self-concepts for boys and weaker math self-concepts for girls, on both implicit and explicit measures. Third, implicit math–gender stereotypes were significantly related to math achievement. These findings show that non-academic factors such as implicit math self-concepts and stereotypes are linked to students' actual math achievement. The findings suggest that measuring individual differences in non-academic factors may be a useful tool for educators in assessing students' academic outcomes.     

Concurrent and longitudinal associations between parental educational involvement,teacher support,and math anxiety: The role of math learning involvement in elementary school children

Environmental and individual factors are regarded as powerful predictors of math anxiety. However, their joint contribution to predicting math anxiety has not been thoroughly explored. To address this, two studies were conducted to examine how parental educational involvement and teacher support related to math evaluation anxiety and learning math anxiety concurrently (Study 1) and longitudinally (Study 2) and whether the effect of parental educational involvement and teacher support on math anxiety needed to go through math learning involvement. Third-grade students (Study 1: N = 1780, Study 2: N = 1850) from three public elementary schools participated in the studies. Concurrent analyses revealed that higher parental educational involvement and teacher support were associated with higher math learning involvement and lower math anxiety. Moreover, math learning involvement partially mediated the relation between parental educational involvement and math evaluation anxiety, teacher support and math evaluation anxiety, teacher support and learning math anxiety, but fully mediated the relation between parental educational involvement and learning math anxiety. Longitudinally, robust associations were found between current parental educational involvement, current teacher support, and subsequent learning math anxiety. But similar patterns did not emerge in math evaluation anxiety. Specifically, the direct effect of parental educational involvement and teacher support on math evaluation anxiety was not significant. These findings suggested the importance of taking into account the dimension of math anxiety when understanding the mechanisms of math anxiety from a dynamic developmental perspective. We demonstrate areas that need improvement and suggest possible future directions.     

Estimating the co-development of executive functions and math achievement throughout the elementary grades using a cross-lagged panel model with fixed effects

Executive functioning (EF) is associated with children’s math skill development, both concurrently and longitudinally. However, it is not known how components of EF might be related to mathematics skills and vice versa over the course of elementary school. The present study addresses this issue by investigating relations between math achievement and two key components of EF -- working memory (WM) and cognitive flexibility (CF) -- from kindergarten to 5th grade, using the large-scale nationally representative dataset (N = 18,174) from the Early Childhood Longitudinal Study-Kindergarten (ECLS-K: 2011). Results from cross-lagged panel models with fixed effects support a transactional theoretical model, demonstrating a long-term reciprocal relationship between WM and math achievement from kindergarten to 5th grade and between CF and math achievement from 2nd grade to 5th grade. However, we found that reciprocal relations decrease as children grow older, suggesting that their math achievement relies less on EF and more on prior math knowledge over time.     

The immigrant paradox and math self-concept: An SES-of-origin-country hypothesis

The immigrant paradox is the phenomenon where recent immigrants have better outcomes than individuals from native-born families. Although limited past research has shown the paradox to exist for math self-concept, neither its exact nature nor a theoretical explanation for its existence have been reported. Using Australian cohort data from the Programme for International Student Assessment (PISA) 2003 (N = 12,551) and 2012 (N = 14,481), we first establish that immigrant students have higher math self-concepts than native students, controlling for gender and absolute parental socioeconomic status (SES), and show that it is similar to—albeit weaker than—the expectation-achievement gap. We then provide an SES-of-origin-country hypothesis as a contextual explanation for this effect; we show that the immigrant paradox for both math self-concept and educational expectations substantially reduces when accounting for parents' SES relative to their country-of-origin. Our findings suggest that the paradox for math self-concept and educational expectations may partly result from immigrant parents’ socioeconomic advantage in their home countries.     

Enhancing children's math motivation with a joint intervention on mindset and gender stereotypes

We tested the effectiveness of the intervention program designed to enhance children's math motivation by simultaneously strengthening their growth mindsets and weakening their gender stereotypes. Both the intervention and control programs consisted of six bi-weekly 40-min sessions that were evenly distributed over three months and administered during regular school hours. Repeated measures analyses of variance with group (between-subject factor: intervention vs. control) and time (within-subject factor: pretest vs. posttest) revealed significant Group × Time interactions for all outcomes but test anxiety. Growth mindset, perceived competence, persistence, and achievement of the intervention group increased, while those of the control group decreased. Gender stereotypic beliefs exhibited the opposite pattern. Also, growth mindset and gender stereotypes correlated negatively only for the intervention group. Path analysis demonstrated that the growth mindset of students after the intervention predicted their math persistence and achievement directly and indirectly via their perceived competence in math.     

The role of numerical and non-numerical ordering abilities in mathematics and reading in middle childhood

This study investigated whether different types of ordering skills were related to mathematics achievement in children (n = 100) in middle childhood, after the effects of age, socio-economic status, IQ, and processing speed were taken into account. The relations between ordering skills and magnitude processing were also investigated, as well as the possibility that some of the shared variance between math and reading is explained by ordering abilities. The ordering tasks included the ordering of familiar numerical and non-numerical sequences, a parental report of children’s everyday ordering skills, and an order working memory task. Three magnitude processing tasks (symbolic and non-symbolic comparison and number line estimation), were also administered, as well as measures of inhibition and spatial working memory. From this set of measures, number ordering, order working memory and number line estimation emerged as the most important predictors of mathematics skills. We found that number ordering mediated the effect of both symbolic and non-symbolic comparison skills on mathematics, further confirming that this task captures some essential skills related to mathematics. Additionally, order working memory mediated the effect of both number comparison and reading skills on math. Finally, whereas non-symbolic comparison and number line estimation are considered important indicators of magnitude processing skills, there was no relationship between these abilities, but there was a correlation between each of these abilities and reading skills, with number line estimation also mediating the effect of reading skills on math. These novel findings could contribute to a better understanding of the basic processes underlying math ability, and why math and reading are strongly related in typical populations and in children with learning difficulties.     

Groupitizing reflects conceptual developments in math cognition and inequities in math achievement from childhood through adolescence

Understanding the cognitive processes central to mathematical development is crucial to addressing systemic inequities in math achievement. We investigate the “Groupitizing” ability in 1209 third to eighth graders (mean age at first timepoint = 10.48, 586 girls, 39.16% Asian, 28.88% Hispanic/Latino, 18.51% White), a process that captures the ability to use grouping cues to access the exact value of a set. Groupitizing improves each year from late childhood to early adolescence (d = 3.29), is a central predictor of math achievement (beta weight = .30), is linked to conceptual processes in mathematics (minimum d = 0.69), and helps explain the dynamic between the ongoing development of non-symbolic number concepts, systemic educational inequities in school associated with SES, and mathematics achievement (minimum beta weight = .11) in ways that explicit symbolic measures may miss.     

It Takes Two: Expectancy-Value Constructs and Vocational Interests Jointly Predict STEM Major Choices

The supply of STEM graduates is an issue in many countries—raising the question of why more students do not choose STEM careers. We aimed to address this question by drawing on two of the most prominent theories on career choices: Eccles et al.'s (1983) expectancy-value theory (EVT) and Holland's (1997) theory of vocational interests. In a large longitudinal data set, we used EVT constructs and vocational interests assessed at the end of high school (T1) to explain differences in math achievement (a critical filter for later STEM choices) at the end of high school (school sample: N = 4,984) and to predict actual STEM major choices in college 2 years later (T2; college sample: N = 2,145). To investigate their distinct and relative contributions, we conducted a set of hierarchical regression analyses (linear and logistic) in which we considered EVT constructs and vocational interests separately and simultaneously. Whereas both groups of constructs were significant predictors of both outcomes, vocational interests were better predictors of STEM major choice (Pseudo-R² = .26) than EVT constructs (Pseudo-R² = .19), and EVT constructs were better predictors of math achievement (R² = .47) than vocational interests (R² = .30) when investigated separately. In addition, the combined analyses revealed that the best predictions of math achievement (R² = .48) and STEM major choice (Pseudo-R² = .28) were achieved when EVT constructs and vocational interests were used jointly. Results suggest that EVT constructs and vocational interests contribute differently to STEM major choices, a finding that may have important implications for research and practice, including the choice of which constructs to target in interventions.     

Cognitive processes and math performance: a study with children at third grade of basic education

The present study aims to examine the relationship between cognitive factors and mathematical achievement in primary education. Participants were 103 Portuguese third grade students, aged 8 and 9. All participants completed a battery for working memory (WMTB-C), a test of general intelligence (Raven's Progressive Color Matrices), a selective attention test (d2), and mathematical exercises (arithmetic story problems and measurement skills). Data suggested significant correlations between math performance, executive, visuospatial sketchpad and g factor. Our findings suggest the importance of the cognitive factors in two mathematical domains considered. In consonance with the research in this area, we conclude that working memory (WM) assumes an important role in different math curricular achievements.     

Optimizing science self-efficacy: A multilevel examination of the moderating effects of anxiety on the relationship between self-efficacy and achievement in science

Extant research has demonstrated that anxiety is negatively associated with self-efficacy, especially in science. However, social cognitive theory also posits that anxiety and self-efficacy are likely to dynamically interact (i.e., moderate), such that a student high in anxiety may not garner the benefits of high self-efficacy. It has been suggested that classrooms may also be characterized in terms of this problematic dynamic, such that class-average anxiety may impede potentially positive effects of class-average self-efficacy. Despite this, very little work has focused on the extent to which anxiety thwarts the positive effects of self-efficacy at either the student- or classroom-level, and none has done so among secondary school students or in science specifically. Thus, the present study examines the main effects of science anxiety and self-efficacy on science achievement, as well as the moderating effects of science anxiety on the relationship between science self-efficacy and achievement, at both the student- and classroom-level. With a sample of N = 1,075 high school students clustered in N = 99 science classrooms, doubly latent multilevel structural equation modelling demonstrated that science self-efficacy positively predicted science achievement at both student- and classroom-levels. Also, at the student-level (but not the classroom-level), science anxiety negatively moderated the effects of science self-efficacy on science achievement, such that students high in self-efficacy with higher anxiety scored lower in science achievement than those with lower anxiety. Interestingly, however, student-level (but not classroom-level) findings also suggested a potentially arousing role of anxiety for students low in self-efficacy. These findings have theoretical implications and suggest that a dual intervention approach (i.e., concurrently promoting science self-efficacy and reducing science anxiety) at student-level and interventions targeting self-efficacy at the classroom-level may be warranted to optimize science achievement.     

The big-fish-little-pond effect on academic self-concept and interest in first- and third-grade students

BackgroundThe big-fish-little-pond effect (BFLPE) postulates that class-average achievement has a negative effect on students’ academic self-concept. Research examining the BFLPE with elementary school students is scarce, especially with first graders.AimsThis study examined the BFLPE of class-average achievement on academic self-concept and interest in the math domain with first and third graders.SampleParticipants were Luxembourgish first graders (N = 5057) and third graders (N = 4925).MethodsA multilevel, doubly latent approach was used to assess a BFLPE model containing achievement (as the predictor) and ASC and interest (as outcomes) in the math domain.ResultsThe BFLPE on math self-concept was supported in both grades, whereas the BFLPE on math interest was supported only for third graders. In both grades, larger effect sizes were observed for the BFLPE on math self-concept than on math interest.ConclusionOur results suggest that the social comparisons underlying the BFLPE play an important role in the formation of math self-concept in both grades, but they play a less substantial—and probably later—role in the formation of math interest in elementary school.     

Killing two birds with one stone: The role of motivational resources in predicting changes in achievement and school well-being beyond intelligence

This study investigated whether motivational resources play a role in predicting changes in students’ achievement and well-being above and beyond the role of intelligence during the transition to secondary school. The motivational resources entailed autonomous and controlled motivation as conceived in Self-Determination Theory and implicit beliefs of intelligence as defined in Dweck's perspective. We used two waves of data from a larger longitudinal study, thereby following 6th grade students in the transition to secondary education (N = 2546, Mage = 11.52 years, 49.8% boys). Results of Latent Change Modeling revealed that, after controlling for the role of intelligence in the prediction of standardized math achievement tests, motivational resources played a supplementary role, both at the level of interindividual differences and at the level of intra-individual change. Students with higher initial levels of autonomous motivation obtained higher initial test scores, reported higher school well-being, and made greater progress in both outcomes across the transition. An increase in autonomous motivation was also related to an increase in both achievement and well-being. A similar, yet opposite, pattern of findings was obtained for controlled motivation. An entity mindset failed to yield any unique associations. Given that autonomous motivation contributes to both achievement and well-being beyond effects of intelligence, it is critical for educators to nurture this motivational resource as it allows them to kill two birds with one stone.     

Attention problems,phonological short-term memory,and visuospatial short-term memory: Differential effects on near- and long-term scholastic achievement

The current study examined individual differences in children's phonological and visuospatial short-term memory as potential mediators of the relationship among attention problems and near- and long-term scholastic achievement. Nested structural equation models revealed that teacher-reported attention problems were associated negatively with composite scholastic achievement (reading, math, language), both initially and at 4-year follow-up in an ethnically diverse sample of children (N = 317). Much of this influence, however, was attenuated by phonological short-term memory's contribution to near-term achievement and visuospatial short-term memory's contribution to long-term achievement. Domain-specific reading and math models showed similar results with some exceptions. In all models, measured intelligence made no contribution to later achievement beyond its initial influence on early achievement. The results contribute to our understanding of the mechanisms associated with individual differences in children's scholastic achievement, and have potential implications for identifying early predictors of children at risk for academic failure, and developing remedial programs targeting phonological and visuospatial short-term memory deficits in children with attention problems.     

Educated fathers and mothers have differential effects on overseas Japanese boys' and girls' math achievement

This chapter summarizes an investigation of the variables connected to the math achievement of 168, 5th- and 6th-grade Japanese students enrolled in an overseas Japanese school located in New York City. A mix of family processes and prior variables, including the language patterns in the home and the time the family had been away from Japan, were incorporated into the path models for analysis. The results of the study show that the education of the fathers and mothers played differential roles for the boys' and girls' math achievement. Educated mothers were found to positively influence their sons' achievement but to negatively influence their daughters' achievement. The authors interpret this finding as an attempt by the mothers to reinforce traditional Japanese values. Highly-educated fathers were found to have positive effects on their daughters' math achievement. This finding suggests educated fathers have a more open view of their daughters' academic potential. SES was found to be much more important to the math achievement of the girls (r=0.36). For both groups, excessive perceived parental pressure and help were found to indirectly undermine children's math achievement. Intellectual resources in the home were found to benefit boys' math achievement but to negatively effect girls' achievement. Overall, a high level of differential socialization was uncovered in this overseas Japanese community.     

Effect of teacher support on students’ math attitudes: Measurement invariance and moderation of students' background characteristics

We examine the effect of students' perceptions of teacher support on attitudes towards math and whether the association varies between students from historically underrepresented groups in STEM. Participants included high school students enrolled in an AP Statistics course (N = 585, M_age = 16.75 years, SD_age = 0.88). Measurement invariance conducted on the basis of student background characteristics (i.e., biological sex, underrepresented race/ethnicity status, and parental educational attainment) provided evidence of metric invariance or greater. Standardized regression coefficients suggested potential differences, such that for students who were female, from an underrepresented racial/ethnicity group in STEM, or had parents with lower levels of education, the effect of teacher support appeared not as strong compared to their counterparts. However, scaled chi-square difference tests comparing nested latent path models did not suggest a moderation effect of these three characteristics. These findings have implications for understanding barriers many students face in receiving the benefits of teacher support.     

Self-fulfilling prophecies in media-based learning: Content relevance moderates quality expectation effects on academic achievement

In the present paper a model of self-fulfilling prophecy effects in media-based learning was developed and tested. The central model assumption was that information about an instructional medium's quality affects students' academic achievement depending on the instructional content's relevance to the student. Experiment 1 (N = 100) demonstrated higher achievement in response to positive compared to negative information, but not the predicted moderating effect of content relevance. Using a revised relevance manipulation, Experiment 2 (N = 199) identified the following moderating function of content relevance: Under moderate relevance positive information led to higher achievement, under high relevance negative information resulted in higher achievement. No differences appeared under low relevance. Path analyses revealed students' cognitive effort as significant mediator for these effects.     

Gender by racial/ethnic intersectionality in the patterns of Adolescents’ math motivation and their math achievement and engagement

Individuals' math motivational beliefs are theorized to shape their STEM achievement and engagement in high school and beyond. Combining situated expectancy-value theory and intersectionality framework, the goals of this study were to (a) identify the unique patterns of U.S. high school students' math motivational beliefs, (b) examine differences in the patterns based on the intersection of gender and race/ethnicity, and (c) test the extent to which these patterns predicted differences in students' math achievement and classroom behavioral engagement for each of the gender by racial/ethnic groups. The current study included 16,120 high schoolers (50% female; 63% White, 17% Latina/o, 11% Black, and 9% Asian Americans; Mage = 14.46 at Grade 9) from the High School Longitudinal Study. There were six unique patterns of students' math motivational beliefs: Overall High, Above Average but not Identified, Identified but Average Value, Average, Low Identity, and Overall Low. Pattern membership at the intersection of gender and race/ethnicity showed nuances that could not be represented by gender or race/ethnicity alone; for example, male and female Asian American adolescents had similar patterns, but many male and female adolescents of other racial/ethnic groups had different patterns. Adolescents' math motivational belief patterns were associated with their Grade 11 math achievement and behavioral engagement even after controlling for prior math achievement and family socioeconomic status, and the associated varied by the gender and racial/ethnic groups.     

Fluid intelligence as a predictor of learning: A longitudinal multilevel approach applied to math

The association between fluid intelligence and inter-individual differences was investigated using multilevel growth curve modeling applied to data measuring intra-individual improvement on math achievement tests. A sample of 166 students (88 boys and 78 girls), ranging in age from 11 to 14 (M = 12.3, SD = 0.64), was tested. These individuals took four math achievement tests, which were vertically equated via Item Response Theory, at the beginning and end of the seventh and eighth grade. The cognitive abilities studied were Numerical Reasoning, Abstract Reasoning, Verbal Reasoning, and Spatial Reasoning (as measured by the Differential Reasoning Test). The general cognitive factor was significantly associated with the parameters of initial level (intercept) and rate of change (slope). A high level of intelligence was associated with higher initial scores, as well as a steeper rise in math scores across the two years.