Elementary school teachers' math anxiety and students' math learning: A large-scale replication.

A solid foundation in math is important for children's long-term academic success. Many factors influence children's math learning-including the math content students are taught in school, the quality of their instruction, and the math attitudes of students' teachers. Using a large and diverse sample of first-grade students (n = 551), we conducted a large-scale replication of a previous study (Proceedings of the National Academy of Sciences of the USA, 2010, 1860; n = 117), which found that girls in classes with highly math anxious teachers learned less math during the school year, as compared to girls whose math teachers were less anxious about math. With a larger sample, we found a negative relation between teachers' math anxiety and students' math achievement for both girls and boys, even after accounting for teachers' math ability and children's beginning of year math knowledge, replicating and extending those previous results. Our findings strengthen the support for the hypothesis that teachers' math anxiety is one factor that undermines children's math learning and could push students off-track during their initial exposure to math in early elementary school.

On the relationship between math anxiety and math achievement in early elementary school: The role of problem solving strategies.

Even at young ages, children self-report experiencing math anxiety, which negatively relates to their math achievement. Leveraging a large dataset of first and second grade students' math achievement scores, math problem solving strategies, and math attitudes, we explored the possibility that children's math anxiety (i.e., a fear or apprehension about math) negatively relates to their use of more advanced problem solving strategies, which in turn relates to their math achievement. Our results confirm our hypothesis and, moreover, demonstrate that the relation between math anxiety and math problem solving strategies is strongest in children with the highest working memory capacity. Ironically, children who have the highest cognitive capacity avoid using advanced problem solving strategies when they are high in math anxiety and, as a result, underperform in math compared with their lower working memory peers.

Intergenerational Effects of Parents' Math Anxiety on Children's Math Achievement and Anxiety.

A large field study of children in first and second grade explored how parents' anxiety about math relates to their children's math achievement. The goal of the study was to better understand why some students perform worse in math than others. We tested whether parents' math anxiety predicts their children's math achievement across the school year. We found that when parents are more math anxious, their children learn significantly less math over the school year and have more math anxiety by the school year's end-but only if math-anxious parents report providing frequent help with math homework. Notably, when parents reported helping with math homework less often, children's math achievement and attitudes were not related to parents' math anxiety. Parents' math anxiety did not predict children's reading achievement, which suggests that the effects of parents' math anxiety are specific to children's math achievement. These findings provide evidence of a mechanism for intergenerational transmission of low math achievement and high math anxiety.

Numerical comparison is spatial-Except when it is not.

The numerical distance effect (NDE) is an important tool for probing the nature of numerical representation. Across two studies, we assessed the degree to which the NDE relates to one's performance on spatial tasks to investigate the role of spatial processing in numerical comparison and, by extension, numerical cognition. We administered numerical comparison tasks and a variety of tasks thought to tap into different aspects of spatial processing. Importantly, we administered both the simultaneous comparison task and the comparison to a standard task, given claims that the NDEs that arise in these two tasks are different. In both studies, the NDEs elicited when comparing simultaneously presented numbers were more strongly negatively correlated with an individual's performance on the spatial tasks than the NDEs elicited when comparing numbers to a standard. The implications of these data for our understanding of numerical comparison tasks and numerical cognition more generally are discussed. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

It is a "small world": Relations between performance on five spatial tasks and five mathematical tasks in undergraduate students.

One of the most robust relations in cognition is that between spatial and mathematical reasoning. One important question is whether this relation is domain general or if specific relations exist between performance on different types of spatial tasks and performance on different types of mathematical tasks. In this study, we explore unique relations between performance on five spatial tasks and five mathematical tasks. An exploratory factor analysis conducted on Data Set 1 (N = 391) yielded a two-factor model, one spatial factor and one mathematical factor with significant cross-domain factor loadings. The general two-factor model structure was replicated in a confirmatory factor analysis conducted in a separate data set (N = 364) but the strength of the factor loadings differed by task. Multidimensional scaling and network-based analyses conducted on the combined data sets reveal one spatial cluster, with a central node and one more tightly interconnected mathematical cluster. Both clusters were interconnected via the math task assessing geometry and spatial sense. The unique links identified with the network-based analysis are representative of a "small-world network." These results have theoretical implications for our understanding of the spatial-mathematical relation and practical implications for our understanding of the limitations of transfer between spatial training paradigms and mathematical tasks. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Transcoding of French numbers for first- and second-language learners in third grade.

Transcoding is the process of translating between spoken and written numbers, and it is correlated with other mathematical skills. In the present study, we investigated the link between French number writing of 49 students in the third grade (aged 7-9 years) and their language skills. Transcoding in French is of particular interest because the spoken number language system does not completely correspond to that of the written digits (e.g., quatre-vingt-dix [four-twenty-ten] and 90). We hypothesised that the complex linguistic structure of spoken numbers in French would be challenging for students who are learning to transcode. First and second French-language learners' accuracy and errors were recorded during a writing task of 3- to 7-digit numbers. Children also completed linguistic tests (e.g., receptive vocabulary, receptive syntax). Results showed that first- and second-language learners did not differ in their transcoding accuracy. Number size, decade complexity of stimulus number words in French (i.e., numbers containing a complex decade, operationalized as a number between soixante-dix, 70, and quatre-vingt-dix-neuf, 99), and receptive vocabulary predicted children's French transcoding skills. Students were more likely to produce errors (e.g., 68 or 6018 for 78) when they transcoded complex decade numbers compared with simple decade numbers. When an error was made on the complex decade portion of a number, it was likely a lexical error. In conclusion, third graders, both first- and second-language learners, found complex decade numbers challenging and their performance was related to their general vocabulary skills.

Examining the Interplay between the Cognitive and Emotional Aspects of Gender Differences in Spatial Processing.

Women reliably perform worse than men on measures of spatial ability, particularly those involving mental rotation. At the same time, females also report higher levels of spatial anxiety than males. What remains unclear, however, is whether and in what ways gender differences in these cognitive and affective aspects of spatial processing may be interrelated. Here, we tested for robust gender differences across six different datasets in spatial ability and spatial anxiety (N = 1257, 830 females). Further, we tested for bidirectional mediation effects. We identified indirect relations between gender and spatial skills through spatial anxiety, as well as between gender and spatial anxiety through spatial skills. In the gender → spatial anxiety → spatial ability direction, spatial anxiety explained an average of 22.4% of gender differences in spatial ability. In the gender → spatial ability → spatial anxiety direction, spatial ability explained an average of 25.9% of gender differences in spatial anxiety. Broadly, these results support a strong relation between cognitive and affective factors when explaining gender differences in the spatial domain. However, the nature of this relation may be more complex than has been assumed in previous literature. On a practical level, the results of this study caution the development of interventions to address gender differences in spatial processing which focus primarily on either spatial anxiety or spatial ability until such further research can be conducted. Our results also speak to the need for future longitudinal work to determine the precise mechanisms linking cognitive and affective factors in spatial processing.

Parental intrusive homework support and math achievement: Does the child's mindset matter?

Prior research shows that when parents monitor, check, and assist in completing homework without an invitation, their children's motivation and academic achievement often decline. We propose that intrusive support from parents might also send the message that children are incompetent, especially if they believe their intelligence is fixed. We tested whether children's mindsets moderate the negative link between parents' intrusive homework support and achievement among first- and second-grade students followed for one academic year (Study 1, N = 563) and middle and high school students for two academic years (Study 2, N = 1,613). The samples were obtained from large urban areas in the United States. In both studies, intrusive homework support more strongly predicted a decrease in achievement over time for children with a fixed mindset. These findings suggest that the belief that intellectual ability cannot be changed may exacerbate the detrimental effects of uninvited help on academic work. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Spatial anxiety and spatial ability: Mediators of gender differences in math anxiety.

Females tend to be more anxious than males while engaging in mathematics, which has been linked to lower math performance and higher math avoidance. A possible repercussion of this gender difference is the underrepresentation of females in STEM fields (science, technology, engineering, and math), as math competencies are an essential part of succeeding in such fields. A related, but distinct, area of research suggests that males tend to outperform females in tasks that require spatial processing (i.e., the ability to mentally visualize, rotate, and transform spatial and visual information). Interestingly, factors from the spatial processing domain (spatial ability and spatial anxiety) are important in explaining gender differences in math anxiety. Here, we examined three types of spatial anxiety and ability (imagery, navigation, and manipulation), as well as math ability, as mediators of gender differences in math anxiety. Undergraduate students (125 male; 286 female) completed assessments of their general level of anxiety, their math anxiety, and their spatial anxiety. They also completed a series of tasks measuring their mathematical skill, their spatial skills, and basic demographics. Results suggest that manipulation anxiety and ability, navigation anxiety, and math ability explained the gender difference in math anxiety, but manipulation anxiety was the strongest mediator of this relation. Conversely, all other measures did not explain the gender difference in math anxiety. These findings help us better understand the gender difference in mathematics, and this is important in reducing the gender gap in STEM fields. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Appraisals of previous math experiences play an important role in math anxiety.

Math anxiety affects many people, from young children through to older adults. While there has been debate concerning the developmental trajectory of math anxiety and negative math attitudes, little attention has been given to the role of appraisals of previous math experiences. We surveyed 308 adults (mean age = 27.56 years, SD = 11.25) and assessed self-reported measures of math anxiety, mathematical resilience, math attitudes, and appraisal of previous math experiences. As hypothesized, all variables were found to be interrelated. Math anxiety was significantly negatively related to appraisal of previous math experiences, mathematical resilience, and math attitudes. Moreover, appraisal of previous math experiences was shown to mediate the relations between (1) math anxiety and math attitudes, and (2) mathematical resilience and math attitudes. The findings demonstrate the importance of considering current appraisals of previous math experiences and are consistent with an interpretation account of math anxiety. This may help inform cognitive-based interventions that focus on one's interpretation of past events to support current and future math learning and engagement.

Testing the specificity of links between anxiety and performance within mathematics and spatial reasoning.

Anxiety within the domains of math and spatial reasoning have consistently been shown to predict performance within those domains. However, little work has focused on how specific these associations are. Across two studies, we systematically tested the degree of specificity in relations between anxiety and performance within math and spatial reasoning. Results consistently showed that anxiety within a cognitive domain predicted performance in that domain even when controlling for other forms of anxiety, providing evidence that cognition-specific anxieties are valuable for understanding cognition-specific performance. We also found that general trait anxiety did not explain a significant portion the anxiety-performance link in either math or spatial reasoning, suggesting that these anxiety-performance associations are not due to the propensity to feel anxious generally. Interestingly, while spatial anxiety did not explain any of the anxiety-performance association in math, math anxiety did explain a significant portion of the anxiety-performance link in spatial reasoning. These results suggest that, while links between anxiety and performance cannot be reduced to a single underlying general anxiety construct, there may nevertheless be overlap between domain anxieties. We end by calling for a more detailed examination of the unique and shared mechanisms linking anxiety and performance across disparate cognitive domains.

Individual differences in the development of children's arithmetic fluency from grades 2 to 3.

In the present research, we provide empirical evidence for the process of symbolic integration of number associations, focusing on the development of simple addition (e.g., 5 + 3 = 8), subtraction (e.g., 5 - 3 = 2), and multiplication (e.g., 5 × 3 = 15). Canadian children were assessed twice, in Grade 2 and Grade 3 (N = 244; 55% girls). All families were English-speaking, and parent education levels ranged from high school to postgraduate, with a median of community college. In Grade 2, children completed general cognitive tasks (i.e., receptive vocabulary, working memory, nonverbal reasoning, and inhibitory control). In both grades, children completed single-digit addition and complementary subtraction problems. In Grade 3, they completed single-digit multiplication problems and measures of applied mathematics, specifically, word-problem solving, algebra, and measurement. We found that addition and subtraction were reciprocally related (controlling for cognitive skills). Subtraction fluency predicted multiplication in Grade 3, whereas addition fluency did not. In Grade 3, both subtraction and multiplication fluency were predictors of applied mathematics, with multiplication partially mediating the relation between subtraction and applied mathematics performance. These findings support the view that learning arithmetic associations is a hierarchical process. As students practice each new skill, individual differences reflect the integration of the novel component into the developing associative network. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Next Directions in Measurement of the Home Mathematics Environment: An International and Interdisciplinary Perspective.

This article synthesizes findings from an international virtual conference, funded by the National Science Foundation (NSF), focused on the home mathematics environment (HME). In light of inconsistencies and gaps in research investigating relations between the HME and children's outcomes, the purpose of the conference was to discuss actionable steps and considerations for future work. The conference was composed of international researchers with a wide range of expertise and backgrounds. Presentations and discussions during the conference centered broadly on the need to better operationalize and measure the HME as a construct - focusing on issues related to child, family, and community factors, country and cultural factors, and the cognitive and affective characteristics of caregivers and children. Results of the conference and a subsequent writing workshop include a synthesis of core questions and key considerations for the field of research on the HME. Findings highlight the need for the field at large to use multi-method measurement approaches to capture nuances in the HME, and to do so with increased international and interdisciplinary collaboration, open science practices, and communication among scholars.

Higher math anxious people have a lower need for cognition and are less reflective in their thinking.

There exists a large body of literature seeking to understand the relation between math anxiety and success in mathematics. While most of this literature focuses on domain specific relations (i.e., how math anxiety impacts thinking about mathematics), in the current work we examine important relations between math anxiety and domain general factors. Specifically, we test three hypotheses: (1) that higher-math-anxious individuals have a lower need for and enjoyment of exerting cognitive effort, (2) that math anxiety mediates a relation between ones' propensity for cognitive effort and their achievement in mathematics, and (3) that higher-math-anxious individuals are less reflective in their thinking, and that this is not limited to questions that are heavily reliant on mathematical reasoning. As predicted, we uncovered relations between math anxiety and the domain-general constructs of need for cognition and cognitive reflection. Importantly, these negative relations hold even after controlling for math ability, general anxiety, and gender of the participant. The results are discussed in terms of implications for our understanding of the construct of math anxiety. Proficiency in mathematics is a major advantage in industrialised nations. Unfortunately, many people experience math-anxiety (Richardson & Suinn, 1972), becoming nervous when engaging in math tasks and avoiding math and math-related professions. As a result, those with math anxiety tend to severely limit their future career and earning opportunities (Chipman, Krantz, & Silver, 1992; Hembree, 1990). The resulting shortage of adults prepared to work in the sciences, technology, engineering, and mathematics field (STEM) has negative consequences at the national level, particularity as societies become increasingly dependent upon technology (Beilock & Maloney, 2015; Chipman et al., 1992; Maloney & Beilock, 2012). Worldwide, increased math-anxiety is linked to decreased math achievement (Foley et al., 2017; Lee, 2009), and this is not limited to academic situations. Math-anxious nurses, for example, are more likely than non-math-anxious nurses to make poor drug calculations (Mcmullan, Jones, & Lea, 2012); math-anxious women are more likely than their peers to engage in poor financial planning (McKenna & Nickols, 1988), and math anxiety is negatively linked to the ability to interpret health statistics (Silk & Parrott, 2014). Given that math-anxiety is related to important and detrimental consequences in people's daily lives, it is vital that we work to understand the behavioural and cognitive differences between those who are high and low in math-anxiety.

Simple arithmetic: not so simple for highly math anxious individuals.

Fluency with simple arithmetic, typically achieved in early elementary school, is thought to be one of the building blocks of mathematical competence. Behavioral studies with adults indicate that math anxiety (feelings of tension or apprehension about math) is associated with poor performance on cognitively demanding math problems. However, it remains unclear whether there are fundamental differences in how high and low math anxious individuals approach overlearned simple arithmetic problems that are less reliant on cognitive control. The current study used functional magnetic resonance imaging to examine the neural correlates of simple arithmetic performance across high and low math anxious individuals. We implemented a partial least squares analysis, a data-driven, multivariate analysis method to measure distributed patterns of whole-brain activity associated with performance. Despite overall high simple arithmetic performance across high and low math anxious individuals, performance was differentially dependent on the fronto-parietal attentional network as a function of math anxiety. Specifically, low-compared to high-math anxious individuals perform better when they activate this network less-a potential indication of more automatic problem-solving. These findings suggest that low and high math anxious individuals approach even the most fundamental math problems differently.

Response to Comment on "Math at home adds up to achievement in school".

Frank presents an alternative interpretation of our data, yet reports largely similar results to those in our original Report. A critical difference centers on how to interpret and test interaction effects. Frank finds no mistakes in our analyses. We stand by our original conclusions of meaningful effects of the Bedtime Learning Together (BLT) math app on children's math achievement.

Jump-Starting Early Childhood Education at Home: Early Learning, Parent Motivation, and Public Policy.

By the time children begin formal schooling, their experiences at home have already contributed to large variations in their math and language development, and once school begins, academic achievement continues to depend strongly on influences outside of school. It is thus essential that educational reform strategies involve primary caregivers. Specifically, programs and policies should promote and support aspects of caregiver-child interaction that have been empirically demonstrated to boost early learning and should seek to impede "motivational sinkholes" that threaten to undermine caregivers' desires to engage their children effectively. This article draws on cognitive and behavioral science to detail simple, low-cost, and effective tools caregivers can employ to prepare their children for educational success and then describes conditions that can protect and facilitate caregivers' motivation to use those tools. Policy recommendations throughout focus on using existing infrastructure to more deeply engage caregivers in effective early childhood education at home.

Math at home adds up to achievement in school.

With a randomized field experiment of 587 first-graders, we tested an educational intervention designed to promote interactions between children and parents relating to math. We predicted that increasing math activities at home would increase children's math achievement at school. We tested this prediction by having children engage in math story time with their parents. The intervention, short numerical story problems delivered through an iPad app, significantly increased children's math achievement across the school year compared to a reading (control) group, especially for children whose parents are habitually anxious about math. Brief, high-quality parent-child interactions about math at home help break the intergenerational cycle of low math achievement.

Anxiety and cognition.

In this review we discuss the interplay between anxiety and cognition, illustrating how anxiety can compromise performance on cognitively-demanding tasks and lead people to perform below their ability. Using math anxiety and test anxiety as examples, we highlight key findings from psychology, cognitive science, and neuroscience, to show that how one approaches an anxiety-inducing situation can have a large impact on how that person ultimately performs. We end by discussing who is most susceptible to anxiety-induced poor performance and suggest promising techniques which may help to reduce the negative impact of anxiety on performance. WIREs Cogn Sci 2014, 5:403-411. doi: 10.1002/wcs.1299 CONFLICT OF INTEREST: The authors have declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website.

Paying attention to attention: evidence for an attentional contribution to the size congruity effect.

Understanding the mechanisms supporting our comprehension of magnitude information represents a key goal in cognitive psychology. A major phenomenon employed in the pursuit of this goal has been the physical size congruity effect-namely, the observation that comparing the relative numerical sizes of two numbers is influenced by their relative physical sizes. The standard account of the physical size congruity effect attributes it to the automatic influence of the comparison of irrelevant physical magnitudes on numerical judgments. Here we develop an alternative account of this effect on the basis of the operation of attention in the typical size congruity display and the temporal dynamics of number comparison. We also provide a test of a number of predictions derived from this alternative account by combining a physical size congruity manipulation with a manipulation designed to alter the operation of attention within the typical size congruity display (i.e., a manipulation of the relative onsets of the digits). This test provides evidence consistent with an attentional contribution to the size congruity effect. Implications for our understanding of magnitude and the interactions between attention and magnitude are discussed.