Elizabeth A. Gunderson

Female teachers’ math anxiety affects girls’ math achievement

People’s fear and anxiety about doing math—over and above actual math ability—can be an impediment to their math achievement. We show that when the math-anxious individuals are female elementary school teachers, their math anxiety carries negative consequences for the math achievement of their female students. Early elementary school teachers in the United States are almost exclusively female (>90%), and we provide evidence that these female teachers’ anxieties relate to girls’ math achievement via girls’ beliefs about who is good at math. First- and second-grade female teachers completed measures of math anxiety. The math achievement of the students in these teachers’ classrooms was also assessed. There was no relation between a teacher’s math anxiety and her students’ math achievement at the beginning of the school year. By the school year’s end, however, the more anxious teachers were about math, the more likely girls (but not boys) were to endorse the commonly held stereotype that “boys are good at math, and girls are good at reading” and the lower these girls’ math achievement. Indeed, by the end of the school year, girls who endorsed this stereotype had significantly worse math achievement than girls who did not and than boys overall. In early elementary school, where the teachers are almost all female, teachers’ math anxiety carries consequences for girls’ math achievement by influencing girls’ beliefs about who is good at math.

The Relation Between Spatial Skill and Early Number Knowledge: The Role of the Linear Number Line

Spatial skill is highly related to success in math and science (e.g., Casey, Nuttall, Pezaris, & Benbow, 1995). However, little work has investigated the cognitive pathways by which the relation between spatial skill and math achievement emerges. We hypothesized that spatial skill plays a crucial role in the development of numerical reasoning by helping children to create a spatially meaningful, powerful numerical representation-the linear number line. In turn, a strong linear number representation improves other aspects of numerical knowledge such as arithmetic estimation. We tested this hypothesis using 2 longitudinal data sets. First, we found that childrens spatial skill (i.e., mental transformation ability) at the beginning of 1st and 2nd grades predicted improvement in linear number line knowledge over the course of the school year. Second, we found that childrens spatial skill at age 5 years predicted their performance on an approximate symbolic calculation task at age 8 and that this relation was mediated by childrens linear number line knowledge at age 6. The results are consistent with the hypothesis that spatial skill can improve childrens development of numerical knowledge by helping them to acquire a linear spatial representation of numbers.

Math Anxiety, Working Memory, and Math Achievement in Early Elementary School

Although math anxiety is associated with poor mathematical knowledge and low course grades (Ashcraft & Krause, 2007), research establishing a connection between math anxiety and math achievement has generally been conducted with young adults, ignoring the emergence of math anxiety in young children. In the current study, we explored whether math anxiety relates to young childrens math achievement. One hundred and fifty-four first- and second-grade children (69 boys, 85 girls) were given a measure of math achievement and working memory (WM). Several days later, childrens math anxiety was assessed using a newly developed scale. Paralleling work with adults (Beilock, 2008), we found a negative relation between math anxiety and math achievement for children who were higher but not lower in WM. High-WM individuals tend to rely on WM-intensive solution strategies, and these strategies are likely disrupted when WM capacity is co-opted by math anxiety. We argue that early identification and treatment of math anxieties is important because these early anxieties may snowball and eventually lead students with the highest potential (i.e., those with higher WM) to avoid math courses and math-related career choices.

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.

Gesture as a window onto children’s number knowledge

Before learning the cardinal principle (knowing that the last word reached when counting a set represents the size of the whole set), children do not use number words accurately to label most set sizes. However, it remains unclear whether this difficulty reflects a general inability to conceptualize and communicate about number, or a specific problem with number words. We hypothesized that childrens gestures might reflect knowledge of number concepts that they cannot yet express in speech, particularly for numbers they do not use accurately in speech (numbers above their knower-level). Number gestures are iconic in the sense that they are item-based (i.e., each finger maps onto one item in a set) and therefore may be easier to map onto sets of objects than number words, whose forms do not map transparently onto the number of items in a set and, in this sense, are arbitrary. In addition, learners in transition with respect to a concept often produce gestures that convey different information than the accompanying speech. We examined the number words and gestures 3- to 5-year-olds used to label small set sizes exactly (1-4) and larger set sizes approximately (5-10). Children who had not yet learned the cardinal principle were more than twice as accurate when labeling sets of 2 and 3 items with gestures than with words, particularly if the values were above their knower-level. They were also better at approximating set sizes 5-10 with gestures than with words. Further, gesture was more accurate when it differed from the accompanying speech (i.e., a gesture-speech mismatch). These results show that children convey numerical information in gesture that they cannot yet convey in speech, and raise the possibility that number gestures play a functional role in childrens development of number concepts.

Reciprocal relations among motivational frameworks, math anxiety, and math achievement in early elementary school

ABSTRACT School-entry math achievement is a strong predictor of math achievement through high school. We asked whether reciprocal relations among math achievement, math anxiety, and entity motivational frameworks (believing that ability is fixed and a focus on performance) can help explain these persistent individual differences. We assessed 1st and 2nd graders’ (N = 634) math achievement, motivational frameworks, and math anxiety 2 times, 6 months apart. Cross-lagged path analyses showed reciprocal relations between math anxiety and math achievement and between motivational frameworks and math achievement. Entity motivational frameworks predicted higher math anxiety. High math achievement was a particularly strong predictor of lower math anxiety and less entity-oriented motivational frameworks. We concluded that reciprocal effects are already present in the first 2 years of formal schooling, with math achievement and attitudes feeding off one another to produce either a vicious or virtuous cycle. Improving both math performance and math attitudes may set children onto a long-lasting, positive trajectory in math.

Parent praise to toddlers predicts fourth grade academic achievement via children’s incremental mindsets.

In a previous study, parent–child praise was observed in natural interactions at home when children were 1, 2, and 3 years of age. Children who received a relatively high proportion of process praise (e.g., praise for effort and strategies) showed stronger incremental motivational frameworks, including a belief that intelligence can be developed and a greater desire for challenge, when they were in 2nd or 3rd grade (Gunderson et al., 2013). The current study examines these same children’s (n = 53) academic achievement 1 to 2 years later, in 4th grade. Results provide the first evidence that process praise to toddlers predicts children’s academic achievement (in math and reading comprehension) 7 years later, in elementary school, via their incremental motivational frameworks. Further analysis of these motivational frameworks shows that process praise had its effect on fourth grade achievement through children’s trait beliefs (e.g., believing that intelligence is fixed vs. malleable), rather than through their learning goals (e.g., preference for easy vs. challenging tasks). Implications for the socialization of motivation are discussed.

The Number Line Is a Critical Spatial-Numerical Representation: Evidence from a Fraction Intervention.

Children’s ability to place fractions on a number line strongly correlates with math achievement. But does the number line play a causal role in fraction learning or does it simply index more advanced fraction knowledge? The number line may be a particularly effective representation for fraction learning because its properties align with the desired mental representation and take advantage of preexisting spatial-numeric biases. Using a pretest-training-posttest design, we examined second and third graders’ fraction learning in 3 conditions: number line training, area model training, and a non-numerical control. Children who received number line training improved at representing fractions with number lines, and children who received area model training improved at representing fractions with area models. Critically, only the number line training led to transfer to an untrained fraction magnitude comparison task. We conclude that the number line plays a causal role in children’s fraction magnitude understanding, and is more beneficial than the widely used area model.

Who Needs Innate Ability to Succeed in Math and Literacy? Academic-Domain-Specific Theories of Intelligence about Peers versus Adults.

Individuals’ implicit theories of intelligence exist on a spectrum, from believing intelligence is fixed and unchangeable, to believing it is malleable and can be improved with effort. A belief in malleable intelligence leads to adaptive responses to challenge and higher achievement. However, surprisingly little is known about the development of academic-domain-specific theories of intelligence (i.e., math vs. reading and writing). The authors examined this in a cross-section of students from 1st grade to college (N = 523). They also examined whether students hold different beliefs about the role of fixed ability in adult jobs versus their own grade. The authors’ adult-specific beliefs hypothesis states that when children learn societally held beliefs from adults, they first apply these beliefs specifically to adults and later to students their own age. Consistent with this, even the youngest students (1st and 2nd graders) believed that success in an adult job requires more fixed ability in math than reading and writing. However, when asked about students in their own grade, only high school and college students reported that math involves more fixed ability than reading and writing. High school and college students’ math-specific theories of intelligence were related to their motivation and achievement in math, controlling for reading and writing-specific theories. Reading and writing-specific theories did not predict reading and writing-specific motivations or achievement, perhaps because students perceive reading and writing as less challenging than math. In summary, academic-domain-specific theories of intelligence develop early but may not become self-relevant until adolescence, and math-specific beliefs may be especially important targets for intervention.

The specificity of parenting effects: Differential relations of parent praise and criticism to children’s theories of intelligence and learning goals

Individuals who believe that intelligence can be improved with effort (an incremental theory of intelligence) and who approach challenges with the goal of improving their understanding (a learning goal) tend to have higher academic achievement. Furthermore, parent praise is associated with childrens incremental theories and learning goals. However, the influences of parental criticism, as well as different forms of praise and criticism (e.g., process vs. person), have received less attention. We examine these associations by analyzing two existing datasets (Study 1: N = 317 first to eighth graders; Study 2: N = 282 fifth and eighth graders). In both studies, older children held more incremental theories of intelligence, but lower learning goals, than younger children. Unexpectedly, the relation between theories of intelligence and learning goals was nonsignificant and did not vary with childrens grade level. In both studies, overall perceived parent praise positively related to childrens learning goals, whereas perceived parent criticism negatively related to incremental theories of intelligence. In Study 2, perceived parent process praise was the only significant (positive) predictor of childrens learning goals, whereas perceived parent person criticism was the only significant (negative) predictor of incremental theories of intelligence. Finally, Study 2 provided some support for our hypothesis that age-related differences in perceived parent praise and criticism can explain age-related differences in childrens learning goals. Results suggest that incremental theories of intelligence and learning goals might not be strongly related during childhood and that perceived parent praise and criticism have important, but distinct, relations with each motivational construct.