Susan C. Levine

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.

Multiple cues for quantification in infancy: Is number one of them?

A review and synthesis of the literature on quantification in infancy and early childhood is provided. In most current conceptualizations, early quantification is assumed to be number based. However, the extant literature provides no clear-cut evidence that infants use number to perform quantitative tasks. Instead, new research suggests that quantification is initially based on nonnumerical cues, such as area and contour length, whether or not a task involves discrete items. The authors discuss the implications of these findings with respect to early quantification and its relation to later numerical development.

Quantitative development in infancy and early childhood

1. Historical Trends and Current Issues 2. Quantification in Infancy 3. Quantification in Early Childhood 4. Quantification of Discrete Sets: A Synthesis 5. Continuous Amount 6. Relative Quantity 7. Nonverbal Representation of Quantity 8. Acquiring Conventional Skills 9. The Whole Child

A mental model for early arithmetic.

The authors examined young childrens ability to solve nonverbal calculation problems in which they must determine how many items are in a hidden array after items have been added into or taken away from it. Earlier work showed that an ability to reliably solve such problems emerges earlier than verbal calculation ability but did not examine when it first appears. The authors propose that the ability to solve such problems involves domain-general symbolic processes similar to those involved in symbolic play and the use of physical models. Hence the ability to calculate should appear at about 2 years and should be related to overall level of intellectual competence. The authors show that the ability to reliably solve nonverbal calculation tasks emerges only after 2 years of age and that performance on nonverbal calculation problems is highly related to overall level of intellectual competence in children between 3 and 4 years of age.

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.

Socioeconomic Status Modifies the Sex Difference in Spatial Skill

We examined whether the male spatial advantage varies across children from different socioeconomic (SES) groups. In a longitudinal study, children were administered two spatial tasks requiring mental transformations and a syntax comprehension task in the fall and spring of second and third grades. Boys from middle-and high-SES backgrounds outperformed their female counterparts on both spatial tasks, whereas boys and girls from a low-SES group did not differ in their performance level on these tasks. As expected, no sex differences were found on the verbal comprehension task. Prior studies have generally been based on the assumption that the male spatial advantage reflects ability differences in the population as a whole. Our finding that the advantage is sensitive to variations in SES provides a challenge to this assumption, and has implications for a successful explanation of the sex-related difference in spatial skill.

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.

Development of Calculation Abilities in Young Children.

This study investigates the development of skills for solving verbally and nonverbally presented calculation problems in children between 4 and 6 years of age. Identical addition and subtraction calculations were presented in three problem-type formats: nonverbal problems, story problems, and number-fact problems. The nonverbal problems involved presenting sets of physical referents that were then transformed either by adding or removing elements. The child saw the initial set and the number of elements that were added or removed, but not the final set. The task was to construct an array that contained the number of elements in the final set. The story problems and number-fact problems were presented orally, without props. Results indicate that children as young as 4 years of age have some success on the nonverbal problems, showing that they can transform sets by adding or subtracting elements. In contrast, children do not achieve comparable levels of success on the story problems or number-fact problems until 5 1/2 to 6 1/2 years of age. Moreover, throughout the age range tested, children performed better on nonverbal problems than on either story problems or number-fact problems. These results suggest that childrens earliest ability to add and subtract is based on experiences combining and separating sets of objects in the world and that this ability precedes the development of conventional verbal methods of calculating.

Differential calculation abilities in young children from middle- and low-income families

This study examined the performance of 42 middleand 42 low-income kindergarten children on arithmetic calculations presented in a nonverbal format as well as in 3 different verbal formats. On the nonverbal task, the child was shown an initial set of disks, which was then hidden with a cover. The set was transformed by adding or removing disks. After the transformation, the childs task was to construct an array of disks that contained the same number of disks as in the final hidden set. A significant interaction between income level and task format was obtained. Although middle-income children performed better than low-income children on each of the verbal calculation tasks, the 2 income groups did not differ in performance on the nonverbal calculation task. The findings suggest that the nonverbal task format is less sensitive to socioeconomic variation than are the verbal task formats.

SOCIOECONOMIC VARIATION, NUMBER COMPETENCE, AND MATHEMATICS LEARNING DIFFICULTIES IN YOUNG CHILDREN

As a group, children from disadvantaged, low-income families perform substantially worse in mathematics than their counterparts from higher-income families. Minority children are disproportionately represented in low-income populations, resulting in significant racial and social-class disparities in mathematics learning linked to diminished learning opportunities. The consequences of poor mathematics achievement are serious for daily functioning and for career advancement. This article provides an overview of childrens mathematics difficulties in relation to socioeconomic status (SES). We review foundations for early mathematics learning and key characteristics of mathematics learning difficulties. A particular focus is the delays or deficiencies in number competencies exhibited by low-income children entering school. Weaknesses in number competence can be reliably identified in early childhood, and there is good evidence that most children have the capacity to develop number competence that lays the foundation for later learning.