Working memory,math performance,and math anxiety

The cognitive literature now shows how critically math performance depends on working memory, for any form of arithmetic and math that involves processes beyond simple memory retrieval. The psychometric literature is also very clear on the global consequences of mathematics anxiety. People who are highly math anxious avoid math: They avoid elective coursework in math, both in high school and college, they avoid college majors that emphasize math, and they avoid career paths that involve math. We go beyond these psychometric relationships to examine the cognitive consequences of math anxiety. We show how performance on a standardized math achievement test varies as a function of math anxiety, and that math anxiety compromises the functioning of working memory. High math anxiety works much like a dual task setting: Preoccupation with one’s math fears and anxieties functions like a resource-demanding secondary task. We comment on developmental and educational factors related to math and working memory, and on factors that may contribute to the development of math anxiety.     

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

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.     

Math Anxiety: Personal, Educational, and Cognitive Consequences

Highly math-anxious individuals are characterized by a strong tendency to avoid math, which ultimately undercuts their math competence and forecloses important career paths. But timed, on-line tests reveal math-anxiety effects on whole-number arithmetic problems (e.g., 46 + 27), whereas achievement tests show no competence differences. Math anxiety disrupts cognitive processing by compromising ongoing activity in working memory. Although the causes of math anxiety are undetermined, some teaching styles are implicated as risk factors. We need research on the origins of math anxiety and on its "signature" in brain activity, to examine both its emotional and its cognitive components.     

Math anxiety: A review of its cognitive consequences,psychophysiological correlates,and brain bases

A decade has passed since the last published review of math anxiety, which was carried out by Ashcraft and Ridley (2005). Given the considerable interest aroused by this topic in recent years and the growing number of publications related to it, the present article aims to provide a full and updated review of the field, ranging from the initial studies of the impact of math anxiety on numerical cognition, to the latest research exploring its electrophysiological correlates and brain bases from a cognitive neuroscience perspective. Finally, this review describes the factors and mechanisms that have been claimed to play a role in the origins and/or maintenance of math anxiety, and it examines in detail the main explanations proposed to account for the negative effects of math anxiety on performance: competition for working memory resources, a deficit in a low-level numerical representation, and inhibition/attentional control deficit.     

The relationships among working memory, math anxiety, and performance.

Individuals with high math anxiety demonstrated smaller working memory spans, especially when assessed with a computation-based span task. This reduced working memory capacity led to a pronounced increase in reaction time and errors when mental addition was performed concurrently with a memory load task. The effects of the reduction also generalized to a working memory-intensive transformation task. Overall, the results demonstrated that an individual difference variable, math anxiety, affects on-line performance in math-related tasks and that this effect is a transitory disruption of working memory. The authors consider a possible mechanism underlying this effect--disruption of central executive processes--and suggest that individual difference variables like math anxiety deserve greater empirical attention, especially on assessments of working memory capacity and functioning.     

Math anxiety, mother's education, and the mathematics performance of adolescent boys and girls: evidence from the United States and Thailand

In this study, I investigated the relationship of mathematics performance to math anxiety, mother's education, and gender. A secondary analysis was conducted using nationally representative samples of 13-year-old children in the United States (N = 4,091) and Thailand (N = 3,613) collected as a part of the Second International Mathematics Study (Garden, 1987). Separate ANOVAs (Math Anxiety x Mother's Education x Gender) were run within each country using a 40-item math performance test as the dependent variable. Math anxiety has an inverse relationship with mathematics performance in the United States (r = -.24) and in Thailand (r = -.14). The relationship between math anxiety and mathematics performance is significant in both countries after controlling for previous achievement, mother's education, and gender, although the data suggest that there is a three-way interaction between math anxiety, mother's education, and gender in Thailand.     

不同数学焦虑成人的算术策略运用差异：ERP研究

采用事件相关电位(ERP)技术和选择/无选法范式, 在两位数加法心算和估算中, 探索高、低数学焦虑个体的算术计算策略运用及其内在机制。行为结果：数学焦虑效应在策略运用的反应时和正确率指标上的差异都不显著; 而脑电结果：高数学焦虑个体的N400波幅显著高于低数学焦虑个体; 选择条件中, 估算与心算的数学焦虑效应的N100波幅差异; 无选条件中, 高低数学焦虑个体N1-P2复合波的波幅和潜伏期差异显著。数学焦虑效应在策略编码(0~250 ms)和策略选择/执行阶段(250 ms之后)存在差异。     

How is anxiety related to math performance in young students? A longitudinal study of Grade 2 to Grade 3 children

Both general and math-specific anxiety are related to proficiency in mathematics. However, it is not clear when math anxiety arises in young children, nor how it relates to early math performance. This study therefore investigated the early association between math anxiety and math performance in Grades 2 and 3, by accounting for general anxiety and by further inspecting the prevalent directionality of the anxiety–performance link. Results revealed that this link was significant in Grade 3, with a prevalent direction from math anxiety to performance, rather than the reverse. Longitudinal analyses also showed an indirect effect of math anxiety in Grade 2 on subsequent math performance in Grade 3. Overall, these findings highlight the importance of monitoring anxiety from the early stages of schooling in order to promote proficient academic performance.     

Math Anxiety,Mother's Education,and the Mathematics Performance of Adolescent Boys and Girls: Evidence from the United States and Thailand

ABSTRACT

In this study, I investigated the relationship of mathematics performance to math anxiety, mother's education, and gender. A secondary analysis was conducted using nationally representative samples of 13-year-old children in the United States (N = 4,091) and Thailand (N = 3,613) collected as a part of the Second International Mathematics Study (Garden, 1987). Separate ANOVAs (Math Anxiety × Mother's Education × Gender) were run within each country using a 40-item math performance test as the dependent variable. Math anxiety has an inverse relationship with mathematics performance in the United States (r = ?.24) and in Thailand (r ?. 14). The relationship between math anxiety and mathematics performance is significant in both countries after controlling for previous achievement, mother's education, and gender, although the data suggest that there is a three-way interaction between math anxiety, mother's education, and gender in Thailand.     

父母教育卷入与小学儿童数学焦虑的纵向联系:数学态度的中介作用

为探讨父母教育卷入与学龄期儿童数学焦虑之间的纵向联系及内在作用机制,从山东省聊城市两所普通小学选取1734名三、四年级学生,对其进行为期一年的追踪研究。结果发现：（1）T1父母教育卷入能够显著负向预测T2儿童数学焦虑,但T1儿童数学焦虑对T2父母教育卷入的预测不显著;（2）在同一时间点上,儿童数学态度在父母教育卷入与儿童数学焦虑之间发挥显著中介作用;（3）在不同时间点上,儿童数学态度的中介作用仍然成立,表明儿童数学态度的中介作用具有跨时间的稳定性。该结果强调了父母教育卷入对学龄期儿童数学焦虑变化的重要作用,亦为从父母教育卷入和数学态度角度降低儿童的数学焦虑水平提供了初步有力证据。     

Self‐construal and students’ math self‐concept,anxiety and achievement: An examination of achievement goals as mediators

This study examines the role of self‐construal in student learning by testing a mediation model: through math achievement goals, self‐construal predicts math self‐concept and anxiety, which further predict math achievement. A sample of 1196 students from 104 secondary classes in Singapore took a survey and a math achievement test. The results from multi‐group structural equation modelling support measurement invariance and equal path coefficients in the mediation model between boys and girls. Interdependent self‐construal positively predicted mastery approach and avoidance goals, through which interdependent self‐construal had a positive total indirect effect on math anxiety. Independent self‐construal positively predicted mastery approach, performance approach and performance avoidance goals, and through the two approach goals, high independent self‐construal was associated with high math self‐concept. Overall, self‐construal was not associated with math achievement. The findings enhance our understanding of achievement motivation from a sociocultural perspective and help explain East Asian students’ relatively higher anxiety and lower self‐concept in comparison with their Western counterparts as reported in international studies.     

Gender and mathematics anxiety: The role of math-related experiences and opinions

Abstract

Research has indicated that women may be particularly prone to experiencing mathematics anxiety and, to account for this, the sex-role socialization hypothesis posits that women are more math anxious because they have had less experience with mathematics and have more negative opinions regarding mathematics. In contrast, the math experiences hypothesis suggests that math anxiety is not truly a gender-related phenomenon, but rather is due to poor mathematical preparation, regardless of gender. The present study pitted the “sex-role” hypothesis against the “math experience” hypothesis in an examination of the relation between gender and math anxiety. One hundred and seventy-one university students completed a measure of math anxiety and a series of questions regarding their math marks, opinions, and experiences throughout their educational history. The findings clearly supported the math experience hypothesis of math anxiety, for differences in math marks, opinions, and experiences were found between non-math-anxious, moderately math-anxious, and highly math-anxious students. The few gender differences that were found indicated that the female students frequently reported higher math marks than those reported by male students. We suggest that the relation between gender and mathematics anxiety may be accounted for by gender-linked reporting biases. The limitations of the study are addressed and suggestions for future research are made.     

乡镇小学生的数学焦虑与数学成绩:数学自我效能感和数学元认知的链式中介作用

采用儿童数学焦虑量表、小学生数学学习自我效能感量表和小学生数学元认知问卷,对508名乡镇中、高年级小学生进行测量,并运用结构方程模型探讨数学焦虑影响数学成绩的内在作用机制。结果发现：（1）数学焦虑显著负向预测数学自我效能感、数学元认知和数学成绩,数学自我效能感显著正向预测数学元认知和数学成绩,数学元认知显著正向预测数学成绩;（2）在数学焦虑对数学成绩的预测中,数学自我效能感和数学元认知均发挥了部分中介作用;（3）数学自我效能感和数学元认知在数学焦虑和数学成绩之间起链式多重中介的作用。因此,数学焦虑除了直接作用于小学生的数学成绩,还可通过数学自我效能感或数学元认知间接影响数学成绩,而且可通过数学自我效能感进而通过数学元认知间接影响数学成绩。文章讨论了上述发现的理论及教育实践含义。     

初中生数学焦虑的调查及其调控研究

数学焦虑既是心理科学研究的对象,又与教育、教学,特别是学科教学密切相关。本文调查发现:部分初中生存在过度的数学焦虑,并且在年级、性别等维度上具有明显差异;教师的评价方式、课堂气氛、数学考试是形成数学焦虑的主要原因。运用三条教学策略的实验研究表明,数学焦虑是可以调控的,而且数学焦虑的缓解对学生数学成绩的提高有一定的促进作用。     

数学焦虑影响大学生/儿童估算策略运用的对比研究

选取66名大学生和40名小学四年级儿童,运用选择/无选法研究范式,采用自编乘法估算材料考察了数学焦虑对成人和四年级儿童算术策略运用的不同影响.研究结果显示:(1)数学焦虑仅影响成人在自由选择条件中策略选择的正确率.(2)数学焦虑影响儿童的策略分布、策略执行的正确率及最佳选择条件中策略选择的正确率.(3)成人和儿童策略选择的适应性(以有选条件下的策略使用正确率为指标)均受到数学焦虑的影响,低数学焦虑者的适应性明显更好.文章讨论了数学焦虑影响成人与儿童算术策略运用的不同潜在机制.     

Exploring the Relationship Between Mathematics Anxiety and Performance: An Eye‐Tracking Approach

The mechanisms underpinning the relationship between math anxiety and arithmetic performance are not fully understood. This study used an eye‐tracking approach to measure a range of eye movements of 78 undergraduate students in response to performance on an arithmetic verification task. Results demonstrated a significant positive relationship between self‐reported math anxiety and response time, indicating reduced processing efficiency. Analysis of eye‐movement data reinforced the utility of an eye‐tracking approach in studying arithmetic performance; specific digit fixations, dwell time, saccades, and regressions all significantly predicted response time. Furthermore, findings highlighted significant positive correlations between math anxiety and fixations, dwell time, and saccades. Despite there being little evidence that eye movements mediate the math anxiety‐to‐performance relationship, relationships observed between math anxiety and eye movements provide a useful starting point for research using an eye‐tracking methodology in studying math anxiety and performance; the present findings suggest future work should focus on calculation strategy. Copyright © 2014 John Wiley & Sons, Ltd.     

The neurodevelopmental basis of math anxiety

Math anxiety is a negative emotional reaction to situations involving mathematical problem solving. Math anxiety has a detrimental impact on an individual's long-term professional success, but its neurodevelopmental origins are unknown. In a functional MRI study on 7- to 9-year-old children, we showed that math anxiety was associated with hyperactivity in right amygdala regions that are important for processing negative emotions. In addition, we found that math anxiety was associated with reduced activity in posterior parietal and dorsolateral prefrontal cortex regions involved in mathematical reasoning. Multivariate classification analysis revealed distinct multivoxel activity patterns, which were independent of overall activation levels in the right amygdala. Furthermore, effective connectivity between the amygdala and ventromedial prefrontal cortex regions that regulate negative emotions was elevated in children with math anxiety. These effects were specific to math anxiety and unrelated to general anxiety, intelligence, working memory, or reading ability. Our study identified the neural correlates of math anxiety for the first time, and our findings have significant implications for its early identification and treatment.     

Mathematics anxiety and coping strategies among middle school students: relations with students’ achievement goal orientations and level of performance

The purpose of this study was to explore relations between students’ prior grades in mathematics, achievement goal orientations in math classes, math anxiety, and students coping strategies in math classes. Three achievement goal orientations (mastery goals, performance-approach goals, and performance-avoidance goals) and two coping strategies (problem-focused and self-protective strategies) were explored. Participants in the study were 939 middle school students. The study was designed as a cross-sectional survey. Data were analyzed by means of zero order correlations and structural equation modeling. The correlations between the three goal perspectives and between the two coping strategies were low. A mastery goal perspective strongly predicted the use of adaptive problem-focused coping strategies whereas this perspective predicted lower levels of math anxiety and less use of maladaptive self-protective coping strategies. A performance-avoidance goal perspective predicted higher math anxiety and more use of self-protective coping strategies. Performance-approach goals were not significantly related to math anxiety or to selfprotective coping strategies. However, they were weakly and negatively associated with problem-focused coping strategies. Prior math grades were positively associated with mastery goals and performance-approach goals and negatively associated with performance-avoidance goals and math anxiety. No direct associations were found between grades and the coping strategies. The associations were indirect, mediated through mastery goals, performance-avoidance goals, and math anxiety.     

When does math anxiety in parents and teachers predict math anxiety and math achievement in elementary school children? The role of gender and grade year

Social Psychology of Education - The study investigated the relationship between math anxiety in parents and teachers and math anxiety and math achievement in first- to third-grade children. The...     

From Janet T. Spence’s Manifest Anxiety Scale to the Present Day: Exploring Math Anxiety and its Relation to Math Achievement

Janet Taylor Spence conducted a great deal of foundational work establishing the negative relation between anxiety and performance. Spence operationalized trait anxiety by creating the Manifest Anxiety Scale, and she conducted numerous studies linking scores on this scale to performance across a variety of cognitive tasks. The field of math anxiety research has built from her work to examine the ways in which negative emotions regarding math can hinder math performance. We discuss the antecedents and development of math anxiety, as well as the ways in which other individual differences, such as working memory, affect the relation between anxiety and performance. Although a rich literature has sprung from Spence’s early work, there is much left to do in terms of fully understanding how specific types of anxiety interact with each other, as well as with other individual differences, to determine performance outcomes.