Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties

Aspects of self-regulated learning and their influence on the mathematics achievement of fifth graders in the context of four different proclaimed curricula

Metacognition is a part of the models of self-regulated learning. The consideration of a broader context resonates with a social cognitive perspective approach to learning which dominates the educational academic field with the theory of self-regulated learning. Metacognition is considered a crucial factor influencing mathematics achievement. Furthermore, the affective field including pupils' self-efficacy, interest and motivation are the phenomena involved in mathematical problem-solving. On the other hand, metacognitive knowledge and metacognitive regulations are not a regular part of mathematics education in the Czech Republic. The main aim of this study was to investigate the relation between pupils' attitude toward mathematics; metacognitive knowledge; self-efficacy and motivation; metacognitive monitoring; and their achievement in solving mathematical problems. All together 1,133 students of Grade 5 from four types of Czech schools participated in the study. There were traditional schools; schools teaching mathematics by genetic constructivism, i.e., Hejný's method; Montessori schools; and Dalton schools were involved. The assessed variables, namely relation to mathematics; metacognitive knowledge; self-efficacy and motivation; metacognitive monitoring; and mathematical achievement were used as an input to regression analysis. Item-response theory was used for assessing the performance of the students and demands of the tasks. The metacognitive monitoring was detected as the most significant predictor of mathematics achievement for higher- and lower-performing students as well as for the item with high and low demands. The study reveals how the different mathematics curricula (un)support the metacognitive processes involved in mathematical problem-solving. The information allows teachers to spend sufficient time with particular types of mathematics problems whose solutions is determined by activation of metacognitive processes. This demonstrates the importance of including the activities for development of metacognitive monitoring in mathematics education.

Cognitive Training in the Domain of Mathematics for Potentially Gifted Children in Primary School

This study examined auditive and visual working memory and metacognitive knowledge in 92 gifted children (aged between eight and twelve), utilising a pre-test-training-post-test design, known as the cognitive training design. This approach was used to examine the working memory and metacognitive knowledge of gifted children concerning the progression after a cognitive training programme in arithmetical problem solving, taking into account the role of intelligence. Children were allocated to one of two experimental conditions: children received training after the pre-test (cognitive training condition) or were provided with training after the post-test (control condition). The results show that all children made significant improvements in working memory and metacognition. Intelligence significantly predicted verbal and visual working memory. However, we did not find a meaningful relationship between intelligence and metacognitive knowledge. The cognitive training in arithmetical problem solving seems to bring additional measurable changes in metacognitive knowledge, but not in working memory.

Anxiety, Motivation, and Competence in Mathematics and Reading for Children With and Without Learning Difficulties

Knowledge of the relations among learners' socio-emotional characteristics and competencies as they engage in mathematics and reading is limited, especially for children with academic difficulties. This study examined the relations between anxiety, motivation, and competence in mathematics and reading, within and across domains, in an academically-diverse set of 8-13-year-old learners (n = 146). To measure anxiety and motivation across domains, we paired existing measures of math anxiety and reading motivation with researcher-developed analogs for reading anxiety and math motivation. Participants completed standardized assessments of mathematics and reading, anxiety and motivation surveys for math and reading, and a measure of nonverbal cognitive ability. Results showed high internal consistency for all anxiety and motivation scales (Cronbach's alpha = 0.76-0.91). Pearson correlations showed that within and across domains, participants with higher competence had lower anxiety and higher motivation. Higher anxiety was also associated with lower motivation. Regression analyses showed that for both math and reading, within-domain motivation was a stronger predictor of competence than anxiety. There was a unidirectional across-domain relation: socio-emotional characteristics for reading predicted math competence, after accounting for nonverbal cognitive ability, age, gender, and within-domain anxiety and motivation. Results contribute to knowledge of the socio-emotional characteristics of children with and without learning difficulties in association with reading and math activities. Implications of a unidirectional socio-emotional link between the two domains can advance research and theory of the relations among socio-emotional characteristics and competence for academically-diverse learners.

Math anxiety relates positively to metacognitive insight into mathematical decision making

The current study reports a pre-registered investigation into the interrelations between mathematics anxiety, metacognition and mathematical decision-making. Although this question has already received some attention in previous work, reliance on self-report measures of metacognition has hindered its interpretation. Here, a novel experimental mathematical decision-making task was used in which participants solved mathematical assignments of varying difficulty, and expressed their level of confidence in the accuracy of their decision both prospectively and retrospectively. Mathematics anxiety was measured using a standardized questionnaire. Both prospective and retrospective confidence judgments predicted unique variation in accuracy; however, the explanatory effect of prospective confidence disappeared after taking task difficulty into account. This suggests that prospective, but not retrospective, confidence is largely based on easily available cues indicative of performance. Results of a multiple regression analysis indicated that individual differences in mathematics anxiety were negatively related to the overall level of confidence (both prospectively and retrospectively), and positively related to metacognitive efficiency (only prospectively). Having insight in these interrelationships is important in the context of remediating mathematics anxiety, which might in turn be useful with regard to the worldwide need for more workers with degrees in science, technology, engineering, or mathematics (STEM).

A meta-analysis of the relation between math anxiety and math achievement

Meta-analyses from the 1990s previously have established a significant, small-to-moderate, and negative correlation between math achievement and math anxiety. Since these publications, research has continued to investigate this relation with more diverse samples and measures. Thus, the goal of the present meta-analysis was to provide an update of the math anxiety-math achievement relation and its moderators. Analyzing 747 effect sizes accumulated from research conducted between 1992 and 2018, we found a small-to-moderate, negative, and statistically significant correlation (r = -.28) between math anxiety and math achievement. The relation was significant for all moderator subgroups, with the exception of the relation between math anxiety and assessments measuring the approximate number system. Grade level, math ability level, adolescent/adult math anxiety scales, math topic of anxiety scale, and math assessments were significant moderators of this relation. There is also a tendency for published studies to report significantly stronger correlations than unpublished studies, but overall, large, negative effect sizes are underreported. Our results are consistent with previous findings of a significant relation between math anxiety and math achievement. This association starts in childhood, remains significant through adulthood, is smaller for students in Grades 3 through 5 and postsecondary school, is larger for math anxiety than for statistics anxiety and for certain math anxiety scales, and is smaller for math exam grades and samples selected for low math ability. This work supports future research efforts to determine effective math achievement and math anxiety interventions, which may be most helpful to implement during childhood. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

How mathematics anxiety affects students' inflexible perseverance in mathematics problem-solving: Examining the mediating role of cognitive reflection

BACKGROUND

Too many students persevere in relying upon one (sometimes suboptimal) strategy for solving a wide range of problems, even when they know more efficient strategies. Although many studies have mentioned such phenomena, few studies have examined how emotional factors could affect this type of inflexible perseverance in strategy use.

AIMS

To examine whether mathematics anxiety could affect students' inflexible perseverance in strategy use and whether this effect could be mediated by cognitive reflection, which is the ability to engage in deliberate reasoning.

SAMPLE AND METHOD

In Study 1, 164 undergraduate students' (18-22 years) mathematics anxiety, cognitive reflection, and performance in overcoming inflexible perseverance were measured by a questionnaire battery. Structural equation models were used to examine the correlations between these variables. In Study 2, 98 undergraduate freshmen (17-18 years) were assigned to two groups, where one group's mathematics anxiety was temporarily induced by task instructions, while the other group served as a control group. Cognitive reflection and inflexible perseverance of the two groups were compared.

RESULTS

Study 1 showed that mathematics anxiety was negatively correlated with students' performance on overcoming inflexible perseverance, while cognitive reflection mediated such an effect. Study 2 showed that compared to the control group, the experimental group showed lower cognitive reflection, which led to lower performance in overcoming inflexible perseverance.

CONCLUSIONS

Mathematics anxiety was showed to impair students' ability to engage in deliberate reasoning and was associated with inflexible use of strategies. Alleviating students' mathematics anxiety should be considered when promoting students' strategic flexibility.

Math anxiety and math achievement: The effects of emotional and math strategy training

Math anxiety (MA) is a specific feeling of tension generated by the manipulation of numerical stimuli in daily life and academic situations (Richardson & Suinn, 1972). This condition has significant repercussions on the individual's life at personal, social, and economic level. Literature on the topic of MA alleviation, however, is still scarce. This study aims at contributing to this field by addressing MA prevention in school-age children. We have developed two different training methods administered to two groups of fourth graders: (a) MA training focusing on identifying and copying with MA-related feelings (N = 76); and (b) Math strategy training focusing on supplementary exercises to enhance calculation strategies (N = 76). We also carried out a Control training involving a range of activities, such as reading comic strips, describing characters in the story, and combining text and images to obtain an original narrative text (N = 72). We evaluated the differential effects of these training methods on MA, general anxiety, and math achievement before and after the training. Results indicate that MA training contributes to a decrease in MA level, although it does not appear to affect math achievement; Math strategy training, on the other hand, results in far transfer on a reduction of MA level as well as near transfer on the improvement of math achievement. Data are discussed in terms of specific mechanisms underlying each type of training method, and with specific focus on the evaluation of educational and developmental opportunities linked to MA prevention and improvement of math abilities in school-age children.