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A brief history of mathematical thought
Emblazoned on many advertisements for the wildly popular game of Sudoku are the reassuring words, \"no mathematical knowledge required.\" Anxiety about math plagues many of us, and school memories can still summon intense loathing. In A Brief History of Mathematical Thought, Luke Heaton shows that much of what many think-and fear-about mathematics is misplaced, and to overcome our insecurities we need to understand its history. To help, he offers a lively guide into and through the world of mathematics and mathematicians, one in which patterns and arguments are traced through logic in a language grounded in concrete experience. Heaton reveals how Greek and Roman mathematicians like Pythagoras, Euclid, and Archimedes helped shaped the early logic of mathematics; how the Fibonacci sequence, the rise of algebra, and the invention of calculus are connected; how clocks, coordinates, and logical padlocks work mathematically; and how, in the twentieth century, Alan Turing's revolutionary work on the concept of computation laid the groundwork for the modern world. A Brief History of Mathematical Thought situates mathematics as part of, and essential to, lived experience. Understanding it requires not abstract thought or numbing memorization but an historical imagination and a view to its origins. -- Provided by publisher.
Book
Spotlight on math anxiety
Anxiety disorders are some of the most widespread mental health issues worldwide. In educational settings, individuals may suffer from specific forms of test and performance anxiety that are connected to a knowledge domain. Unquestionably, the most prominent of these is math anxiety. Math anxiety is a widespread problem for all ages across the globe. In the international assessments of the Programme for International Student Assessment (PISA) studies, a majority of adolescents report worry and tension in math classes and when doing math. To understand how math anxiety takes effect, it has to be regarded as a variable within an ensemble of interacting variables. There are antecedents that facilitate the development of math anxiety. They concern environmental factors such as teachers' and parents' attitudes toward their students' and children's ability in math, societal stereotypes (eg, on females' math abilities), or personal factors such as traits or gender. These antecedents influence a number of variables that are important in learning processes. Math anxiety interacts with variables such as self-efficacy or motivation in math, which can intensify or counteract math anxiety. Outcomes of math anxiety concern not only performance in math-related situations, they can also have long-term effects that involve efficient (or not-so-efficient) learning as well as course and even vocational choices. How can math anxiety be counteracted? A first step lies in its correct diagnosis. Questionnaires for the assessment of math anxiety exist for all age groups, starting at primary education level. Help against math anxiety can be offered on different levels: by educational institutions, by teachers and a change in instructional approaches, by parents, or by the affected person. However, much more research is needed to develop effective measures against math anxiety that are tailored to an individual's characteristics and needs.
Journal Article
Math curse
When the teacher tells her class that they can think of almost everything as a math problem, one student acquires a math anxiety which becomes a real curse.
Book
Tackling Anxiety in Primary
This book provides teacher educators with an understanding of the issues around mathematics anxiety and a framework of teaching strategies to support undergraduates, trainee teachers and established professionals in primary settings in developing confidence in learning and teaching mathematics.
The existence of mathematics anxiety in adults is both prevalent and well documented, and there is a real concern that adults who are anxious or lacking in confidence in their own mathematical ability may affect the quality of teaching and learning for those in their care. Research has identified that there are lower levels of mathematical confidence in adults working with children in primary rather than secondary schools, and that where adults are anxious this can be passed on to the pupils with whom they work. This book addresses issues related to the effect that mathematics anxiety has on those teaching and working with primary aged children and supports teacher educators to develop confidence in both trainee teachers and established professionals.
eBook
Development and Validation of the Brief Math Anxiety Scale (BMAS) in University Students
Background:: This study developed the Brief Math Anxiety Scale (BMAS), a brief version of the Shortened Math Anxiety Rating Scale (sMARS), maintaining its original three-factor structure, by applying item response theory. Method:: The sMARS was administered to 1,349 undergraduates, along with other questionnaires to measure their math ability, trait and test anxieties, and attitudes toward mathematics. Results:: Results showed that the original scale could be reduced to nine items (three for each subscale). We provided evidence of good psychometric properties: strong internal consistency, adequate 7-week test-retest reliability, and good convergent/discriminant validity. Conclusions:: In conclusion, the BMAS provides valid interpretations and reliable scores for assessing math anxiety in university students, and is especially useful in situations with time constraints where the longer form is impractical.
Journal Article
Metacognitive Cues, Working Memory, and Math Anxiety: The Regulated Attention in Mathematical Problem Solving (RAMPS) Framework
Mathematical problem solving is a process involving metacognitive (e.g., judging progress), cognitive (e.g., working memory), and affective (e.g., math anxiety) factors. Recent research encourages researchers who study math cognition to consider the role that the interaction between metacognition and math anxiety plays in mathematical problem solving. Problem solvers can make many metacognitive judgments during a math problem, ranging from global judgments such as, “Do I care to solve this problem?” to minor cue-based judgments such as, “Is my current strategy successful in making progress toward the correct solution?” Metacognitive monitoring can hinder accurate mathematical problem solving when the monitoring is task-irrelevant; however, task-relevant metacognitive experiences can lead to helpful control decisions in mathematical problem solving such as checking work, considering plausibility of an answer, and considering alternate strategies. Worry and negative thoughts (i.e., math anxiety) can both interfere with the accuracy of metacognitive experiences as cues in mathematical problem solving and lead to avoidance of metacognitive control decisions that could otherwise improve performance. The current paper briefly reviews and incorporates prior literature with current qualitative reports (n = 673) to establish a novel framework of regulated attention in mathematical problem solving (RAMPS).
Journal Article
Factor Structure and Gender Invariance of the Abbreviated Math Anxiety Scale (AMAS) in Middle School Students
Given the potential short and long-term consequences of math anxiety in children and adolescents, it is important to have psychometrically sound measures that assess math anxiety in this population. The purpose of the current study was to examine the factor structure and equivalence of the factor structure of the Abbreviated Math Anxiety Scale
(
AMAS) in middle school girls and boys. Participants were 604 children recruited from two middle schools in Texas. A single-factor, two-factor, and bifactor model were tested using a Confirmatory Factor Analysis (CFA). A Multigroup Confirmatory Factor Analysis (MGCFA) was used to investigate whether the AMAS demonstrated measurement invariance across the sample of middle school girls and boys. The bifactor model provided an excellent fit and the best fit of the three models tested (
CFI
= .99,
TLI
= .99,
SRMR
= .02,
RMSEA
= .03). Results of the MGCFA supported configural, metric, and scalar invariance of the AMAS across middle school boys and girls. These results suggest that the AMAS demonstrates strong factorial invariance across gender for middle school students and can be used to assess potential differences in math anxiety between middle school girls and boys in an unbiased manner.
Journal Article
Learning Engagement as a Moderator between Self-Efficacy, Math Anxiety, Problem-Solving Strategy, and Vector Problem-Solving Performance
Vector problem-solving abilities are fundamental to everyday life and higher education; thus, improving them is important in education and research. However, the role of cognitive and affective factors and learning engagement in vector problem-solving performance is still unclear. This study examines the processes associated with vector problem-solving performance, focusing on the problem-solving strategy as a cognitive factor and math anxiety and task-specific self-efficacy as affective factors. In addition, this study examines the impact of learning engagement as a moderator in this process. A total of 245 Japanese 11th-grade high school students completed questionnaires. A multiple-group structural equation modelling revealed that (1) task-specific self-efficacy, math anxiety, and problem-solving strategies contribute to vector problem-solving performance when learning engagement is above average; (2) task-specific self-efficacy contributes to math anxiety, whereas task-specific self-efficacy and math anxiety contribute to problem-solving strategies when learning engagement is above average and stable; (3) task-specific self-efficacy is a positive predictor of vector problem-solving performance regardless of learning engagement. The results suggest that learning engagement moderates the association between math anxiety, task-specific self-efficacy, problem-solving strategy, and vector problem-solving performance. In addition, task-specific self-efficacy is a strong predictor of vector problem-solving performance.
Journal Article
The Content Specificity and Generality of the Relationship between Mathematical Problem Solving and Affective Factors
Research has revealed that both cognitive factors, such as knowledge, problem solving strategies and affective factors, such as motivation and emotions, strongly influence mathematical problem solving. However, few studies have examined the content specificity and generality of the relationship between mathematical problem solving and affective factors. This study examines the content specificity and generality of the relationship between mathematical problem solving, task value, math anxiety and engagement among high school students. Japanese second-year high school students (n = 240) completed questionnaires. The multilevel structural equation modelling revealed that utility value for entrance examinations and emotional engagement positively affected mathematical problem solving via cognitive engagement between various contents level. Emotional engagement positively affected mathematical problem solving via cognitive engagement within a certain content level. The results suggest that promoting the perception that learning mathematics has high utility value for university entrance examinations across various contents can increase students’ cognitive engagement and, therefore, improve mathematical problem solving. Furthermore, both increasing students’ emotional engagement only when they learn certain content and consistently increasing it may improve cognitive engagement and, therefore, allow learners to better solve mathematical problems. The study’s findings have significant implications for educational practice and mathematical problem-solving research.
Journal Article