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Math-ish : finding creativity, diversity, and meaning in mathematics
Mathematics is a fundamental part of life, yet every one of us has a unique relationship with learning and understanding the subject. Working with numbers may inspire confidence in our abilities or provoke anxiety and trepidation. Stanford researcher, mathematics education professor, and the leading expert on math learning Dr. Jo Boaler argues that our differences are the key to unlocking our greatest mathematics potential. In Math-ish, Boaler shares new neuroscientific research on how embracing the concept of \"math-ish\"--a theory of mathematics as it exists in the real world--changes the way we think about mathematics, data, and ourselves. When we can see the value of diversity among people and multi-faceted approaches to learning math, we are free to truly flourish. --Provided by publisher.
Book
A Meta-analysis of the Worked Examples Effect on Mathematics Performance
Abstract The current meta-analysis quantifies the average effect of worked examples on mathematics performance from elementary grades to postsecondary settings and to assess what moderates this effect. Though thousands of worked examples studies have been conducted to date, a corresponding meta-analysis has yet to be published. Exclusionary coding was conducted on 8033 abstracts from published and grey literature to yield a sample of high quality experimental and quasi-experimental work. This search yielded 43 articles reporting on 55 studies and 181 effect sizes. Using robust variance estimation (RVE) to account for clustered effect sizes, the average effect size of worked examples on mathematics performance outcomes was medium with g = 0.48 and p = 0.01. Moderators assessed included example type (correct vs. incorrect examples alone or in combination with correct examples), pairing with self-explanation prompts, and timing of administration (i.e., practice vs. skill acquisition). The inclusion of self-explanation prompts significantly moderated the effect of examples yielding a negative effect in comparison to worked examples conditions that did not include self-explanation prompts. Worked examples studies that used correct examples alone yielded larger effect sizes than those that used incorrect examples alone or correct examples in combination with incorrect examples. The worked examples effect yields a medium effect on mathematics outcomes whether used for practice or initial skill acquisition. Correct examples are particularly beneficial for learning overall, and pairing examples with self-explanation prompts may not be a fruitful design modification. Theoretical and practical implications are discussed.
Journal Article
Math Performance and Academic Anxiety Forms, from Sociodemographic to Cognitive Aspects: a Meta-analysis on 906,311 Participants
The relationship between anxiety and mathematics has often been investigated in the literature. Different forms of anxiety have been evaluated, with math anxiety (MA) and test anxiety (TA) consistently being associated with various aspects of mathematics. In this meta-analysis, we have evaluated the impact of these forms of anxiety, distinguishing between different types of mathematical tasks. In investigating this relationship, we have also included potential moderators, such as age, gender, working memory, type of task, and type of material. One hundred seventy-seven studies met the inclusion criteria, providing an overall sample of 906,311 participants. Results showed that both MA and TA had a significant impact on mathematics. Sociodemographic factors had modest moderating effects. Working memory (WM) also mediated the relationship between MA and TA with mathematics; however, this indirect effect was weak. Theoretical and educational implications, as well as future directions for research in this field, are discussed.
Journal Article
Not a One-Way Street: Bidirectional Relations Between Procedural and Conceptual Knowledge of Mathematics
There is a long-standing and ongoing debate about the relations between conceptual and procedural knowledge (i.e., knowledge of concepts and procedures). Although there is broad consensus that conceptual knowledge supports procedural knowledge, there is controversy over whether procedural knowledge supports conceptual knowledge and how instruction on the two types of knowledge should be sequenced. A review of the empirical evidence for mathematics learning indicates that procedural knowledge supports conceptual knowledge, as well as vice versa, and thus that the relations between the two types of knowledge are bidirectional. However, alternative orderings of instruction on concepts and procedures have rarely been compared, with limited empirical support for one ordering of instruction over another. We consider possible reasons for why mathematics education researchers often believe that a conceptual-to-procedural ordering of instruction is optimal and why so little research has evaluated this claim. Future empirical research on the effectiveness of different ways to sequence instruction on concepts and procedures is greatly needed.
Journal Article
Math at home adds up to achievement in school
With a randomized field experiment of 587 first-graders, we tested an educational intervention designed to promote interactions between children and parents relating to math. We predicted that increasing math activities at home would increase children's math achievement at school. We tested this prediction by having children engage in math story time with their parents. The intervention, short numerical story problems delivered through an iPad app, significantly increased children's math achievement across the school year compared to a reading (control) group, especially for children whose parents are habitually anxious about math. Brief, high-quality parent-child interactions about math at home help break the intergenerational cycle of low math achievement.
Journal Article
Early Predictors of High School Mathematics Achievement
Identifying the types of mathematics content knowledge that are most predictive of students' long-term learning is essential for improving both theories of mathematical development and mathematics education. To identify these types of knowledge, we examined long-term predictors of high school students' knowledge of algebra and overall mathematics achievement. Analyses of large, nationally representative, longitudinal data sets from the United States and the United Kingdom revealed that elementary school students' knowledge of fractions and of division uniquely predicts those students' knowledge of algebra and overall mathematics achievement in high school, 5 or 6 years later, even after statistically controlling for other types of mathematical knowledge, general intellectual ability, working memory, and family income and education. Implications of these findings for understanding and improving mathematics learning are discussed.
Journal Article
Stereotype Threat in High School Classrooms: How It Links to Teacher Mindset Climate, Mathematics Anxiety, and Achievement
As stereotype threat was initially examined in experimental settings, the effects of such threats have often been tested by temporarily manipulating social identity threats. This study expands the literature by examining 9th-grade adolescents’ naturalistic stereotype threat, using data from the National Study of Learning Mindsets in the United States (n ~= 6040, age: 13–17, Mage = 14.31, 6.9% Black boys, 6.5% Black girls, 13.1% Latinos, 12.3% Latinas, 31.5% White boys, 29.7% White girls). The results indicate that Black and Latinx students experience higher levels of stereotype threat in high school mathematics classrooms than do their White peers. When students perceive that their teachers have created fixed mindset climates, they experience greater stereotype threat. Stereotype threat, in turn, negatively predicts Black and Latino boys and White girls’ later achievement via anxiety. These findings highlight the importance of creating mathematics classrooms that cultivate a growth mindset and minimize social identity threat.
Journal Article
Impact of math self-efficacy, math anxiety, and growth mindset on math and science career interest for middle school students
This study tested a proposed model consisting of mathematics anxiety, mathematics self-efficacy, and implicit theories of intelligence in predicting mathematics and science career interest in middle school students, while controlling for student math level. One hundred fifty-two seventh-grade students in a middle school in the USA participated in the study. Results revealed both similarities and differences on the relation among the intended variables by gender. The path analyses showed that, for boys, mathematics self-efficacy mediated the relation between implicit theories of intelligence and mathematics and science career interest. In addition, student mathematics level exerted a direct impact on mathematics anxiety, growth mindset, and career interest for boys. For girls, mathematics anxiety exerted a direct impact on their career interest. Implications of the results are discussed.
Journal Article
The Relationship between Visuospatial Working Memory and Mathematical Performance in School-Aged Children: a Systematic Review
The body of research surrounding the relationship between visuospatial working memory (VSWM) and mathematics performance remains in its infancy. However, it is an area generating increasing interest as the performance of school leavers comes under constant scrutiny. In order to develop a coherent understanding of the literature to date, all available literature reporting on the relationship between VSWM and mathematics performance was included in a systematic, thematic analysis of effect sizes. Results show a significant influence of the use of a standardised mathematics measure, however, no influence of the type of VSWM or mathematics being assessed, on the effect sizes generated. Crucially, the overall effect size is positive, demonstrating a positive association between VSWM and mathematics performance. The greatest implications of the review are on researchers investigating the relationship between VSWM and mathematics performance. The review also highlights as yet under-researched areas with scope for future research.
Journal Article