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Teaching and learning in lower secondary schools in the era of PISA and TIMSS
\"Based on extensive video documentation from science, math and reading classrooms in Norwegian secondary schooling, this book explores teaching and learning in lower secondary classroomsin the three PISA domains science, mathematics and reading. It analyzes how offered and experienced teaching and learning opportunities in these three subject areas support students' learing\"-- Back cover.
Book
The Relation Between Mathematics Anxiety and Mathematics Performance Among School-Aged Students: A Meta-Analysis
The purpose of this meta-analysis was to examine the relation between mathematics anxiety (MA) and mathematics performance among school-aged students, and to identify potential moderators and underlying mechanisms of such relation, including grade level, temporal relations, difficulty of mathematical tasks, dimensions of MA measures, effects on student grades, and working memory. A meta-analysis of 131 studies with 478 effect sizes was conducted. The results indicated that a significant negative correlation exist between MA and mathematics performance, r = -.34. Moderation analyses indicated that dimensions of MA, difficulty of mathematical tasks, and effects on student grades differentially affected the relation between MA and mathematics performance. MA assessed with both cognitive and affective dimensions showed a stronger negative correlation with mathematics performance compared to MA assessed with either an affective dimension only or mixed/unspecified dimensions. Advanced mathematical task that require multistep processes showed a stronger negative correlation to MA compared to foundational mathematical tasks. Mathematics measures that affected/reflected student grades (e.g., final exam, students 'course grade, GPA) had a stronger negative correlation to MA than did other measures of mathematics performance that did not affect student grades (e.g., mathematics measures administered as part of research). Theoretical and practical implications of the findings are discussed.
Journal Article
Unpacking the Male Superiority Myth and Masculinization of Mathematics at the Intersections: A Review of Research on Gender in Mathematics Education
Gender research in mathematics education has experienced methodological and theoretical shifts over the past 45 years. This article offered a review of gender research in mathematics education with analysis of its findings as well as conceptual and empirical contributions. Implications for future gender research, particularly the adoption of intersectionality theory, were raised to inform more nuanced analyses.
Journal Article
Effect size measures for multilevel models: definition, interpretation, and TIMSS example
Effect size reporting is crucial for interpretation of applied research results and for conducting meta-analysis. However, clear guidelines for reporting effect size in multilevel models have not been provided. This report suggests and demonstrates appropriate effect size measures including the ICC for random effects and standardized regression coefficients or f2 for fixed effects. Following this, complexities associated with reporting R2 as an effect size measure are explored, as well as appropriate effect size measures for more complex models including the three-level model and the random slopes model. An example using TIMSS data is provided.
Journal Article
Mathematical errors made by high performing candidates writing the National Benchmark Tests
When the National Benchmark Tests (NBTs) were first considered, it was suggested that the results would assess entry-level students’ academic and quantitative literacy, and mathematical competence, assess the relationships between higher education entry-level requirements and school-level exit outcomes, provide a service to higher education institutions with regard to selection and placement, and assist with curriculum development, particularly in relation to foundation and augmented courses. We recognise there is a need for better communication of the findings arising from analysis of test data, in order to inform teaching and learning and thus attempt to narrow the gap between basic education outcomes and higher education requirements. Specifically, we focus on identification of mathematical errors made by those who have performed in the upper third of the cohort of test candidates. This information may help practitioners in basic and higher education. The NBTs became operational in 2009. Data have been systematically accumulated and analysed. Here, we provide some background to the data, discuss some of the issues relevant to mathematics, present some of the common errors and problems in conceptual understanding identified from data collected from Mathematics (MAT) tests in 2012 and 2013, and suggest how this could be used to inform mathematics teaching and learning. While teachers may anticipate some of these issues, it is important to note that the identified problems are exhibited by the top third of those who wrote the Mathematics NBTs. This group will constitute a large proportion of first-year students in mathematically demanding programmes. Our aim here is to raise awareness in higher education and at school level of the extent of the common errors and problems in conceptual understanding of mathematics. We cannot analyse all possible interventions that could be put in place to remediate the identified mathematical problems, but we do provide information that can inform choices when planning such interventions.
Journal Article
Teaching Students What They Already Know? The (Mis)Alignment Between Mathematics Instructional Content and Student Knowledge in Kindergarten
Kindergarten mathematics skills are important for subsequent achievement, yet mathematics is underemphasized in kindergarten classrooms. Using nationally representative data, this study explored the relationship between students' school-entry math skills, classroom content coverage, and end-of-kindergarten math achievement. Although the vast majority of children entered kindergarten having mastered basic counting and able to recognize simple geometric shapes, their teachers reported spending the most mathematics time—typically about 13 days per month—on this content. On average, exposure to this basic mathematics content was negatively associated with math achievement across kindergarten. Importantly, children with the lowest levels of math skills benefited from exposure to this basic mathematics content whereas other children benefited from exposure to more advanced content.
Journal Article
Developing Ambitious Mathematics Instruction Through Web-Based Coaching: A Randomized Field Trial
This article describes and evaluates a web-based coaching program designed to support teachers in implementing Common Core–aligned math instruction. Web-based coaching programs can be operated at relatively lower costs, are scalable, and make it more feasible to pair teachers with coaches who have expertise in their content area and grade level. Results from our randomized field trial document sizable and sustained effects on both teachers’ ability to analyze instruction and on their instructional practice, as measured by the Mathematical Quality of Instruction instrument and student surveys. However, these improvements in instruction did not result in corresponding increases in math test scores as measured by state standardized tests or interim assessments. We discuss several possible explanations for this pattern of results.
Journal Article
A systematic literature review of the current discussion on mathematical modelling competencies
Mathematical modelling competencies have become a prominent construct in research on the teaching and learning of mathematical modelling and its applications in recent decades; however, current research is diverse, proposing different theoretical frameworks and a variety of research designs for the measurement and fostering of modelling competencies. The study described in this paper was a systematic literature review of the literature on modelling competencies published over the past two decades. Based on a full-text analysis of 75 peer-reviewed studies indexed in renowned databases and published in English, the study revealed the dominance of an analytical, bottom-up approach for conceptualizing modelling competencies and distinguishing a variety of sub-competencies. Furthermore, the analysis showed the great richness of methods for measuring modelling competencies, although a focus on (non-standardized) tests prevailed. Concerning design and offering for fostering modelling competencies, the majority of the papers reported training strategies for modelling courses. Overall, the current literature review pointed out the necessity for further theoretical work on conceptualizing mathematical modelling competencies while highlighting the richness of developed empirical approaches and their implementation at various educational levels.
Journal Article
Quality Assurance in Teacher Education and Outcomes: A Study of 17 Countries
This study investigated the relationship between policies related to the recruitment, selection, preparation, and certification of new teachers and (a) the quality of future teachers as measured by their mathematics content and pedagogy content knowledge and (b) student achievement in mathematics at the national level. The study used data collected for the Teacher Education and Development Study in Mathematics, which compared the ways in which 17 countries prepared teachers of mathematics for the primary and secondary levels. A consistent positive association was found between the strength of a country's quality assurance arrangements and future teachers' knowledge of mathematics and mathematics pedagogy. Countries with strong policies for assuring the quality of new teachers were also found to be among the strongest performers on international tests of mathematics achievement.
Journal Article
Creativity as a function of problem-solving expertise: posing new problems through investigations
This study was inspired by the following question: how is mathematical creativity connected to different kinds of expertise in mathematics? Basing our work on arguments about the domain-specific nature of expertise and creativity, we looked at how participants from two groups with two different types of expertise performed in problem-posing-through-investigations (PPI) in a dynamic geometry environment (DGE). The first type of expertise—MO—involved being a candidate or a member of the Israeli International Mathematical Olympiad team. The second type—MM—was comprised of mathematics majors who excelled in university mathematics. We conducted individual interviews with eight MO participants who were asked to perform PPI in geometry, without previous experience in performing a task of this kind. Eleven MMs tackled the same PPI task during a mathematics test at the end of a 52-h course that integrated PPI. To characterize connections between creativity and expertise, we analyzed participants’ performance on the PPI tasks according to proof skills (i.e., auxiliary constructions, the complexity of posed tasks, and correctness of their proofs) and creativity components (i.e., fluency, flexibility and originality of the discovered properties). Our findings demonstrate significant differences between PPI by MO participants and by MM participants as reflected in the more creative performance and more successful proving processes demonstrated by MO participants. We argue that problem posing and problem solving are inseparable when MO experts are engaged in PPI.
Journal Article