This case study carried out during the 2020 coronavirus disease of 2019 (COVID-19) lockdown used online data collection means to investigate the distribution of cognitive demand levels of probability and counting principles (PCP) learning tasks in a popular online Grade 12 mathematics textbook, based on the PCP teachers' rating. The teachers'…

Preschoolers' experiences with shapes are important because geometry is foundational to aspects of mathematics and it is now part of the Common Core for school-readiness. Exposure to shapes also provides experiences that are key to developing spatial thinking more broadly. Yet achieving a strong conceptual understanding of geometric categories can…

The difficulties introductory statistics students have with formal statistical inference are well known in the field of statistics education. "Informal" statistical inference has been studied as a means to introduce inferential reasoning well before and without the formalities of formal statistical inference. This mixed methods study…

The theme of this year's conference is "Sin Fronteras: Questioning Borders with(in) Mathematics Education." This theme is intended to encourage research presentations, discussion, and reflection on the variety of borders within mathematics education, as well as those that might be probed, challenged, explained, enhanced and/or…

This document presents a review of evidence commissioned by the Education Endowment Foundation to inform the guidance document "Improving Mathematics in Key Stages Two and Three" (Education Endowment Foundation, 2017). The review draws on a substantial parallel study by the same research team, funded by the Nuffield Foundation, which…

Some intensive quantities, such as slope, velocity, or likelihood, are perceptually privileged in the sense that they are experienced as holistic, irreducible sensations. However, the formal expression of these quantities uses "a/b" analytic metrics; for example, the slope of a line is the quotient of its rise and run. Thus, whereas students'…

Many approaches to the transfer problem argue that transfer depends on the recognition of the same or similar abstract "structure" in 2 different situations. However, mainstream cognitive perspectives and contrasting Piagetian constructivist accounts differ in their conceptualizations of structure. These differences, not clearly articulated in the…

A student might find a certain representational format (e.g., diagram, text) more attractive than other formats for learning. Computer technology offers opportunities to adjust the formats used in learning environments to the preferences of individual learners. The question addressed in the current study was: does the match between a student's…

This volume, a comprehensive survey and critical analysis of today's issues in mathematics education, distills research to build knowledge and capacity in the field. The compendium is a valuable new resource that provides the most comprehensive evidence about what is known about research in mathematics education. The 38 chapters present five…

College students' misconceptions about probability are common and widespread. These misconceptions impede students' ability to make sound judgments in situations of uncertainty and master fundamental concepts of inferential statistics. In this paper the authors report the results of a study undertaken with the objective of correcting three common…

Probability theory has long been taken as the self-evident norm against which to evaluate inductive reasoning, and classical demonstrations of violations of this norm include the conjunction error and base-rate neglect. Many of these phenomena require multiplicative probability integration, whereas people seem more inclined to linear additive…

Four experiments investigated college students' judgments of inter-event contingency. Subjects were asked to judge the effect of a discrete response (tapping a wire) on the occurrence of a brief outcome (a radio's buzzing). Pairings of the possible event-state combinations were presented in a summary table, an unbroken time line, or a broken time…

The effects of a teaching program in probability devised for students in grades five to seven were analyzed. Most of the notions were too difficult for fifth graders; 60-70 percent of the sixth graders and 80-90 percent of the seventh graders were able to understand and use correctly most of the concepts. (MNS)

Describes a study to determine middle school children's representational strategies to form part-whole or part-part relationships for relational numbers such as proportions, ratios, or fractions. Quantitative and qualitative analysis revealed that children prefer a part-part representation to solve relational quantity problems. (15 references)…