We developed and tested strategies for using spatial representations to help students understand core probability concepts, including the multiplication rule for computing a joint probability from a marginal and conditional probability, interpreting an odds value as the ratio of two probabilities, and Bayesian inference. The general goal of these…

In quantum mechanics, probability amplitudes are complex numbers and the relative phases between the terms in superposition states have measurable effects. This article describes an investigation into sophomore- and junior-level students' reasoning patterns in relating relative phases and real-world quantum phenomena. The investigation involved…

We tested a method for solving Bayesian reasoning problems in terms of spatial relations as opposed to mathematical equations. Participants completed Bayesian problems in which they were given a prior probability and two conditional probabilities and were asked to report the posterior odds. After a pretraining phase in which participants completed…

This study analyzed how the earliest teaching and learning of probability was organized in Singapore, the US, and Indonesia through an analysis of textbook as an intended mathematics curriculum. An analytical framework was developed comprising four perspectives: representational forms, cognitive demand levels, contextual features, and organization…

One of the highest ambitions in educational technology is the move towards personalized learning. To this end, computerized adaptive learning (CAL) systems are developed. A popular method to track the development of student ability and item difficulty, in CAL systems, is the Elo Rating System (ERS). The ERS allows for dynamic model parameters by…

These proceedings are a written record of the research presented at the 42nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) held in Mazatlán, Mexico, virtually beginning May 27, 2021 and in-person June 2-6, 2021. The conference was originally scheduled to take place…

This article was written as a response to Ayres, Lowrey, Douglas, and Sievers (2011) who commented on the degree to which promoting the teaching of functional skills had a higher probability of leading to a more independent life for students with severe disabilities. In doing so, the authors take issue with the use of a standards-based curriculum…

The teaching of Probability Theory constitutes a new trend in mathematics education internationally. The purpose of this research project was to explore the degree to which preschoolers understand key concepts of probabilistic thinking, such as sample space, the probability of an event and probability comparisons. At the same time, we evaluated an…

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…

Distinguishing between good and bad science is not easy. Evaluating whether or not a claim really is supported by good research is like buying a car. There is an optimal solution to the problem, which is to read and digest all of the relevant research, but most people do not have time to execute the optimal solution. What they need is a good…

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…

Most students love to play games. Ernest (1986) believed that games could be used to teach mathematics effectively in four areas: motivation, concept development, reinforcement of skills, and practice of problem-solving strategies. Fifteen is an interesting and thought-provoking game that helps students learn mathematics at the same time. Playing…

This study used an ecobehavioral approach to investigate the conditional probability that English language learning (ELL) students would engage in academic tasks in urban middle school content area classrooms within different instructional grouping configurations. These configurations included whole class, small group, one-to-one, and individual…

The relationships among types of errors observed during probability problem solving were studied. Subjects were 50 graduate students in an introductory probability and statistics course. Errors were classified as text comprehension, conceptual, procedural, and arithmetic. Canonical correlation analysis was conducted on the frequencies of specific…

This issue of the journal contains abstracts and critical comments for 10 published reports on research in mathematics education. The reports concern children's school mobility and achievement, preservice teachers' sources of decisions, spatial visualization in boys and girls, rote versus conceptual emphases in teaching probability, using drawings…