These proceedings are a written record of the research presented at the 41st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) held in St. Louis, Missouri, November 14-17, 2019. This year's conference theme is "...against a new horizon." The papers comprise 67…

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…

The paper presents inequalities between four descriptive statistics that can be expressed in the form [P-E(P)]/[1-E(P)], where P is the observed proportion of agreement of a "kappa x kappa" table with identical categories, and E(P) is a function of the marginal probabilities. Scott's "pi" is an upper bound of Goodman and Kruskal's "lambda" and a…

This article proposes a procedure, based on a global statistic, for assessing intra-individual consistency in a test-retest design with a short-term retest interval. The procedure is developed within the framework of parametric item response theory, and the statistic is a likelihood-based measure that can be considered as an extension of the…

We consider how probability theory can be used to increase one's chances of winning in the new television game show "The Colour of Money."

In spite of the growing interest in cross-cultural research and assessment, there is little research on statistical procedures that can be used to simultaneously assess the differential item functioning (DIF) across multiple groups. The chief objective of this work is to show a unified framework for the analysis of DIF in multiple groups using one…

In this paper I discuss some concerns related to the analysis of focus groups: (a) the issue of generalisation; (b) the problems of using numbers and quantifying in the analysis; (c) how the concrete situation of the focus groups could be included in the analysis, and (d) what formats can be used when quoting from focus groups. Problems with…

In a recent paper, Alcock and Inglis (in press) noted a distinction between the way that Weber (in press) and they defined syntactic and semantic proof productions. Weber argued that "a syntactic proof production occurs when one works predominantly within the representation system of proof [...] Alternatively, a semantic proof production occurs…

This report presents results of the 2009 National Assessment of Educational Progress (NAEP) in mathematics at grades 4 and 8. The results from the 2009 assessment presented in this report are compared to those from previous years, showing how students' performance in mathematics has progressed over time. Results for students in the nation, the 50…

Bayesian statistical inference is unfamiliar to many educational evaluators. While the classical model is useful in educational research, it is not as useful in evaluation because of the need to identify solutions to practical problems based on a wide spectrum of information. The reason Bayesian analysis is effective for decision making is that it…

Examines possible differences in secondary students' conceptions of randomness before and after instruction in probability, which occurs for Spanish students between the ages of 14 and 17. Indicates that students' subjective understanding of randomness is close to some interpretations of randomness throughout history. Contains 16 references.…

This assessment sample provides information on the Missouri Assessment Program (MAP) for grade 8 mathematics. The sample consists of three items taken from the test booklet and scoring guides for the three items. The items assess number theory, data analysis, probability and statistics, and patterns and relationships. (MM)

Presented is a description of the experimental first-year algebra materials "Algebra Through Applications"; a description of the procedure used in evaluating these materials; and recommendations for changes in the materials, implementation, evaluation, and funding. The evaluation indicates that these materials can be effectively used in a variety…

Presented are review questions and exercises for several mathematics topics. The first five sections cover the following major topics of the course: algebra, geometry, logic, probability, and statistics. Each of these five units follows a similar format. Each major topic is broken into several subtopics, with examples for each topic taken from…

The changing role of mathematics in society may require a different mathematics curriculum in the schools. Curriculum builders work constructing pieces of the new mathematics curriculum. To last, this new curriculum must be based on a foundation of experience and research. This book provides access to that foundation for secondary schools and…