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…

We represent the main stages of the process of mathematical modelling as fuzzy sets in the set of the linguistic labels of negligible, low intermediate, high and complete success by students in each of these stages and we use the total possibilistic uncertainty as a measure of students' modelling capacities. A classroom experiment is also…

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…

The approaches taken to psychological research are discussed. Studies are classified as axiomatic, classical, stochastic or statistical, or structural. The mathematical models used in each type of study are discussed. (SD)

Using the concepts of conditional probability, conditional expectation, and conditional independence, the main results of the classical test theory model can be derived in a very few steps with minimal assumptions. The present effort explores the possibility that present classical test theories can be further condensed. (Author/RC)

Using conventional mental test theory, item parameters of an aptitude or achievement test vary with each group of examinees, and as such are somewhat limited in their use and interpretation. Within the last 25 years, measurement models have emerged in which item parameters are considered to be invariant. Generically referred to as latent trait…

A model permitting construction of algorithms for the polynomial conjoint analysis of similarities is presented. This model, which is based on concepts used in nonmetric scaling, permits one to obtain the best approximate solution. The concepts used to construct nonmetric scaling algorithms are reviewed. Finally, examples of algorithmic models for…

Latent trait theory supposes that, in testing situations, examinee performance on a test can be predicted (or explained) by defining examinee characteristics, referred to as traits, estimating scores for examinees on these traits and using the scores to predict or explain test performance (Lord and Novick, 1968). In view of the breakthroughs in…

The Proceedings of PME-XVIII have been published in four separate volumes because of the large number of individual conference papers reported. Volume I contains brief reports for 11 Working Groups and 8 Discussion Groups, 55 "Short Oral Communications," 28 Posters, 5 Plenary Panel reports, and 4 Plenary Session reports. Volume II…