Because new learning technologies are enabling students to build and explore probability models, we believe that there is a need to determine the big enduring ideas that underpin probabilistic thinking and modeling. By uncovering the elements of the thinking modes of expert users of probability models we aim to provide a base for the setting of…

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…

In this proposal, I introduce a method for modeling the dynamics of a sixth-grade student's accommodation of his fractions scheme to include a disembedding operation (Steffe & Olive, 2010). I will describe a three-part approach consisting of a constructivist teaching experiment, retrospective analysis, and stochastic modeling of the student's…

The paper is focused on students of Mathematical methods in economics at the Czech university of life sciences (CULS) in Prague. The idea is to create a model of students' progress throughout the whole course using the Markov chain approach. Each student has to go through various stages of the course requirements where his success depends on the…

Propensity score analysis (PSA) is a methodological technique which may correct for selection bias in a quasi-experiment by modeling the selection process using observed covariates. Because logistic regression is well understood by researchers in a variety of fields and easy to implement in a number of popular software packages, it has…

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…

Radical behaviorism considers private events to be a part of ongoing observable behavior and to share the properties of public events. Although private events cannot be measured directly, their roles in overt action can be inferred from mathematical models that relate private responses to external stimuli and reinforcers according to the same…

Consider the nonparametric regression model Y = m(X)+ [tau](X)[epsilon], where X and [epsilon] are independent random variables, [epsilon] has a median of zero and variance [sigma][squared], [tau] is some unknown function used to model heteroscedasticity, and m(X) is an unknown function reflecting some conditional measure of location associated…

Earlier Analyses are shown to involve special cases of the equations developed here; also that a general four-state chain has the same parameter space as an all-or-none model if and only if its representation with an observable absorbing state is lumpable into a Markov chain with three states. (Author/GS)

Several steps are taken to develop methods for analyzing systems that involve probabilistic causation. The basic ideas and distinctions are illustrated for systems with dichotomous variables. It is shown that these basic ideas have analogous counterparts in causal systems with continuous variables. By using a generalized conditional probability…

The use of a Bayesian approach in evaluating data from clinical trials with many treatment centers and from many studies is discussed. The main distinction between a metaanalysis and an analysis of a multicenter trial is that different studies may have very different designs, while the centers in a multicenter trial usually follow the same…

The present article reviews the procedures that have been developed for measuring the reliability of human observers' judgments when making direct observations of behavior. These include the percentage of agreement, Cohen's Kappa, phi, and univariate and multivariate agreement measures that are based on quasi-equiprobability and quasi-independence…

Work performed persuant to grant number 1-06, 1819-2240 from the U.S. Office of Education.

Presents and discusses the results of research into similarity measures for search request formulations which employ Boolean combinations of index terms. The use of a weighting mechanism to indicate the importance of attributes in a search formulation is described. A 16-item reference list is included. (JL)

Two techniques for interpretation of fitted log-linear models in contingency table analysis are discussed. The use of odds ratios as opposed to direct interpretation of the fitted model is argued for. (Author/JKS)