One of the most vexing challenges facing developmental researchers today is the statistical modeling of two or more behaviors as they unfold jointly over time. Although quantitative methodologists have studied these issues for more than half a century, no widely agreed-upon principled strategy exists to empirically analyze codevelopmental…

In recent years, mathematical models of decision making, such as the diffusion model, have been endorsed in individual differences research. These models can disentangle different components of the decision process, like processing speed, speed-accuracy trade-offs, and duration of non-decisional processes. The diffusion model estimates individual…

Using data from teaching experiments and theories from quantitative reasoning, we built second-order accounts of students' mathematics with regards to how they conceived rate of change through operating on existing quantities. In this report, we explain three different ways STEM undergraduates structurally conceive rate of change as they…

As climate change becomes an increasingly important topic for science educators, it is critical to learn how teachers may be able to increase students' knowledge about it. We conducted two consecutive quasi-experimental studies that investigated the role of interest in predicting middle school students' knowledge gains from a unit about how…

Another year of COVID-19 meant another virtual meeting but the Canadian Mathematics Education Study Group/Groupe Canadien d'Étude en Didactique des Mathématiques (CMESG/GCEDM) made the best of the situation and found ways to learn together and share connections. Having learned a lot from the 2021 virtual meeting, the executive was able to once…

Information changes as it is passed from person to person, with this process of cultural transmission allowing the minds of individuals to shape the information that they transmit. We present mathematical models of cultural transmission which predict that the amount of information passed from person to person should affect the rate at which that…

Niche construction is the modification of components of the environment through an organism's activities. Humans modify their environments mainly through ontogenetic and cultural processes, and it is this reliance on learning, plasticity and culture that lends human niche construction a special potency. In this paper we aim to facilitate…

Functions provide powerful tools for describing change, but research has shown that students find difficulty in using functions to create and interpret models of changing phenomena. In this study, we drew on a models and modeling perspective to design an instructional approach to develop students' abilities to describe and interpret rates of…

Unemployment Insurance (UI) is the major social insurance program that protects against lost earnings resulting from involuntary unemployment. Existing literature finds that low-earning unemployed workers experience difficulty accessing UI benefits. The most prominent policy reform designed to increase rates of monetary eligibility, and thus UI…

This paper explores the use of spreadsheets to develop an exploratory environment where mathematics students can develop their own understanding of the parameters of commonly encountered families of functions: linear, logarithmic, exponential and power. The key to this understanding involves opening up the definition of rate of change from the…

The relationship between hierarchical linear modeling (HLM) notation and mixed model notation is illustrated by explicitly mapping the parameters across notations for a concrete example involving the hierarchical modeling of change. (Author/SLD)

Describes the individual chapters of this collection and notes that, although the book lacks consistency in some respects, it contains state-of-the-art reflections on the modeling of change and should stimulate discussion for experts and practitioners. (SLD)

Two Statistical Analysis System (SAS) macros are presented that perform the modified principal components approach of L. R. Tucker (1966) to modeling generalized learning curves analysis up to a rotation of the components. Three SAS macros are described that rotate the factor patterns to have characteristics Tucker considered desirable. (SLD)

The problem of chance model modifications under varying levels of sample size, model size, and severity of misspecification in confirmatory factor analysis models was examined through Monte Carlo simulations. Findings suggest that practitioners should exercise caution when interpreting modified models unless sample size is quite large. (SLD)

Methods for studying relationships between patterns of change on different variables are considered, showing how the multilevel modeling framework, often used to study univariate change, can be extended to the multivariate case to yield estimates of covariances of parameters representing aspects of change for different variables. (SLD)