We examine the challenges of teaching probability through the use of modelling. We argue how an integrated modelling approach might facilitate a coordinated understanding of distribution by marrying theoretical and data-oriented perspectives and present probability as more connected to the social lives of modern-day students. Research is, however,…

A fundamental aspect of statistical inference is representation of real-world data using statistical models. This article analyzes students' articulations of statistical models and modeling during their first steps in making informal statistical inferences. An integrated modeling approach (IMA) was designed and implemented to help students…

This research examines issues regarding model estimation and robustness in the use of Bayesian Inference Networks (BINs) for measuring Learning Progressions (LPs). It provides background information on LPs and how they might be used in practice. Two simulation studies are performed, along with real data examples. The first study examines the case…

A. Redish et al. (2007) proposed a reinforcement learning model of context-dependent learning and extinction in conditioning experiments, using the idea of "state classification" to categorize new observations into states. In the current article, the authors propose an interpretation of this idea in terms of normative statistical inference. They…

Stochastic understanding of probability distribution undergirds development of conceptual connections between probability and statistics and supports development of a principled understanding of statistical inference. This study investigated the impact of an instructional course intervention designed to support development of stochastic…

This article reports on a case study from a design-based research project that investigated how students make sense of the disciplinary tools they are taught to use, and specifically, what personal, interpersonal, and material resources support this process. The probability topic of binomial distribution was selected due to robust documentation of…

Dealing with alternative causes is necessary to avoid making inaccurate causal inferences from covariation data. However, information about alternative causes is frequently unavailable, rendering them unobserved. The current article reviews the way in which current learning models deal, or could deal, with unobserved causes. A new model of causal…

In 3 experiments, the authors investigated learning of the value of money from product prices in an unfamiliar currency when the prices are proportional to quantity. In support of the second stage of a hypothesized 2-stage process of learning, Experiment 1, in which 32 undergraduates participated, shows that response times for inferences of…

Languages are transmitted from person to person and generation to generation via a process of iterated learning: people learn a language from other people who once learned that language themselves. We analyze the consequences of iterated learning for learning algorithms based on the principles of Bayesian inference, assuming that learners compute…