Modeling First: Applying Learning Science to the Teaching of Introductory Statistics

Abstract

Students learn many concepts in the introductory statistics course, but even our most successful students end up with rigid, ritualized knowledge that does not transfer easily to new situations. In this article we describe our attempt to apply theories and findings from learning science to the design of a statistics course that aims to help students build a coherent and interconnected representation of the domain. The resulting practicing connections approach provides students with repeated opportunities to practice connections between core concepts (especially the concepts of statistical model, distribution, and randomness), key representations (R programming language and computational techniques such as simulation and bootstrapping), and real-world situations statisticians face as they explore variation, model variation, and evaluate and compare statistical models. We provide a guided tour through our curriculum implemented in an interactive online textbook (CourseKata.org) and then provide some evidence that students who complete the course are able to transfer what they have learned to the learning of new statistical techniques.

Statistics education from a data‐centric perspective

“…The “General Linear Model” [45] modeling approach gives a coherent view of statistical problem‐solving. Modeling emphasizes the correlation of input (independent) and output (dependent) variables, it explicates data generating processes (where possible) and sets the necessary (but not sufficient) scene for causal reasoning.…”

“…Early in our courses, in the section on exploratory data analysis, we start with the simplest model as a starting point for students' inquiry: the mean (Equation [1]). The rest, called by Son, Blake, Fries, et al [45]. “some other stuff,” is the deviation of each observation to the mean.…”

“…At this point of the PPDCAC cycle, the task is to explore and model the data based on the problem and hypotheses. Teachers will want to discuss the loss in degrees of freedom, which are “the currency of statistical power” [45], the trade‐off between complexity and interpretability, questions such as bias and variance, and the fundamental difference between explanation and prediction [44], among others. Another advantage of the modeling approach is that most statistical tests can be expressed by linear models [23].…”

“…Compared to the parallelly developed curriculum by Son, Blake, Fries, et al [45], we start somewhat later with the data generating process in our curriculum, but we both come to the same modeling approach.…”

Instructed Hand Movements Affect Students’ Learning of an Abstract Concept From Video

“…Although most people get introduced to the concept of modeling when they take graduate‐level statistics, the concept is rarely taught in the introductory undergraduate course. The current studies are situated within a broader project in which we are exploring what it would look like to teach everything in connection with modeling, and then to understand the effects of such an approach on students’ understanding and transfer (Stigler et al, 2020; Son, Blake, Fries, & Stigler, 2020).…”