Fostering Transfer in Intro Stats: A Modeling-First Curriculum Grounded in Practicing Connections Pedagogy

• In Event: AER Roundtable Session Friday 1:45 pm - Gold 4
  In Roundtable Session: Reimagining Introductory Statistics: A Research-Practice Partnership Model for Impactful Statistics Education

Abstract

Theoretical Framework and Objectives
Learning sciences emphasizes the value of helping students make connections across concepts, representations, and contexts. Yet, traditional introductory statistics instruction often fragments learning, presenting hypothesis tests as isolated decision rules rather than part of a larger system. In contrast, our approach draws on the Practicing Connections Hypothesis (Fries et al., 2021) and introduces a modeling-first approach centered on the general linear model (GLM) to support deeper, more connected understanding. Framing an introductory statistics curriculum around Data = Model + Error provides a coherent structure that helps students build conceptual knowledge and extend it across contexts. The aims of this presentation are to describe how this curriculum (which includes an interactive textbook and in-class activities) supports students in making connections to the core concept of Data = Model + Error and to present evidence from a course using this curriculum that this approach not only enhances in-course learning but also fosters transfer to more advanced models.

Methods and Implementation
In the course, students encounter the Data = Model + Error framework early, starting with intuitive word equations (e.g., Lung Function = Smoking + Other Stuff). These word equations serve as a starting off point for representing the idea that Smoking can help us predict Lung Function, with some degree of error. This same idea is then translated into visualizations of these relationships, as well as R code for fitting the model, while also learning to interpret the model coefficients, and connecting the model's output directly to the data it describes. See
Figure 1 for examples of these representations (word equations, R code, visualizations, and GLM notation). The goal of this is to help students make connections between these various representations, across a variety of contexts, rather than feeling like they are learning a bunch of disconnected bits of information. In our presentation, we will share trends in student work from one specific class as they progress through the course and develop their understanding of this core concept.

Results: Evidence of Transfer
To assess whether the modeling first approach fosters both in-course learning and transfer to more advanced GLM concepts, we gathered preliminary data from an introductory statistics course for psychology majors at UCLA (N=458). Students had not studied multivariate models, but were given optional extra credit questions after the final exam to evaluate their ability to extend their understanding. They were asked questions (see Figures 2-5) designed to assess their ability to reason about and represent a multivariate model. Results showed that most students were able to successfully stretch their understanding from single-predictor models to a multivariate model.

Significance
A modeling-first approach, grounded in a practicing connections pedagogy, provides students with meaningful entry points into the broader world of statistical modeling, fostering flexible understanding that extends beyond introductory content. Such grounding not only supports immediate course learning but also prepares students to transfer their knowledge to advanced topics such as polynomial models, multivariate methods, and even neural networks.

Authors

• Caylor Davis, CourseKata

• Mariela Rivas, University of California - Los Angeles