Five key representations for introductory statistics: verbal descriptions, visualizations, word equations, GLM notation, and R code

Design · All designs
Evidence · no claims cited

Description

The textbook asks students to repeatedly translate and connect among five representations: "verbal descriptions, visualizations, word equations, GLM (general linear model) notation, and R code." Students describe models in words, write word equations (e.g., Thumb Length = Height + other stuff), map them to DATA = MODEL + ERROR, write R code, and learn GLM notation, which the authors value for its generalizability, alignability with other representations, and ecological validity. Algebra was deliberately excluded because students do not find it accessible or useful.

Design Implications

Context

Requirements

• Selected representations must be accessible to novices, important for the field, and productive for making connections
• Learning a representational system requires an investment of time and effort, so the set must be limited

Constraints

• GLM notation is described as a difficult representational system for students to learn

Target Learners

• Novice college students in introductory statistics

Learning Goals

• Using and connecting multiple representations of statistical models
• Participating in computational, reproducible data analysis practices

Claims

Related Designs

Examples

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Key Sources

• Fries, L., Son, J. Y., Givvin, K. B., & Stigler, J. W. (2020). Practicing Connections: A Framework to Guide Instructional Design for Developing Understanding in Complex Domains. Educational Psychology Review. https://doi.org/10.1007/s10648-020-09561-x

Page metadata

Field	Value
type	design
id	statistics-five-key-representations
title	Five key representations for introductory statistics: verbal descriptions, visualizations, word equations, GLM notation, and R code
description	The textbook asks students to repeatedly translate and connect among five representations: "verbal descriptions, visualizations, word equations, GLM (general linear model) notation, and R code." Students describe mode...
status	review
generated	by process:settle-candidates on 2026-10-20
trust	unverified — no one has confirmed this page's content
sources	1 — fries-2020

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