A Case Study: Zander Reasons With Incomplete Contingency Tables and Mosaic Plots

Abstract

Reasoning across multiple representations and incorporating reversibility can enhance and reveal an in-depth view of a student’s understanding. In this paper, we explore how a school-age student reasons about the independence of two categorical variables using contingency tables and mosaic plots. This case study reveals some fine-grained reasoning that highlights the differences between mathematical and statistical thinking, shows an inclination to use a part-part or odds approach, and demonstrates how a mosaic plot was used to solve a problem with incomplete contingency. Ultimately, this study supports the use of incomplete contingency tables and mosaic plots for students to reason about statistical independence.