S07: Design aspects of contingency tables and student reasoning

Information

Categorical data is growing in prevalence, thus it is increasingly important for students to understand bivariate categorical data. It is important that we understand how students reason and I report insight into student reasoning about independence from a qualitative study with middle and high school students who have demonstrated an aptitude for prerequisite proportional reasoning. These students who have not yet had AP Statistics reasoned efficiently and differently based on different aspects of the data provided and they used both an odds and risk-based approach. In this poster, I present a flowchart and framework for student reasoning. The way we sequence instruction matters. From a simple two-by-two table to one with higher dimensions, there are many aspects of contingency tables besides dimensions to consider. Some aspects, like contradictory contexts (e.g., smoking and lung disease) have been studied repeatedly, but others like whether there is a clear explanatory and response variable or whether there is a population comparison are absent from the literature. These aspects can impact how students reason and should be considered when designing and sequencing instructional material. In this poster, I identify nine different aspects of contingency tables and include related findings from the literature.