Informal Inferential Reasoning on Simple Linear Regression Encouraging Critical Thinking

Abstract

Informal inferential reasoning (IIR), described as making evidence-based generalizations about a population based on samples, is considered important for the development of argumentation-, inference-, critical thinking - and aggregate thinking abilities. This article aims to explore how undergraduate students’ IIR can develop in an inquiry problem-solving session on simple linear regression, through individual think-aloud protocols with follow-up conversations with five students. Our findings suggest that enabling and supporting the students to grapple with their own hypotheses is important for their development of IIR encouraging critical thinking. From initial hypotheses with limited argumentation and little regard to the probabilistic nature of statistical inferences, the students’ reasoning evolved in terms of making probabilistic generalizations from data when they were given time and concurrent probing to elaborate on, and question, their own arguments and inferences. We also suggest that in addition to emphasize the signal in the noise, giving attention to the noise around the signal can be fruitful for their IIR.