Studying the Relationship Between Students’ Perception of the Mean and Their Understanding of Variance

• Activity Number: 125 - SPEED: Modernization of What, How, and Where We Teach Statistics Part 1
• Type: Contributed
• Date/Time: Monday, July 29, 2019 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and Data Science Education
• Author(s): Robert Sigley* and Layla Guyot and Alexander White
• Companies: Texas State University and Texas State University and Texas State University
• Keywords: Introduction to Statistics; perspectives of the mean; variance

Abstract

A key idea in an Introduction to Statistics course is the mean as not only a measure of central tendency but as a measure of variability. Policy documents (e.g., Gaise Report) stress the importance of students having multiple conceptions of the mean such as a measure of center and as a balance point. In this talk, we intend to explore how a student’s conception of the mean influences their thinking about variation. This qualitative study took place at a large four-year college in the United States. The participants (n=7) viewed the mean through different representations (e.g., balance beam, leveling off) and expressed what they attended to when determining the mean and variation of a dataset. When viewing the mean as a balance point, the participants focused on the mode and symmetry of the data around the mode leading to faulty inferences about the variation. In the leveling off approach, the participants focused on the distance of the data points from the mean which they used to make correct inferences about variation. This talk will highlight the differences in both approaches among the participants and discuss the implications for teaching this topic in courses.