Examining Student Conceptions of Covariation: A Focus on the Line of Best Fit

Abstract

The purpose of this research study was to learn about students' conceptions concerning the line of best fit just prior to their introduction to the topic. Task-based interviews were conducted with thirty-three students, focused on five tasks that asked them to place the line of best fit on a scatterplot and explain their reasoning throughout the process. The results include descriptions and categorizations of students' meanings, criteria and methods for placement, accuracy of placement, and interpretation of the line of best fit. The discussion addresses how students' prior study of mathematics and statistics impacted their conceptualizations of the line of best fit as well as implications for the teaching and learning of the line of best fit.

Slope and Line of Best Fit: A Transfer of Knowledge Case Study

“…This presents a challenge for students when they are asked to reason about modeling data with an LOBF. Approximately one‐fourth of the students in Casey's () study challenged the notion of fitting a straight line to data that was not straight (i.e., noncollinear), asking if they could connect the points on the scatterplot to make a “jagged line” instead. Students who are able to place a line informally develop their own criteria for doing so.…”

“…Students who are able to place a line informally develop their own criteria for doing so. Common criteria for both secondary and university students are placing the line so an equal number of data points are on each side of the line and closest to all of the points (Casey, ; Sorto, White, & Lesser, ). Another common approach used by secondary students is to place the LOBF through as many data points as possible (Casey, ).…”

“…Common criteria for both secondary and university students are placing the line so an equal number of data points are on each side of the line and closest to all of the points (Casey, ; Sorto, White, & Lesser, ). Another common approach used by secondary students is to place the LOBF through as many data points as possible (Casey, ). To understand factors that influence students’ approaches to place the LOBF, we must consider the mathematical knowledge that is transferred to the new learning context.…”

“…Our analysis focuses on task‐based interviews with two students, Claire and Sasha (pseudonyms), who participated in a larger study of 33 U.S. eighth grade students and their conceptions of and approaches to placing an LOBF informally (Casey, ). The study was conducted the week before the teaching of LOBF in the mathematics curricula the students were studying, so both students had received instruction on topics considered prerequisite by the curriculum authors (e.g., coordinate graphing, linear functions) and were prepared to study LOBF.…”

“…The term “transitionary student” is used to describe a student who placed an inaccurate LOBF on the first one or two tasks during the interview, but transitioned to placing an accurate LOBF on both tasks three and four. (Accuracy was measured based on proximity to the least‐squares regression line; see Casey, for details.) Claire and Sasha were both identified as transitionary students.…”