Understanding Student Attempts to Find a Line of Fit

Abstract

Summary The least squares method of fitting a line is not one that naturally occurs to students. We present three tasks to understand student views on how lines may be fit.

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

“…In accordance with the work of Sorto et al (2011), this type of task was deemed effective at eliciting students' conceptions regarding the line of best fit; thus the protocol for this study included posing five similar tasks to the participants. The students followed this procedure for a series of five scatterplots for contextual data sets with eight ordered pairs each.…”

“…Next the students were presented with Task 6, an adaption of the third task used by Sorto et al (2011). The scenario for this task was that two students, Angelo and Barbara, were given the same task the participating students were given in Task 1: to find the line of best fit for the data on a golf ball's drop height and bounce height.…”

“…The current study builds on research by Sorto et al (2011) who investigated university students' methods for drawing the line that best fit the data and whether these methods agree with the method of least-squares. The most relevant part of this study for the purposes of the present study was its methodology.…”

“…Informally finding a line of best fit, where students are naturally developing their own methods, criteria, and properties for the line of best fit, has been included in curriculum standards for more than two decades (e.g., National Council of Teachers of Mathematics (NCTM) 1989; NCTM 2000), yet students' conceptions of line of best fit are largely undocumented. A review of the literature found only one study that examined university students' conceptions of the line of best fit (Sorto, White, and Lesser 2011). Most significantly, empirical research has not examined what conceptions are held by younger (ages 11-14) students who are studying this topic for the first time.…”

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

“…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, ).…”