"Learning from Misconceptions in Mathematics Instruction: Testing Teacher Intuitions"

SRCD 2019 Biennial Conference
March 21-23, 2019
Baltimore, Maryland

Title: Learning from Misconceptions in Mathematics Instruction: Testing Teacher Intuitions (Poster)
Session: Education, Schooling
Authors: Emily A. Lyons, Lindsey Richland

Abstract: Background: In order to be prepared for advanced math and eventual STEM careers, students must develop conceptual frameworks for quantitative reasoning. Comparing and contrasting solution strategies, including misconceptions, is a powerful instructional strategy that can promote deep conceptual understanding by encouraging students to think relationally (Rittle-Johnson & Star, 2007, Durkin & Rittle-Johnson, 2012). Discussion of misconceptions can encourage students to more critically assess the rationale behind correct solution strategies (VanLehn, 1999). However, when presenting a misconception during instruction there is also the risk that students will adapt the incorrect solution strategy. In a previous study, we interviewed 5th grade math teachers on including discussion of a common misconception when teaching ratio. These teachers had strong intuitions about when misconception discussion would be more vs. less useful. Specifically, many teachers suggested that discussion of misconceptions would be more useful when the incorrect solution strategy was student-generated (as opposed to presented by the teacher) and among students with higher prior knowledge. Teachers also worried that presenting an incorrect strategy could lead students with poor attention to adapt that misconception.

Building upon these teacher intuitions, the current study tests whether student’s self-generation of the misconception, attentional control, and prior knowledge predict learning and interest during a math lesson on ratio that compared a correct strategy (lowest common multiple) with a common misconception (subtraction). Study participants were 181 socioeconomically and racially diverse 5th grade students drawn from 5 schools in the Chicago area.

Study procedures were administered in three sessions. In session 1, students completed a pretest. During session 2, students viewed a video lesson on ratio that compared a correct strategy with a common misconception. After the lesson, students completed an immediate posttest and a situational interest survey. At session 3, students completed a delayed posttest and the d2 measure of attentional control (Brickenkamp & Zillmer, 1998).

Findings were grouped in three categories.

1. Student Generation of misconception: Students who, at pretest, generated the misconception on their own had larger immediate, F(1,179)=17.04, p<0.001, and sustained, F(1,179)=13.09, p <0.001, gains in correct content than students who did not attempt subtraction at the pretest (p < 0.01). These students also reported higher interest during the lesson (p <0.05).
2. Student attentional control: Students higher in attentional control learned more from the lesson. Students’ d2 score predicted larger immediate, r (179)= 0.17, p <0.05, and sustained, r(179)=0.27, p<0.01, gains in correct content and smaller immediate, r (179)= -0.21, p<0.01, and sustained, r (179)=-0.24, p<0.01, uptake of the misconception, but did not predict interest.
3. Prior Knowledge: Students use of correct content at the pretest did not predict immediate or sustained gains or interest.

Partially corroborating the teachers’ intuitions, we found that students higher in attentional control and who generated the misconception on their own at the pretest learned more from the lesson, but that students who performed poorly on the pretest learned just as much from the lesson as their counterparts with higher initial math knowledge.