Mistakes on display: Incorrect examples refine equation solving and algebraic feature knowledge

Abstract

SummaryAlthough findings from cognitive science have suggested learning benefits of confronting errors (Metcalfe, 2017), they are not often capitalized on in many mathematics classrooms (Tulis, 2013). The current study assessed the effects of examples focused on either common mathematical misconceptions and errors or correct concepts and procedures on algebraic feature knowledge and solving quadratic equations. Middle school algebra students (N = 206) were randomly assigned to four conditions. Two errorful conditions either displayed errors and asked students to explain or displayed correct solutions and primed students to reflect on potential errors by problem type. A correct example condition and problem‐solving control group were also included. Studying and explaining common errors displayed in incorrect examples improved equation‐solving ability. An aptitude‐by‐treatment interaction revealed that learners with limited understandings of algebraic features demonstrated greater benefits. Theoretical implications about using examples to promote learning from errors are considered in addition to suggestions for educational practice.