Erroneous Examples as Desirable Difficulty

Abstract

Abstract.Erroneous examples, an unusual and challenging form of learning material, are arguably a type of desirable difficulty for students that could lead to deeper learning. In a series of studies we have done over the past three years involving web-based math instruction, the learning benefits of erroneous examples we have observed occured on delayed tests, as occurs in the desirable difficulties literature. This short paper briefly reviews the literature, summarizes our results, and speculates on how an adaptive version of our materials could better leverage desirable difficulties theory and lead to deeper student learning.Keywords: erroneous examples, interactive problem solving, adaptation of problems, self-explanation, decimals, mathematics education IntroductionErroneous examples are step-by-step descriptions of how to solve a problem in which one or more of the steps are incorrect. In the studies we have done with erroneous examples over the past three years, focused on learning decimals using web-based, interactive materials, middle school students are prompted to find, explain, and fix error(s) in order to more deeply learn how to solve decimal problems. Presenting students with challenge is central to the notion of learning with erroneous examples. Research on desirable difficulties has shown that it is possible to achieve long-term benefits if lessons are designed (or altered) to make them more challenging during learning [1,2]. Examples of desirable difficulties include mixing the order of tasks for practice (rather than providing tasks in blocked fashion); varying the frequency and timing of feedback (rather than providing immediate feedback); and varying tasks with a focus on generalizability. These changes to standard instructional practice have been shown to slow the rate of improvement in students' understanding during the learning process but lead to long-term benefits [1,2].The erroneous examples we work with can be viewed as presenting desirable difficulties for students in two ways. First, they are an unusual and challenging form of problem, in which students must find, explain, and correct errors, as opposed to the more standard practice of simply solving problems. Although this characteristic is not

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

“…Some prior work on incorrect worked examples suggests that benefits occur at a delay rather than immediate posttest (Adams et al, 2014; Durkin & Rittle‐Johnson, 2012). These delayed benefits are explained as being a result of desirable difficulties while working with errors invoking deeper processing of material which would not show immediate benefits but rather deeper learning over time (Adams, McLaren, Mayer, Goguadze, & Isotani, 2013). Prior work has demonstrated that altering instruction to make it more challenging during learning leads to long‐term benefits (Bjork & Bjork, 2011; Schmidt & Bjork, 1992).…”