To Err Is Human, to Explain and Correct Is Divine: A Study of Interactive Erroneous Examples with Middle School Math Students

McLaren, Bruce M.; Adams, Deanne M.; Durkin, Kelley; Goguadze, George; Mayer, Richard E.; Rittle‐Johnson, Bethany; Sosnovsky, Sergey; Isotani, Seiji; Velsen, Martin van

doi:10.1007/978-3-642-33263-0_18

Cited by 33 publications

(42 citation statements)

References 17 publications

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“…We have conducted two previously published studies with interactive erroneous examples [10,11]. In the first study [10] an interactive erroneous examples condition did not lead to learning benefits compared to a worked examples condition and problem solving condition.…”

Section: Our Erroneous Examples Studies and Resultsmentioning

confidence: 99%

“…Our second study [11] was conducted after revising the interactive erroneous examples along these two dimensions (i.e., simplifying the self-explanation step by prompting for only a single sentence completion phrase and prompting students to correct errors). With 100+ students in each of two conditions -interactive erroneous examples and supported problem solving -an effect was found: students who worked with the interactive erroneous examples did significantly better than the problem solving students on a delayed posttest (but not on an immediate posttest).…”

Section: Our Erroneous Examples Studies and Resultsmentioning

confidence: 99%

“…Our third study, which will be published in a forthcoming journal article, employed the same materials as described in [11] but entailed a much larger population of students. More specifically, our latest results are a combination of the [11] results and the running of the study five more times at three additional schools over the course of a year.…”

Section: Our Erroneous Examples Studies and Resultsmentioning

confidence: 99%

Section: Our Erroneous Examples Studies and Resultsmentioning

confidence: 99%

“…More specifically, our latest results are a combination of the [11] results and the running of the study five more times at three additional schools over the course of a year. The total number of subjects per condition is more than three times that of [11] -over 300 students per condition. In addition, a third condition of 82 students, in which subjects were presented with erroneous examples in adaptive fashion, based on a Bayes Net assessment of their misconceptions on the pretest, was included in the final three versions of the study.…”

Section: Our Erroneous Examples Studies and Resultsmentioning

confidence: 99%

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Erroneous Examples as Desirable Difficulty

Adams

McLaren

Mayer

et al. 2013

Lecture Notes in Computer Science

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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

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Section: Our Erroneous Examples Studies and Resultsmentioning

confidence: 99%

Section: Our Erroneous Examples Studies and Resultsmentioning

confidence: 99%

Section: Our Erroneous Examples Studies and Resultsmentioning

confidence: 99%

Section: Our Erroneous Examples Studies and Resultsmentioning

confidence: 99%

Section: Our Erroneous Examples Studies and Resultsmentioning

confidence: 99%

See 3 more Smart Citations

Erroneous Examples as Desirable Difficulty

Adams

McLaren

Mayer

et al. 2013

Lecture Notes in Computer Science

Self Cite

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The potential of learning from erroneous models: comparing three types of model instruction

Wijnen

Mulder

Alessi

et al. 2015

System Dynamics Review

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Learning from computer models is a promising approach to learning. This study investigated how three types of learning from computer models can be applied to teach high-school students (aged 14-17) about the process of glucose-insulin regulation. Two traditional forms of learning from models (i.e. simulating a predefined model and constructing a model) were compared to learning from an erroneous model. In this innovative form of learning from computer models, students are provided with a model that contained errors to be corrected. As such, students do not have to engage in the difficult task of constructing a model. Rather, they are challenged to work with and correct the model in order for the simulation to generate correct output. As predicted, learning from erroneous models enhances learning of domain-specific knowledge better than running a simulation or constructing a model.

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