Erroneous examples versus problem solving: Can we improve how middle school students learn decimals? 

D. Adams, K. Durkin, R.E. Mayer, B. Rittle-Johnson, S. Isotani, M. Van Velsen, Bruce McLaren

In: Naomi Miyake , David Peebles , Richard P. Cooper (Hrsg.). Building Bridges Across Cognitive Sciences Around the World. Annual Conference of the Cognitive Science Society (CogSci-2012) Proceedings of 34th Meeting of the Cognitive Science Society August 1-4 Sapporo Japan ISBN 978-1-62276-304-7 e-media with Curran Associates, Inc. 11/2012.


Erroneous examples versus problem solving: Can we improve how middle school students learn decimals? In N. Abstract Worked examples have been found to be effective tools in reducing cognitive load and supporting learning. Erroneous examples are worked examples that include incorrect steps and are intended to help students learn how to identify important principles and errors to avoid. The current study examines whether using erroneous examples in an online intelligent tutoring system can help middle-school children learn decimals beyond simple problem solving with feedback. Results showed that although students did not differ between the two conditions on an immediate posttest, students in the erroneous examples group performed better on a delayed posttest. This suggests that working with errors, and thus processing the decimal problems at a deeper level, helped students retain more about decimals and build upon that understanding over time. Worked Examples and Math Learning One effective method that has been applied to mathematics education to increase learning is worked-out-examples (also called worked examples). Worked examples consist of a problem formation, the steps taken Worked examples may be effective because they facilitate learning by helping to manage intrinsic processing levels (i.e. cognitive processing required to learn the material presented in a lesson); decreasing extraneous processing (i.e., cognitive processing that does not support the instructional goal); and by encouraging generative processing (i.e., cognitive processing that enables deeper learning). According to the cognitive theory of multimedia learning (Mayer, 2009) and cognitive load theory from which it is derived (Moreno and Park, 2010) learners have a limited processing capacity in working memory and every learning task has an intrinsic level of processing required to understand and learn the task. During problem solving such as mathematics, students use strategies such as means-ends analyses to solve problems, comparing the state of the problem to the goal state and trying to reduce the differences (Renkl and Atkinson, 2010). Over time they develop procedural and schematic knowledge that facilitates problem solving. Worked examples can decrease both intrinsic and extraneous cognitive processing during learning by showing the students the solution procedures to follow. The freed up cognitive resources can then be applied to understanding and eventually to automatizing the different steps in the problem's procedure. A study by Cooper and Sweller (1987) compared learning by doing/traditional problem solving and learning from worked examples. The results showed that participants in the learning by examples group could answer …

Deutsches Forschungszentrum für Künstliche Intelligenz
German Research Center for Artificial Intelligence