Worked Examples and Self Explanation

• In Event: Bridging Research and Practice: From Cognitive Principles to Design Principles of Curriculum, Instruction, and Assessment

Abstract

Replacing half of the problems in a practice session with examples of how to solve a problem improves student learning (Zhu & Simon, 1987; Clark & Mayer, 2003) because worked examples focus learners on trying to understand the concepts that support correct problem solving instead of guessing at appropriate problem-solving steps and acquiring knowledge or habits that may work for some problems but do not generalize well (Zhu & Simon, 1987; Sweller, 1999). When examining worked examples, students should be prompted to explain them. Such explanation facilitates integration of new information with prior knowledge and forces the learner to make their new knowledge explicit (Chi, 2000; Roy & Chi, 2005). Typical implementation involves providing a correct example and asking students to explain why the solution is correct. However, a growing body of literature suggests that explaining a combination of correct and incorrect examples (i.e., explain why a common incorrect strategy is wrong) can be more beneficial than explaining correct examples alone (Siegler, 2002; Siegler & Chen, 2008; Rittle-Johnson, 2006; Grosse & Renkl, 2007).

Adaptation of the CMP2 curriculum according to the worked example and self-explanation principle is less straightforward than it would be for traditional mathematics textbooks, which tend to present long lists of similar homework problems. Because CMP2 implements a wider variety of different types of homework problems than traditional curricula, we cannot simply replace half of the problems with examples as would be recommended by the practice guide (Pashler et al., 2007a), or students may never have the opportunity to use some procedures demonstrated by worked examples. Instead, we implement the principle in the following way:

The first time a skill is introduced in a homework assignment, we replace the problem with a fully worked out example, in which a fictitious character is said to have solved the problem correctly, all steps of the problem toward finding a solution are presented in handwriting, and a follow-up self-explanation prompt is included to focus the student’s attention on the critical ideas in the problem. The next time that skill is invoked, we provide a partially worked example in which the student is told that a fictitious character started to solve the problem but got stuck. The student is asked to fill in any gaps in the presented work and finish solving the problem and then to complete subsequent problems on his or her own. In addition, one clearly-marked incorrect example is included in each homework assignment; the prompts for correct fully worked examples also often ask students to explain why it would not be appropriate to try to solve the problem using a certain incorrect procedure.

In accordance with learning theory and literature on worked examples, preliminary analysis of think aloud studies involving our adapted CMP2 indicates students are learning and self-correcting as they refer to prior worked examples and problems. In addition, anecdotal evidence suggests students may prefer learning from worked examples as compared to traditional problem solving.

Authors

• Julie L. Booth, Temple University

• Kenneth R. Koedinger, Carnegie Mellon University

• Kenneth R. Koedinger, Carnegie Mellon University