When non-experts learn new concepts, it is more effective for them to study step-by-step solutions to solved problems (worked examples) than to attempt solving problems. Worked examples are effective only when learners self-explain the solutions and when multiple, varied worked examples of the same concept are provided. Worked examples are most effective for non-experts (i.e. most of our students most of the time). Experts benefit more from attempting to solve problems than from studying worked examples.

- Provide learners fully worked examples and require them to self-explain solutions through asking students follow-up questions (ex: ‘Why was this strategy used?’, ‘What principle is being applied and why?’), annotating solutions, identifying an error in a solution or asking students to compare solutions of two contrasting examples.
- As learners become more expert with a concept, fade support by asking them to solve more and more steps within a problem.

18.02 Multivariable Calculus | Denis Auroux**:**

Worked examples are used extensively in 18.02. Most units in the course contain recitation videos, which provide step-by-step guidance for solving problems, as well as a large number of written worked examples. In 18.02, students are encouraged to watch the recitation videos and study multiple worked examples. To reinforce self-explanations, which are crucial to obtain the worked example effect, instructors should intersperse a worked example recitation video or class demonstration with questions to get students to think about how a given problem is being solved.

Key resource:

- Renkl, A. (2014). Learning from worked examples: How to prepare students for meaningful problem solving. In V. A. Benassi, C. E. Overson, & C. M. Hakala (Eds.).
*Applying science of learning in education: Infusing psychological science into the curriculum.*HTTP (downloaded PDF available)

Additional:

- Chi, M., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems.
*Cognitive Science*, 13(2), 145–182. DOI - Cooper, G., & Sweller, J. (1987). Effects of schema acquisition and rule automation on mathematical problem-solving transfer.
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*Journal of Educational Psychology*, 93(3), 579–588. DOI - Kalyuga, S., & Renkl, A. (2010). Expertise reversal effect and its instructional implications: Introduction to the special issue.
*Instructional Science*, 38(3), 209–215. DOI - Paas, F., & Van Merriënboer, J. (1994). Variability of worked examples and transfer of geometrical problem-solving skills: A cognitive-load approach.
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*Educational Psychology Review*, 22(4), 379–392. DOI - Schwonke, R., Renkl, A., Krieg, C., Wittwer, J., Aleven, V., & Salden, R. (2009). The worked-example effect: Not an artifact of lousy control conditions.
*Computers in Human Behavior*, 25(2), 258–266. DOI - Schworm, S., & Renkl, A. (2007). Learning argumentation skills through the use of prompts for self-explaining examples.
*Journal of Educational Psychology*, 99(2), 285–296. DOI - Sweller, J., & Cooper, G. A. (1985). The use of worked examples as a substitute for problem solving in learning algebra.
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