European Journal of Psychology of Education

, Volume 14, Issue 4, pp 477–488 | Cite as

Learning mathematics from worked-out examples: Analyzing and fostering self-explanations

  • Alexander Renkl


Recent research has shown that learning from worked-out examples is of major importance for initial skill acquisition in well-structured domains such as mathematics. However, only those learners who actively process the presented examples profit noticeably from this learning mode. Specifically, the learning outcomes depend on how well the learners explain the solution steps presented in the examples to themselves (‘self-explanation effect”). In a series of studies on learning mathematics from examples, learners’ spontaneous self-explanations and instructional means used to encourage self-explanations were investigated. In this research, the following main findings were obtained. Most learners were rather passive with respect to their spontaneous self-explanations. Among the active and successful learners, two subgroups employing different self-explanation styles could be identified. With regard to the instructional means used to induce effective example processing, it turned out that to employ “learning by teaching” in order to stimulate explanation activities was of very limited use. Attempts to directly train for or elicit certain types of self-explanations were more successful. However, even in the latter case, self-explanations had inherent deficits (e.g., proneness to errors). Thus, we sought to design learning arrangements that try to integrate self-explanations with well-timed and well-adapted instructional explanations (e.g., from tutors) in order to enhance students’ problem-solving skills.


Metacognitive Knowledge Successful Learner Solution Step Instructional Explanation Comprehension Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Instituto Superior de Psicologia Aplicada, Lisbon, Portugal/ Springer Netherlands 1999

Authors and Affiliations

  1. 1.Department of Educational PsychologyUniversity of FreiburgFreiburgGermany

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