Learning from solution examples

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Learning from solution examples is a teaching method . A complete solution example consists of a task, the solution path and the solution to the task. In the method, the students follow several examples of the same solution in order to recognize the underlying solution principle. Through a special sequencing with targeted variation of the solution principle and / or the contextual integration (surface feature) of the examples, near and far knowledge transfer can be stimulated. The method uses the solution example effect and the effectiveness can be explained by the cognitive load theory . To increase the effectiveness of the method, it has proven useful to include questions for self-explanations with the examples. These are intended to stimulate active examination of the examples and to prevent superficial consumption. The method is suitable at the beginning of a new topic. With the help of incomplete or incorrect solution examples, it can also be used to close a topic. With increasing expertise in a subject area, the strength of the solution example effect or the learning effectiveness of the method decreases. This fact is known as the expertise reversal effect . Use cases of the method are well documented, especially in mathematics. But there are also suggestions from the field of industrial-technical, commercial and medical training.

Theoretical background

Name factor in the method is the solution as effect (Worked-example effect). This describes the superiority of learning with worked out solution examples over problem solving. This effect can be explained with the help of the cognitive load theory : It is assumed that the cognitive load (intrinsic cognitive load) is much higher when solving problems than when learning from solution examples. This is why more cognitive resources (German Load) are available for the process of understanding and acquiring schemes when learning with example solutions than when solving problems.

In addition to the cognitive psychological justification, there is also a motivational psychological justification: Instead of solving a problem (performance orientation) with the associated “trial and error” and the thought “the main thing is to have a solution”, the learners concentrate on understanding examples. The method is perceived as targeted and efficient. Therefore, learners prefer to use this method when they have the choice between an example and a textual explanation.
With the increasing expertise of the learners, the above-mentioned expertise reversal effect threatens to occur. Didactic measures such as structuring and learning aids, which help novices learn, become superfluous for experts and hinder the acquisition of knowledge.

Classic solution examples in the context of lessons

Usually, solution examples are used in the classroom as follows:

  1. A theorem is developed by the teacher or presented by the textbook.
  2. The teacher provides an example for this theorem or a completely solved task follows in the textbook. This example is intended to illustrate the application of the theory.
  3. After the students have followed the example, they should solve similar tasks independently.

The transition from step 2 (sample study) to step 3 (task processing / problem solving) takes place too quickly and places too high demands on the learners.

The method

The learners receive several (at least two) solution examples. These are based on the same solution principle. The learners try to understand this example solution. Finally, the knowledge gained is discussed in the plenary and recorded in writing.

Questions about self-declaration

Self-explanatory questions should be used to control the sample study and to avoid passive sample consumption. These can not only be questions, but also tasks. Possible examples are:

  • Find subheadings for steps 1 - 4!
  • Why can the root be pulled in step 3? (State requirements)
  • Which law was used for the solution?
  • With what aim was the root pulled in step 3?

For inexperienced learners, self-declaration training can increase the quality of the self-declaration and thus also the learning effectiveness. The teacher works on an example and follows each step in the solution thinking out loud. Then the learners work on a similar example. You can get the help of the teacher. Learners without prior knowledge in particular benefit greatly from self-explanatory training.

Example sequences that accentuate surfaces and principles

The solution principle of an example can be repeated in different contextual embeddings. For example with the rule of three with a proportional structure:

  • Surface feature "pumping the flooded basement empty": more pumps - more power
  • Surface feature "painting the wall": more assistants - more performance

Since the surface features that are irrelevant to the solution are varied and the underlying solution structure remains the same, this is referred to as a principle-accentuating example sequence.
Furthermore, it is possible to deal with different solution principles in the same content-related embedding. For example, the rule of three with proportional and anti-proportional structure:

  • Surface feature "pumping the flooded basement dry", inversely: more pumping - less time
  • Surface feature "pumping the flooded basement dry", proportional: more pumps - more power

Such a sequence is therefore called surface accentuating. With the help of the targeted variation of these characteristics, a near to further transfer can be stimulated. The different types of sequencing of the examples is also referred to as an inter-example feature.
The graphic and textual design of an individual example is referred to as intra-example characteristics. In particular, the term " integrated format " is often mentioned. Information that belongs together is arranged in such a way that the allocation performance is as low as possible.

Incomplete and incorrect solution examples

In the advanced learning process, there are incomplete solution examples. The solution is deliberately presented with gaps. The learners then have to complete the solution. At the end of a topic, if the learners should be experts in the topic, incorrect solution examples can be used. The learners then have to find the mistake in the wrong solution. The expertise reversal effect can be avoided through incomplete and incorrect solution examples.

The transition to problem solving

The learner can be introduced to a problem by gradually reducing the number of solution hints (incomplete solution examples). If you leave out all help, he is faced with a problem.

Criticism of the method

Frequently mentioned points of criticism of the method are:

  1. Only algorithms can be learned.
  2. It does not encourage deeper understanding.
  3. Multiple solutions are not possible.
  4. The solution examples are only worked through superficially.
  5. It reduces the incentive to find your own (creative) solutions.

The first two points can be invalidated since there have been successful tests with heuristic solution examples. The third and fourth points of criticism can be avoided by designing appropriate examples. Only the last point of criticism cannot be refuted. For this reason, and because of the expertise reversal effect mentioned above, the method cannot (and should) not be used in every phase of the learning process.

Individual evidence

  1. ↑ Tatjana S. Hilbert, Alexander Renkl, Lars Holzäpfel: Oh, that's how it works! Practice with solution examples. In: Teaching Mathematics. No. 147, 2008.
  2. ↑ Tatjana S. Hilbert et al: Cognitively active - but how? Learning with self-explanations and solution examples. In: Teaching Mathematics. No. 135, 2006.
  3. ↑ Simone Herold: Complete or incomplete? An experimental study on learning with solution examples at the vocational school. Master thesis, Heidelberg 2010.
  4. ↑ Andreas Schelten, Alfred Riedl, Robert Geiger: Teaching-learning processes in a constructivist learning environment for control engineering lessons. DFG final report. 2003.
  5. ↑ Robin Stark among others: Learning with solution examples in the initial commercial training. Attempts to optimize a learning method. In: Klaus Beck, Rolf Dubs (Hrsg.): Competence development in vocational training: cognitive, motivational and moral dimensions of commercial qualification processes. Steiner, Stuttgart 1998 ( Journal for Vocational and Business Education: Supplements ), pp. 24–37. (online at: epub.uni-regensburg.de )
  6. ↑ Veronika Kopp, Robin Stark, Martin R. Fischer: Promotion of diagnostic competence in medical training by implementing an approach to case-based learning from solution examples. In: GMS Journal for Medical Education. 24, No. 2, 2007. (online at: egms.de )
  7. ↑ Luzia Zöttl: Promote modeling skills with heuristic solution examples. Franzbecker, Hildesheim et al. 2010, ISBN 978-3-88120-499-6 , p. 21f.
  8. ↑ Alexander Renkl, Silke Schworm, Rudolf Vom Hofe: Learning with solution examples. In: Teaching Mathematics. No. 109, 2001, p. 15.
  9. ↑ Tatjana S. Hilbert et al: Cognitively active - but how? Learning with self-explanations and solution examples. In: Teaching Mathematics. No. 135, 2006, p. 62.
  10. ↑ Tatjana S. Hilbert, Alexander Renkl, Lars Holzäpfel: Oh, that's how it works! Practice with solution examples. In: Teaching Mathematics. No. 147, 2008, p. 47.
  11. ↑ Luzia Zöttl: Promote modeling skills with heuristic solution examples. Franzbecker, Hildesheim et al. 2010, ISBN 978-3-88120-499-6 , p. 24f.
  12. ↑ Alexander Renkl, Silke Schworm, Rudolf Vom Hofe: Learning with solution examples. In: Teaching Mathematics. No. 109, 2001, p. 15.
  13. ↑ Helmut M. Niegemann, Steffi Domagk, Silvia Hessel: Compendium Multimedia Learning. Springer, Dordrecht 2007, ISBN 978-3-540-37226-4 , p. 54.
  14. ↑ John Sweller, Graham A. Cooper: The Use of Worked Examples as a substitute for Problem Solving in learning algebra. In: Cognition and Instruction. No. 1, 1985. (online at: jstor.org )
  15. ^ Jill L. Quilici, Richard E. Mayer: Role of examples in how students learn to categorize statistics word problems. In: Journal of Educational Psychology. 88, No. 1, 1996.
  16. ↑ Xinming Zhu, Herbert A. Simon: Learning Mathematics from Examples and by Doing. In: Cognition and Instruction. 4, No. 3, 1987. (online at: jstor.org )
  17. ↑ Robin Stark: Analysis and Promotion of Example-Based Learning - Application of an Integrative Research Paradigm. Unpublished Habilitation thesis, Munich 2001, p. 128ff. quoted from: Simone Herold: Complete or incomplete? An experimental study on learning with solution examples at the vocational school. Master's thesis, Heidelberg University of Education, 2010, p. 17ff.
  18. ↑ Alexander Renkl, Silke Schworm, Rudolf Vom Hofe: Learning with solution examples. In: Teaching Mathematics. No. 109, 2001, p. 16.
  19. ↑ Alexander Renkl, Silke Schworm, Rudolf Vom Hofe: Learning with solution examples. In: Teaching Mathematics. No. 109, 2001, p. 16.
  20. ↑ Margit Frackmann, Michael Tärre: learning and problem solving in vocational training. Method manual. Bertelsmann, Bielefeld 2009, ISBN 978-3-7639-1124-0 , p. 209.
  21. ↑ Alexander Renkl, Silke Schworm: Learning to teach with solution examples. 263 In: Manfred Prenzel, Jörg Doll (Hrsg.): Educational quality of school. School and extracurricular conditions for mathematical, scientific and interdisciplinary skills. Beltz, Weinheim et al. 2002, ISBN 3-407-41146-4 , pp. 259-270. (PDF; 678 kB)
  22. ↑ Alexander Renkl, Silke Schworm, Rudolf Vom Hofe: Learning with solution examples. In: Teaching Mathematics. No. 109, 2001, p. 262f.
  23. ↑ Alexander Renkl, Silke Schworm, Rudolf Vom Hofe: Learning with solution examples. In: Teaching Mathematics. No. 109, 2001, p. 16f.
  24. ↑ Robin Stark, Veronika Kopp, Martin R. Fischer: Promotion of diagnostic competence in medical students through situated, case-based learning with solution examples. the influence of mistakes and feedback. In: Psychology in Education and Teaching. 56, No. 2, 2009.
  25. ↑ Alexander Renkl, Silke Schworm, Tatjana S. Hilbert: Learning from solution examples. an effective, but rarely used option to design lessons. In: Jörg Doll (Hrsg.): Educational quality of school. Teacher professionalization, lesson development and student advancement as strategies of quality development. Waxmann, Münster / New York / Munich / Berlin 2004, ISBN 3-8309-1399-0 , pp. 88-89.
  26. ↑ Luzia Zöttl: Promote modeling skills with heuristic solution examples. Franzbecker, Hildesheim et al. 2010, ISBN 978-3-88120-499-6 .
  27. ↑ Alexander Renkl, Silke Schworm, Tatjana S. Hilbert: Learning from solution examples. an effective, but rarely used option to design lessons. In: Jörg Doll (Hrsg.): Educational quality of school. Teacher professionalization, lesson development and student advancement as strategies of quality development. Waxmann, Münster / New York / Munich / Berlin 2004, ISBN 3-8309-1399-0 , pp. 88f.