Learning to prove in geometry: Learning from heuristic examples and how it can be supported

Tatjana S. Hilbert, Alexander Renkl, Stephan Kessler, Kristina Reiss

Research output: Contribution to journalArticlepeer-review

73 Scopus citations


This field experiment tested whether a special type of worked-out examples (i.e., heuristic examples) helps learners develop better conceptual knowledge about mathematical proving and proving skills than a control condition focussing on mathematical contents. Additionally, we analysed the benefits of self-explanation prompts and completion requirements in a 2 × 2-design. The participants' (N = 111 student teachers) proving skills and their conceptual knowledge were significantly better when learning with heuristic examples as compared to the control condition. Completion requirements impaired learning especially in combination with self-explanation prompts. The sole provision of self-explanation prompts, in contrast, fostered conceptual knowledge as well as skills.

Original languageEnglish
Pages (from-to)54-65
Number of pages12
JournalLearning and Instruction
Issue number1
StatePublished - Feb 2008
Externally publishedYes


  • Heuristic examples
  • Learning to prove
  • Self-explanations
  • Worked-out examples


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