Learning Mathematics From Examples and by Doing

@article{Zhu1987LearningMF,
  title={Learning Mathematics From Examples and by Doing},
  author={Xinming Zhu and Herbert A. Simon},
  journal={Cognition and Instruction},
  year={1987},
  volume={4},
  pages={137-166}
}
This article demonstrates the feasibility and effectiveness of teaching several mathematical skills by presenting students with carefully chosen sequences of worked-out examples and problems - without lectures or other direct instruction. Thinking-aloud protocols of 20 students learning factorization by this method are analyzed to determine the kinds and depth of understanding students attained. Students did not simply memorize procedures but were able to recognize when the procedures were… 
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