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Effects of solving related proofs on memory and transfer in geometry problem solving
1Department of Psychology, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213-3890.
Summary
Diagrams are key to geometry problem-solving memory. Solving similar problems interferes with memory, impacting future problem-solving transfer, especially when steps conflict.
Area of Science:
- Cognitive Psychology
- Educational Psychology
- Mathematics Education
Background:
- Memory plays a crucial role in cognitive tasks.
- Understanding how memory influences problem-solving is vital for effective learning.
Purpose of the Study:
- To investigate the relationship between memory and problem-solving in geometry theorem proving.
- To determine the factors influencing memory recall and problem-solving transfer.
Main Methods:
- Three experiments were conducted involving geometry theorem proving tasks.
- Examined retroactive interference and problem-solving transfer based on diagram similarity and logical steps.
Main Results:
- Memory for geometry problems is primarily based on diagrams, not logical similarity.
- Problem-solving transfer is reduced when initial problems share the same diagram.
- Memory interference, particularly with conflicting steps, significantly impairs transfer.
Conclusions:
- The visual structure (diagrams) is a critical component of memory in geometry problem-solving.
- The quality and structure of problem-solving memories directly impact the ability to transfer knowledge to new problems.