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Effects of instructions and representation on mathematical problem-solving.
Naoko Kuriyama1, Kimihiko Yamagishi, Takashi Kusumi
1Graduate School of Decision Science and Technology, Tokyo Institute of Technology, Japan. naoko.kuriyama@nifty.com
Psychological Reports
|December 3, 2003
Summary
Specific instructions shape how problems are represented, influencing errors in permutation problem-solving. Subgoal instructions significantly reduced common mistakes compared to control groups.
Area of Science:
- Cognitive Psychology
- Educational Psychology
- Problem-Solving Research
Background:
- Understanding how task representations influence problem-solving is crucial.
- Investigating the impact of specific instructional methods on error patterns is needed.
Purpose of the Study:
- To determine if different instructions create distinct representations for permutation problems.
- To ascertain if task representations primarily affect error direction in problem-solving.
Main Methods:
- 39 participants were randomly assigned to three groups: equation instruction, subgoal instruction, and control.
- Participants were given an identical problem description but varied instructions.
- Performance and error types were analyzed across groups.
Main Results:
- Treatment groups (equation and subgoal instructions) solved the problem more accurately than the control group.
- Subgoal instructions, providing a set of steps, notably decreased typical errors.
- Instruction type significantly influenced the direction of common mistakes.
Conclusions:
- Instructional framing impacts cognitive representations of problems.
- Subgoal instructions offer a promising strategy to mitigate specific errors in permutation tasks.
- Findings have direct implications for designing effective educational interventions.