Trade-offs between grounded and abstract representations: evidence from algebra problem solving.

Area of Science:

• Cognitive Psychology
• Mathematics Education
• Learning Sciences

Background:

• Grounded representations (e.g., story problems) are concrete and familiar.
• Abstract representations (e.g., algebraic symbols) are concise but lack physical referents.
• Prior research showed a verbal advantage for simple problems.

Purpose of the Study:

• To investigate the trade-offs between grounded and abstract representations in early algebra.
• To extend prior findings to both simple and complex problems.
• To examine these effects in college student samples.

Main Methods:

• Comparing problem-solving performance on analogous story problems and equations.
• Analyzing performance across simple and complex algebraic problems.
• Utilizing two samples of college students.

Main Results:

• A verbal advantage was replicated for simple problems, with students performing better on story problems.
• A symbolic advantage emerged for complex problems, with students performing better on equations.
• Performance differences highlight the complementary nature of representation types.

Conclusions:

• Grounded, verbal representations are advantageous for simpler early algebra tasks.
• Abstract, symbolic representations are advantageous for more complex early algebra tasks.
• A trade-off exists, suggesting optimal representation choice depends on problem complexity.