Inducing mental set constrains procedural flexibility and conceptual understanding in mathematics

Area of Science:

• Cognitive Psychology
• Mathematics Education

Background:

• Flexible strategy use and conceptual understanding are key goals in mathematics.
• Mental set, induced by problem context, can impede strategy flexibility.

Purpose of the Study:

• To investigate how problem-solving context influences the use of efficient strategies in mathematical equivalence.
• To examine the impact of problem order on procedural flexibility and conceptual understanding.

Main Methods:

• Undergraduate and middle school students (N=128) solved mathematical equivalence problems under two conditions: complex-first or shortcut-first.
• Problems involved either multistep strategies or readily available shortcut strategies.

Main Results:

• Students in the complex-first condition were less likely to use the efficient shortcut strategy when available.
• This group also showed reduced procedural flexibility and conceptual understanding on subsequent assessments.

Conclusions:

• The order in which mathematical problems are presented significantly impacts strategy selection and flexibility.
• Problem-solving contexts can either facilitate or obstruct deeper conceptual engagement with mathematical equivalence.