The effects of early schema acquisition on mathematical problem solving

Area of Science:

• Cognitive Psychology
• Educational Psychology
• Mathematics Education

Background:

• Effective learning strategies are crucial for mathematical problem-solving.
• The timing of instructional interventions can significantly impact learning outcomes.
• Worked examples are known to facilitate learning, but their effect on transfer is less understood.

Purpose of the Study:

• To investigate the impact of early versus late schema training on mathematical word problem-solving.
• To examine how the ratio of worked examples to problem-solving practice affects learning and transfer.
• To extend the understanding of the worked example effect to near and far transfer problems.

Main Methods:

• Participants were randomly assigned to one of four conditions manipulating schema training timing and worked example/practice ratio.
• Mathematical word problems, modeled after Graduate Record Examination (GRE) questions, were used for training and testing.
• Performance was assessed on both near and far transfer problems.

Main Results:

• Early schema training led to superior performance compared to late schema training, particularly on far transfer tasks.
• A higher ratio of worked examples to problem-solving practice resulted in better performance than the inverse ratio.
• These findings indicate that instructional design impacts the ability to solve novel mathematical problems.

Conclusions:

• Schema training is most effective when introduced at the outset of learning mathematical word problems.
• Optimizing the balance between worked examples and practice enhances problem-solving transfer.
• Early schema instruction combined with ample worked examples can improve mathematical problem-solving efficacy.