Removing opportunities to calculate improves students' performance on subsequent word problems

Area of Science:

• Cognitive Psychology
• Educational Psychology
• Mathematics Education

Background:

• Investigated the impact of removing calculation opportunities on students' word problem-solving skills.
• Two studies explored whether hindering calculation enhances relational understanding of mathematical problems.

Purpose of the Study:

• To determine if preventing calculation improves students' ability to solve novel word problems.
• To test the hypothesis that removing calculation opportunities promotes relational thinking over instrumental thinking.

Main Methods:

• Participants explained either typical word problems or the same problems with numbers removed.
• The non-calculable problem group was expected to engage more in relational thinking.
• Performance on subsequent transfer problems was measured.

Main Results:

• Students explaining non-calculable problems significantly outperformed those explaining calculable problems on transfer tasks.
• The manipulation did not entirely eliminate the desire to calculate; some students invented numbers.
• Higher frequency of invented numbers correlated positively with self-reported math anxiety.

Conclusions:

• Preventing calculation appears to foster relational thinking, leading to better problem-solving transfer.
• Educational interventions for math difficulties should consider students' dispositions towards mathematics.
• Focusing on relational understanding may be more effective than solely addressing skill deficits.