The mathematical flexibility of college students: The role of cognitive and affective factors

Background: Traditional math instruction that emphasizes procedures and rote memorization is common in math classes, particularly within the United States. Students may be able to perform steps and recite information, but flexible thinking in math is also an important ability. Lay theories assume that extensive experience in math would lead to increased flexibility, but some research has posited a change-resistant account, which argues that experience with traditional instruction may make it difficult to think flexibly about even simple concepts.

Aims: The current study explored the mathematical flexibility of college students who completed their K-12 education in the United States, and investigated how affective and cognitive factors contributed to flexible thinking.

Sample: Participants were 128 undergraduate students at a competitive U.S. public university.

Method: Mathematical flexibility was measured through a novel task that asked participants to generate as many strategies as they could for a simple arithmetic problem. These strategies were coded to create scores of fluency (number of strategies) and flexibility (number of unique strategies).

Results and conclusions: On average, participants were only able to provide little more than three unique strategies beyond the primary strategy taught in K-12 classrooms. Measures of math anxiety, math identity, need for cognition, and working memory were all unrelated to flexibility. However, student perceptions of how many possible solutions exist were significantly related to flexibility. These results provide evidence for a change-resistance account and provide further evidence that math flexibility is a unique construct.