Overcoming the gap between knowledge and use in mathematical flexibility: Examining the role of inhibitory control

Abstract

Background

Previous research in the domain of equation solving has shown that although students obtain knowledge of multiple strategies, they often use a standard but less efficient strategy. This phenomenon has been framed as a gap between knowledge and use.

Aims

We aim to examine whether using a standard strategy might be a dominant response and whether inhibitory control is needed for students to overcome the knowledge-use gap.

Samples

284 college students participated in the study (n_{Pilot study} = 114, n_Study1 = 62, n_Study2 = 108).

Methods

A time-pressure and a no-choice design was used to examine the frequency of using standard strategies, and the accuracy and speed of using the standard and efficient strategies, respectively (Pilot study). Students completed a dual-inhibition task and a negative priming (NP) task (Study 1). Students’ strategy use was examined in a delayed NP adaptation and a delay intervention in the classroom (Study 2).

Results

Students used standard strategies more frequently under time pressure, indicating the dominance of the standard strategy, even though using efficient strategies was faster. Their performance of using efficient strategies was impaired when inhibition resources were occupied; the observed NP effect reflected the inhibition of the standard strategy when using efficient strategies. A delay intervention improved students’ inhibition process and facilitated their flexibility performance.

Conclusion

This study revealed that applying the standard strategy is often the default tendency for solving algebra equations, and inhibitory control is critical in bridging the gap between possessing knowledge of various strategies and implementing them in mathematical practice.