# The Priming Effect of Auxiliary Line Construction on Mathematical Creative Thinking: An fNIRS Study

## TL;DR

This study shows that practicing geometric problem-solving with auxiliary lines boosts mathematical creativity, as shown by brain activity and test results.

## Contribution

It demonstrates that short-term auxiliary line construction primes mathematical creative thinking through specific brain activation and connectivity changes.

## Key findings

- The auxiliary line group scored higher in fluency and originality of mathematical creative thinking.
- The auxiliary line group showed stronger activation in the right superior frontal gyrus during the priming phase.
- Post-test brain connectivity showed a lower clustering coefficient and reduced small-world network properties in the auxiliary line group.

## Abstract

Auxiliary line construction has been identified as a crucial approach to fostering mathematical creative thinking. However, existing studies have only focused on the correlations between auxiliary line construction tasks and mathematical creative thinking, without investigating whether engaging in auxiliary line construction can improve mathematical creativity. As a well-established research paradigm, cognitive priming can elicit changes in thinking within a short period. Based on this idea, the present study adopted the cognitive priming paradigm combined with functional near-infrared spectroscopy (fNIRS) technology, and randomly assigned 42 Chinese college students to an auxiliary line group or a control group. The students’ brain activity was monitored in real time during the priming phase (the auxiliary line group completed geometric problems requiring auxiliary line construction, while the control group finished proof problems with pre-set auxiliary lines) and the post-test phase (both groups completed a mathematical creative thinking test). The behavioral results showed that the auxiliary line group achieved significantly higher scores in fluency and originality of mathematical creative thinking than the control group in the post-test phase. The fNIRS data revealed that during the priming phase, the auxiliary line group exhibited stronger activation of the right superior frontal gyrus and higher variability in dynamic functional connectivity; meanwhile, in the post-test phase, the right superior frontal gyrus and right middle frontal gyrus maintained robust neural activation, and brain functional connectivity exhibited a lower clustering coefficient and attenuated small-world network properties. This study confirms that short-term engagement in auxiliary line construction exerts a priming effect on the fluency and originality of mathematical creative thinking, which may be associated with the enhanced activation of specific brain regions and the dynamic adjustment of brain functional connectivity. These findings provide theoretical and empirical evidence for the cultivation of mathematical creative thinking.