# The Performance of Learners’ Strategic Flexibility and Its Relationship with External Factors and Cognitive Flexibility: A Survey of High School Mathematics in China

## TL;DR

This study explores how high school students in China use flexible strategies in math and how this relates to their cognitive abilities and external factors.

## Contribution

The study introduces a new framework linking strategic flexibility in trigonometry with cognitive flexibility and external factors in high school education.

## Key findings

- Actual strategic flexibility in trigonometry is higher than potential strategic flexibility among students.
- Cognitive flexibility positively influences both potential and actual strategic flexibility.
- Subject combinations, but not gender or class, impact strategic flexibility in math.

## Abstract

As a behavioral ability, flexibility plays an indispensable role in human learning activities. However, the analysis of flexibility in specific disciplines has not yet been fully explored. In response, through trigonometry of mathematics, this study investigated the strategic flexibility of high school level students, examining the influence of external factors such as gender and class on flexibility, and exploring the relationship between cognitive and strategic flexibility. Based on the four-stage flexibility test and the cognitive flexibility questionnaire survey of 237 11th-grade students in China, the current research yielded the following findings: (1) There is a positive correlation between potential strategic flexibility and actual strategic flexibility, and the actual strategic flexibility level of students is higher than that of potential strategic flexibility. (2) Gender and class have no significant relationship with strategic flexibility, but different subject combinations have a certain impact on flexibility. (3) Cognitive flexibility has a positive effect on both potential strategic flexibility and actual strategic flexibility. These findings have provided some research basis for understanding students’ external performance and adjusting teachers’ teaching behaviors, proposing a certain adjustment direction for the focus of teaching, students’ learning content, and classroom teaching methods.