Flexibility Before Fluency: Exploring How Flexible Strategies Emerge through Collaborative Problem-Solving

Abstract

In K-12 math education, it is important not only to foster fluency but also flexibility in the problem-solving process. Prior works have focused on measuring learning in terms of efficiency or productivity by examining the extent to which students can optimize their problem-solving paths to involve the fewest number of steps. Limited work has paid attention to the notion of flexibility, or the ability to understand and navigate different paths to the same problem. In this study, we examine how middle school students’ use a dynamic notation tool to explore flexible solution paths during collaborative problem solving (CPS) activity. Results show that there are differences in patterns of CPS process between students who demonstrated greater flexibility and those who did not. Specifically, they differed in their engagement with higher-level operations. We discuss the implications for supporting students’ flexible problem solving and teachers in orchestrating CPS for similar goals in classrooms.

Materials

• Full BibTeXapi.crossref.org

Cite

@inproceedings{lee2026flexibility,
  author = {Lee, Seiyon and Zhang, Shan and Li, Hongming and Lee, Ji-Eun and Closser, Avery and Botelho, Anthony F.},
  title = {Flexibility Before Fluency: Exploring How Flexible Strategies Emerge through Collaborative Problem-Solving},
  booktitle = {Proceedings of the 19th International Conference on Computer-Supported Collaborative Learning - CSCL 2026},
  year = {2026},
  pages = {244--253},
  publisher = {International Society of the Learning Sciences},
  doi = {10.22318/cscl2026.591401},
  url = {https://repository.isls.org/handle/1/12470}
}