Exploring students’ ability to translate between mathematical representations in solving quadratic function problems

Abstract

Background: Students often encounter difficulties in translating between mathematical representations when solving quadratic function problems, resulting in fragmented conceptual understanding. These difficulties indicate that the source representation may influence how students construct mathematical meaning across verbal, graphical, and symbolic forms.

Aim: This study explores students' ability to translate between mathematical representations in solving quadratic function problems by examining the influence of different source representations and identifying the characteristics of their translation processes.

Method: This qualitative study adopted an exploratory case study design. Participants were selected through purposive sampling based on variations in their representation translation ability. Data were collected through written problem-solving tasks and semi-structured interviews and analyzed using Braun and Clarke's Reflexive Thematic Analysis.

Results: Students demonstrated different translation patterns depending on the source representation. Verbal and graphical representations were more frequently translated into other forms, whereas symbolic representations were generally retained without further transformation. Three translation characteristics were identified: isolated, sequential, and fragmented, reflecting varying levels of representational coordination.

Conclusion: Students' ability to translate between mathematical representations is influenced by the source representation used during problem solving. Mathematics instruction should explicitly connect verbal, graphical, and symbolic representations to strengthen conceptual understanding and promote more meaningful representation translation.