The Effect of Integrated Mathematical Modeling and GeoGebra on Students’ Learning of Trigonometric Functions: A Mixed-Methods Study

Document Type : Original Article

Authors

1 PhD student, Department of Mathematics, Institute of Convergin Sciences and Technologies, SR.C., Islamic Azad University ,Tehran, Iran

2 Professor, Department of Mathematics, Tarbiat Modares University, Tehran, Iran

3 Associate Professor, Department of Mathematics, Institute of Convergin Sciences and Technologies, SR. C., Islamic Azad University ,Tehran, Iran

4 Associate Professor, Department of Statistics, Institute of Convergin Sciences and Technologies, SR. C., Islamic Azad University ,Tehran, Iran

Abstract

The present study investigated the effect of an integrative instructional intervention combining mathematical modeling activities with GeoGebra on students’ performance in learning trigonometric functions. A quasi-experimental pretest–posttest design with two main groups (experimental and control) was employed. The final sample included 270 eleventh-grade students (132 in four experimental subgroups and 138 in four control subgroup). Data were collected using problem-based tests grounded in mathematical modeling and analyzed based on students’ technical skills in GeoGebra and conceptual modeling levels. The experimental group received GeoGebra-based mathematical modeling instruction, whereas the control group was taught using traditional methods without technology. Quantitative analyses using one-way ANCOVA indicated significant improvements in students’ performance (p < 0.001) with large effect sizes for digital technology (η² = 0.715) and mathematical modeling (η² = 0.712). Comparison of the two interventions showed no significant difference (p = 0.339), indicating the positive impact of both approaches. Qualitative findings revealed that students’ active learning, group interaction, and deeper conceptual understanding were enhanced. Overall, integrating digital technology and mathematical modeling provides an effective model for interactive instruction and improving students’ performance in complex mathematical topics.

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History

  • Receive Date: 29 November 2025
  • Revise Date: 09 February 2026
  • Accept Date: 18 April 2026
  • First Publish Date: 15 June 2026
  • Publish Date: 23 September 2026

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