Investigation of the Contribution of ACE Based Designed Mathematical Modelling Instruction to the Modelling Skills of International Baccalaureate Students in the Light of APOS Theory

Authors : Gökçe Kayhan Gencer, Menekşe Seden Tapan Broutin

Pages : 2697-2722

Doi:10.15869/itobiad.1743272

View : 41 | Download : 110

Publication Date : 2025-12-31

Article Type : Research Paper

Abstract :This qualitative study was conducted to investigate the contribution of an instructional program structured on the APOS theory to improve high school students\\\' mathematical modelling skills. The research focused on the first two phases of the modelling process namely, understanding the problem and simplifying the problem. The study was designed as a teaching experiment and conducted during the 2022–2023 academic year with 12 students registered in the International Baccalaureate program at a religious high school in Bursa, Turkey. During the research process, the genetic decomposition of the concept of mathematical modelling was developed based on the literature review and the pilot implementation. Afterwards, a teaching program consisting of approximately 14 to 18 class hours was designed and implemented based on the ACE (Activities, Classroom Discussions, Exercises) instructional cycle. The activities in the program were designed at the of guiding students through higher-order mental processes such as analysing real-life problems, identifying key variables, formulating realistic assumptions, and constructing mathematical representations. Data were collected through open-ended modelling tasks, researcher observation notes, transcripts of clinical interviews, and detailed lesson journals. The data were analysed using descriptive analysis. The findings revealed that students were considerably insufficient in understanding problem contexts before the implementation; however, they demonstrated high-level performance in this skill by the end of the instruction and especially in the retention test. In terms of simplifying the problem, students were initially at a basic proficiency level, but after the program, they exhibited more detailed and well-justified strategies. The results of the study are consistent with prior research demonstrating the effectiveness of structured instructional programs in developing students\\\' modelling abilities. Moreover, the study provides a contribution to the literature by integrating APOS theory with the teaching of mathematical modelling.
Keywords : ACE, APOS, Matematiksel Modelleme, Öğretim Deneyi, Lise Öğrencileri

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