Investigation de la contribution de l’enseignement de la modélisation mathématique conçu sur la base de ACE aux compétences en modélisation des élèves du Baccalauréat International à la lumière de la théorie APOS

Yıl 2025, Cilt: 14 Sayı: 5, 2697 - 2722, 31.12.2025

Gökçe Kayhan Gencer , Menekşe Seden Tapan Broutin

https://doi.org/10.15869/itobiad.1743272

Öz

Cette étude vise à examiner l’efficacité d’un programme d’enseignement structuré selon la théorie APOS pour améliorer les compétences en modélisation mathématique des élèves du secondaire. La recherche se concentre particulièrement sur les deux premières phases du processus de modélisation : la compréhension du problème et sa simplification. L’étude a été conçue comme une expérience d’enseignement et menée au cours de l’année scolaire 2022–2023 auprès de 12 élèves inscrits au programme du Baccalauréat International (IB) dans un lycée religieux à Bursa, en Turquie. Au cours du processus de recherche, une décomposition génétique du concept de modélisation mathématique a été élaborée sur la base d’une revue de littérature et d’une étude pilote. Par la suite, un programme d’enseignement d’environ 14 à 18 heures de cours a été conçu et mis en œuvre en s’appuyant sur le cycle d’instruction ACE (Action–Process–Object–Schema). Les activités du programme visaient à guider les élèves à travers des processus cognitifs de haut niveau tels que l’analyse de problèmes de la vie réelle, l’identification des variables clés, la formulation d’hypothèses réalistes et la construction de représentations mathématiques. Les données ont été collectées à l’aide de tâches de modélisation ouvertes (pré-test, post-test, test de rétention), de notes d’observation du chercheur, de transcriptions d’entretiens cliniques et de journaux de cours détaillés. Les données ont été analysées par analyse descriptive. Les résultats ont révélé que les élèves avaient des lacunes importantes dans la compréhension du contexte des problèmes avant l’implémentation ; cependant, ils ont démontré des performances de haut niveau dans cette compétence à la fin de l’enseignement et notamment lors du test de rétention. En ce qui concerne la simplification du problème, les élèves étaient initialement à un niveau de compétence de base, mais après le programme, ils ont présenté des stratégies plus détaillées et bien justifiées. Les résultats de l’étude sont cohérents avec les recherches antérieures démontrant l’efficacité des programmes d’enseignement structurés pour développer les compétences en modélisation des élèves. De plus, l’étude apporte une contribution théorique et pratique originale à la littérature en intégrant la théorie APOS à l’enseignement de la modélisation mathématique.

Anahtar Kelimeler

ACE , APOS , Modélisation mathématique , Expérience d’enseignement , Lycée

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

Öz

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.

Anahtar Kelimeler

ACE , APOS , Mathematical Modelling , Teaching Experiment , High School Students

ACE Kapsamında Tasarlanan Matematiksel Modelleme Eğitiminin, Uluslararası Bakalorya Öğrencilerinin Modelleme Becerilerine Katkısının APOS Teorisi Işığında İncelenmesi

Öz

Bu araştırma, lise düzeyindeki öğrencilerin matematiksel modelleme becerilerini geliştirmek amacıyla APOS teorisini temel alan bir öğretim programının katkılarını incelemeyi amaçlamaktadır. Çalışma, matematiksel modelleme sürecinin ilk iki basamağı olan “problemi anlama” ve “problemi sadeleştirme” yeterliklerine odaklanmaktadır. Araştırma deseni olarak öğretim deneyi tercih edilmiş ve 2022–2023 eğitim-öğretim yılında Bursa ilinde bir imam hatip lisesinde öğrenim gören Uluslararası Bakalorya programına dahil olan 12 öğrenci çalışma grubunu oluşturmuştur. Araştırma sürecinde öncelikle literatür taramasına ve pilot uygulamaya dayalı olarak matematiksel modelleme kavramının genetik çözümlemesi yapılmış, ardından ACE (Activities, Classroom Discussions, Exercises) öğretim döngüsü esas alınarak yaklaşık 14–18 ders saatinden oluşan bir öğretim programı tasarlanmış ve uygulanmıştır. Geliştirilen etkinlikler, öğrencilerin gerçek yaşam problemlerini analiz etme, önemli değişkenleri ayırt etme, gerçekçi varsayımlar oluşturma ve matematiksel temsiller geliştirme gibi üst düzey bilişsel süreçlere yönlendirilmesini hedeflemiştir. Veriler; açık uçlu modelleme etkinlik kağıtları, araştırmacı gözlem notları, klinik görüşme dökümleri ve ayrıntılı ders günlüklerinden elde edilmiştir. Veriler betimleyici analiz yöntemiyle değerlendirilmiştir. Bulgular, öğrencilerin uygulama öncesinde problem durumu anlama konusunda oldukça yetersiz olduklarını, ancak öğretim süreci sonunda ve özellikle kalıcılık testi sürecinde bu becerilerde üst düzey performans sergilediklerini ortaya koymuştur. Problemi sadeleştirme açısından ise öğrenciler uygulama öncesinde temel düzeyde yeterli bulunmuş, öğretim sonrasındaysa bu beceriyi daha ayrıntılı ve gerekçelendirilmiş biçimde ortaya koymuşlardır. Çalışmanın bulguları, yapılandırılmış öğretim programlarının modelleme becerilerinin gelişiminde etkili olduğunu gösteren araştırmalarla tutarlılık göstermektedir. Çalışma, matematiksel modelleme öğretimi ile APOS teorisini bir araya getirerek literatüre teorik ve uygulamalı bir katkı sunmaktadır.

Anahtar Kelimeler

ACE , APOS , Matematiksel Modelleme , Öğretim Deneyi , Lise Öğrencileri

Kaynakça

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