Matematiksel Modellemeyi Anlamak

Abstract

Bu çalışmanın amacı, matematiksel modellemenin eğitim bağlamında sıkça karşılaşılan kavramsal belirsizliklerini gidermek ve “doğru anlama”yı destekleyen uygulanabilir ve bütüncül bir çerçeve sunmak adına matematiksel modelleme kavramını tanımlamak, döngüleri hakkında bilgi vermek, matematiksel modelleme yeterlikleri, nitelikli matematiksel modelleme etkinliklerinin ayırt edici özellikleri ile matematiksel modelleme sürecinin yürütülmesi ve değerlendirilmesini açıklamaktır. Çalışmada, matematiksel modellemenin problem çözmede izlenecek özel bir yol olduğu, matematiksel modelleme yeterliklerinin yalnızca bilişsel alt becerilerden ibaret olmadığı; bilişsel, üstbilişsel, duyuşsal ve sosyal boyutları içeren çok bileşenli bir yetkinlik alanı olduğu ortaya konulmaktadır. Matematiksel modelleme etkinliklerinin seçimi ve tasarımına yönelik farklı kuramsal çerçevelerin bütünleştirilmesiyle, bu etkinliklerin öğretim programıyla uyumlu, gerçek yaşamla ilişkili, açık uçlu, çoklu çözüme imkân veren ve öğrencilerin düşünme süreçlerini görünür kılan görevler olarak yapılandırılması gerektiği vurgulanmaktadır. Ayrıca matematiksel modelleme sürecinin planlanması, yürütülmesi ve rubrikler, öz–akran değerlendirme, projeler, gözlemler ve yazılı testler gibi çoklu araçlarla değerlendirilmesine ilişkin ilkeler sunulmaktadır.

Keywords

• Matematik Eğitimi
• Matematiksel Modelleme
• Problem Çözme

Understanding Mathematical Modelling

Abstract

The purpose of this study is to clarify the conceptual ambiguities frequently encountered in the educational use of mathematical modeling and to propose a practical and comprehensive framework that supports a “correct understanding” of the construct. To this end, the study aims to define mathematical modeling, present major modeling cycles, describe mathematical modeling competencies, outline the distinguishing characteristics of high-quality modeling tasks, and explain how the modeling process is implemented and assessed. The study highlights that mathematical modeling constitutes a specific pathway for problem solving and that modeling competencies extend beyond cognitive subskills; rather, they represent a multifaceted domain that encompasses cognitive, metacognitive, affective, and social dimensions. By integrating various theoretical frameworks on the selection and design of modeling tasks, the study underscores that such tasks must be aligned with the curriculum, grounded in real-life contexts, open-ended in nature, allow for multiple solution approaches, and make students’ thinking processes visible. Furthermore, the study outlines principles for planning, conducting, and evaluating the mathematical modeling process using multiple assessment tools, including rubrics, self- and peer assessment, projects, observations, and written tests.

Keywords

• Mathematics Education
• Mathematical Modelling
• Problem-solving

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