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Model Oluşturma Etkinlikleri: Kuramsal Yapısı ve bir Örneği

Model Eliciting Activities: The Theoretical Structure and Its Example

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Abstract (2. Language): 
The purpose of the study is to introduce the theoretical structure of model eliciting activities considered to an important tool for mathematics education, to exemplify a model eliciting activity constructed by mathematics teachers and to explain its application process. In a general way, the model eliciting activities are basically defined as real life problem solving activities required constructing mathematical model/models. Model eliciting activities defining non-routine complex real world situations are ill-defined and open ended problems requiring students to reason and interpret about the situation, and to define and formulize the process mathematically to help clients who benefit from this situation (Lesh, Hoover, hole, Kelly, & Post, 2000; Chamberlin & Moon, 2008). These activities were firstly developed by many mathematics teachers, students, researchers, and mathematics and teacher educators in the framework of the fifteen-week seminars named multi-tiered teaching experiments. During these seminars, it was revealed that the model eliciting activities continuously tested and improved to provide some criteria. In this context, to become a model eliciting activity, it must meet the criteria named reality principle, model construction principle, self-assessment principle, construct documentation principle, model generalization principle, effective prototype principle. The reality principle means that the context of the situation should be meaningful and relevant to the students and the solution should be real and meaningful in the students‘ everyday lives. The model construction principle means that the product obtained at the end of the model eliciting activities should be model/models constructed by the students. According to the self-assessment principle, the students should decide whether their solution approaches and the accuracy of their constructed model/models are true and sufficient or not. In this context, the students assess their own approaches in their working groups which the practices are carried out. The model documentation principle requires the students should state their thinking towards solutions in a detail way. Due to the nature of the model eliciting activities, the students develop/advise a model/models to help a client and it is wanted for the developed model /models to be conveyed to the client by a letter or e-mail. These also indicate the model documentation principle. The model generalization principle refers that the solutions created by students are generalizable or easily adapted to other similar situations. This principle also ensures that students' models are communicated in a clear understandable manner that allows them to be used by others. Finally the effective prototype principle means that the developed model/models should provide a prototype for interpreting other problems with the same underlying structure. Each model eliciting activity asks students to interpret a complex real-world situation mathematically and requires the formation of a mathematical description, procedure, or method for the purpose of making a decision for a realistic client. The model eliciting activities has four central components named the newspaper article and the readiness or warm-up questions, the problem situation and the presentation of solutions. The implementation process of these activities is as follows: The newspaper article and the readiness or warm-up questions are given to the students as individual homework a lesson before the class application. The so-called readiness questions as for the article content contains questions. Some of these questions are reading comprehension questions and some of them are aimed to reveal the students‘ original thoughts. Students come to the course by reading the newspaper article and responding the readiness questions firstly and then discuss their answers with their classmates. After that, the students in working groups of 3 or 4 people begin to solve the problem situation distributed them. In this process, teachers only can guide students in the event of difficulties in understanding the problem situation. Otherwise students in the group should be able to decide themselves the effectiveness of the approaches to their solution. Within the time specified by the contents of the problem difficulty and the level of students, the groups completing their solutions present their solutions/models to their classmates. During this component referred to as the presentation of solutions, a student from each group is expected to make presentations. Although there are different model eliciting activities for different levels in the foreign literature, there are no original ones in Turkey. So the Fuel Problem constructed by three mathematics teachers is presented in this study as an example. The components of Fuel Problem are explained in a detailed way and the implementation process is identified. Finally, it is emphasized the importance of model eliciting activities in mathematics education. There is required different model eliciting activities to be implemented in different levels in Turkey.
Abstract (Original Language): 
Bu çalışmanın amacı matematik öğretimi için önemli bir araç olduğu düşünülen Model Oluşturma Etkinliklerinin kuramsal yapısını, bir örneğini ve bu örneğin uygulama sürecini tanıtmaktır. Model oluşturma etkinlikleri ürün olarak matematiksel bir modelin oluşturulmasını gerektiren gerçek yaşam problemlerini çözme etkinlikleri olarak tanımlanmaktadır. Çalışma kapsamında model oluşturma etkinliklerini kuramsal olarak tanıtmak için, öncelikle bu etkinliklerin ortaya çıkış süreci kronolojik olarak verilmekte ve alan yazında farklı araştırmacılar tarafından nasıl tanımlandıkları ifade edilmektedir. Daha sonra ayrıntılı bir şekilde model oluşturma etkinliklerinin prensipleri olan, gerçeklik, model oluşturma, öz değerlendirme, yapı belgelendirme, model genelleme ve etkili prototip prensipleri açıklanmaktadır. Model oluşturma etkinliklerinin matematik öğretimindeki önemi, bileşenleri ve bu bileşenlere paralel olarak derslerde nasıl uygulanması gerektiğine de yer verilmektedir. Yabancı alan yazında örnekleri bulunmasına karşılık ulusal çalışmalarda özgün örnekleri bulunmaması sebebiyle, çalışmanın devamında matematik öğretmenleri tarafından geliştirilen Yakıt Problemi isimli bir model oluşturma etkinliği örneği verilmekte ve ayrıntılı olarak tüm bileşenleri sunulmaktadır. Son olarak bu model oluşturma etkinliğinin uygulama sürecinden bahsedilmektedir.

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