Model Eliciting Activities: The Theoretical Structure and Its Example
Journal Name:
- Ondokuz Mayıs Üniversitesi Eğitim Fakültesi Dergisi
Key Words:
Keywords (Original Language):
| Author Name | University of Author | Faculty of Author |
|---|---|---|
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.
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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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