Matematiksel Çalışmanın Doğasına Bilişsel ve Epistemolojik Bir Yaklaşım: Duru’nun Matematiksel Çalışma Uzayı

Abstract

Matematiksel Çalışma Uzayı (MWS) sınıf ortamında öğretmen ve öğrencilerin gerçekte ne ile meşgul olduklarını anlamlandırmamıza olanak sağlayan kapsamlı analiz çerçevesi sunan bir kuramdır. Matematiksel çalışmanın karakteristiğini epistemolojik düzlemiyle matematik, bilişsel düzlemiyleyse öğrenci aktivitesi üzerinden açıklamaktadır. Bu çalışmayla kuramın yurtiçi literatürde tanınırlığının artırılması, matematiksel çalışmayı açıkladığı kavramları gerçek bir çalışma süreci ile ifade edilmesi amaçlanmıştır. Araştırma tamamlanmış bir matematiksel çalışmanın ortaya konulması amacıyla BİLSEM’e devam eden 8. sınıf öğrencisi ile gerçekleştirilmiştir. Araştırmada MWS’de ifade edilen zengin içerikli matematiksel görev olarak şekilsiz geometri problemi kullanılmıştır. Nitel desende gerçekleştirilen çalışmada veriler yapılandırılmış gözlem formu, öğrenci çalışma kağıtları, alan notları, görüşme ile elde edilmiştir. Problemin analiz a priorisi ve oluşturulan analiz çerçevesi kullanılarak öğrencinin çalışma uzayı tanımlanmıştır. Elde edilen bulgular öğrencinin çalışma uzayında MWS’nin semiyotik, enstrümantal ve söylemsel oluşumlarının ve yönelimlerinin belirlenebildiğini göstermiştir. Sonuç olarak MWS’nin etkili görev tasarımı, matematiksel çalışmanın analiz a priori- posteriorinin gerçekleştirilmesi, kişisel çalışma uzaylarını tanımlama, öğrenme ortamında karşılaşılan zorlukları belirleme gibi pek çok başlıkta araştırmacılara destek sağlayabilecek potansiyeli ortaya konulmuştur. Araştırmacılara MWS’yi matematiğin farklı alanlarında ve farklı bağlamlarda matematiksel çalışma sürecinin incelenmesinde kullanmaları önerilmektedir.

Keywords

• Matematiksel çalışma
• MWS
• Çalışma uzayı

A Cognitive and Epistemological Approach to the Nature of Mathematical Work: Duru’s Mathematical Working Space

Abstract

The Mathematical Working Space (MWS) is a theoretical framework that provides a comprehensive analytical lens for understanding what teachers and students actually engage with in the classroom. It characterizes mathematical activity through two planes: the epistemological plane, which concerns mathematics itself, and the cognitive plane, which is grounded in students’ activity. The aim of this study is to increase the visibility of the framework within the national literature and to illustrate the concepts through which it explains mathematical work by presenting an authentic working process. The research was conducted with an 8th-grade student attending a Science and Art Center (BİLSEM) to present a completed mathematical working process. In the study, a figureless geometry problem was used as a mathematically rich task, as defined within the MWS framework. Employing a qualitative research design, data were collected through a structured observation form, student worksheets, field notes, and an interview. Using the a priori analysis of the problem together with the constructed analytical framework, the student’s working space was identified. The findings indicate that the semiotic, instrumental, and discursive geneses and orientations of the MWS could be clearly observed within the student's working space. In conclusion, the study demonstrates the potential of the MWS framework to support researchers in several areas, including effective task design, conducting a priori and a posteriori analysis of mathematical work, identifying personal working spaces, and determining difficulties encountered in learning environments. It is recommended that researchers apply the MWS framework to examine mathematical working processes across different domains of mathematics and in various contexts.

Keywords

• Mathematical work
• MWS
• Working space

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