Ortaokul Öğretmenlerinin İspatla İlişkili Etkinliklere Katılımlarının Doğasının İncelenmesi

Year 2019, Volume: 48 Issue: 1, 100 - 130, 21.04.2019

Muhammed Fatih Dogan

Abstract

Akıl yürütme ve ispat matematik öğrenmede ve öğretmede çok önemli olmasına ve okul matematiğinde daha fazla yer edinmiş olmasına rağmen, hem öğrenciler hem öğretmenler, ispatla ilgili etkinliklerde büyük zorluklarla karşılaşmaktadır. Bu tür zorluklara neden olan önemli potansiyel neden, öğretmenlerin ispat kavramı ile ilgili anlayışları olabilir. Buna rağmen ortaokulda görev yapan matematik öğretmenlerinin gerekçelendirme ve ispat kavramlarını nasıl öğrendiklerini araştıran çok az çalışma vardır. Bu nedenle, alan yazındaki boşluğu doldurmak için, bu çalışma ortaokul öğretmenlerinin akıl yürütme ve ispat ile ilgili etkinliklerle etkileşimlerine odaklanan yüksek lisans düzeyindeki bir mesleki gelişim dersinin gözlemsel verilerini incelemektedir. Bu çalışmadan elde edilen bulgular, ö ğretmenlerin ispat etkinliklerini çözmede oldukça başarılı olduklarını, ancak tümdengelimsel argümanlar üretmede zorlandıklarını göstermektedir. Bu başarısızlığın arkasındaki bazı nedenler, öğretmenlerin etkinliklere çözüm üretmeyi ispatı tamamlamak olarak görerek ispat yapma ihtiyacı duymamaları ve cebirsel ifadeleri (simgeleştirmeyi) matematiksel fikirleri ifade etmek için uygun bir araç olarak görmemeleri olabilir.

Keywords

Matematik öğretmen eğitimi, Mesleki gelişim, Akıl yürütme, gerekçelendirme ve ispat

The Nature of Middle School In-Service Teachers’ Engagements in Proving-Related Activities

Abstract

Although reasoning and proof in learning and teaching mathematics is crucial and have gained more presence in school mathematics, both students and their teachers face great difficulties when engaging in proving activities. One potential cause for such difficulties might be due to teachers’ conception of proof. However, to date, there are few, if any, studies that have examined how secondary school in-service mathematics teachers learn justification and proof. Thus, in order to fill this gap, this study examines secondary school in-service teachers’ engagement in proving activities by providing observational data from a master’s level professional development course that focuses on teaching reasoning and proof. The findings from this work show that teachers were very successful at engaging in exploration of the proving tasks, but they fail to produce complete-deductive arguments. Some reasons behind this failure were teachers’ lack of a perceived need for justification and proof after exploring the task, and their lack of seeing algebraic symbolization as a viable means of expressing mathematical ideas.

Keywords

Mathematics teacher education, Professional Development, Reasoning, Justification and Proof

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