Publication: Matematik felsefesi temelli geometri etkinliklerinin öğrencilerin matematik inançları ve kaygıları üzerine etkisi
Abstract
Matematik felsefesi temelli geometri etkinliklerinin öğrencilerin matematik inançları ve kaygıları üzerine etkisi Geometri felsefesi, matematikle özellikle de geometriyle ilgili olan felsefi soruları ve kavramları inceleyen bir alandır. Geometri felsefesi matematiksel nesnelerin ve kavramların varlığı, doğası, gerçekliği üzerine düşündürmeyi önemser. Matematikteki nesnelerin var olup olmadığı, varsa bunların doğası, geometrik yapıların ne tür bilgi sağladığı, matematikteki gerçeklik ve somut dünya ile ilişkisinin ne olduğunu incelemektedir. Geometri felsefesi etkinliklerinin sonucunda öğrenciler bu dersi nasıl sorgulamaları gerektiğini, matematiksel düşünmenin nasıl daha etkili yapılabileceğini, derslerde işlenilen kavramların veya teoremlerin gerçek hayatta nerelerde karşımıza çıktığını yani bu yapıların somut dünya ile ilişkisini daha iyi idrak edebileceklerdir. Böylece yaptıkları işlemlerin uygulamalarının nasıl tezahür ettiğini daha rahat kavrayabileceklerdir. Tüm bunların sonucunda kaygı düzeylerinin azalması ve matematik yapabileceklerine karşı inançlarının artması amaçlanmaktadır. İncelenen araştırmalarda geometri felsefesinin eğitime katkısı özelinde yeterli çalışma olmadığı tespit edilmiştir. Günümüz koşullarını göz önüne alırsak bilgi ulaşılması çok kolay bir haldedir, ancak nitelikli bilgiyi bulmak büyük bir sorgulama sürecini gerektirmektedir. Bu çalışmada matematik derslerini öğrenirken gerekli sorgulamaları yapabilecekleri etkinlikler ile yol gösterilmiştir. Araştırma sürecinde, nicel yöntem çerçevesinde ön test ve son test uygulamalarının yer aldığı, kontrol gruplu yarı deneysel bir desen kullanılmıştır. Araştırmanın çalışma grubunu İstanbul'da bir devlet lisesinde 11. sınıfa devam eden 60 öğrenci oluşturmaktadır. Bu lisede bulunan iki şubeden biri amaclı orneklem yoluyla deney grubu olarak, diğer şube de kontrol grubu olacak şekilde belirlenmiştir. Deney grubunda kontrol grubundan farklı olarak Matematik Felsefesi temelli Geometri etkinlikleri içeren öğretim yapılmıştır. Deney ve kontrol grubuna kaygı ve inanç ölçekleri ön test olarak uygulanmıştır. Sonrasında 2023-2024 eğitim öğretim yılının 2. Döneminde deney grubunda kazanımlar Matematik Felsefesi temelli geometri etkinliklerini de içerecek şekilde işlenmiştir, kontrol grubunda ise yapılandırmacı öğretim yaklaşımı ile ders işlenmeye devam edilmiştir. Çalışma sonucunda deney ve kontrol gruplarındaki öğrencilere kaygı ve inanç ölçekleri son test olarak sunulmuştur. Ön test - son testlerden veriler elde edilmiştir. Daha sonra elde edilen veriler nicel araştırma yönteminde yer alan bağımsız örneklem t testi ve bağımlı örneklem t testi yapılarak karşılaştırılmıştır. Deney ve kontrol grupları uygulama öncesinde uygulama sırasında uygulama sonrasında gösterdikleri gelişimleri bakımından incelenmiş ve elde edilen veriler analiz edilmiştir. Bu araştırmada, deney ve kontrol gruplarının matematiğe yönelik inançları ve matematik kaygıları üzerinde Matematik Felsefesi temelli Geometri etkinliklerinin etkisi incelenmiştir. İnanç düzeylerine ilişkin hem gruplar arası hem de grup içi karşılaştırmalarda anlamlı bir fark bulunmamıştır. Ancak matematik kaygısı açısından kontrol grubunda son testte anlamlı bir artış gözlemlenirken, deney grubunda anlamlı bir değişim görülmemiştir. Deney grubunda uygulanan etkinlikler, öğrencilerin kaygı seviyelerinde artışa engel olmuş ve bu durum Cohen's d değeriyle de orta düzeyde bir etki olarak doğrulanmıştır. Bu sonuçlar, Matematik Felsefesi temelli Geometri etkinliklerinin öğrencilerin matematik kaygısını azaltmada etkili olabileceğini göstermektedir.
The effect of philosophy of mathematics-based geometry activities on students’ mathematical beliefs and anxiety The philosophy of geometry is a field that examines philosophical questions and concepts related to mathematics, particularly geometry. It emphasizes encouraging reflection on the existence, nature, and reality of mathematical objects and concepts. It explores whether mathematical entities truly exist, the nature of such entities if they do exist, the type of knowledge provided by geometric structures, and how mathematical reality relates to the physical world. As a result of philosophy of geometry activities, students will better understand how to critically question the subject, how to engage in more effective mathematical thinking, and where the concepts or theorems covered in lessons appear in real life—thus grasping more clearly the connection between abstract structures and the concrete world. Consequently, they will be able to comprehend how the operations they perform manifest in real-life applications. Ultimately, these activities aim to reduce students’ anxiety levels and increase their belief in their ability to do mathematics. The reviewed studies have revealed that there is a lack of sufficient research specifically focused on the contributions of geometry philosophy to education. Considering the conditions of today’s world, access to information is quite easy; however, identifying qualified and reliable information requires a deep process of inquiry. This study offers students guidance through activities designed to help them develop the habit of questioning while learning mathematics. In the research process, a quasi-experimental design with a control group was employed within the framework of quantitative methods, involving pre-test and post-test applications. The study group consisted of 60 eleventh-grade students attending a public high school in Istanbul. Two classes at this school were selected, with one class chosen as the experimental group through purposive sampling, and the other serving as the control group. The experimental group received instruction that included Geometry activities based on the Philosophy of Mathematics, differing from the control group. Anxiety and belief scales were administered as pre-tests to both groups. Subsequently, during the second semester of the 2023-2024 academic year, the experimental group was taught the curriculum incorporating Philosophy of Mathematics-based geometry activities, while the control group continued with a constructivist teaching approach. At the end of the study, anxiety and belief scales were administered as post-tests to both groups. Data collected from the pre- and post-tests were analyzed using independent samples t-tests and paired samples t-tests, which are part of quantitative research methods. The progress shown by the experimental and control groups before, during, and after the intervention was examined, and the obtained data were analyzed accordingly. This study examined the effect of Geometry activities based on the Philosophy of Mathematics on students' mathematical beliefs and math anxiety in both the experimental and control groups. No significant differences were found in belief levels, either between the groups or within the groups. However, in terms of math anxiety, a significant increase was observed in the control group's post-test results, whereas no significant change was detected in the experimental group. The activities applied in the experimental group prevented an increase in students’ anxiety levels, and this was confirmed as a medium-level effect through the Cohen's d value. These findings suggest that Geometry activities grounded in the Philosophy of Mathematics may be effective in reducing students’ math anxiety.
The effect of philosophy of mathematics-based geometry activities on students’ mathematical beliefs and anxiety The philosophy of geometry is a field that examines philosophical questions and concepts related to mathematics, particularly geometry. It emphasizes encouraging reflection on the existence, nature, and reality of mathematical objects and concepts. It explores whether mathematical entities truly exist, the nature of such entities if they do exist, the type of knowledge provided by geometric structures, and how mathematical reality relates to the physical world. As a result of philosophy of geometry activities, students will better understand how to critically question the subject, how to engage in more effective mathematical thinking, and where the concepts or theorems covered in lessons appear in real life—thus grasping more clearly the connection between abstract structures and the concrete world. Consequently, they will be able to comprehend how the operations they perform manifest in real-life applications. Ultimately, these activities aim to reduce students’ anxiety levels and increase their belief in their ability to do mathematics. The reviewed studies have revealed that there is a lack of sufficient research specifically focused on the contributions of geometry philosophy to education. Considering the conditions of today’s world, access to information is quite easy; however, identifying qualified and reliable information requires a deep process of inquiry. This study offers students guidance through activities designed to help them develop the habit of questioning while learning mathematics. In the research process, a quasi-experimental design with a control group was employed within the framework of quantitative methods, involving pre-test and post-test applications. The study group consisted of 60 eleventh-grade students attending a public high school in Istanbul. Two classes at this school were selected, with one class chosen as the experimental group through purposive sampling, and the other serving as the control group. The experimental group received instruction that included Geometry activities based on the Philosophy of Mathematics, differing from the control group. Anxiety and belief scales were administered as pre-tests to both groups. Subsequently, during the second semester of the 2023-2024 academic year, the experimental group was taught the curriculum incorporating Philosophy of Mathematics-based geometry activities, while the control group continued with a constructivist teaching approach. At the end of the study, anxiety and belief scales were administered as post-tests to both groups. Data collected from the pre- and post-tests were analyzed using independent samples t-tests and paired samples t-tests, which are part of quantitative research methods. The progress shown by the experimental and control groups before, during, and after the intervention was examined, and the obtained data were analyzed accordingly. This study examined the effect of Geometry activities based on the Philosophy of Mathematics on students' mathematical beliefs and math anxiety in both the experimental and control groups. No significant differences were found in belief levels, either between the groups or within the groups. However, in terms of math anxiety, a significant increase was observed in the control group's post-test results, whereas no significant change was detected in the experimental group. The activities applied in the experimental group prevented an increase in students’ anxiety levels, and this was confirmed as a medium-level effect through the Cohen's d value. These findings suggest that Geometry activities grounded in the Philosophy of Mathematics may be effective in reducing students’ math anxiety.