The Case of Time Axis Fallacy: 11th Grade Students’ Intuitively-based Misconception in Probability and Teachers’ Corresponding Practices

Abstract

This case study aimed to investigate whether mathematics teachers’ instructional practices were effective in resolving eleventh grade students’ intuitively-based misconceptions regarding time axis fallacy. The participants were three mathematics teachers from different high schools and their students. Students were administered a diagnostic test comprising questions related to intuitively-based misconceptions in probability. The test was administered before and after students received teachers’ instructions for probability subject. Teachers were interviewed about their knowledge of students’ difficulties and misconceptions. Teachers’ instructions for probability were observed and videotaped. Content analysis method was used in the data analysis. Considering the findings, it was observed that teachers did not give emphasis on unfamiliar situations related to time axis fallacy. Comparing the test results, there was slight increase in the number of students who fell into time axis fallacy. Based on the findings, it can be asserted that practitioners should be aware of possible intuitively-based misconceptions in probability and organize their instructions accordingly.

Keywords

• Intuition,misconceptions,probability,time axis fallacy,mathematics teachers

Zaman Etkisi Örneği: 11. Sınıf Öğrencilerinin Olasılıkta Sezgi Temelli Kavram Yanılgısı ve Öğretmenlerin İlgili Uygulamaları

Öz

Bu durum çalışmasının amacı, matematik öğretmenlerinin öğretim uygulamalarının on birinci sınıf öğrencilerinin sezgi temelli kavram yanılgıları bağlamında olasılık konusunda zaman etkisi yanılgısını gidermede etkili olup olmadığını incelemektir. Bu çalışmanın katılımcılarını farklı liselerde çalışan üç matematik öğretmeni ve bu öğretmenlerin öğrencileri oluşturmaktadır. Öğrencilere olasılıkta sezgi temelli kavram yanılgılarıyla ilgili sorular içeren bir tanı testi uygulanmıştır. Test, öğretmenlerin olasılık konusunun öğretiminin öncesi ve sonrasında uygulanmıştır. Ayrıca öğrencilerin zorlandıkları noktalar ve kavram yanılgılarına yönelik öğretmenler ile mülakatlar yapılmıştır. Öğretmenlerin olasılık öğretimleri sırasında hem gözlem yapılmış hem de dersler video kaydı altına alınmıştır. Verilerin analizinde içerik analiz yöntemi kullanılmıştır. Bulgular göz önüne alındığında, zaman etkisi kavram yanılgısıyla ilgili aşina olunmayan durumlara öğretmenlerin odaklanmadığı gözlemlenmiştir. Test sonuçları karşılaştırıldığında, zaman etkisi yanılgısına düşen öğrenci sayısında az bir artış olduğunu göstermiştir. Bulgular ışığında, uygulayıcıların olasılıkta sezgi temelli kavram yanılgılarından haberdar olmaları ve öğretimlerini bu bağlamda düzenlemeleri gerektiği söylenebilir.

Anahtar Kelimeler

• Sezgi,kavram yanılgıları,olasılık,zaman etkisi yanılgısı,matematik öğretmenleri

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