Ortaokul Matematik Öğretmeni Adaylarının Olasılık Alan Bilgilerinin Olasılığın Farklı Anlamları Açısından İncelenmesi

Year 2020, Volume: 11 Issue: 3, 706 - 732, 15.12.2020

Gamze Kurt , Orkun Coşkuntuncel

https://doi.org/10.16949/turkbilmat.728122

Abstract

Olasılık öğretiminin uluslararası alanda gördüğü ilgi, Türkiye’de olasılığın ayrı bir öğrenme alanı olarak ele alınmasını sağlamış olsa da ortaokul matematik programında yoğunluğu azaltılmış ve hafifletilmiştir. Buna rağmen, ilköğretim matematik öğretmen adaylarının lisans öğrenimleri boyunca istatistik ve olasılık derslerine ayrıca yer verilmesi onların bu konuların öğretiminde yetiştirilmesi gerekliliğini göstermektedir. Fakat öğretmen adaylarının öğrenimleri boyunca aldıkları olasılık öğretiminin yeterli olmadığı, olasılığı farklı yaklaşımlarla öğrenemedikleri ve dolayısıyla da olasılığı öğretmek için gerekli yeterliğe sahip olmadıkları iddia edilmektedir. Bu durum, matematik öğretmeni adaylarının olasılığı öğretebilmek için gereken temel alan bilgisi, ileri düzeyde alan bilgisi ve uzman düzey alan bilgisi bakımından olasılık bilgilerinin incelenmesi gerekliliğini ortaya koymuştur. Bu çalışmada, matematik öğretmeni adaylarının olasılık alan bilgileri (temel, ileri ve özel) olasılığın farklı anlamları (klasik, sıklıkçı ve öznel) bağlamında incelenmiştir. Türkçe’ye çevrilerek uyarlanan olasılık alan bilgisi testinin 98 öğretmen adayına uygulanması ile elde edilen genel bulgulara göre, katılımcıların en başarılı oldukları alan bilgisinin temel düzeyde alan bilgisi olduğu ve olasılığın klasik anlamı için yeterli düzeyde bir anlayışa sahip oldukları görülmüştür. Fakat ileri düzeyde ve uzman düzey alan bilgisi için öğretmen adaylarının eksiklerinin bulunduğu, olasılığın sıklıkçı ve öznel yaklaşımına dair anlayışlarının yetersiz olduğu tespit edilmiştir. Çalışmada elde edilen sonuçlara göre, üniversite eğitimleri sırasında verilen istatistik ve olasılık derslerinin kapsamının iyileştirilmesi ve genişletilmesi ve paralel bir şekilde ortaokul matematik programlarının da olasılığın yalnızca klasik değil diğer anlamlarını da ön plana çıkarır şekilde yeniden yapılandırılması önerilmektedir.

Keywords

Olasılık alan bilgisi, olasılığın farklı anlamları, ortaokul matematik öğretmeni adayları

Assessment of Elementary Mathematics Teachers’ Probability Content Knowledge in terms of Different Meanings of Probability

Abstract

Although the international interest in teaching probability has allowed probability to be treated as a separate learning area in Turkey, its intensity has been reduced and mitigated in the middle school mathematics program. Despite this, the addition of statistics and probability courses for middle school mathematics teacher candidates during their undergraduate education shows the need for them to be trained in these subjects’ teaching. However, it is claimed that the probability knowledge that teacher candidates receive in their undergraduate years is not sufficient; they cannot learn probability with different approaches, and therefore do not have the necessary competence to teach probability. In this case, it is necessary to examine the probability knowledge in terms of common content knowledge (CCK), advanced content knowledge (ACK), and specialized content knowledge (SCK) required to teach the probability of mathematics teacher candidates. In this study, probability content knowledge (CCK, ACK, and SCK) of mathematics teacher candidates was examined in the context of different meanings of probability (classical, frequentist, and subjective). According to the general results obtained by applying the probability content knowledge test, which was adapted to Turkish to 98 teacher candidates, it was found that the content knowledge in which participants were most successful was CCK and had a sufficient level of understanding for the classical meaning of probability. However, it was found that there are deficiencies in teacher candidates for ACK and SCK, and their understanding of the frequentist and subjective approach of probability is insufficient. It was recommended to improve and expand the scope of statistics and probability courses given during university education. In parallel, restructuring middle school mathematics programs could be applied to emphasize classical and other meanings of probability

Keywords

Probability content knowledge, preservice elementary mathematics teachers, meanings of probability

References

• Arican, M., & Kuzu, O. (2020). Diagnosing preservice teachers’ understanding of statistics and probability: Developing a test for cognitive assessment. International Journal of Science and Mathematics Education, 18, 771–790.
• Ata, A. (2014). Öğretmen adaylarının olasılık konusuna ilişkin kavramsal ve işlemsel bilgi düzeylerinin incelenmesi (Yayımlanmamış yüksek lisans tezi). Eskişehir Osmangazi Üniversitesi, Eğitim Bilimleri Enstitüsü, Eskişehir.
• Azcárate, P. (1995). El conocimiento profesional de los profesores sobre las nociones de aleatoriedad y probabilidad. (Unpublished doctoral dissertation). University of Cádiz, Spain.
• Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching. What makes it special? Journal of Teacher Education, 59(5), 389-407.
• Batanero, C., Chernoff, E. J., Engel, J., Lee, H. S., & Sánchez, E. (2016). ICME-13 Topical Surveys: Research on teaching and learning probability. Springer, Cham.
• Batanero, C., & Díaz, C. (2012). Training school teachers to teach probability: Reflections and challenges. Chilean Journal of Statistics, 3(1), 3-13.
• Batanero, C., Garfield, J. B., & Serrano, L. (1996). Heuristics and biases in secondary school students’ reasoning about probability. In L. Puig & A. Gutiérrez (Eds.), Proceedings of the Twentieth Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 51-59). Valencia, Spain: IGPME.
• Batanero, C., Godino, J. D., & Roa, R. (2004). Training teachers to teach probability. Journal of Statistics Education, 12(1).
• Batanero, C., Godino, J. D., & Cañizares, M. J. (2005). Simulation as a tool to train pre-service school teachers. In J. Adler (Ed.), Proceedings of first ICMI African regional conference. Johannesburg: First Africa Regional Congress of ICMI on Mathematical Education (AFRICME-1). Witwatersrand University, Johannesburg, South Africa.
• Batanero, C., Henry, M., & Parzysz, B. (2005). The nature of chance and probability. In G. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 15-37). New York: Springer.
• Bursalı, G. G., & Gökkurt-Özdemir, B. (2019). Instructional explanations of mathematics teachers and pre-service teachers on misconceptions: The subject of probability. Journal of Computer and Education Research, 7(14), 642-672. DOI: 10.18009/jcer.639384
• Chernoff, E. J. (2011). Investigating relative likelihood comparisons of multinomial, contextual sequences. In M. Pytlak, T. Rowland, & E. Swoboda (Eds), Proceedings of the Seventh Conference of the European Society for Research in Mathematics Education (591-600). Rzeszow: European Society for Research in Mathematics Education (ERME).
• Danişman, Ş., & Tanışlı, D. (2017). Examination of mathematics teachers’ pedagogical content knowledge of probability. Malaysian Online Journal of Educational Sciences, 5(2), 16-34.
• Díaz, C., & Batanero, C. (2009). University students’ knowledge and biases in conditional probability reasoning. International Electronic Journal of Mathematics Education, 4(3), 131-162.
• Estrada, A., Batanero, C., & Díaz, C. (2018). Exploring teachers’ attitudes towards probability and its teaching. In C. Batanero, E. J. Chernoff (Eds), Teaching and Learning
• Stochastics: Advances in Probability Education Research (pp. 313-332). Cham, Switzerland: Springer International Publishing.
• Falk, R., & Wilkening, F. (1998). Children’s construction of fair chances: Adjusting probabilities. Developmental Psychology, 34(6), 1340-1357.
• Fischbein, E., & Gazit, A. (1984). Does the teaching of probability improve probabilistic intuitions? Educational Studies in Mathematics, 15(1), 1-24.
• Fraenkel, J. R., & Wallen, N. E. (2006). How to design and evaluate research in education (6th ed.). New York: McGraw-Hill.
• Gómez-Torres, E., Batanero, C., Díaz, C., & Contreras, J. M. (2016). Developing a questionnaire to assess the probability content knowledge of prospective primary school teachers. Statistics Education Research Journal, 15(2), 197-215.
• Green, D. R. (1982). Probability concepts in school pupils aged 11-16 years. (Unpublished Doctoral Dissertation) The Loughborough University of Technology, The United Kingdom.
• Green, D. R. (1983). From thumbtacks to inference. School Science and Mathematics, 83(7), 541-551.
• Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372-400.
• Hourigan, M., & Leavy, A. M. (2019). Pre-service teachers’ understanding of probabilistic fairness: Analysis of decisions around task design. International Journal of Mathematical Education in Science and Technology, 1-23.
• Jones, G. A., & Thornton, C.A. (2005). An overview of research into the teaching and learning of probability. In G. A. Jones (Ed.) Exploring Probability in School (pp. 65-92). Boston: Springer US.
• Karaaslan, K. G. ve Ay, Z. S. (2017). Öğretmen adaylarının olasılık konusuna ilişkin alan bilgilerinin kavramsal-işlemsel bilgi kapsamında incelenmesi. Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi, 17(2), 716-736.
• Karasar, N. (2005). Bilimsel araştırma yöntemi. (15. Baskı). Ankara: Nobel Yayın Dağıtım.
• Koparan, T. (2019). Teaching game and simulation-based probability. International Journal of Assessment Tools in Education, 6(2), 235-258.
• Kurt-Birel, G. (2017). The investigation of pre-service elementary mathematics teachers’ subject matter knowledge about probability. Mersin Üniversitesi Eğitim Fakültesi Dergisi, 13(1), 348-362.
• Langrall, C. W. (2018). The status of probability in the elementary and lower secondary school mathematics curriculum: The rise and fall of probability in school mathematics in the United States. In C. Batanero, E. J. Chernoff (Eds), Teaching and Learning Stochastics: Advances in Probability Education Research (pp. 39-50). Cham, Switzerland: Springer International Publishing.
• Shaughnessy, J. M., & Ciancetta, M. (2002). Students’ understanding of variability in a probability environment. In B. Phillips (Ed.), Proceedings of the Sixth International Conference on the Teaching of Statistics, Cape Town, South Africa. [CD-ROM] Voorburg, The Netherlands: International Statistical Institute. Retrieved from: https://iase-web.org/documents/papers/icots6/6a6_shau.pdf?1402524962
• Millî Eğitim Bakanlığı [MEB]. (2013). Ortaokul Matematik Dersi (5, 6, 7 ve 8. Sınıflar) Öğretim Programı. Ankara: MEB Yayınları.
• Millî Eğitim Bakanlığı [MEB]. (2018). Ortaöğretim Matematik Dersi (9, 10, 11 ve 12. Sınıflar) Öğretim Programı. Ankara: MEB Yayınları.
• Moore, D. S. (1997). New pedagogy and new content: The case of statistics. International Statistical Review, 65(2), 123-137.
• Olpak, Y. Z., Baltaci, S., & Arican, M. (2018). Investigating the effects of peer instruction on pre-service mathematics teachers’ achievements in statistics and probability. Education and Information Technologies, 23(6), 2323-2340.
• Quinn, R. J. (1997). Effects of mathematics methods courses on the mathematical attitudes and content knowledge of preservice teachers. The Journal of Educational Research, 91(2), 108-114.
• Shaughnessy, J. M. (1977). Misconceptions of probability: An experiment with a small-group, activity-based, model building approach to introductory probability at the college level. Educational Studies in Mathematics, 8, 285-316.
• Stohl, H. (2005). Probability in teacher education and development. In G. A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 345–366). New York: Springer.