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Assessment of a Middle-School Mathematics Teacher’s Knowledge for Teaching the 5th-Grade Subject of Fractions

Yıl 2021, Cilt: 12 Sayı: 1, 96 - 138, 05.02.2021
https://doi.org/10.16949/turkbilmat.742136

Öz

This study has aimed at revealing the knowledge for teaching a middle-school mathematics teacher has in teaching the 5th-grade subject of fractions. For this purpose, the Mathematics Knowledge for Teaching (MKT) was used. The study adopted the holistic single-case study, one of the qualitative study designs. The study was implemented with a teacher assigned at a public school and who volunteered for the study. The study data were collected by semi-structured interviews held with the teacher and observations during the teaching process of the subject of fractions, on which the teacher’s knowledge was sought to be assessed. Consequent to the study, it was revealed that the middle-school mathematics teacher possesses insufficient content knowledge on fractions, operations with fractions and meanings and models of fractions. It was concluded that his insufficient content knowledge also had an adverse impact on this knowledge for teaching and therefore, restricted the teacher’s teaching process. Based on the study, it was concluded that due to the teacher’s limited content knowledge and pedagogical content knowledge, he has an insufficient mathematical knowledge for teaching.

Kaynakça

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  • Bailey, D. H., Hoard, M. K., Nugent, L., & Geary, D. C. (2012). Competence with fractions predicts gains in mathematics achievement. Journal of Experimental Child Psychology, 113(3), 447-455. doi: 10.1016/j.jecp.2012.06.004
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  • Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., Klusmann, U., Krauss, S., Neubrand, M., & Yi-Miau, T. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, 47(1), 133-180. doi:10.3102/0002831209345157
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Ortaokul Matematik Öğretmeninin 5. Sınıf Kesirler Konusundaki Öğretme Bilgisinin İncelenmesi

Yıl 2021, Cilt: 12 Sayı: 1, 96 - 138, 05.02.2021
https://doi.org/10.16949/turkbilmat.742136

Öz

Bu çalışmada 5. sınıf kesirler konusunun öğretiminde bir ortaokul matematik öğretmeninin öğretme bilgisinin ortaya konulması amaçlanmıştır. Bu amaç doğrultusunda Öğretmek için Matematik Bilgisi (ÖMB) modeli kullanılmıştır. Araştırmada nitel araştırma desenlerinden bütüncül tek durum çalışması benimsenmiştir. Araştırma, devlet ortaokulunda görev yapan ve çalışmaya katılmaya gönüllü olan bir matematik öğretmeni ile yürütülmüştür. Araştırmanın verileri öğretmen ile gerçekleştirilen yarı yapılandırılmış görüşmeler ve öğretmen bilgisinin incelendiği kesirler konusunun öğretimi sürecinde yapılan gözlemler yolu ile toplanmıştır. Araştırmada elde edilen verilerin analizinde betimsel analiz yöntemi kullanılmıştır. Araştırma sonucunda çalışmada yer alan ortaokul matematik öğretmeninin kesir, kesirlerle işlemler, kesirlerin anlamları ve modellerine ilişkin yetersiz alan bilgisine sahip olduğu ortaya konulmuştur. Yetersiz alan bilgisinin, öğretmenin öğretme bilgisini de olumsuz etkilediği ve öğretim sürecinin de bu doğrultuda kısıtlı kaldığı ortaya konulmuştur. Çalışma sonucunda öğretmenin alan bilgisi ve pedagojik alan bilgisinin kısıtlı olması sonucu matematik öğretme bilgisinin de yeterli olmadığı sonucuna ulaşılmıştır.

Kaynakça

  • Amato, A. S. (2005). Developing students’ understanding of the concept of fractions as numbers. Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, Australia.
  • Aslan-Tutak, F., & Köklü, O. (2016). Öğretmek için matematik bilgisi. E. Bingölbali, S. Arslan & İ. Ö. Zembat (Eds.), Matematik eğitiminde teoriler içinde (s. 701-720). Ankara: Pegem Akademi.
  • Baek, J. M., Wickstrom, M. H., Tobias, J. M., Miller, A. L., Safak, E., Wessman-Enzinger, N., & Kirwan, J. V. (2017). Preservice teachers’ pictorial strategies for a multistep multiplicative fraction problem. The Journal of Mathematical Behavior, 45, 1-14. doi: 10.1016/j.jmathb.2016.10.005
  • Bailey, D. H., Hoard, M. K., Nugent, L., & Geary, D. C. (2012). Competence with fractions predicts gains in mathematics achievement. Journal of Experimental Child Psychology, 113(3), 447-455. doi: 10.1016/j.jecp.2012.06.004
  • Ball, D. L., Lubienski, S., & Mewborn, D. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.), Handbook of research on teaching (pp. 433-456). Washington, DC: American Educational Research Association.
  • 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. doi: 10.1177/0022487108324554
  • Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., Klusmann, U., Krauss, S., Neubrand, M., & Yi-Miau, T. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, 47(1), 133-180. doi:10.3102/0002831209345157
  • Begle, E. (1979). Critical variables in mathematics education: Findings from a survey of the empirical literature. Washington, DC: The Mathematical Association of America and the National Council of Teachers of Mathematics.
  • Behr, M. J., Harel, G., Post, T., & Lesh, R. (1992). Rational number, ratio, and proportion. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 296-333). New York: Macmillan.
  • Brownell, M. T., Ross, D. D., Colon, E. P., & McCallum, C. L. (2005). Critical features of special education teacher preparation: A comparison with general teacher education. The Journal of Special Education, 38(4), 242-252.
  • Charalambous, C. Y., & Pitta-Pintazi, D. (2005). Revisiting a theoretical model on fractions: Implications for teaching and research. Chick, H. L. & Vincent, J. L. (Eds.), Proceedings of the 29th conference of the international group for the psychology of mathematics education, 2, 233-240.
  • Chestnut-Andrews, A. (2007). Pedagogical content knowledge and scaffolds: Measuring teacher knowledge of equivalent fractions in a didactic setting. (Doctoral Dissertation). City University of New York.
  • Clarke, D. M., Roche, A., & Mitchell, A. (2008). 10 practical tips for making fractions come alive and make sense. Mathematics Teaching in The Middle School, 13(7), 372-380.
  • Cramer, K., Wyberg, T., & Leavitt, S. (2008). The role of representations in fraction addition and subtraction. Mathematics Teaching in The Middle School, 13(8), 490-496. doi: 10.5951/MTMS.13.8.0490
  • Davis, G. E. (2003). Teaching and classroom experiments dealing with fractions and proportional reasoning. The Journal of Mathematical Behavior, 22(2), 107-111. doi:10.1016/S0732-3123(03)00016-6
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  • Vamvakoussi, X. & Vosniadou, S. (2004). Understanding the structure of the set of rational numbers: a conceptual change approach. Learning and Instruction, 14(5), 453-467. doi: 10.1016/j.learninstruc.2004.06.013
  • Vamvakoussi, X., Van Dooren, W., & Verschaffel, L. (2012). Naturally biased? In search for reaction time evidence for a natural number bias in adults. The Journal of Mathematical Behavior, 31(3), 344-355. doi: 10.1016/j.jmathb.2012.02.001
  • Van de Walle, Karp, & Bay-Williams (2013). Elementary and middle school mathematics: Teaching developmentally (8th Edition). Boston: Pearson.
  • Van Dooren, W., Lehtinen, E., & Verschaffel, L. (2015). Unraveling the gap between natural and rational numbers. Learning and Instruction, 37, 1-4. https://doi.org/10.1016/j.learninstruc.2015.01.001
  • Warrington, M. A. (1997). How children think about division with fractions. Mathematics Teaching in the Middle School, 2(6), 390-94.
  • Webel, C., & DeLeeuw, W. W. (2016). Meaning for fraction multiplication: Thematic analysis of mathematical talk in three fifth grade classes. The Journal of Mathematical Behavior, 41, 123-140. doi: 10.1016/j.jmathb.2015.12.003
  • Wu, H. H. (2011). Understanding elementary school mathematics. Washington, DC: Mathematical Association of America.
  • Yanık, H. B. (2013). Rasyonel sayılar. İ. Ö. Zembat, M. F. Özmantar, E. Bingölbali, H. Şandır & A. Delice (Eds.), Tanımları ve tarihsel gelişimleriyle matematiksel kavramlar içinde (s. 95-110). Ankara: Pegem Akademi.
  • Yıldırım, A., & Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin Yayıncılık.
  • Yin, R. K. (2003). Applications of case study research. Beverly Hills, CA: Sage Publishing.Zhou, Z., Peverly, S. T., & Xin, T. (2006). Knowing and teaching fractions: A cross cultural study of American and Chinese mathematics teachers. Contemporary Educational Psychology, 31(4), 438-457. doi:10.1016/j.cedpsych.2006.02.001
Toplam 95 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Alan Eğitimleri
Bölüm Araştırma Makaleleri
Yazarlar

Ceylan Şen 0000-0002-6384-7941

Yayımlanma Tarihi 5 Şubat 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 12 Sayı: 1

Kaynak Göster

APA Şen, C. (2021). Assessment of a Middle-School Mathematics Teacher’s Knowledge for Teaching the 5th-Grade Subject of Fractions. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 12(1), 96-138. https://doi.org/10.16949/turkbilmat.742136
AMA Şen C. Assessment of a Middle-School Mathematics Teacher’s Knowledge for Teaching the 5th-Grade Subject of Fractions. Turkish Journal of Computer and Mathematics Education (TURCOMAT). Şubat 2021;12(1):96-138. doi:10.16949/turkbilmat.742136
Chicago Şen, Ceylan. “Assessment of a Middle-School Mathematics Teacher’s Knowledge for Teaching the 5th-Grade Subject of Fractions”. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, sy. 1 (Şubat 2021): 96-138. https://doi.org/10.16949/turkbilmat.742136.
EndNote Şen C (01 Şubat 2021) Assessment of a Middle-School Mathematics Teacher’s Knowledge for Teaching the 5th-Grade Subject of Fractions. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12 1 96–138.
IEEE C. Şen, “Assessment of a Middle-School Mathematics Teacher’s Knowledge for Teaching the 5th-Grade Subject of Fractions”, Turkish Journal of Computer and Mathematics Education (TURCOMAT), c. 12, sy. 1, ss. 96–138, 2021, doi: 10.16949/turkbilmat.742136.
ISNAD Şen, Ceylan. “Assessment of a Middle-School Mathematics Teacher’s Knowledge for Teaching the 5th-Grade Subject of Fractions”. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12/1 (Şubat 2021), 96-138. https://doi.org/10.16949/turkbilmat.742136.
JAMA Şen C. Assessment of a Middle-School Mathematics Teacher’s Knowledge for Teaching the 5th-Grade Subject of Fractions. Turkish Journal of Computer and Mathematics Education (TURCOMAT). 2021;12:96–138.
MLA Şen, Ceylan. “Assessment of a Middle-School Mathematics Teacher’s Knowledge for Teaching the 5th-Grade Subject of Fractions”. Turkish Journal of Computer and Mathematics Education (TURCOMAT), c. 12, sy. 1, 2021, ss. 96-138, doi:10.16949/turkbilmat.742136.
Vancouver Şen C. Assessment of a Middle-School Mathematics Teacher’s Knowledge for Teaching the 5th-Grade Subject of Fractions. Turkish Journal of Computer and Mathematics Education (TURCOMAT). 2021;12(1):96-138.