Matematik Öğretmen Adaylarının Klinik Görüşmeler Aracılığıyla Öğrenci Düşüncelerine Yönelik Tespitleri ve Yorumları

Year 2019, Volume: 13 Issue: 2, 759 - 788, 31.12.2019

Makbule Gözde Didiş Kabar Berna Tataroğlu Taşdan

https://doi.org/10.17522/balikesirnef.538365

Cited By: 1

Abstract

Bu çalışmanın amacı ortaokul matematik öğretmen
adaylarının gerçekleştirdikleri klinik görüşmeler sürecinde kesirler
konusundaki öğrenci düşüncelerine yönelik tespitlerinin ve bu tespitlerine yönelik yorumlarının incelenmesidir.
Çalışmanın katılımcıları 41 dördüncü sınıf ortaokul matematik öğretmen
adayıdır. Çalışmada öğretmen adayları bir dönem boyunca 3-4 haftalık
aralıklarla toplam üç kez, farklı başarı düzeylerine sahip öğrencilerle
“kesirler” konusunda birebir görüşmeler gerçekleştirmişlerdir. Bu çalışmanın
veri kaynaklarını öğretmen adaylarının her bir klinik görüşme uygulamasından
sonra verilen değerlendirme formundaki sorulara grupça verdikleri yazılı cevapları,
öğretmen adaylarına ait gözlem notları ve klinik görüşmelerin  yazılı dökümleri oluşturmaktadır. Çalışmanın
verileri nitel araştırma yöntemlerinden içerik analizi kullanılarak analiz
edilmiştir. Çalışmanın bulguları matematik öğretmen adaylarının klinik
görüşmeler sürecinde, öğrencilerin yanlış bilgileri ve doğru bilgileri ile
ilgili, öğrencilerin kullandıkları çözüm stratejileri ve çözümlerini
açıklayabilmeleri ile ilgili tespitlerde bulunduklarını göstermiştir. Öğretmen
adaylarının öğrenci düşünceleri ile ilgili tespitlerini yorumlarken ise “öğrenci”
veya “öğretmen” ile ilişkilendirdikleri belirlenmiştir. 

Keywords

kesirler, klinik görüşme, öğrenci düşüncesi, matematik öğretmen adayları

Pre-Service Mathematics Teachers’ Identifications and Interpretations about Students’ Thinking through Clinical Interviews

Abstract

The
aim of this study was to examine the pre-service elementary school mathematics
teachers’ identifications and interpretations of the students’ thinking about
fractions through clinical interviews. The participants of this case study were
41 fourth grade pre-service mathematics teachers. In the study, pre-service
teachers conducted three interviews with the students, who had different
success levels, at 3-4 week intervals during the semester. The data sources for
the study consisted of the written responses of the pre-service teachers to the
questions in the given evaluation form, the
observation notes of pre-service teachers and the transcriptions of each
interview. Qualitative content analysis was used for analyzing the data. The
findings of the study showed that pre-service teachers identified the students’
correct and incorrect knowledge, the students' solution strategies and students’
ability to explain their solutions. It was also found that while the pre-service
teachers were interpreting students’ thinking they identified during
interviews, they associated their interpretations with “the student” or “ the teacher”. 

Keywords

clinical interviews, fractions, pre-service elementary school mathematics teachers, student thinking

References

• Ambrose, R., Nicol, C., Crespo, S., Jacobs, V., Moyer, P., & Haydar, H. (2004). Exploring the use of clinical interviews in teacher development. In D. E. McDougall & J. A. Ross (Eds.) Proceedings of the Twenty-Sixth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 89-91). Toronto, Ontario, Canada.
• An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school, mathematics teachers in China and the US. Journal of Mathematics Teacher Education, 7(2), 145-172.
• Ball, D. L. (1997). What do students know? Facing challenges of distance, context, and desire in trying to hear children. In B. Biddle, T. Good, & I. Goodson (Eds.), International handbook on teachers and teaching (Vol. II, pp. 679–718). Dordrecht: Kluwer Press.
• 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.
• Boaler, J., & Brodie, K. (2004). The importance, nature and impact of teacher questions. D. E. McDougall & J. A. Ross (Eds.), Proceedings of the twenty-sixth annual meeting North American chapter of international group for the psychology of mathematics education (Vol. 2, pp.773-782). North America: Toronto, Canada.
• Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C. P., & Loef, M. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26(4), 499–531.
• Chamberlin, M. (2002). Teacher investigation of students’ work: The evaluation of teacher’s social process and interpretations of students’ thinking. Unpublished doctoral dissertation, Purdue University, Indiana, U.S.
• Clarke, D. M., Roche, A., & Mitchell, A. (2008). Ten practical tips for making fractions come alive and make sense. Mathematics Teaching in the Middle School, 13(7), 372-380.
• Crespo, S. (2000). Seeing more than right and wrong answers: prospective teachers’ interpretations of students’ mathematical work. Journal of Mathematics Teacher Education, 3(2), 155–181.
• Crespo, S., & Nicol, C. (2003). Learning to investigate students’ mathematical thinking: The role of student interviews. In N. A. Pateman, B. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th International Group for the Psychology of Mathematics Education Conference (Vol. 2, pp. 261–268). Honolulu, HI: University of Hawai’i.
• Dunphy, E. (2010). Exploring young children's (mathematical) thinking: Preservice teachers reflect on the use of the one-to-one interview. International Journal of Early Years Education, 18(4), 331-347.
• Even, R., & Tirosh, D. (1995). Subject-matter knowledge and knowledge about students as sources of teacher presentations of the subject-matter. Educational Studies in Mathematics, 29(1), 1–20.
• Even, R., & Wallach, T. (2004). Between student observation and student assessment: A critical reflection. Canadian Journal of Science, Mathematics and Technology Education, 4(4), 483–495.
• Franke, M. L., Webb, N. M., Chan, A. G., Ing, M., Freund, D., & Battey, D. (2009). Teacher questioning to elicit students’ mathematical thinking in elementary school classrooms. Journal of Teacher Education, 60(4), 380-392.
• Ginsburg, H. (1997). Entering the child’s mind: The clinical interview in psychological research and practice. Cambridge: Cambridge University Press.
• Groth, R. E., Bergner, J. A., & Burgess, C. R. (2016). An exploration of prospective teachers' learning of clinical interview techniques. Mathematics Teacher Education and Development, 18(2), 48-71.
• Haser, Ç., & Ubuz, B. (2002). Kesirlerde kavramsal ve işlemsel performans. Eğitim ve Bilim, 27(126), 53-61.
• Heng, M. A., & Sudarshan, A. (2013). “Bigger number means you plus!” – Teachers’ learning to use clinical interviews to understand students’ mathematical thinking. Educational Studies in Mathematics, 83(3), 471-485.
• 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.
• Jacobs, V. R., Lamb, L. L. C., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169–202.
• Jenkins, O. F. (2010). Developing teachers’ knowledge of students as learners of mathematics through structured interviews. Journal of Mathematics Teacher Education, 13(2), 141–154.
• McDonough, A., Clarke, B., & Clarke, D. M. (2002). Understanding, assessing and developing children’s mathematical thinking: The power of a one-to-one interview for preservice teachers in providing insights into appropriate pedagogical practices. International Journal of Educational Research, 37(2), 211-226.
• Milli Eğitim Bakanlığı [MEB] (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar). Ankara: Talim ve Terbiye Kurulu Başkanlığı.
• Moyer, S., & Milewicz, E. (2002). Learning to questions: Categories of questioning used by preservice teachers during diagnostic mathematics interviews. Journal of Mathematics Teacher Education, 5(4), 293–315.
• National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
• Paoletti, T., Krupnik, V., Dimitrios, P., Olsen, J., Fukawa-Connelly, T., & Weber, K. (2018). Teacher questioning and invitations to participate in advanced mathematics lectures. Educational Studies in Mathematics, 98(1), 1-17.
• Pesen, C. (2007). Öğrencilerin kesirlerle ilgili kavram yanılgıları. Eğitim ve Bilim, 32(143), 79-88.
• Piaget, J. (1952). The child’s conception of number (translated by C. G. & F. M. Hodgson). London: Routledge & Kegan Paul Ltd.
• Şahin, A., & Kulm, G. (2008). Sixth grade mathematics teachers’ intentions and use of probing, guiding, and factual questions. Journal of Mathematics Teacher Education, 11(3), 221-242.
• Schorr, R. Y. (2001). A study of the use of clinical interviewing with prospective teachers. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 153–160). Utrecht, The Netherlands: Freudenthal Institute.
• Sherin, M., & van Es, E. (2005). Using video to support teachers’ ability to notice classroom interactions. Journal of Technology and Teacher Education, 13(3), 475-491.
• Shifter, D. (2001). Learning to see the invisible: What skills and knowledge are needed to engage with students' mathematical ideas? In Wood, T., Nelson, B. S., & Warfield, J. (Eds.) Beyond classical pedagogy: Teaching elementary school mathematics (pp. 109–134). Mahwah, NJ: Lawrence Erlbaum.
• Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
• Sowder, J. T. (2007). The mathematical education and development of teachers. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 157–223). Charlotte, NC: Information Age Publishing.
• Söğüt, G. Y., & Yazgan, Y. (2018). 7. Sınıf öğrencilerinin kesirleri karşılaştırırken kullandıkları referans noktası stratejileri. Kastamonu Eğitim Dergisi, 26(3), 823-833.
• Stockero, S. L., Rupnow, R. L., & Pascoe, A. E. (2017). Learning to notice important student mathematical thinking in complex classroom interactions. Teaching and Teacher Education, 63, 384-395.
• Ulusoy, F., & Çakıroğlu, E. (2018). Using video cases and small-scale research projects to explore prospective mathematics teachers’ noticing of student thinking. EURASIA Journal of Mathematics, Science and Technology Education, 14(9), 1-14.
• Van de Walle, J. A. (2007). Elementary and middle school mathematics: Teaching developmentally (6th ed.). Boston, MA: Pearson.
• Van Es, E. A., Cashen, M., Barnhart, T., & Auger, A. (2017). Learning to notice mathematics Instruction: Using video to develop preservice teachers' vision of ambitious pedagogy. Cognition and Instruction, 35(3), 165-187.
• Wallach, T., & Even, R. (2005). Hearing students: The complexity of understanding what they are saying, showing, and doing. Journal of Mathematics Teacher Education, 8(5), 393–417.
• Yetkin-Özdemir, İ. E., & Kayhan-Altay, M. (2016). Sınıf öğretmeni adaylarının öğrencilerin matematiksel düşüncelerini ortaya çıkarma ve yorumlama becerileri. İlköğretim Online, 15(1), 23-39.
• Yıldırım, A., & Şimşek, H. (2006). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin Yayıncılık.