Matematik Öğretmen Adaylarının Öğrencilerin Aritmetik Ortalamaya Yönelik Düşünüşünü Fark Etme Becerilerinin Geliştirilmesi: Bir Öğretim Deneyi

Öz

Bu çalışmanın amacı, ilköğretim matematik öğretmen adaylarının aritmetik ortalamaya yönelik mesleki fark etme becerilerinin belirlenmesi ve öğretim deneyi yöntemiyle geliştirilmesidir. Çalışmada, istatistik öğretimini kapsayan 8 haftalık öğretim dizisinde yaklaşık 4 hafta süren aritmetik ortalama öğretimine odaklanılmıştır. Çalışmanın verileri 3. sınıfta öğrenim gören 35 öğretmen adayından ön test, son test, yarı yapılandırılmış görüşmeler ve öğretmen adaylarının öğretim deneyi sürecinde tutmuş oldukları günlükler vasıtasıyla toplanmıştır. Öğrencilerin Matematiksel Düşünmelerine Yönelik Mesleki Fark Etme kuramsal çerçevesinin üç bileşenine yönelik soruların olduğu ön-test ve son-test, aritmetik ortalamaya yönelik bir problem ve bu probleme ait üç öğrenci çözümü içermektedir. Veriler, aynı kuramsal çerçeve temel alınarak hazırlanan kodlama tablosu kullanılarak analiz edilmiştir. Ön-test sonuçları öğretmen adaylarının öğrenci düşünüşü odaklı istatistik öğretimine katılmadan önce öğrencilerin aritmetik ortalamaya yönelik problemlerdeki çözüm stratejilerini dikkate alma, öğrencilerin matematiksel kavrayışlarını yorumlama ve öğrencilere karşılık verme becerilerinin düşük olduğunu göstermektedir. Öğrenci düşünüşü odaklı istatistik öğretiminin sonunda, öğretmen adaylarının, dikkate alma, yorumlama ve karşılık verme becerilerini önemli derecede geliştirdikleri görülmektedir. Bu bulgular doğrultusunda, ,amaca yönelik planlanan ve sistemli bir şekilde yürütülen matematik eğitimi dersleri ile öğretmen adaylarının fark etme becerilerinin geliştirilebileceği söylenebilir.

Anahtar Kelimeler

• Mesleki fark etme becerisi
• aritmetik ortalama
• matematik öğretmen adayları

Development of Prospective Mathematis Teachers' Noticing Skills of Students’ Thinking regarding the Mean: A Teaching Experiment

Öz

This study aims to determine the prospective mathematics teachers’ (PSTs) professional noticing skills regarding mean and to develop their noticing skills through teaching experiment method. In the study, it was focused on teaching arithmetic mean, lasting approximately 4 weeks in an 8-week teaching series including teaching statistics. The data were collected through pre-test, post-test, semi-structured interviews and diaries that PSTs kept during the teaching experiment process from 35 third grade PSTs. The pre-test and post-test, containing questions about three facets of theoretical framework of Professional Noticing of Children’s Mathematical Thinking, include a problem about mean and three student solutions to this problem. The data were analysed using a coding table prepared based on same theoretical framework. The pre-test results showed that before participating in student thinking-focused statistics teaching, PSTs had low skills in attending to students' solution strategies related to mean, interpreting students' mathematical understandings, and responding to students. At the end of the student thinking-focused statistics teaching, it is seen that PSTs significantly improved their attending, interpreting and responding skills. In line with these findings, it can be said that the PST’s noticing skills can be improved with mathematics education courses that are purposefully planned and systematically conducted.

Anahtar Kelimeler

• Professional noticing skills
• mean
• prospective matematics teachers

Kaynakça

1. Amador, J. M., Carter, I., & Hudson, R. A. (2016). Analyzing preservice mathematics teachers’ professional noticing. Action in Teacher Education, 38(4), 371- 383.
2. Amador, J. M., & Carter, I. S. (2018). Audible conversational affordances and constraints of verbalizing professional noticing during prospective teacher lesson study. Journal of Mathematics Teacher Education, 21, 5-34.
3. Anantharajan, M. (2020). Teacher noticing of mathematical thinking in young children’s representations of counting. Journal for Research in Mathematics Education, 51(3), 268-300.
4. Aydın, Ş. (2020). Sekizinci sınıf öğrencilerinin merkezi eğilim ölçülerine yönelik istatistiksel düşünmelerinin incelenmesi (Tez No. 644516). [Yüksek lisans tezi, Hacettepe Üniversitesi]. Yüksek Öğretim Kurulu Ulusal Tez Merkezi.
5. Bastian, A., Kaiser, G., Meyer, D., Schwarz, B., & König, J. (2022). Teacher noticing and its growth toward expertise: An expert–novice comparison with pre-service and in-service secondary mathematics teachers. Educational Studies in Mathematics, 110(2), 205-232.
6. Birgin, O., & Eryılmaz, E. (2022). Türkiye’de Matematik Eğitimi Alanında Öğretmenin Fark Etmesi Konusunda Yapılan Çalışmaların Sistematik İncelenmesi. International Journal of Educational Studies in Mathematics, 9(3), 184-203.
7. Birinci, M. (2018). Bir ortaokul matematik öğretmeninin mesleki gelişiminden yansımalar: Kesir öğretiminde fark etme becerisinin işe koşulması [Yayımlanmamış doktora tezi, Karadeniz Teknik Üniversitesi Eğitim Bilimleri Enstitüsü]. Yüksek Öğretim Kurulu Ulusal Tez Merkezi.
8. Blömeke, S., Gustafsson, J.-E., & Shavelson, R. (2015). Beyond dichotomies: Competence viewed as a continuum. Zeitschrift für Psychologie, 223(1), 3–13. https://doi.org/10.1027/2151-2604/a000194

9. Bütüner, S. Ö. (2020). Türkiye’de okutulan ortaokul matematik ders kitaplarının aritmetik ortalama kavramına ilişkin öğrencilere sunduğu öğrenme fırsatları. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 11(1), 157-187.
10. Callejo, M. L., & Zapatera, A. (2017). Prospective primary teachers’ noticing of students’ understanding of pattern generalization. Journal of Mathematics Teacher Education, 20(4), 309-333.
11. 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.
12. Cobb, P., Confrey, J., DiSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9-13.
13. Confrey, J., & Lachance, A. (2000). Transformative teaching experiments through conjecture-driven research design. In A. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 231–265). Mahwah, NJ: Lawrence Erlbaum Associates.
14. Cooper, S. (2009). Preservice teachers' analysis of children's work to make instructional decisions. School Science and Mathematics, 109(6), 355-362.
15. Doğan-Coşkun, Tekin-Sitrava, R., & Işıksal-Bostan, M. (2023). Pre-service elementary teachers’ noticing expertise of students’ mathematical thinking: The case of fractions. International Journal of Mathematical Education in Science and Technology, 54(6), 982-999.
16. Czarnocha, B., & Maj, B. (2008). A teaching experiment. In B. Czarnocha (Ed.), Handbook of mathematics teaching research -a tool for teachers- researchers (pp. 47–58). Poland: University of Reszów.
17. Fernández, C., Llinares, S., & Valls, J. (2013). Primary school teacher’s noticing of students’ mathematical thinking in problem solving. The Mathematics Enthusiast, 10(1), 441–468.
18. Dick, L. K. (2017). Investigating the relationship between professional noticing and specialized content knowledge. In E. Schack, M. Fisher, & J. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 339-358). Springer.
19. Dişbudak-Kuru, Ö., Ucuzoğlu, A. N., Işıksal-Bostan, M., Yemen-Karpuzcu, S., & Tekin-Sitrava, R. (2022). Ortaokul matematik öğretmenlerinin mesleki fark etme becerileri: dikdörtgenler prizmasının hacmine ilişkin problem durumu. Mersin Üniversitesi Eğitim Fakültesi Dergisi, 18(2), 154-174.
20. Dreher, A., & Kuntze, S. (2015). Teachers’ professional knowledge and noticing: The case of multiple representations in the mathematics classroom. Educational Studies in Mathematics, 88, 89-114.
21. Enisoğlu, D. (2014). Yedinci sınıf öğrencilerinin sütun grafiği gösteriminde verilen aritmetik ortalama, ortanca ve tepe değer kavramları ile ilgili problemleri çözerken kullandıkları olası çözüm stratejileri, yaptıkları hatalar ve yanlış yorumlamaları (Tez No: 381685) [Yüksek lisans tezi, Orta Doğu Teknik Üniversitesi]. Yüksek Öğretim Kurulu Ulusal Tez Merkezi.
22. Fernández, C., Llinares, S., & Valls, J. (2013). Primary school teacher’s noticing of students’ mathematical thinking in problem solving. The Mathematics Enthusiast, 10(1), 441-468.
23. Gal, I. (1995). Statistical tools and statistical literacy: The case of the average. Teaching Statistics, 17(3), 97-99.
24. Girit-Yildiz, D., Osmanoglu, A., & Gundogdu Alayli, F. (2023). Providing a video-case-based professional development environment for prospective mathematics teachers to notice students’ misconceptions in measurement. Journal of Mathematics Teacher Education, 26(2), 179-209.
25. González, G., & Vargas, G. E. (2020). Teacher noticing and reasoning about student thinking in classrooms as a result of participating in a combined professional development ıntervention. Mathematics Teacher Education and Development, 22(1), 5-32
26. Groth, R.E. (2009). Characteristics of teachers' conversations about teaching mean, median, and mode. Teaching and Teacher Education, 25, 707-716.
27. Güner, P., & Akyüz, D. (2017). Ders imecesi (lesson study) mesleki gelişim modeli: Öğretmen adaylarının fark etme becerilerinin incelenmesi. İlköğretim Online, 16(2), 428-452.
28. Güner, P., & Akyüz, D. (2020). Noticing student mathematical thinking within the context of lesson study. Journal of Teacher Education, 71(5), 568–583. https://doi.org/10.1177/0022487119892964
29. Gürbüz, S. ve Şahin, F. (2018). Sosyal bilimlerde araştırma yöntemleri (5. baskı). Ankara: Seçkin Yayıncılık.
30. Gürel, R. (2016). Ortaokul matematik öğretmenlerinin merkezi eğilim ve yayılım ölçülerine ilişkin öğretim bilgilerinin incelenmesi. (Tez No: 443569). [Yüksek lisans tezi, Hacettepe Üniversitesi]. Yüksek Öğretim Kurulu Ulusal Tez Merkezi.
31. Gürsoy, P. (2019). Bir matematik öğretmeninin cebir öğretim sürecinden yansımalar: Fark etme becerisi. [Yayımlanmamış Yüksek Lisans Tezi, Karadeniz Teknik Üniversitesi Eğitim Bilimleri Enstitüsü]. Yüksek Öğretim Kurulu Ulusal Tez Merkezi.
32. Hino, K., Stylianides, G. J., Eilerts, K., Lajoie, C., & Pugalee, D. (2017). Topic study group no. 47: Pre-service mathematics education of primary teachers. In G. Kaiser (Ed.), Proceedings of the 13th International Congress on Mathematical Education, ICME-13 Monographs (pp. 593–597). https://doi.org/10.1007/978-3-319-62597-3_74
33. Hoth, J., Kaiser, G., Busse, A., Doehrmann, M., Koenig, J., & Blömeke, S. (2017). Professional competences of teachers for fostering creativity and supporting high-achieving students. ZDM, 49, 107-120.
34. Ivars, P., Fernández, C., & Llinares, S. (2020). A learning trajectory as a scaffold for pre-service teachers’ noticing of students’ mathematical understanding. International Journal of Science and Mathematics Education, 18, 529-548.
35. Jacobbe, T. (2007). Elementary school teachers’ understanding of essential topics in statistics and the influence of assessment instruments and a reform curriculum upon their understanding [Unpublished doctoral dissertation]. Clemson University.
36. Jacobs, V. R., & Empson, S. B. (2016). Responding to children’s mathematical thinking in the moment: An emerging framework of teaching moves. ZDM, 48(1–2), 185–197.
37. 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.
38. Kaiser, G., Busse, A., Hoth, J., König, J. & Blömeke, S. (2015). About the complexities of video-based assessments: Theoretical and methodological approaches to overcoming shortcomings of research on teachers‘ competence. International Journal of Science and Mathematics Education, 13(2), 369–387.
39. Konold, C., & Pollatsek, A. (2002). Data analysis as the search for signals in noisy processes. Journal for Research in Mathematics Education, 33(4),259-289.
40. Lampert, M. (2001). Teaching problems and the problems of teaching. New Haven, CT: Yale University Press. LaRochelle, R. M. (2018). Secondary teachers’ professional noticing of students’ mathematical thinking. [Unpublished doctoral dissertation]. UC San Diego, California, USA.
41. LaRochelle, R., Nickerson, S. D., Lamb, L. C., Hawthorne, C., Philipp, R. A., & Ross, D. L. (2019). Secondary practising teachers' professional noticing of students' thinking about pattern generalisation. Mathematics Teacher Education and Development, 21(1), 4-27.
42. Leavy, A., & O’Loughlin, N. (2006). Preservice teachers understanding of the mean: Moving beyond the arithmetic average. Journal of Mathematics Teacher Education, 9, 53-90.
43. Makar, K. (2014). Young children's explorations of average through informal inferential reasoning. Educational Studies in Mathematics, 86, 61-78.
44. Miles, M. B., & Huberman, A. M. (1994). Qualitative Data Analysis: An Expanded Source Book. Sage Publications.
45. Nickerson, S. D., Lamb, L., & LaRochelle, R. (2017). Challenges in measuring secondary mathematics teachers’ professional noticing of students’ mathematical thinking. In E. Schack, M. Fisher, & J. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 381–398). Springer.
46. Sánchez-Matamoros, G., Fernández, C., & Llinares, S. (2019). Relationships among prospective secondary mathematics teachers’ skills of attending, interpreting and responding to students’ understanding. Educational Studies in Mathematics, 100(1), 83-99.
47. Santagata, R., König, J., Scheiner, T., Nguyen, H., Adleff, A. K., Yang, X., & Kaiser, G. (2021). Mathematics teacher learning to notice: A systematic review of studies of video-based programs. ZDM–Mathematics Education, 53(1), 119-134.
48. Scheiner, T. (2021). Towards a more comprehensive model of teacher noticing. ZDM, 53(1), 85-94.
49. Sherin, M. G., Jacobs, V., & Philipp, R. (Eds.). (2011). Mathematics teacher noticing: Seeing through teachers’ eyes. Routledge.
50. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
51. Sorto, M. A. (2004). Prospective middle school teachers' knowledge about data analysis and its application to teaching. [Unpublished doctoral dissertation]. Michigan State University, USA.
52. Star J. R., Lynch K. H., Perova N. (2011). Using video to improve mathematics’ teachers’ abilities to attend to classroom features: A replication study. In Sherin M. G., Jacobs V. R., Philipp R. A. (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 117-133). New York, NY: Routledge.
53. Star, J. R., & Strickland, S. K. (2008). Learning to observe: Using video to improve preservice mathematics teachers’ ability to notice. Journal of Mathematics Teacher Education, 11(2), 107–125.
54. Steffe, L. P., & Thomson, P. (2000). Teaching experiments methodology: Underlying principles and essential characteristics. Research Design in Mathematics and Science Education, Hillsdale, Nj: Laurence Erlbaum.
55. Şermetoğlu, H., & Baki, M. (2019). Investigation of the Rate and Ratio’s Teaching Process in the Context of a Mathematics Teacher's Noticing. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 10(2), 394-425.
56. Tekin-Sitrava, R., Kaiser, G., & Işıksal-Bostan, M. (2022). Development of prospective teachers’ noticing skills within initial teacher education. International Journal of Science and Mathematics Education, 20(7), 1611-1634.
57. Toluk-Uçar, Z., & Akdoğan, E. N. (2009). 6-8. sınıf öğrencilerinin ortalama kavramına yüklediği anlamlar. İlköğretim Online, 8(2), 391-400.
58. Ulusoy, F., & Çakıroğlu, E. (2021). Exploring prospective teachers’ noticing of students' understanding through micro-case videos. Journal of Mathematics Teacher Education, 24, 253-282.
59. Van, de, Walle, J., Karp, K., & Bay-Williams, J. (2015). Elementary and middle school mathematics: Teaching developmentally (9th ed.). Essex, UK: Pearson Education
60. Van Es, E. A. (2011). A framework for learning to notice student thinking. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 134–151). Routledge.
61. van Es, E. A., & Sherin, M. G. (2002). Learning to notice: Scaffolding new teachers’ interpretations of classroom interactions. Journal of Technology and Teacher Education, 10(4), 571–596.
62. van Es, E. A., & Sherin, M. G. (2021). Expanding on prior conceptualizations of teacher noticing. ZDM, 53, 17-27.
63. Warshauer, H. K., Starkey, C., Herrera, C. A., & Smith, S. (2021). Developing prospective teachers’ noticing and notions of productive struggle with video analysis in a mathematics content course. Journal of Mathematics Teacher Education, 24, 89-121.
64. Yılmaz, H. K., & Özdemir-Baki, G. (2023). Bir ortaokul matematik öğretmeninin fark etme becerisinin alan ölçme öğretimine yansımaları. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi, (55), 95-118.