Reflections from the Lesson Study for the Development of Techno-Pedagogical Competencies in Teaching Fractal Geometry

Abstract

Technological Pedagogical Content Knowledge (TPACK) is a model that explains how teachers use technology more effectively in the context of technological, pedagogical, and content knowledge. Teachers' TPACK competencies play great importance in this regard. Lesson study has also been playing significant roles in the development of teachers' professional trainings. When the researches on TPACK and lesson study have been analyzed, the research is expected to provide significant contributions to the literature. This study aims to present reflections from a lesson study practice that carried out to urge techno-pedagogical competencies of the secondary school mathematics teachers and to reveal the development of teachers’ progress. The study used case study method, and it was conducted with three in-service teachers. The research data were collected through semi-structured interviews, voice recorder, and observation notes. To analyze the collected data, descriptive analysis method was used. The results have revealed that teachers have made much more progress in designing, implementing, and problem solving in terms of TPACK competencies. It has also been determined that teachers’ development of openness to the innovations was limited. This limitation appeared to emerge as a result of teachers’ time anxiety and insufficient knowledge regarding the use of technology.

Keywords

• Lesson study, Techno-pedagogical competencies, Secondary school mathematics teachers, Fractal geometry

References

1. Akkaya, E. (2009). Matematik ogretmen adaylarinin turev kavramina iliskin teknolojik pedagojik alan bilgilerinin ogrenci zorluklari baglaminda incelenmesi [Investigating technological pedagogical content knowledge for derivative concept: Knowledge of student difficulties] (Unpublished Doctoral Thesis), Marmara University, Istanbul, Turkey.
2. Altan, M. Z. (1998). A call for change and pedagogy: A critical analysis of teacher education in Turkey. European Journal of Education, 33(4), 407-417.
3. Anderson, S. E., & Maninger R. M. (2007). Preservice teachers' abilities, beliefs and intentions regarding technology integration. Journal of Educational Computing Research, 37(2), 151-172.
4. Angeli, C., & Valanides, N. (2009). Epistemological and methodological issues for the conceptualization, development, and assessment of ICT–TPCK: Advances in technological pedagogical content knowledge (TPCK). Computers & Education, 52, 154-168.
5. Archambault, L., & Crippen, K. (2009). Examining TPACK among K-12 online distance educators in the united states. Contemporary Issues in Technology and Teacher Education, 9(1), 71-88.
6. Argon, T., Ismetoglu, M., & Celik Yilmaz, D. (2015). The opinions of branch teachers about their technopedagogical education competencies and induvial innovativeness levels. Journal of Research in Education and Teaching, 4(2), 319-333.
7. Ay, Y. (2015). Ogretmenlerin teknolojik pedagojik alan bilgisi (TPAB) becerilerinin uygulama modeli baglaminda degerlendirilmesi [Evaluation of teachers’ technological pedagogical content knowledge (TPACK) within the framework of practical model] (Unpublished Doctoral Thesis). Eskisehir Osmangazi University, Eskisehir, Turkey.
8. Back, J., & Joubert, M. (2011, February). Lesson study as a process for professional development: Working with teachers to effect significant and changes in practice. Proceedings of 7th Congress of the European Society for Research in Mathematics Education, Rzeszow, Poland.

9. Baki, A. (2001). Bilisim teknolojisi isigi altinda matematik egitiminin degerlendirilmesi [Evaluation of mathematics education under the light of information technology]. Milli Egitim Dergisi, 149, 26-31.
10. Baki, M. (2012). Sinif ogretmeni adaylarinin matematigi ogretme bilgilerinin gelisiminin incelenmesi: Bir ders imecesi (lesson study) calismasi [Investigating development of prospective primary teachers’ mathematical pedagogical content knowledge: Lesson study] (Unpublished Doctoral Thesis). Karadeniz Technical University, Trabzon, Turkey.
11. Butun, M. (2012). Ilkogretim matematik ogretmeni adaylarinin uygulanan zenginlestirilmis program surecinde matematigi ogretme bilgilerinin gelisimi [The development of pedagogical content knowledge of preservice mathematics teachers in the process of applied enriched program] (Unpublished Doctoral Thesis), Karadeniz Technical University, Trabzon, Turkey.
12. Bos, B. (2011). Professional development for elementary teachers using TPACK. Contemporary Issues in Technology and Teacher Education, 11(2), 167-183.
13. Carlson, M. P., & Bloom, I. (2005). The cyclic nature of problem solving: An emergent multidimensional problem-solving framework. Educational Studies in Mathematics, 58, 45–75.
14. Chai, C. S., Koh, J. H. L., & Tsai, C. C. (2010). Facilitating preservice teachers' development of technological, pedagogical, and content knowledge (TPACK). Educational Technology & Society, 13(4), 63–73.
15. Crawford, A. R., Chamblee, G. E., & Rowlett, R. J.(1998). Assessing concerns of algebra teachers during a curriculum reform: A constructivist approach. Journal of In-service Education, 24(2), 317–327.
16. Cox, S. (2008). A conceptual analysis of technological pedagogical content knowledge [Unpublished Doctoral Dissertation]. Brigham Young University, USA.
17. Demir, S., & Bozkurt, A. (2011). Ilkogretim matematik ogretmenlerinin teknoloji entegrasyonundaki ogretmen yeterliklerine iliskin gorusleri [Primary mathematics teachers’ views about their competencies concerning the integration of technology]. Elementary Education Online, 10(3), 850-860.
18. Demirel, O., & Kaya, Z. (2003). Ogretmenlik meslegine giris [Introduction to teaching profession]. Ankara: Pegem Yayincilik.
19. Depaepe, F., Corte, E., & Verschaffel, L. (2010). Teachers’ approaches towards word problem solving: Elaborating or restricting the problem context. Teaching and Teacher Education, 26, 152-160.
20. Doruk, B. K., Aktumen, M., & Aytekin, C. (2013). Pre-service elementary mathematics teachers' opinions about using GeoGebra in mathematics education with reference to 'teaching practices'. Teaching Mathematics and Its Aplication. 32(3), 140-157.
21. Erbas, A. K., Cetinkaya, B., & Ersoy, Y. (2009). Ogrencilerin basit dogrusal denklemlerin cozumunde karsilastiklari guclukler ve kavram yanilgilari [Student difficulties and misconceptions in solving simple linear equations]. Education and Science, 34(152), 44-59.
22. Fernandez, C., & Yoshida, M. (2004). Lesson study A Japanese approach to improving mathematics teaching and learning. New Jersey, Lawrence Erlbaum Associates.
23. Fraboni, M., & Moller, T. (2008). Fractals in the classroom. Mathematics Teacher, 102(3), 197.
24. Graham, C. R. (2011). Theoretical considerations for understanding technological pedagogical content knowledge (TPACK). Computers & Education, 57, 1953- 1960.
25. Groth, R., Spickler, D., Bergner, J., & Bardzell, M. (2009). A qualitative approach to assessing technological pedagogical content knowledge. Contemporary Issues in Technology and Teacher Education, 9(4), 392-411.
26. Guzey, S. S., & Roehrig, G.H. (2009). Teaching science with technology: Case studies of science teachers’ development of technology, pedagogy, and content knowledge. Contemporary Issues in Technology and Teacher Education, 9(1), 25-45.
27. Gundogmus, N. (2013). Ogretmen adaylarinin teknolojik pedagojik alan bilgileri ile ogrenme stratejileri arasindaki iliskinin incelenmesi [Analysis of relationship between technological pedagogical and learning strategies of teacher candidates] (Unpublished Master Thesis), Necmettin Erbakan University, Konya, Turkey.
28. Handal, B., & Herrington, A. (2003). Mathematics teachers’ beliefs and curriculum reform. Mathematics Education Research Journal, 15(1) 59-69.
29. Harris, J. B., & Hofer, M. J. (2011). Technological pedagogical content knowledge (TPACK) in action: A descriptive study of secondary teachers' curriculum based, technology-related instructional planning. Journal of Research on Technology in Education, 43(3), 211-229.
30. Hermans, R, Tondeur, J., van Braak, J., & Valcke, M. (2008) The impact of primary school teachers’ educational beliefs on the classroom use of computers. Computers & Education, 51, 1499-1509.
31. Inoue, N. (2011). Zen and the art of neriage: Facilitating consensus building in mathematics inquiry lessons through lesson study. Journal of Mathematical Teacher Education, 14, 5-23.
32. Isiksal, M., & Cakiroglu, E. (2006). Ilkogretim matematik ogretmen adaylarinin matematige ve matematik ogretimine yonelik yeterlik algilari [Pre-service mathematics teachers’ efficacy beliefs toward mathematics and mathematics teaching]. Hacettepe Universitesi Egitim Fakultesi Dergisi, 31,74-84.
33. Jaipal, K., & Figg, C. (2010). Unpacking the “Total package”: Emergent TPACK chracteristics from a study of preservice teachers teaching with technology. Journal of Technology and Teacher Education, 18(3), 415-441.
34. Jang, S. J., & Chen, K. C. (2010). From PCK to TPACK: Developing a transformative model for pre-service science teachers. Journal of Science Education and Technology, 19(6), 553-564.
35. Kabakci Yurdakul, I., Odabasi, H. F., Kilicer, K., Coklar, A. N., Birinci, G., & Kurt, A. A. (2014). Constructing technopedagogical education based on teacher competencies in terms of national standards. Elementary Education Online, 13(4), 1185-1202.
36. Karakus, F. (2007). Ilkogretim ogrencilerinin fraktal geometri etkinliklerine yonelik gorusleri [Elementary school students’ views on fractal geometry activities]. First National Primary Congress, Hacettepe University, Ankara, Turkey.
37. Karakus, F. (2010). Fraktal kart etkinligiyle fraktal geometriye giris [Introduction to fractal geometry with fractal card activity]. Elementary Education Online, 9 (1), 1-6.
38. Koehler, M. J., Mishra, P., & Yahya, K. (2007). Tracing the development of teacher knowledge in a design seminar: Integrating content, pedagogy and technology. Computers & Education, 49(3), 740-762.
39. Koh, J. L., Chai, C. S., & Tsai, C. C. (2013). Examining practicing teachers’ perceptions of technological pedagogical content knowledge (TPACK) pathways: A structural equation modeling approach. Instructional Science, 41(4), 793-809.
40. Lewis, C., Perry, R., Hurd, J., & O’Cannell, M. P. (2006). Lesson study comes of age in North America. 88, 273-281. Phi Delta Kappan.
41. Lewis, C., Perry, R., & Hurd, J. (2009). Improving mathematics instruction through lesson study: A theoretical model and North American case. Journal of Mathematics Teacher Education, 12, 285-304.
42. Lornell, R., & Westerberg, J. (1999). Fractals in high school: Exploring a new geometry. Mathematics Teacher, 92(3), 260–269.
43. Mishra, P., & Koehler, M. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. The Teachers College Record, 108(6), 1017-1054.
44. Murata, A. (2011). Conceptual overview of lesson study: Introduction. In L. Hart, A. Alston & A. Murata (Eds.), Lesson Study Research and Practice in Mathematics Education: Learning Together, pp. 1-12, NY: Springer.
45. Niess, M. L. (2005). Preparing teachers to teach science and mathematics with technology: Developing a technology pedagogical content knowledge. Teaching and Teacher Education, 21(5), 509-523.
46. Ong, E. G., Lim, C. S., & Ghazali, M. (2010). Examining the changes in novice and experienced mathematics teachers’ questioning techniques through the lesson study process. Journal of Science and Mathematics Education in Southeast Asia, 33(1), 86-109.
47. Saito, E., Harun, I., Kuboki, I., & Tachibana, H. (2006). Indonesian lesson study in practice: Case study of Indonesian mathematics and science teacher education project. Journal of In-service Education, 32(2), 171–184.
48. Sarkar Arani, M. R., Keisuke, F., & Lassegard, J. P. (2010). “Lesson Study” as professional culture in Japanese schools: An historical perspective on teacher classroom practices. Japan Review, 22, 171-200.
49. Senge, P., Cambron-McCabe, N., Lucas, T., Smith, B., Dutton, J., & Kleiner, A. (2000). Schools that learn: A fifth discipline field book for educators, parents, and everyone who cares about education. NY: Doubleday / Currency.
50. Simsek, O., Demir, S. Bagceci, B., & Kinay, I. (2013). Ogretim elemanlarinin teknopedagojik egitim yeterliliklerinin cesitli degiskenler acisindan incelenmesi [Examining technopedagogical knowledge competencies of teacher trainers in terms of some variables]. Ege Journal of Education, 14(1), 1-23.
51. Tokmak, H. S., Konokman, G.Y., & Yelken, T.Y. (2013). Mersin Universitesi Okul oncesi ogretmen adaylarinin teknolojik pedagojik alan bilgisi (TPAB) oz guven algilarinin incelenmesi [An investigation of Mersin University early childhood pre-service teachers’ self-confidence about their technological pedagogical content knowledge (TPACK)]. Journal of Kirsehir Education Faculty, 14(1), 35–51.
52. Yildiz, A. (2013). Ders imecesinin matematik ogretmenlerinin problem cozme ortamlarinda ogrencilerinin ustbilislerini harekete gecirmeye yonelik davranislarina etkisi [The effect of lesson study to the behaviours of mathematics teachers intended to promote the metacognitions of the students in the problem solving environment] (Unpublished Doctoral Thesis), Karadeniz Technical University, Trabzon, Turkey.
53. Yildirim, A., & Simsek, H. (2005). Sosyal bilimlerde nitel arastirma yontemleri [Qualitative research methods in the social sciences]. Seckin Yayincilik. Ankara.
54. Yin, R. K. (2003). Case study research: Design and methods. Thousand Oaks, CA: Sage.
55. Yoshida, M., & Jackson, W., C. (2011). Ideas for developing mathematical pedagogical content knowledge through lesson study. In L, C, Hart., A. Alston and A. Murata (Eds.), Lesson Study Research and Practice in Mathematics Education (pp, 279- 288), Dordrecht, The Netherlands: Springer.
56. Werhoef, N. C., & Tall, D. O. (2011). Lesson study: The effect on teacher’s professional development. In Ubuz, B.(Ed.). Proceedings of the 35th Conference of the International for the Psychology of Mathematics Education, 4, 297-304, Ankara, Turkey: PME.