Bir Ortaokul Matematik Öğretmeni ve Bir Öğretmen Adayının Matematiksel Söylemleri

Year 2017, Volume: 8 Issue: 2, 161 - 185, 05.04.2017

Tangül Kabael , Ayla Ata Baran

https://doi.org/10.17569/tojqi.266930

Abstract

Bu
araştırmada matematiksel iletişim bağlamında eğitim almış bir ortaokul
matematik öğretmen adayı ile mesleki deneyime sahip bir ortaokul matematik
öğretmeninin matematiksel söylemlerinin ve matematiksel söylemleri analiz etme
biçimlerinin incelenmesi ve matematiksel iletişim bağlamındaki eğitimin ve
mesleki deneyimin bunlar üzerindeki etkileri konusunda ileriki çalışmalara ışık
tutulması amaçlanmaktadır. Bu amaçla fenomenoloji deseni kullanılan bu
araştırmanın verileri araştırmacılar tarafından tasarlanan bir öğretim
senaryosu ile klinik görüşmeler ve ders gözlemleri yapılarak toplanmıştır.
Araştırmanın katılımcıları 10 yıllık mesleki deneyime sahip bir ortaokul
matematik öğretmeni ile bir ortaokul matematik öğretmen adayıdır.
Katılımcıların matematiksel söylem analizleri ve ders gözlemlerinden elde
edilen veriler odaksal analiz yöntemi ile analiz edilirken, klinik
görüşmelerden elde edilen veriler ise içerik analizi yöntemi ile analiz
edilmiştir. Araştırma sonucunda matematik öğretmeni ve öğretmen adayının hem
matematiksel söylemleri hem de matematiksel söylemleri analiz etme biçimlerinin
birbirinden oldukça farklı olduğu görülmüştür. 

Keywords

Matematiksel söylem, söylem analizi, odaksal analiz

One Middle School Mathematics Teacher’s and One Senior Prospective Teacher’s Mathematical Discourse

Abstract

The
purpose of this study was to investigate mathematical discourse and discourse
analysis of one senior prospective teacher who is educated about mathematical
communication and one experienced middle school mathematics teacher. Besides it
was aimed to shed light on future studies about the effects of education about
mathematical communication and teaching experience on mathematical discourse
and discourse analysis. The study was designed as phenomenological study. In
the process of data collection, a teaching scenario was developed by the
researchers. Afterwards clinical interviews and lesson observations were
conducted with the participants. The participants of this study were a middle
school mathematics teacher who has 10 years of experience in teaching and a
senior prospective teacher. Data related to discourse analysis and classroom
discourse was analyzed qualitatively by using focal analysis technique and data
collected from clinical interviews was analyzed by content analysis. According
to the findings, it was seen that the participants’ mathematical discourse and
their discourse analysis was quite different from each other. 

Keywords

Mathematical discourse; discourse analysis; focal analysis

References

• Adler, J. (1997). A participatory-inquiry approach and the mediation of mathematical knowledge in a multilingual classroom. Educational Studies in Mathematics, 33, 235–258.
• Baroody, A. J. (1993). Problem solving, reasoning and communicating, K-8: Helping children think mathematically. New York: Macmillan Publishing Co.
• Chapin, S., O’Connor, C., & Anderson, N. (2003). Classroom Discussions: Using Math Talk to Help Students Learn. Math Solutions Publications: Sausalito, CA.
• Clement, J. (2000). Analysis of clinical interviews: Foundations and model viability. In R. Lesh & A. Kelly (Eds.), Handbook of research methodologies for science and mathematics education (pp. 341-385). Hillsdale, NJ: Lawrence Erlbaum.
• Creswell, J. W. (2013). Qualitative inquiry & research design: Choosing among five approaches. Los Angeles: SAGE Publications.
• Esty, W. W. (2004/ unpublished manuscript). The language of mathematics.
• Esty, W. W. & Teppo, A. R. (1994). A general-education course emphasizing mathematical language and reasoning. Focus on Learning Problems in Mathematics, 16 (1), 13-35.
• Funahashi, Y. & Hino, K. (2014). Teacher’s role in guiding children’s mathematical ideas toward meeting lesson objectives. ZDM—The International Journal on Mathematics Education, 46 (3). Doi: 10.1007/s11858-014-0592-0
• Gee, J. P. & Green, J. L. (1998). Discourse analysis, learning and social practice: A methodological study. Review of Research in Education, 23, 119-169.
• Gillies, R. (2004). The effects of communication training on teachers’ and students’ verbal behaviours during cooperative learning. International Journal of Educational Research, 41, 257-279.
• Gillies, R. & Khan, A. (2008). The effects of teacher discourse on students’ discourse, problem solving and reasoning during cooperative learning. International Journal of Educational Research, 47, 323-340.
• Güçler, B. (2016). Matematiksel bilişe iletişimsel yaklaşım. In E. Bingölbali, S. Arslan ve İ. Ö. Zembat (Ed.), Matematik eğitiminde teoriler, (ss. 629-641). Ankara: Pegem Akademi.
• Hamm, J. & Perry, M. (2002). Learning mathematics in first grade classrooms: On whose authority? Journal of Educational Psychology, 94, 126-137.
• Hattie, J. & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77 (1), 81-112. http://dx.doi.org/10.3102/003465430298487.
• Hiebert, J., Morris, A. K., & Glass, B. (2003). Learning to learn to teach: An "experiment" model for teaching and teacher preparation in mathematics. Journal for Mathematics Teacher Education, 6, 201-222.
• Kersaint, G. (2015). Orchestrating mathematical discourse to enhance student learning. Curriculum Associates, LLC.
• Lee, C. (2006). Language for Learning Mathematics - Assessment for Learning in Practice. Buckingham: Open University Press.
• Lynch, S. D. & Bolyard, J. J. (2012). Putting mathematical discourse in writing. Mathematics Teaching in the Middle School, 17 (8), 486-492.
• Macgregor, M. & Stacey, K. (1997). Students’ understanding of algebraic notation: 11-15. Educational Studies in Mathematics, 33, 1-19.
• Martino, A. M. & Maher, C. A. (1999). Teacher questioning to promote justification and generalization in mathematics: What research practice has taught us. Journal of Mathematical Behavior, 18 (1), 53-78.
• McMillan, J. H. (2004). Educational research. Fundamentals for the consumer. Boston, MA: Pearson Education.
• Moschkovich, J. (2003). What counts as mathematical discourse? International Group for the Psychology of Mathematics Education, 3, 325-332.
• Nakamura, S. K. (2009). Tesseracting to a fourth space: A teacher's journey in supporting kindergartners in appropriating sophisticated mathematical discourse (Doctoral dissertation). Available from ProQuest Dissertations and Theses Database. (Document ID 3391960).
• Nathan, M. J. & Knuth, E. J. (2003). A study of whole classroom mathematical discourse and teacher change. Cognition and Instruction, 21 (2), 175–207.
• National Council of Teachers of Mathematics (NCTM), (1991). Professional Standards for Teaching Mathematics. [Online]: Retrieved on 12-January-2015, at URL: http://www.nctm.org/flipbooks/standards/professionalteaching/index.html
• National Council of Teachers of Mathematics (NCTM), (2014). Principles to Actions: Ensuring Mathematical Success for All. Reston, VA: NCTM.
• Peressini, D. & Knuth, E. (1998). Why are you talking when you could be listening? The role of discourse in the professional development of mathematics teachers. Teaching and Teacher Education 14 (1), 107–125.
• Pimm, D. (1987). Speaking mathematically: Communication in mathematics classrooms. London: Routledge & Kegan Paul.
• Razfar, A. (2012). Discoursing mathematics: Using discourse analysis to develop and sociocultural and critical perspective of mathematics education. The Mathematics Educator, 22 (1), 39-62.
• Sfard, A. (2000). Steering (dis)course between metaphor and rigor: Using focal analysis to investigate the emergence of mathematical objects. Journal for Research in Mathematics Education, 31 (3), 296-327.
• Sfard, A. (2001). There is more to discourse than meets the ears: Looking at thinking as communication to learn more about mathematical learning. Educational Studies in Mathematics, 46 (1-3), 13-57.
• Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses and mathematizing. Cambridge, U.K.: Cambridge University Press.
• Spangler, D. & Hallman-Thrasher, A. (2014). Using task dialogues to enhance preservice teachers’ abilities to orchestrate discourse. Mathematics Teacher Educator, 3, 58–75.
• Stein, C. C. (2007). Let’s talk: Promoting mathematical discourse in the classroom. Mathematics Teacher, 101 (4), 285-289.
• Trocki, A., Taylor, C., Starling, T., Sztajn, P., & Heck, D. (2014). Using the think aloud strategy to launch a discourse-rich mathematics lesson: Introducing a mathematical think aloud. Teaching Children Mathematics, 21 (4).
• Truxaw, M. P. & DeFranco, T. C. (2007). Lessons from Mr. Larson, an inductive model of teaching for orchestrating discourse. Mathematics Teacher, 101 (4), 269-272.
• Walshaw, M. & Anthony, G. (2008). The teacher’s role in classroom discourse: A review of recent research into mathematics classrooms. Review of Educational Research, 78 (3), 516–551.
• Wille, A. M. (2016). Developing mathematical language proficiency in preservice teacher education: A case study. 13th International Congress on Mathematical Education, Hamburg, 24-31 July 2016.
• Yıldırım, H. & Şimşek, A. (2011). Sosyal bilimlerde nitel araştırma yöntemleri (8. Baskı). Ankara: Seçkin.