Prospective Middle School Mathematics Teachers’ Mathematical Communication, Mathematical and Pedagogical Knowledge

Year 2017, Volume: 25 Issue: 5, 1909 - 1924, 15.09.2017

Tangül Kabael Ayla Ata Baran

Abstract

The purpose of this study was to investigate prospective teachers’ mathematical
communication and to explore whether there was a relationship between their forms of
communication and mathematical and pedagogical knowledge. Data was collected through
clinical interviews. Data related to participants’ interviews was analyzed by focal and
preoccupational analysis and data related to researchers’ interviews was analyzed by content
analysis. According to the findings the participant communicated effectively had strong
algebraic thinking skill and her pedagogical explanations were based on her own mathematical
understanding. The participant communicated ineffectively had poor algebraic thinking skill
and her pedagogical explanations were based on external sources. 

Keywords

Mathematical communication, mathematical knowledge, pedagogical knowledge, middle school mathematics teacher

Ortaokul Matematik Öğretmen Adaylarının Matematiksel İletişimleri, Matematik ve Pedagoji Bilgileri

Abstract

Bu araştırmada ortaokul matematik öğretmen adaylarının matematiksel iletişimleri ve
varsa matematik ve pedagoji bilgileri ile iletişim biçimleri arasındaki ilişkileri derinlemesine
incelemek amaçlanmaktadır. Araştırmanın verileri klinik görüşmeler aracılığıyla toplanmıştır.
Katılımcıların gerçekleştirdikleri görüşme verileri odaksal ve etkileşimsel analiz yöntemleriyle,
katılımcılar ile gerçekleştirilen görüşme verileri ise içerik analizi yöntemiyle analiz edilmiştir.
Araştırma sonucunda ortaokul öğrencisi ile etkili iletişim kurabilen öğretmen adayının güçlü
cebirsel düşünme becerisine sahip olduğu ve pedagoji bilgisine ilişkin açıklamalarını kendi
matematiksel anlamlandırmasına dayandırdığı görülmüştür. Ortaokul öğrencisi ile etkili
iletişim kuramayan öğretmen adayının ise cebirsel muhakeme becerisinin zayıf olduğu ve
pedagoji bilgisine ilişkin açıklamalarını dışsal kaynaklara dayandırdığı görülmüştür. 

Keywords

Matematiksel iletişim, matematik bilgisi, pedagoji bilgisi, ortaokul matematik öğretmen adayı

References

• Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal, 90(4), 449–466.
• Barwell, R. (2008). Discourse, mathematics and mathematics education. In N. H. Hornberger (Ed.), Encyclopedia of language and education (pp. 317-328). New York: Springer
• Blanke, B. L. (2009). Understanding mathematical discourse in the elementary classroom: A case study (Doctoral dissertation). Available from ProQuest Dissertations and Theses Database. (Document ID 3352007).
• Brendefur, J., & Frykholm, J. (2000). Promoting mathematical communication in the classroom: Two preservice teachers’ conceptions and practices. Journal of Mathematics Teacher Education, 3, 125-153.
• Cazden, C. B. (2001). Classroom Discourse: The Language of Teaching and Learning, (2nd ed.), Portsmouth, NH: Heinemann.
• Charlesworth, B. (2005). Prekindergarten mathematics: Connecting with national standards. Early Childhood Education Journal, 32(4), 229–236
• Griffin, S. (2004). Building number sense with number worlds: A mathematics program for young children. Early Childhood Research Quarterly, 19, 173–180.
• Hufferd-Ackles, K., Fuson, K. C., & Sherin, M. G. (2004). Describing levels and components of a math-talk learning community. Journal for Research in Mathematics Education, 35 (2),81-116.
• Jung, H. Y., & Reifel. S. (2011). Promoting children’s communication: A kindergarten teacher’s conception and practice of effective mathematics instruction. Journal of Research in Childhood Education, 25, 194-210.
• Lee, C. (2006). Language for Learning Mathematics - Assessment for Learning in Practice. Buckingham: Open University Press.
• Morrissey, R. (2011). An examination of the discourse in a graduate mathematics methods course. Dissertations, Theses and Capstone Projects. Paper 432.
• Moyer, P. S., & Milewicz, E. (2002). Learning to question: Categories of questioning used by preservice teachers during diagnostic mathematics interviews. Journal of Mathematics Teacher Education, 5, 293-315
• 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.
• Sfard, A., & Kieran, C. (2001). Preparing teachers for handling students' mathematical communication: Gathering knowledge and building tools. In F. L. Lin & T. J. Cooney (Eds.), Making sense of mathematics teacher education (pp. 187-205). Dordrecht, The Netherlands: Kluwer.
• Silver, E. A., & Smith, M. S. (1996). Building discourse communities in mathematics classrooms: A worthwhile but challenging journey. In P. C. Elliot & M. J. Kenney (Eds.), Communication in mathematics, K-12 and beyond (pp. 20-28). Reston, VA: National Council of Teachers of Mathematics.
• Yackel, E., Cobb, P., & Wood, T. (1990). The interactive constitution of mathematical meaning in one second grade classroom: An illustrative example. Journal of Mathematical Behaviour, 11(2), 469-488.
• Yıldırım, H. ve Şimşek, A. (2011). Sosyal bilimlerde nitel araştırma yöntemleri (8. Baskı). Ankara: Seçkin.