EXAMINING PRE-SERVICE MATHEMATICS TEACHERS’ WRITTEN MATHEMATICAL COMMUNICATION SKILLS

Abstract

This study aims to investigate pre-service mathematics teachers’ written mathematical communication skills. The examined skills were to what extent the participants used mathematical language and terminology in their written explanations, and their proficiency in comprehending, interpreting, and applying mathematical definitions. Within this context, data were collected from 40 junior pre-service mathematics teachers via two data collection tools consisting of open-ended questions. In the first data collection tool, participants were given seven well-known mathematical statements and were asked to explain why these statements were true. In the second data collection tool, they were given definitions of angle and fraction and were asked to answer questions based on these definitions, and then to express the triangle, the circle, and the closed disc symbolically. Data were analyzed via content analysis and a rubric was utilized to determine the participants’ written mathematical communication levels. Results show that 27% of PSMTs’ written explanations were incorrect or unrelated to the statement, 40% consisted of low-level mathematical communication, 19% moderate-level communication, and 13% high-level communication. Participants used words at the most and visual expressions at the least in their written explanations. They could not interpret and apply the definitions in an expected level and performed a low-level success in using symbolic language to express geometrical concepts. Suggestions are made regarding how mathematics teaching programs can help pre-service teachers to develop their mathematical communication.

Keywords

• pre-service mathematics teachers,mathematical communication,mathematical language,written mathematical language

İlköğretim Matematik Öğretmen Adaylarının Yazılı Matematiksel İletişim Becerilerinin İncelenmesi

Abstract

Bu araştırmada ilköğretim matematik öğretmen adaylarının yazılı matematiksel iletişim becerilerinin incelenmesi amaçlanmıştır. Öğretmen adaylarının matematiksel düşüncelerini yazılı olarak ifade ederken matematiksel dil ve terminolojiyi ne derece etkin kullandıkları ve kendilerine verilen matematiksel bir tanımı anlama, yorumlama ve benzer durumlara uygulama düzeyleri incelenmiştir. Bu kapsamda veriler 40 üçüncü sınıf ilköğretim matematik öğretmen adayından iki açık uçlu form aracılığıyla toplanmıştır. Bu formlardan ilkinde, öğretmen adaylarından belirtilen yedi matematiksel ifadenin niçin doğru olduğunu açıklamaları istenirken, ikinci formda açı ve kesir tanımı verilmiş ve bu tanımlara göre kendilerine sorulan soruları cevaplamaları beklenmiş ve üçgen, çember ve daire kavramlarını sembolik olarak açıklamaları istenmiştir. Öğretmen adaylarının yazılı matematiksel iletişim düzeylerinin belirlenmesi amacıyla bir rubrik kullanılmış ve öğretmen adaylarından elde edilen tüm veriler içerik analizi aracılığıyla analiz edilmiştir. Elde edilen buğular, öğretmen adaylarının açıklamalarının %27’sinin yanlış veya madde ile ilgisiz olduğu, yarıya yakınında (%40) matematiksel dilin düşük seviyede kullanıldığı, %19’unda matematiksel dilin orta seviyede kullanıldığı ve yalnızca %13’ününde ise matematiksel dilin yüksek seviyede kullanıldığını göstermektedir. Öğretmen adayları matematiksel düşüncelerini yazılı olarak belirtirken en çok sözel en az ise görsel ifadeler kullanmayı tercih etmişler, tanımları yeterli seviyede yorumlayıp uygulayamamışlar ve üçgen, çember ve daireyi sembolik olarak ifade etmede düşük bir başarı göstermişlerdir.  Öğretmen adaylarının matematiksel fikirlerini yazılı bir biçimde ifade edecekleri etkinliklerle daha çok meşgul olmaları, matematiksel dilin kullanımına ilişkin akran ve uzman değerlendirmesi ile matematiksel dili kullanma düzeylerinin farkına varmaları ve tanımlar üzerinde durarak tanımların temel bileşenlerini kavramalarını ve farklı durumlara yorumlamalarını sağlayacak bir öğretim programının düzenlenmesi önerilebilir.

Keywords

• İlköğretim matematik öğretmen adayları,matematiksel iletişim,matematik dili,yazılı matematiksel iletişim

References

1. Alcock, L. (2008). Mathematicians’ perspectives on the teaching and learning of proof. CBMS Issues in Mathematics Education, 16, 73-100.
2. 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.
3. Argün, Z., Arıkan, A., Bulut, S., ve Halıcıoğlu, S. (2014). Temel Matematik Kavramların Künyesi. Ankara: Gazi.
4. Baker, D. & Campbell, C. (2004). Fostering the development of mathematical thinking: observations from a proofs course. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 14(4), 345-353.
5. Baykul, Y. (2000). İlköğretimde Matematik Öğretimi: 1-5. Sınıflar İçin. Pegem A. Yayıncılık. Ankara
6. Borasi, R., & Rose, B. J. (1989). Journal writing and mathematics instruction. Educational Studies in Mathematics, 20(4), 347-365.
7. Brendefur, J., & Frykholm, J. (2000). Promoting mathematical communication in the classroom: Two preservice teachers' conceptions and practices. Journal of Mathematics Teacher Education, 3(2), 125-153.
8. Cai, J., Jakabcsin, M. S., & Lane, S. (1996). Assessing students' mathematical communication. School Science and Mathematics, 96(5), 238-246.

9. Capraro, M. M. & Joffrion, H. (2006). Algebraic equations: can middle-school students meaningfully translate from words to mathematical symbols? Reading Psychology, 27 (2), 147-164.
10. Chapin, S. H., O'Connor, C., & Anderson, N. C. (2009). Classroom Discussions: Using Math Talk to Help Students Learn, Grades K-6. Sausalito, CA: Math Solutions.
11. Colwell, J., & Enderson, M.C. (2016). “When I hear literacy”: Using pre-service teachers’ perceptions of mathematical literacy to inform program changes in teacher education. Teaching and Teacher Education,53, 63-74.
12. Cunningham, F. & Roberts, A. (2010). Reducing the mismatch of geometry concept definitions and concept images held by pre-service teachers. IUMPS The Journal, 1, 1-17.
13. Demiray, E. (2013). Ortaokul matematik öğretmen adaylarının matematiksel ispat başarı düzeylerinin ve yanlış anlamlandırma nedenlerinin incelenmesi (Unpublished Master Thesis). Middle East Technical University, Ankara, Turkey.
14. Doğan, M., ve Güner, P. (2012). İlköğretim matematik öğretmen adaylarının matematik dilini anlama ve kullanma becerilerinin incelenmesi. X. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi, Niğde Üniversitesi, Niğde.
15. Fennema A., & Franke, M. L. (1992). Teachers’ knowledge and its impact. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning, (pp. 147-164). New York: Macmillan Publishing Company.
16. Gay, A. S. (2008). Helping teachers connect vocabulary and conceptual understanding. Mathematics Teacher,102(3), 218-223.
17. Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. Teachers College Press, Teachers College, Columbia University.
18. Güner, R. P., & Gülten, D. Ç. (2016). Pre-service primary mathematics teachers’ skills of using the language of mathematics in the context of quadrilaterals. International Journal on New Trends in Education & Their Implications, 7(1), 13-27.
19. Hiebert, J. (1992). Reflection and communication: Cognitive considerations in school mathematics reform. International Journal of Educational Research, 17(5), 439-456.
20. Kabasakalian, R. (2007). Language and thought in mathematics staff development: A problem probing protocol. Teachers College Record,109(4), 1-21.
21. Kaya, D., & Aydın, H. (2016). Elementary mathematics teachers' perceptions and lived experiences on mathematical communication. Eurasia Journal of Mathematics, Science & Technology Education, 12(6), 1619-1629.
22. Kenney, J. M. (2005). Literacy strategies for improving mathematics instruction. Alexandria, VA: Association for Supervision and Curriculum Development.
23. Kosko, K. V., & Wilkins, J. L. M. (2010). Mathematical communication and its relation to the frequency of manipulative use, International Electronic Journal of Mathematics Education, 5(2), 79-90.
24. Kotsopoulos, D. (2007). Mathematics discourse. It’s like hearing a foreign language. Mathematics Teacher,101(4), 301-305.
25. Köğce, D. (2013). İlköğretim matematik öğretmen adaylarının ispatın matematik öğrenmeye katkısı ile ilgili görüşleri ve ispat düzeyleri. International Periodical for the Languages, Literature and History of Turkish and Turkic, 8(12), 765-776.
26. Lomibao L., Luna, C.A., & Namoco, R.A. (2016). The influence of mathematical communication on students’ mathematics performance and anxiety. American Journal of Educational Research, 4(5),378-382.
27. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.
28. Marks, R. (1990). Pedagogical content knowledge: From a mathematical case to a modified conception. Journal of Teacher Education, 41(3), 3-11.
29. Millî Eğitim Bakanlığı (MEB) (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. sınıf) öğretim programı. 13.04.2019 tarihinde http://ttkb.meb.gov.tr/www/ogretim-programlari/icerik/72 adresinden erişilmiştir.
30. Mooney, C., Briggs, M., Gomm, R., Hansen, A., & McCullouch, J. (2012). Primary mathematics: Teaching theory and practice. Exeter: Learning Matters.
31. Moore, R. C. (1990). College students’ difficulties in learning to do mathematical proofs (Unpublished PhD dissertation). University of Georgia, Athens, USA.
32. National Council of Teachers of Mathematics (NCTM). (1995). Assessment standards for school mathematics. Reston, VA: Author.
33. National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics (Vol. 1). Reston, VA: National Council of Teachers of Mathematics.
34. Pape, S. J., Bell, C. V., & Yetkin, İ. E. (2003). Developing mathematical thinking and self-regulated learning: A teaching experiment in a seventh-grade mathematics classroom. Educational Studies in Mathematics, 53(3), 179-202.
35. Pourdavood, R.G., & Wachira, P. (2015). Importance of mathematical communication and discourse in secondary classrooms. Global Journal of Science Frontier Research: F Mathematics and Decision Sciences, 15(10), 9-20.
36. Rajagukguk, W. (2016). Incorporating learning motivation and self-concept in mathematical communicative ability. International Education Studies, 9(4), 155-164.
37. Sfard, A. (2001). There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning. Educational Studies in Mathematics, 46(1-3), 13-57.
38. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational researcher, 15(2), 4-14.
39. Sür, B., & Delice, A. (2016). The examination of teacher student communication process in the classroom- mathematical communication process model. SHS Web of Conferences, 26, 01059. DOI: 10.1051/shsconf/20162601059
40. Uğurel, I., Moralı, S., Koyunkaya, M. Y., & Karahan, Ö. (2016). Pre-service secondary mathematics teachers' behaviors in the proving process. Eurasia Journal of Mathematics, Science & Technology Education, 12(2).
41. Wahyuningrum, E., & Suryadi, D. (2014). Association of mathematical communication and problem-solving abilities: Implementation of MEAs strategy in junior high school, SAINSAB, 17, 38-50.
42. Yang, D. C., Reys, R. E., & Reys, B. J. (2009). Number sense strategies used by pre-service teachers in Taiwan. International Journal of Science and Mathematics Education, 7(2), 383-403.
43. Yeşildere, S. (2007). İlköğretim matematik öğretmen adaylarının matematiksel alan dilini kullanma yeterlikleri. Boğaziçi Üniversitesi Eğitim Dergisi, 24(2), 61-70.