How to Introduce Function Concept in Textbooks?: Evaluations of Pre-Service Mathematics Teachers
Year 2020,
, 240 - 270, 30.06.2020
Zuhal Yılmaz
Hande Gülbağcı Dede
,
Hatice Akkoç
Abstract
Textbooks are one of the most commonly used
instructional resources by teachers. Using textbooks without critical
evaluation has a direct impact on instruction. For this reason, it is important
to examine how pre-service teachers evaluate and criticize textbooks. The aim
of this study is to examine how pre-service mathematics teachers evaluate the
introductory sections of three different mathematics textbooks on functions
each of which embraces a different function idea. In the study, pre-service
teachers’ written evaluation reports on the introductory sections were
examined. It was found that they could evaluate the introductory sections of
the books with a critical lens along with providing mathematical and
pedagogical justification. However, a significant weakness of pre-service
teachers’ mathematical justifications is the difficulty in supporting their
ideas about the limitations and affordances of function ideas. A major weakness
in pedagogical justifications was that the examples of daily life were privileged
regardless of to what extent they represented the mathematical meaning of
function.
Supporting Institution
Marmara Üniversitesi
Project Number
EGT-K-091116-0515
References
- Ayalon, M., Watson, A., & Lerman, S. (2017). Students’ conceptualisations of function revealed through definitions and examples. Research in Mathematics Education, 19(1), 1-19.
- Aydın, N., Camus, A. ve Kaya, M. (2018). Ortaöğretim matematik ders kitabı 10. Ankara: Aydın Yayıncılık.
- Bağrıaçık, M., Şişman, M., Lökçü, M., Çolak, Ö., Keskin, Ç., Atak, Ö. ve diğerleri. (2010). Ortaöğretim matematik 9. sınıf ders kitabı (5. Baskı). Ankara: Devlet Kitapları.
- Ball, D. L., & Feiman-Nemser, S. (1988). Using textbooks and teachers’ guides: A dilemma
for beginning teachers and teacher educators. Curriculum Inquiry, 18(4), 401–423.
- Banilower, E. R., Smith, P. S., Malzahn, K. A., Plumley, C. L., Gordon, E. M., Hayes, M. L. (2018). Report of the 2018 NSSME+. Chapel Hill, NC: Horizon Research.
- Beyer, C. J., & Davis, E. A. (2012). Learning to critique and adapt science curriculum materials: Examining the development of preservice elementary teachers' pedagogical content knowledge. Science Education, 96(1), 130-157.
- Cady, J. A., Hodges, T. E., & Collins, R. L. (2015). A comparison of textbooks' presentation of fractions. School Science and Mathematics, 115(3), 105-116.
- Cady, J., Meier, S. L., & Lubinski, C. A. (2006). Developing mathematics teachers: The transition from preservice to experienced teacher. The Journal of Educational Research, 99(5), 295-306.
- Collopy, R. (2003). Curriculum materials as a professional development tool: How a mathematics textbook affected two teachers' learning. The Elementary School Journal, 103(3), 287-311.
- Cooney, T. J., Beckmann, S., Lloyd, G. M., Wilson, P. S., & Zbiek, R. M. (2010). Developing essential understandings of functions for teaching mathematics in grades 9–12. Reston, VA: NCTM.
- Davis, J. D. (2009). Understanding the influence of two mathematics textbooks on prospective secondary teachers’ knowledge. Journal of Mathematics Teacher Education, 12(5), 365-389.
- DeMarois, P., & Tall, D. (1999). Function: Organizing principle or cognitive root? In O. Zaslavsky (Ed.), Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 257–264). Haifa, Israel: PME.
- Doorman, M., Drijvers, P., Gravemeijer, K., Boon, P., & Reed, H. (2012). Tool use and the development of the function concept: From repeated calculations to functional thinking. International Journal of Science and Mathematics Education, 10(6), 1243–1267.
- Drake, C., & Sherin, M. G. (2009). Developing curriculum vision and trust: changes
in teachers' curriculum strategies. In J. Remillard, B. Herbel-Eisenmann, & G. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction (pp. 321-337). New York: Routledge.
- Elsaleh, I. (2010). Research in brief: Teachers' interactions with curriculum materials in mathematics. School Science and Mathematics, 110(4), 177-179.Gök, M., Erdoğan, A., & Erdoğan, E. Ö. (2019). Transpositions of function concept in mathematics curricula and textbooks from the historical development perspective. International Journal of Instruction, 12(1), 1189-1206.
- Grossman, P., & Thompson, C. (2008). Learning from curriculum materials: Scaffolds for new teachers? Teaching and Teacher Education, 24(8), 2014-2026.Grouws, D. A., & Cebulla, K. J. (2000). Elementary and middle school mathematics at the crossroads. In T. L. Good (Ed.), American education, yesterday, today, and tomorrow (Vol. 2, pp. 209–255). Chicago, IL: University Press.
- İskenderoğlu, T., & Baki, A. (2011). İlköğretim 8. sınıf matematik ders kitabındaki soruların PISA matematik yeterlik düzeylerine göre sınıflandırılması. Eğitim ve Bilim, 36(161), 287-301.
- Jacobs, V. R., Lamb, L. L., & Philipp, R. A. (2010). Professional noticing of children's mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169-202.
- Jamieson-Proctor, R., & Byrne, C. (2008). Primary teachers' beliefs about the use of mathematics textbooks. In M. Goos, R. Brown, K. Makar (Eds.), Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia, (pp. 295-302). Brisbane, QLD: MERGA.
- Johansson, M. (2006). Teaching mathematics with textbooks: A classroom and curricular perspective. Unpublished doctoral dissertation, Lulea University of Technology, Sweden.
- Karakuyu, E., & Bağcı, O. (2013). Ortaöğretim matematik 9. sınıf ders kitabı. Ankara: Dikey Yayıncılık.
- Kerpiç, A., & Bozkurt, A. (2011). Etkinlik tasarım ve uygulama prensipleri çerçevesinde 7. sınıf matematik ders kitabı etkinliklerinin değerlendirilmesi. Mustafa Kemal Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 8(16), 303-318.
- Krippendorff, K. (2004). Content analysis: An introduction to its methodology. Thousand Oaks, CA: Sage.
- Mayring P. (2004). Qualitative content analysis. In: Flick U, von Kardoff E, Steinke I,. (Eds.) A companion to qualitative research (p. 266-269). London, UK: Sage.
- Milli Eğitim Bakanlığı [MEB], (2005). İlköğretim matematik dersi öğretim programı ve kılavuzu (6-8. sınıflar). Ankara: Devlet Kitapları Müdürlüğü.
- Milli Eğitim Bakanlığı [MEB]. (2013). Ortaöğretim matematik 9. sınıf 2. kitap. Ankara: Yazar.National Council of Teachers of Mathematics [NCTM]. (1989). Curriculum and evaluation standards for school mathematics. Reston: NCTM.
- Nicol, C. C., & Crespo, S. M. (2006). Learning to teach with mathematics textbooks: How preservice teachers interpret and use curriculum materials. Educational Studies in Mathematics, 62(3), 331-355.
- Niss, M. A. (2014). Functions learning and teaching. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 238-241). Dordrecht: Springer Netherlands.
- Robitaille, D. F., & Travers, K. J. (1992). International studies of achievement in mathematics. In D. A. Grouws (Ed.), Handbook of research in mathematics teaching and learning (pp. 687–709). New York: Macmillan.
- Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers' mathematics subject knowledge: The knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8(3), 255-281.
- Sağlam, R., & Alacacı, C. (2012). A comparative analysis of quadratics unit in Singaporean, Turkish and IMDP mathematics textbooks. Turkish Journal of Computer and Mathematics Education, 3(3), 131-147.
- Semerci, Ç. (2004). İlköğretim türkçe ve matematik ders kitaplarının genel değerlendirme ölçeği. Cumhuriyet Üniversitesi Sosyal Bilimler Dergisi, 28(1), 49-54.
- Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1-36.
- Steele, M. D., Hillen, A. F., & Smith, M. S. (2013). Developing mathematical knowledge for teaching in a methods course: The case of function. Journal of Mathematics Teacher Education, 16(6), 451-482.
- Tall, D. (1991). Advanced mathematical thinking. Dordrecht: Kluwer Academic Publishers.
- Tall, D.O. (2013). How humans learn to think mathematically: exploring the three worlds of mathematics. Cambridge: Cambridge University Press.
- Valverde, G. A., Bianchi, L. J., Wolfe, R. G., Schmidt, W. H., & Houang, R. T. (2002). According to the book: Using TIMSS to investigate the translation of policy into practice through the world of textbooks. Dordrecht, The Netherlands: Kluwer.
- Vinner, S. (1983). Concept definition, concept image and the notion of function. International Journal of Mathematical Education in Science and Technology, 14(3), 293-305.
- Watson, A., Jones, K., & Pratt, D. (2013). Key ideas in teaching mathematics: Research-based guidance for ages 9-19. Oxford: Oxford University Press.
- Yazarlar, (2016). Mathematics Teacher Education and Development, xx(x), xx-xx.
- Yıldırım, A., & Şimşek, H. (2018). Sosyal bilimlerde nitel araştırma yöntemleri (11. Baskı). Ankara: Seçkin Yayınları.
Ders Kitaplarında Fonksiyon Kavramına Nasıl Giriş Yapılıyor?: Matematik Öğretmen Adaylarının Değerlendirmeleri
Year 2020,
, 240 - 270, 30.06.2020
Zuhal Yılmaz
Hande Gülbağcı Dede
,
Hatice Akkoç
Abstract
Özet – Ders kitapları öğretmenlerin en çok kullandıkları ders materyalleri
arasında yer almaktadır. Ders kitaplarının değerlendirilmeden derslerde bire
bir kullanılması
öğretimi doğrudan etkilemektedir. Bu sebeple göreve başlayacak olan öğretmen
adaylarının ders kitaplarını nasıl değerlendiklerinin incelenmesi önemlidir. Bu
çalışmanın amacı matematik öğretmen adaylarının fonksiyona ait üç farklı fikri
benimseyen üç farklı ders kitabını nasıl değerlendirdiklerini belirlemektir.
Çalışmada adayların ders kitaplarının fonksiyona giriş bölümleri için
yazdıkları değerlendirme raporları incelenmiştir. Çalışma sonucunda adayların
ders kitaplarındaki farklı fonksiyon girişlerine matematiksel ve pedagojik
gerekçeler göstererek eleştirel bir gözle bakabildikleri ortaya çıkmıştır. Buna
rağmen adayların sundukları matematiksel gerekçeleri yeterli düzeyde
açıklayamadığı görülmüştür. Ayrıca adayların giriş bölümlerinde var olan günlük
hayat örneklerine çok fazla önem verdikleri fakat bu örneklerin fonksiyonu
matematiksel olarak temsil edip etmediğini yeterince irdelemedikleri
görülmektedir.
Project Number
EGT-K-091116-0515
References
- Ayalon, M., Watson, A., & Lerman, S. (2017). Students’ conceptualisations of function revealed through definitions and examples. Research in Mathematics Education, 19(1), 1-19.
- Aydın, N., Camus, A. ve Kaya, M. (2018). Ortaöğretim matematik ders kitabı 10. Ankara: Aydın Yayıncılık.
- Bağrıaçık, M., Şişman, M., Lökçü, M., Çolak, Ö., Keskin, Ç., Atak, Ö. ve diğerleri. (2010). Ortaöğretim matematik 9. sınıf ders kitabı (5. Baskı). Ankara: Devlet Kitapları.
- Ball, D. L., & Feiman-Nemser, S. (1988). Using textbooks and teachers’ guides: A dilemma
for beginning teachers and teacher educators. Curriculum Inquiry, 18(4), 401–423.
- Banilower, E. R., Smith, P. S., Malzahn, K. A., Plumley, C. L., Gordon, E. M., Hayes, M. L. (2018). Report of the 2018 NSSME+. Chapel Hill, NC: Horizon Research.
- Beyer, C. J., & Davis, E. A. (2012). Learning to critique and adapt science curriculum materials: Examining the development of preservice elementary teachers' pedagogical content knowledge. Science Education, 96(1), 130-157.
- Cady, J. A., Hodges, T. E., & Collins, R. L. (2015). A comparison of textbooks' presentation of fractions. School Science and Mathematics, 115(3), 105-116.
- Cady, J., Meier, S. L., & Lubinski, C. A. (2006). Developing mathematics teachers: The transition from preservice to experienced teacher. The Journal of Educational Research, 99(5), 295-306.
- Collopy, R. (2003). Curriculum materials as a professional development tool: How a mathematics textbook affected two teachers' learning. The Elementary School Journal, 103(3), 287-311.
- Cooney, T. J., Beckmann, S., Lloyd, G. M., Wilson, P. S., & Zbiek, R. M. (2010). Developing essential understandings of functions for teaching mathematics in grades 9–12. Reston, VA: NCTM.
- Davis, J. D. (2009). Understanding the influence of two mathematics textbooks on prospective secondary teachers’ knowledge. Journal of Mathematics Teacher Education, 12(5), 365-389.
- DeMarois, P., & Tall, D. (1999). Function: Organizing principle or cognitive root? In O. Zaslavsky (Ed.), Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 257–264). Haifa, Israel: PME.
- Doorman, M., Drijvers, P., Gravemeijer, K., Boon, P., & Reed, H. (2012). Tool use and the development of the function concept: From repeated calculations to functional thinking. International Journal of Science and Mathematics Education, 10(6), 1243–1267.
- Drake, C., & Sherin, M. G. (2009). Developing curriculum vision and trust: changes
in teachers' curriculum strategies. In J. Remillard, B. Herbel-Eisenmann, & G. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction (pp. 321-337). New York: Routledge.
- Elsaleh, I. (2010). Research in brief: Teachers' interactions with curriculum materials in mathematics. School Science and Mathematics, 110(4), 177-179.Gök, M., Erdoğan, A., & Erdoğan, E. Ö. (2019). Transpositions of function concept in mathematics curricula and textbooks from the historical development perspective. International Journal of Instruction, 12(1), 1189-1206.
- Grossman, P., & Thompson, C. (2008). Learning from curriculum materials: Scaffolds for new teachers? Teaching and Teacher Education, 24(8), 2014-2026.Grouws, D. A., & Cebulla, K. J. (2000). Elementary and middle school mathematics at the crossroads. In T. L. Good (Ed.), American education, yesterday, today, and tomorrow (Vol. 2, pp. 209–255). Chicago, IL: University Press.
- İskenderoğlu, T., & Baki, A. (2011). İlköğretim 8. sınıf matematik ders kitabındaki soruların PISA matematik yeterlik düzeylerine göre sınıflandırılması. Eğitim ve Bilim, 36(161), 287-301.
- Jacobs, V. R., Lamb, L. L., & Philipp, R. A. (2010). Professional noticing of children's mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169-202.
- Jamieson-Proctor, R., & Byrne, C. (2008). Primary teachers' beliefs about the use of mathematics textbooks. In M. Goos, R. Brown, K. Makar (Eds.), Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia, (pp. 295-302). Brisbane, QLD: MERGA.
- Johansson, M. (2006). Teaching mathematics with textbooks: A classroom and curricular perspective. Unpublished doctoral dissertation, Lulea University of Technology, Sweden.
- Karakuyu, E., & Bağcı, O. (2013). Ortaöğretim matematik 9. sınıf ders kitabı. Ankara: Dikey Yayıncılık.
- Kerpiç, A., & Bozkurt, A. (2011). Etkinlik tasarım ve uygulama prensipleri çerçevesinde 7. sınıf matematik ders kitabı etkinliklerinin değerlendirilmesi. Mustafa Kemal Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 8(16), 303-318.
- Krippendorff, K. (2004). Content analysis: An introduction to its methodology. Thousand Oaks, CA: Sage.
- Mayring P. (2004). Qualitative content analysis. In: Flick U, von Kardoff E, Steinke I,. (Eds.) A companion to qualitative research (p. 266-269). London, UK: Sage.
- Milli Eğitim Bakanlığı [MEB], (2005). İlköğretim matematik dersi öğretim programı ve kılavuzu (6-8. sınıflar). Ankara: Devlet Kitapları Müdürlüğü.
- Milli Eğitim Bakanlığı [MEB]. (2013). Ortaöğretim matematik 9. sınıf 2. kitap. Ankara: Yazar.National Council of Teachers of Mathematics [NCTM]. (1989). Curriculum and evaluation standards for school mathematics. Reston: NCTM.
- Nicol, C. C., & Crespo, S. M. (2006). Learning to teach with mathematics textbooks: How preservice teachers interpret and use curriculum materials. Educational Studies in Mathematics, 62(3), 331-355.
- Niss, M. A. (2014). Functions learning and teaching. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 238-241). Dordrecht: Springer Netherlands.
- Robitaille, D. F., & Travers, K. J. (1992). International studies of achievement in mathematics. In D. A. Grouws (Ed.), Handbook of research in mathematics teaching and learning (pp. 687–709). New York: Macmillan.
- Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers' mathematics subject knowledge: The knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8(3), 255-281.
- Sağlam, R., & Alacacı, C. (2012). A comparative analysis of quadratics unit in Singaporean, Turkish and IMDP mathematics textbooks. Turkish Journal of Computer and Mathematics Education, 3(3), 131-147.
- Semerci, Ç. (2004). İlköğretim türkçe ve matematik ders kitaplarının genel değerlendirme ölçeği. Cumhuriyet Üniversitesi Sosyal Bilimler Dergisi, 28(1), 49-54.
- Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1-36.
- Steele, M. D., Hillen, A. F., & Smith, M. S. (2013). Developing mathematical knowledge for teaching in a methods course: The case of function. Journal of Mathematics Teacher Education, 16(6), 451-482.
- Tall, D. (1991). Advanced mathematical thinking. Dordrecht: Kluwer Academic Publishers.
- Tall, D.O. (2013). How humans learn to think mathematically: exploring the three worlds of mathematics. Cambridge: Cambridge University Press.
- Valverde, G. A., Bianchi, L. J., Wolfe, R. G., Schmidt, W. H., & Houang, R. T. (2002). According to the book: Using TIMSS to investigate the translation of policy into practice through the world of textbooks. Dordrecht, The Netherlands: Kluwer.
- Vinner, S. (1983). Concept definition, concept image and the notion of function. International Journal of Mathematical Education in Science and Technology, 14(3), 293-305.
- Watson, A., Jones, K., & Pratt, D. (2013). Key ideas in teaching mathematics: Research-based guidance for ages 9-19. Oxford: Oxford University Press.
- Yazarlar, (2016). Mathematics Teacher Education and Development, xx(x), xx-xx.
- Yıldırım, A., & Şimşek, H. (2018). Sosyal bilimlerde nitel araştırma yöntemleri (11. Baskı). Ankara: Seçkin Yayınları.