Habits of Mind in Teaching of Geometric Patterns: Investigation of Textbooks

Year 2021, Volume: 5 Issue: 1, 62 - 78, 26.04.2021

Deniz Eroğlu

https://doi.org/10.32960/uead.878814

Cited By: 2

Abstract

The purpose of this study is to examine the parts of patterns in middle school seventh grade books in the context of habits of mind related to algebra and to discuss the implementation of a geometric pattern activity in order to develop students' algebraic thinking and gain habits of mind. For this purpose, the research consists of two parts. In the first part, the pattern sections of two different seventh grade textbooks taught by the Ministry of National Education were analyzed using the document analysis method. In the second part, it was explained how mental habits can be developed by adapting a pattern problem in the book of the Ministry of National Education. This research will guide academicians who conduct algebraic thinking studies, mathematics teachers, and program developers who organize the curriculum in the development of students' algebraic thinking.

Keywords

habits of mind, algebraic thinking, patterns, seventh grade, mathematics textbooks, document analysis

Yedinci Sınıf Ders Kitaplarındaki Örüntüler Konusunun “Zihinsel Alışkanlıklar” Perspektifinden İncelenmesi

Abstract

Bu çalışmanın amacı, ortaokul yedinci sınıf kitaplarında yer alan örüntüler konusunun cebirle ilişkili zihinsel alışkanlıklar bağlamında incelenmesi ve bu konuda öğrencilerin cebirsel düşünme becerilerini geliştirmek ve onlara zihinsel alışkanlıklar kazandırmak için bir geometrik şekil örüntüsü etkinliğinin uygulanma sürecini tartışmaktır. İlk bölümde öncelikle MEB tarafından okutulan iki farklı yedinci sınıf ders kitabının örüntüler bölümleri döküman analizi yöntemi kullanılarak analiz edilmiştir. İkinci bölümde ise MEB’in kitabında yer alan bir örüntü probleminin uyarlaması yapılarak, zihinsel alışkanlıkların nasıl geliştiriebileceği açıklanmıştır. Bu araştırma cebirsel düşünme çalışmaları yapan akademisyenlere, matematik öğretmenlerine ve öğretim programını düzenleyen program geliştiricilere, öğrencilerin cebirsel düşünme becerilerinin geliştirilmesinde yol gösterecek niteliktedir.

Keywords

zihinsel alışkanlıklar, cebirsel düşünme, örüntüler, yedinci sınıf, matematik ders kitabı, doküman analizi

References

• Arcavi, A. (2008). Modelling with graphical representations. For the Learning of Mathematics, 28(2), 2-10.
• Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special. Journal of teacher education, 59(5), 389-407.
• Blanton, M. L., & Kaput, J. J. (2005). Characterizing a classroom practice that promotes algebraic reasoning. Journal for research in mathematics education, 36(5), 412-446.
• Bowen, G.A. (2009), "Document Analysis as a Qualitative Research Method", Qualitative Research Journal, 9(2), 27-40.
• Council of Chief State School Officers (CCSSO). (2021). Common core state standards initiative. Washington, DC: Author. Retrieved from http://www.corestandards.org/
• Costa, A. L., & Kallick, B. (2008). Habits of mind in the curriculum. Learning and leading with habits of mind, 16, 42-58.
• Cuoco, A., Goldenberg, E. P., & Mark, J. (1996). Habits of mind: An organizing principle for mathematics curricula. The Journal of Mathematical Behavior, 15(4), 375-402.
• Cuoco, A., Goldenberg, E. P., & Mark, J. (2010). Contemporary curriculum issues: Organizing a curriculum around mathematical habits of mind. The Mathematics Teacher, 103(9), 682-688.
• Driscoll, M. (1999). Fostering algebraic thinking: A guide for teachers, Grades 6-10. Portsmouth, NH: Heinemann.
• Driscoll, M. J., DiMatteo, R. W., Nikula, J., & Egan, M. (2007). Fostering geometric thinking: A guide for teachers, grades 5-10. Portsmouth, NH: Heinemann.
• Erşen, Z, Bülbül, B, Güler, M . (2021). Analysis of Solved Examples in Mathematics Textbooks Regarding the Use of Geometric Habits of Mind. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 12 (1), 349-377. DOI: 10.16949/turkbilmat.850882
• Foster, D. (2007). Making meaning in algebra examining students’ understanding and misconceptions. In A. H. Schoenfeld (Ed.), Assessing Mathematical Proficiency (pp.163-176). Berkeley: Cambridge University Press.
• Friel, S. N., & Markworth, K. A. (2009). A framework for analyzing geometric pattern tasks. Mathematics teaching in the Middle school, 15(1), 24-33.
• Harel, G. (2008). What is mathematics? A pedagogical answer to a philosophical question. In B. Gold & R. Simons (Eds.), Current issues in the philosophy of mathematics from the perspective of mathematicians. Washington, DC: Mathematical American Association.
• Kaput, J. J. (1999). Teaching and learning a new algebra. In E. Fennema & T. A. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 133-155). Mahwah, NJ: Lawrence Erlbaum Associates.
• Kilpatrick, J., & Izsák, A. (2008). A history of algebra in the school curriculum. Algebra and algebraic thinking in school mathematics, 70, 3-18.
• Lannin, J. K. (2004). Developing mathematical power by using explicit and recursive reasoning. The Mathematics Teacher, 98(4), 216-223.
• Lee, L., & Freiman, V. (2006). Developing algebraic thinking through pattern exploration. Mathematics teaching in the middle school, 11(9), 428-433.
• Mark, J., Cuoco, A., Goldenberg, E. P., & Sword, S. (2010). Contemporary curriculum issues: Developing mathematical habits of mind. Mathematics Teaching in the Middle School, 15(9), 505-509.
• Mason, J. (2008). Being mathematical with and in front of learners: Attention, awareness, and attitude as sources of differences between teacher educators, teachers and learners. In International Handbook of Mathematics Teacher Education: Volume 4 (pp. 31-55). Brill Sense.
• Matsuura, R., Sword, S., Piecham, M., B., Stevens, G., & Cuoco, A. (2013). Mathematical habits of mind for teaching: Using language in algebra classrooms. The Mathematics Enthusiast, 10(3), 735-776.
• MEB (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar). Ankara: Milli Eğitim Bakanlığı. Moyer, J., Huinker, D., & Cai, J. (2004). Developing algebraic thinking in the earlier grades: A case study of the US Investigations curriculum. The Mathematics Educator, 8(1), 6-38.
• National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics NCTM. Reston: VA.
• Radford, L., & Peirce, C. S. (2006). Algebraic thinking and the generalization of patterns: A semiotic perspective. In Proceedings of the 28th conference of the international group for the psychology of mathematics education, North American chapter (Vol. 1, pp. 2-21).
• Radford, L. (2011). Embodiment, perception and symbols in the development of early algebraic thinking. In 35th Conference of the International Group for the Psychology of Mathematics Education Developing Mathematical Thinking (Vol. 93).
• Radford, L. (2008). Connecting theories in mathematics education: Challenges and possibilities. ZDM, 40(2), 317-327.
• Radford, L. (2000). Signs and meanings in students' emergent algebraic thinking: A semiotic analysis. Educational studies in mathematics, 42(3), 237-268.
• Rivera, F. D., & Becker, J. R. (2011). Formation of pattern generalization involving linear figural patterns among middle school students: Results of a three-year study. In Early algebraization (pp. 323-366). Springer, Berlin, Heidelberg.
• Seaman, C. E., & Szydlik, J. E. (2007). Mathematical sophistication among preservice elementary teachers. Journal of Mathematics Teacher Education, 10(3), 167-182.
• Warren, E., & Cooper, T. (2008). Generalising the pattern rule for visual growth patterns: Actions that support 8 year olds’ thinking. Educational Studies in mathematics, 67(2), 171-185.
• Yıldırım, A., & Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri. Seçkin yayıncılık: Ankara.