Mathematical knowledge of two middle school mathematics teachers in planning and teaching pattern generalization


GİRİT D., AKYÜZ D.

Elementary Education Online, cilt.19, sa.4, ss.2098-2117, 2020 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 19 Sayı: 4
  • Basım Tarihi: 2020
  • Doi Numarası: 10.17051/ilkonline.2020.763457
  • Dergi Adı: Elementary Education Online
  • Derginin Tarandığı İndeksler: Scopus, EBSCO Education Source, Directory of Open Access Journals, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.2098-2117
  • Anahtar Kelimeler: Lesson planning, Mathematical knowledge for teaching, Pattern generalization, Students’ generalization strategies
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

© 2020, Ankara University. All rights reserved.Examining the knowledge of teachers in practice may shed light on understanding how students learn and finding out why they have difficulty in learning. This paper focused on teachers' knowledge of pattern generalization in instruction with the consideration of students' generalization strategies in planning. The multiple-case study design was used for this study to compare and contrast two middle school mathematics teachers’ lesson planning and instruction. Lesson plans, pre-observation interviews, observations and post-observation interviews were used as the data collection tools. The data were analyzed by using the Mathematical Knowledge for Teaching (MKT) model. The findings showed that the two teachers used numerical reasoning in all representations, but they had difficulties in using figural reasoning. They generally used the tabular representation effectively to underlie the relationship of generalization. While one of the teachers defined the pattern concept correctly and always emphasized analyzing the relationship between the position number and the term, the other teacher defined the pattern concept partially correctly, and her inadequate explanations of functional thinking caused some misunderstandings of students about generalization. It was also observed that the students’ lack of knowledge about algebraic expressions prevented them from obtaining a general rule. Through the cases of these two teachers, it was noted that teachers need to have a good conceptual mathematical understanding and also knowledge of students’ thinking to design effective lessons.