ISSN 1305-3515
 

Research Article 


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

Dilek Girit Yildiz,Didem Akyuz.

Abstract
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 teachersí 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 studentsí 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 studentsí thinking to design effective lessons.

Key words: Lesson planning, mathematical knowledge for teaching, pattern generalization, studentsí generalization strategies


 
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Pubmed Style

Dilek Girit Yildiz,Didem Akyuz. Mathematical knowledge of two middle school mathematics teachers in planning and teaching pattern generalization. EEO. 2020; 19(4): 2098-2117. doi:10.17051/ilkonline.2020.763457


Web Style

Dilek Girit Yildiz,Didem Akyuz. Mathematical knowledge of two middle school mathematics teachers in planning and teaching pattern generalization. http://ilkogretim-online.org//?mno=121832 [Access: August 11, 2020]. doi:10.17051/ilkonline.2020.763457


AMA (American Medical Association) Style

Dilek Girit Yildiz,Didem Akyuz. Mathematical knowledge of two middle school mathematics teachers in planning and teaching pattern generalization. EEO. 2020; 19(4): 2098-2117. doi:10.17051/ilkonline.2020.763457



Vancouver/ICMJE Style

Dilek Girit Yildiz,Didem Akyuz. Mathematical knowledge of two middle school mathematics teachers in planning and teaching pattern generalization. EEO. (2020), [cited August 11, 2020]; 19(4): 2098-2117. doi:10.17051/ilkonline.2020.763457



Harvard Style

Dilek Girit Yildiz,Didem Akyuz (2020) Mathematical knowledge of two middle school mathematics teachers in planning and teaching pattern generalization. EEO, 19 (4), 2098-2117. doi:10.17051/ilkonline.2020.763457



Turabian Style

Dilek Girit Yildiz,Didem Akyuz. 2020. Mathematical knowledge of two middle school mathematics teachers in planning and teaching pattern generalization. Elementary Education Online, 19 (4), 2098-2117. doi:10.17051/ilkonline.2020.763457



Chicago Style

Dilek Girit Yildiz,Didem Akyuz. "Mathematical knowledge of two middle school mathematics teachers in planning and teaching pattern generalization." Elementary Education Online 19 (2020), 2098-2117. doi:10.17051/ilkonline.2020.763457



MLA (The Modern Language Association) Style

Dilek Girit Yildiz,Didem Akyuz. "Mathematical knowledge of two middle school mathematics teachers in planning and teaching pattern generalization." Elementary Education Online 19.4 (2020), 2098-2117. Print. doi:10.17051/ilkonline.2020.763457



APA (American Psychological Association) Style

Dilek Girit Yildiz,Didem Akyuz (2020) Mathematical knowledge of two middle school mathematics teachers in planning and teaching pattern generalization. Elementary Education Online, 19 (4), 2098-2117. doi:10.17051/ilkonline.2020.763457