Date

2015

Author

Sofuoğlu, Sevgi

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The purpose of this study is to investigate high school students’ and prospective mathematics teachers’ graphing, their reasoning and the relation between their graphing and reasoning in the context of a modeling task that requires graphing and covariational reasoning. This study is conducted within a larger project designed to develop in-service and prospective mathematics teachers’ knowledge and skills about modeling and using modeling in mathematics education. Qualitative method is used in the study and high school students and prospective mathematics teachers are treated as two cases. 24 prospective mathematics teachers and 107 10th and 11th grade level high school students participated in the study. Data for the study is collected through worksheets, and audio and video recordings. Qualitative data analysis methods are used to analyze the data. Analysis of data revealed that students’ graphs can be categorized into four groups: smooth, smooth chunk, uniform chunks, non-uniform chunks; and their covariational reasoning related to rate of change can be categorized into three groups: i) using extensive quantities, ii) creating intensive quantity-comparing intensities, iii) creating intensive quantity-consider variation in intensity. While, the prospective mathematics teachers constructed graphs in smooth or smooth chunks and considered variance in the intensity, the high school students rarely drew smooth graphs and usually constructed graphs in smooth chunks, uniform chunks and non-uniform chunks. Furthermore, the high school students considered variance of intensities, compared intensities, and extensive quantities in their reasoning. There exists a consistency between participants’ sketches of graphs and their reasoning about rate of change. The students who constructed smooth graphs considered variation in intensities with a global approach. All the students who drew smooth graphs took slope of the graph into consideration. Students who sketched graphs in smooth chunk considered variation in intensity, and compared intensities with a more local approach. Students who drew chunky graphs used extensive quantities with a local approach. However, some students who drew non-uniform chunks changed the slope of the graph to represent variation similar to students who drew smooth graphs. Associating students’ sketches of graphs with their reasoning provided us a further insight into how students interpret a covariational situation; and how students’ understanding of covariation can be deduced from their graphing.

Subject Keywords

Mathematics, Calculus of variations, Graphic methods, Mathematics teachers., Student teachers, Teaching, Learning, Psychology of.

URI

http://etd.lib.metu.edu.tr/upload/12619697/index.pdf
https://hdl.handle.net/11511/25387

Collections

Graduate School of Natural and Applied Sciences, Thesis