An Integrated use of vectorial approach with analytical and synthetic approaches: a teaching experiment with eleventh grade students on quadrilaterals

Mut, Ali İhsan
The purposes of this research were to investigate the contributions of the instruction in which vectorial approach was integrated with synthetic and analytic approaches on quadrilaterals to the eleventh grade students’ problem solving strategies, to determine how the participants decided the type of approach to be utilized while solving problems on quadrilaterals, to specify major components of the instruction, and to examine the reflections of the participants’ on the instruction. Teaching experiment methodology was utilized to achieve the purposes of the research. Three eleventh grade students from a public high school in one of the cities located in Central Anatolian Region participated in 6-month teaching experiment, which included 37 teaching episodes during 2012-2013 spring semester and summer holiday. Data was collected by means of pre- and post-interviews, and pre- and post-tests. Moreover, the participants were presented geometry problems containing “proofbased problems” and “classic type-problems” related to quadrilaterals at the end of the chapters. The participants’ solutions to these problems were used as another source of the data for this study. While the interviews were analyzed by means of content analysis method, the students’ solutions in the pre- and post-tests, and their solutions for the problems at the end of each chapter were analyzed through descriptive analysis method. Frequency tables were provided for the findings from all of the participants’ works. According to the findings of the study, getting the skills to utilize vector representations, to integrate analytic, synthetic and vectorial approaches within a problem, and to make flexible transitions among these approaches can be stated as the main contributions of the instruction to the participants’ problem solving strategies. In addition, the students utilized vectorial approach especially in geometry problems on quadrilaterals that have perpendicular diagonals, that have pair of parallel sides or perpendicular sides, and quadrilaterals that are given on analytic coordinate plane. Furthermore, their solutions indicated that there were some changes in their preferences of approaches depending on the context of the problem. At the end of the instruction, the participants gained skills in comparing the approaches in terms of their advantages and disadvantages, and deciding the approach through which they could solve the problem more conveniently and efficiently.
Citation Formats
A. İ. Mut, “An Integrated use of vectorial approach with analytical and synthetic approaches: a teaching experiment with eleventh grade students on quadrilaterals,” Ph.D. - Doctoral Program, Middle East Technical University, 2016.