The Effect Of Dynamic Geometry Software On ...

TOJET: The Turkish Online Journal of Educational Technology – July 2015, Special Issue 2 for INTE 2015

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The Effect Of Dynamic Geometry Software On Prospective Teachers’ Achievement About Locus Problems Timur Koparan Bülent Ecevit University, Turkey [email protected]

ABSTRACT Geometric locus problems are topics that students find difficult to understand. To solve these problems, students must obtain the ability to think abstractly. Nevertheless, in the courses carried out with pen and paper, these skills are not enough to understand the geometric locus problems. The lack of moving structures and monitoring in traditional environment requires the need for alternative learning environment. Dynamic geometry software constitutes different learning environments for teachers and students. This software has features such as dynamic free dragging, dynamic measurements, transformations, animation and locus (Gao, 1998). The aim of this study is to determine the effect of dynamic geometric software on prospective mathematics' teachers’ achievement on locus problems. For this aim, quasi experimental design was used. The study took place during the 2014–2015 spring semester at Bülent Ecevit University in Zonguldak city of Turkey. Of the 65 prospective teachers who participated in the study, 32 were in the control group. The remaining 33 prospective teachers were in the experimental group. Locus problems were solved in experimental group with dynamic software (Cabri and Geogebra). In the control group classes were conducted in traditional learning environment. A data collection tool has been developed which consists of 10 open-ended questions. This tool was applied before and after the implementation in both group. The findings showed that the dynamic geometry software has a positive effect on prospective teachers’ achievement on locus problems. INTRODUCTION Development of technology has led the educators to take step towards the integration of computer into learning environment (Akkaya, Tatar, & Kağızmanlı, 2011). Computers have changed the way we teach mathematics. The use of computers in the teaching of mathematics is receiving increasing attention from teachers and researchers. Computers are the most preferred and utilized tools in education among the available technologies, and they have many properties. Computer-aided teaching helps students develop high level of cognitive skills and allow students to live experiences of a mathematician and construct their own mathematics (Baki, Güven & Karataş, 2002). The aim of using computer in mathematics instruction is to increase students’ interest towards the subject and to help them understand the concepts visually easier where they have difficulty to imagine via traditional instruction (Yıldız, Güven & Koparan, 2010). Since geometry is founded on abstract structures, some difficulties may be encountered in understanding some geometrical concepts such as locus (Açıkgül & Aslaner, 2012; Güven, & Karataş, 2009). The concept of locus; defined as a cluster of points with the same characteristics (Sarıgül, 2001). Most students will not move the point in a structure and even it is almost impossible to imagine for students. Because of the difficulty in visualizing geometric problems they are often not included in textbooks (Cha & Moss, 2004). Locus problems are different from each other and thus it is very difficult for them to develop materials in traditional media. At the same time, locus problems in the traditional learning environment where work carried out using pencil and paper are quite difficult (Güven & Karataş, 2009). The majority of the studies in the literature for solving the locus problems are to emphasize the dynamic geometry software (Antohe, 2009; Baki, Çekmez, & Kösa, 2009; Botana & Valcarce, 2003; Botana, Aba´ Nades & Escribano, 2011; De Villiers, 2008 Gorghiu et al., 2009). Dynamic geometry software is a highly effective tool to solve these problems related to locus (Güven, 2008; Güven & Karatas, 2009; Jahn, 2002; Real & Leung, 2006). They have features such as track and locus. These properties offer new possibilities for locus problems (Cha & Moss, 2004; Jahn, 2002). Thanks to these features, locus of a point can be easily visualized. Thus, students can determine the locus of a point relative to another point in the structure. Dynamic geometry software interactively offers students the opportunity to explore how the locus occurred. There is different qualitative research on the use of dynamic geometry software in the process of solving locus problems in the literature. However, the effect of dynamic geometry software on student or prospective teachers’ achievement about locus problems has not been studied so much up to now. The purpose of this study is to investigate the effect of dynamic geometry software on prospective mathematics' teachers achievement related to locus problems and it is also evaluating opportunities offered by the dynamic geometry software.

Copyright © The Turkish Online Journal of Educational Technology

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THE STUDY Quasi experimental design was used in this study. All participant solved problems by using paper-pencil approach before the implementation. At the beginning of the study, technical features of Cabri II and Geogebra software was introduced to experimental group. Emphasis was given on how to give computer-assisted instruction in geometry courses using this software; after then, they used software for making their solutions. During the study, the prospective teachers were observed in their natural environment. In the control group, classes were conducted in traditional learning environment. The study took place at Bülent Ecevit University in Zonguldak city of Turkey. It was carried out in the spring semester of 2014-2015 academic year on 65 prospective teachers who are third-year university students in a department of elementary school mathematics teaching. Of the 65 prospective mathematics teachers who participated in the study, 32 were in the control group. The remaining 33 prospective teachers were in the experimental group. The prospective teachers in the sample group volunteered for the study. The data in this study were collected using a test developed related to geometry. The test was developed by two researchers working in the field of geometry education. This test consists of ten open ended questions related to locus problems and concept. These ten open-ended questions are shapeless. A pilot study was conducted before the actual implementation. Thus probable deficiencies were sought related to the questions. In this way, the appropriateness of the questions was tested. Participants are asked the following questions; What is the circle? Please define. What is the parabola? Please define. What is an ellipse? Please define. What is the hyperbola? Please define. What is the locus of the intersection of the central pillar of the beams in a circle? What is the locus of the intersection of the edge of the central pillar of a triangle? What is the geometric point of equal distance from two fixed points in the plane? What is the locus of the intersection of the internal bisector of a triangle? Draw a triangle on the circle. What is the locus according to a corner of the triangle's center of gravity? Draw an angle of 120 degrees. Draw an equilateral triangle with two corners on the arm angles. What is the locus of the third corner? The study has completed a total four weeks. First and last week pre-test and post-test are conducted. The application process was carried out in the computer lab for six hours. Quasi-experimental design was used in this study and activities lasted 4 weeks. In the pre-test all prospective teachers were asked to solve locus problems with paper and pencil. Then half of the class was defined as experimental group and the rest as control group. Subjects in the experimental group were held in computerized environments (3 hours per week for 2 weeks). Cabri II and Geogebra software was used as the software and various applications about locus subject were carried out. In the control group, the same procedure was followed without using dynamic geometry software. These problems are solved sometimes by students, sometimes by the instructor. A majority of the solutions showed an algebraic characteristic Prospective teachers’ answers to questions about locus before and after application were examined. The obtained data were used for statistical analysis with SPSS. At the same time, the differences between answers of experimental and control group were qualitatively examined. FINDINGS The findings from the questions related to locus problems are given in this section. The results were presented as findings from quantitative data and the findings from qualitative data. The findings from quantitative data The data obtained from the quantitative were analyzed using SPSS programme (t test and covariance analysis). Independent t-test was performed to determine whether a significant difference exists between the pre-test scores of the prospective teacher in experimental and control groups and the results were given in Table 1.

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! Table 1. Independent two sample t test results Group N Mean Pre-test

Exp. Cont.

33 32

34,54 32,50

SD 12,01 13,91

SD Error Mean 2,09 2,45

sd

t

p

63

0,635

0,528

Looking at the measures of the two groups pre-test averages are very close to each other (34,54 and 32,50). The result of the experimental and control groups compared to pretest before the implementation by the t test results, there is no difference between groups t(63) = 0,635, p > 0,05. Experimental group t test result was given in Table 2. Table 2. Experimental group pre-test and post-test t test results Exp. N Mean SD SD Error Group Mean Pre-test 33 34,54 12,01 2,09 Post-test 33 65,15 13,94 2,42

sd

t

32

-11,898

p 0,000

Looking at the results of the experimental groups the average score of prospective teachers at the pre-test was 34,54 (SD = 12,01), while the average score at post was 65,15 (SD = 2,42). Results from a dependent t-test indicate that this difference was significant, t(32) = -11,898, p < 0,05. Supported with dynamic geometry software learning approach may be regarded as a positive effect on prospective teachers’ achievement. Control group t test result was given in Table 3. Table 3. Control group pre-test and post-test t test results Control N Mean SD SD Error Group Mean Pre-test 32 32,50 13,91 2,45 Post-test 32 43,43 11,53 2,03

sd

t

p

31

-5,536

0,000

Looking at the result of the control groups, the average score of prospective teachers at the pre-test was 32,50 (SD = 13,91), while the average score at post-test was 43,43 (SD = 11,53). Results from a dependent t-test indicate that this difference was significant, t(31) = -5,536, p