The effectiveness of teaching via constructed examples by using GeoGebra software in learning high school geometry theorems

The purpose of this study is to investigate the use of researcher-made examples by GeoGebra software as an educational tool to increase the learning skills of geometric theorems and assess the attitude of 11th-grade math students towards geometry and provide a practical model for teaching geometry.

 This research is a quasi-experimental type with an experimental group and a control group. It uses pre-test and post-test and is applied in terms of purpose. The statistical population of the present study included all-female high school students in the eleventh grade of mathematics in the districts three and four of Isfahan in the academic year 2021-2022. The statistical sample consisting of 120 students was purposefully selected using the available sample method. A pre-test of geometry course 1 as well as a three-scale Cattell intelligence test were administered to all groups in the same manner. A researcher-created questionnaire on a five-point Likert scale was given to all groups to assess the students' attitudes towards geometry before and after the research. The opinions of experienced education consultants and teachers were used to assess the validity of the questionnaire, and after correction, it was made available to students. The Cronbach's alpha coefficient was used to determine the reliability of the questions. Reliability was 0.93 indicating the high reliability of the questionnaire. The experimental group was taught how to use, construct simple shapes, and measure the components of shapes in GeoGebra via cyberspace, and their problems were solved by the researcher in five one-hour sessions.A researcher- created nine practical examples related to the sections of the circle and transformation sections in Geometry 2 using the opinions of five experienced professors and teachers, their answers were designed using GeoGebra software, and they were provided to the experimental group. Using this software, they guessed the components and checked their accuracy. The correct answers were then given to them. They also deduced the original form of the relevant theorems and demonstrated them. During this time, the control groups were given the contents of this section of the book in the traditional manner. The post-test was administered equally for all groups at the end of this period. The inferential part of SPSS 25 software, which included MANCOVA analysis, Kolmogorov-Smirnov test, Levin test, and M box test, was used to analyze the obtained data.

The results of MANCOVA analysis show that the use of examples made by GeoGebra software compared to traditional teaching has a statistically significant effect on students' ability to guess and learn geometric theorems. In addition, the questionnaire given to the students show that they value the use of GeoGebra to solve these examples and guess and prove the theorems related to them and have more motivation to participate in the geometry class.

According to the findings, the teaching method of proving a geometric theorem by using examples made by GeoGebra software increases the amount of learning in the classroom and increases students' motivation to learn geometry, and makes the classroom more attractive to them. This method increases students' creativity and causes them to be more involved in the learning process and becomes more active in the classroom, and these skills enable students and facilitate learning in the geometry classroom. There were some issues with the research. Some school principals, for example, refused to allow this method of teaching geometry. Some geometry teachers were also unfamiliar with GeoGebra software. In-service courses in this area are ideal for math teachers who want to help their students learn geometry more effectively and enthusiastically.