The impact of the GeoGebra dynamic program on the learning of functions in lower secondary school - Pihlap, Sirje (LUMAT-B: International Journal on Math, Science and Technology Education, 2026)
Functions are a fundamental topic in school mathematics. Understanding the concept of functions requires students to understand various representations of functions and their interconnections. Finding relationships among different representations can be challenging because it often necessitates viewing multiple forms simultaneously. In traditional learning, where graphs are drawn by hand, plotting various graphs is time-consuming and may involve additional difficulties in calculation and drawing. In this context, using a computer program offers distinct advantages: it enables the rapid, simultaneous display of a function’s graph and equation, allowing students to immediately observe how changes in one representation affect another. Nevertheless, it is also important for students to learn how to draw graphs by hand to understand how a graph emerges from another representation, such as an equation or a table. The focus of the present dissertation was on lower secondary school students’ learning of functions using the dynamic geometry program GeoGebra, in addition to more traditional teaching methods. The thesis aimed to investigate (1) the impact of the use of the GeoGebra dynamic program on the learning outcomes of the students who learn functions in basic school, (2) how do students participating in GeoGebra-assisted intervention and students in traditional instruction explain their answers when matching the equation of a linear function to the graph, and (3) students’ attitudes and affects of using GeoGebra dynamic geometry program in two different contexts – inside school and outside school. In order to test whether supplementing traditional instruction with GeoGebra can lead to a better conceptual understanding of functions and to explore how the use of GeoGebra influences students’ attitudes toward mathematics, two experiments were conducted. The results of these experiments are presented in three empirical studies (Study I, II, and III). Additionally, three competitions were organized in which students created GeoGebra-based projects linking the topic of functions to everyday life. For example, in one competition, students had to create a fireworks display, in another competition, they had to create a movement in some real-life context. Students’ opinions about using GeoGebra outside school are presented in Study IV. Study I examined the effect of GeoGebra on learning linear functions and inverse variation among seventh-grade students. The quasi-experimental design involved 212 students, with 128 in the experimental group using GeoGebra in addition to traditional learning and 84 in the control group receiving only traditional instruction without computer programs. There was no statistically significant difference in the learning results between the experimental and control groups neither in the pre-test nor in the post-test. Students’ ratings of the necessity, interest, and enjoyment of learning functions were lower while their difficulty ratings were higher in both the experimental and control classes than the same ratings of learning mathematics in general. However, students in the experimental group reported in the post-questionnaire that the use of computers made learning functions easier and more enjoyable. Notably, 42% of the experimental group students indicated that using GeoGebra improved their attitude towards mathematics. Study II explored how GeoGebra impacts students’ understanding of the relationships between different representations of linear functions and developing their graphing skills. In this study, two tasks from the final test of the first experiment were analysed. In the first task, the equation and graph of a linear function were matched and the basis for the match was explained. In the second task, the graph of a linear function was drawn based on the given equation. The results, involving the same student groups as Study I, indicated that the preferred reasoning of students using GeoGebra was using the values of the coefficients a and b, while students in the control class preferred to create a table. The experimental group performed significantly better at matching linear function graphs with their corresponding equation. However, both groups required further development in explaining. There was no difference between the experimental and control group students in the graph drawing task. This suggests that dynamic geometry software GeoGebra can be a valuable tool for teaching linear functions, provided that tasks are designed to help students discover links between different representations. Study III explored the impact of computer use on learning quadratic functions in ninth grade. The quasi-experiment included five classes of 9th-graders using GeoGebra alongside traditional methods and five classes with only traditional methods when learning functions. A total of 199 students participated in the study, 105 of them belonged to the control classes and 94 to the experimental classes. The results indicated no significant differences in learning outcomes between the two groups. However, the students who used computers had better attitudes toward learning functions, and 33% of the experimental group students who responded to the question found that their attitudes towards mathematics improved. While using GeoGebra may not directly improve test scores, it can enhance student engagement and interest in mathematics. Study IV highlighted the role of GeoGebra in increasing students’ interest in mathematics through creative competitions. These competitions, held over three years, involved students creating GeoGebra applets on various topics such as patterns from graphs of functions, fireworks, and moving objects. With participation numbers of 232, 160, and 167 respectively, the competitions demonstrated that according to the students themselves, they learned more about GeoGebra and improved their mathematical skills. Participants reported that the competitions made mathematics more enjoyable and relevant, and they appreciated the opportunity to see the practical applications of mathematical concepts. The results of the four empirical studies suggest that when teaching students about functions in lower secondary school the students can gain a better understanding when they have an opportunity to use the dynamic geometry program GeoGebra. In order to develop students’ explanation skills, in addition to solving tasks, students could also be directed to explain their solution process or way of thinking. This gives the teacher valuable information about how the students have understood the topic and what needs to be paid attention to. Using the GeoGebra program makes learning more enjoyable for students. Solving creative tasks related to real life and art provides a lot of challenges and joy for doing mathematics.