Abstraction Processes of Grade 9 students in modelling activities(A qualitative research)

This study integrates activities that begin from real life situations related to the angles topic for grade 9 students. Students engaged in these activities are expected to elicit mathematical models out of the real life situations, here with the help of technology, namely GeoGebra. Using the Abstraction in Context (AiC) theoretical model, students’ learning processes of the circle topic were analyzed. More specifically, the current research attempted to answer the question: what are the characteristics of the abstraction processes that grade 9 students perform when they are engaged in carrying out modelling activities in the circle topic with the help of technology? The researcher built a learning unit that included modelling activities related to the circle topic and fit grade 9 students. Three groups of grade 9 students carried out the activities with the help of GeoGebra. The students’ work was videoed, coded and then analyzed using the Abstraction in Context model. The results of the research indicate that the participating students succeeded to abstract the circle concepts (for example the inscribed and the central angles) and relations (the central angle is twice the inscribed angle) by carrying out modelling activities with GeoGebra. Doing so, the students went through the four stages of AiC model (need, recognizing, building with, constructing and consolidating). The research results indicate that modelling activities carried out with the help of technology help students arrive at the abstraction of mathematical concepts, so it is recommended to integrate such activities in the mathematics classroom, especially in geometry lessons. Carrying out these activities in groups, student collaborate to overcome the difficulties of such activities, so group work is recommended when carrying out modelling activities. The technology also helped the participating student to carry out the modelling activities and arrive at the geometric concepts and relations, so it is recommended that technology be integrated in modelling activities to facilitate students’ work. Furthermore, it is recommended that future qualitative researches be conducted, using AiC model to verify students’ abstraction processes with technology in other mathematical topics.