Investigation of the process of forming knowledge about probability at the 8th grade level in the context of the RBC+C model

The aim of this study is to determine and compare the distribution of behaviors exhibited by groups of students with different achievement levels in the same activities related to the process of abstracting probability information according to the RBC+C model. In addition, it was aimed to determine which steps students with different achievement levels had difficulty in these activities according to the RBC+C model and how they progressed in the encountered difficulties. The case study method, which is one of the qualitative research methods, was adopted in the study. The study group was determined using the maximum variation method, which is one of the purposeful sampling methods. The study was conducted with a total of eight volunteer 8th grade students with high (2), medium (2), and low (4) levels of mathematical success. The data of the study were collected through clinical interviews, observations, audio recordings, and documents containing student solutions. In the data collection process, a probability test containing 11 open-ended questions was used to reveal the processes of students' formation of the concept of probability. The probability test was solved in four stages by groups of two students. During the solution process, students were free to communicate with their groupmates and the teacher. In this process, students were encouraged to think aloud in order to provide more evidence for the research. In the analysis of the data, the audio recordings taken during the interviews were converted into written texts and examined together with the student answer sheets. The obtained data were analyzed according to the stages of the RBC+C model with the descriptive analysis method. The results of the study showed that groups consisting of students with different success levels generally exhibited different numbers of behaviors in the stages of the RBC+C model. The quantitative distribution of these behaviors in each group and stage was presented as the first result of the study. The second result of the study determined that students at high and medium success levels were able to progress on their own in the recognition and use stages of the process of creating probability knowledge, while students at low success levels had difficulty from time to time. It was seen that students at low success levels were able to perform epistemic actions with support from their friends in the group and the researcher. It was observed that other success groups also interacted with the teacher as the abstraction process became more complex. Although feedback was provided by the teacher in the lack of information seen in the research process, it was observed that the students were also affected by their group friends, discussed their thoughts about the problems with each other, approved each other when they agreed, and corrected their mistakes. Therefore, when students have difficulty in performing epistemic actions related to probability knowledge, it may be recommended to provide peer interaction in addition to teacher support.