Investigation of Probabilistic Reasoning Levels of Secondary School Students

The aim of this study is to investigate the probabilistic reasonings of secondary school students at subjective, transitive, informal quantitative and quantitative levels. Besides, in this study it is aimed to investigate that how students' probabilistic reasonings change according to grade level and mathematics achievement. The study was conducted in a public secondary school with students in a low socio-economic status in Edremit district of Balıkesir provience during the I. and II. semester of the 2018-2019 academic year. The participants of the study consist of twenty-four 5, 6, 7 and 8. grade students in this school. Students were selected from 5, 6, 7 and 8 grade students with six students of each grade according to maximum diversity sampling. This selection was made according to the students' mathematics grade points avarages of the previous year where two students were selected from three achievement levels of low, medium and high from each grade. Data related to the students' probabilistic reasonings were obtained from the semi-structured interviews and students' solutions and drawings during the interviews. In the interviews, 16 problems were used for subjective, transitional, informal quantitative and numerical levels. Data were analyzed by content analysis. Data analysis was based on the "Framework for Explaining Probability Reasonings of Students" developed by Jones, Thornton, Langrall and Tarr (1999). In the study, students' probabilistic reasoning levels were investigated for 6 concepts of probability (sample space, experimental probability of an event, theoretical probability of an event, comparison of probabilities, conditional probability and independence). The results of the study revealed that the students progressed through all 4 levels of probabilistic reasoning for each probabilistic concept. 2 students from 24 students were in the same level for all concepts. 11 students were in the same level for five of the 6 concepts. It was determined that the other students countinued to be consistently at one level down or one level up in general. According to the results of the study, students were mostly in the second level (transitional) of probabilistic reasoning for all 6 concepts. As the grade level increases, it was found that the students' probabilistic reasoning levels increase consistently. In addition, when students' levels of probabilistic reasoning were investigated according to their mathematics achievement level it was determined that students who have high level of mathematics achievement were also in higher levels of probabilistic reasoning.