Abstract
Probabilistic thinking is one type of thinking skills which belongs to the Higher Order Thinking Skills (HOTS). Students need to have the probabilistic thinking ability to face the life which is full of uncertainty. The purpose of this research is to formulate the stages of mathematical probabilistic thinking processes in solving probability problems. It was a descriptive qualitative research involving eight students of the 9 th grade of SMP Muhammadiyah 3 Mlati Sleman Yogyakarta as the subjects. We administered a probabilistic thinking test and then observed and interviewed them to get the data. The data were then analyzed using triangulation method. This study resulted the five stages of mathematical probabilistic thinking process. They are: (1) understanding the problem of uncertainty that needs to be solved; (2) identifying all possibilities that will occur from a problem; (3) grouping the results of the identified event; (4) determining the probability of the occurred events; and (5) verifying the results.
Highlights
Probabilistic thinking is one type of thinking skills which belongs to the HigherOrder Thinking Skills (HOTS)
It is in line with Piaget's classification in the characterization of cognitive development that logic and probability are positioned at the formal stage of operation at the age of more than 11 years old, characterized by abstract thinking, hypothesis, deductive, inductive, logical, and probability (Aseeri, 2020)
Based on the previous theories of the probabilistic thinking stages, we tried to consider the stages in the problem-solving process, types of thinking, probabilistic thinking level indicators, and characteristics of probabilistic thinking
Summary
Probabilistic thinking is one type of thinking skills which belongs to the Higher. It is in line with Piaget's classification in the characterization of cognitive development that logic and probability are positioned at the formal stage of operation at the age of more than 11 years old, characterized by abstract thinking, hypothesis, deductive, inductive, logical, and probability (Aseeri, 2020). A decade later, it became a concern among researchers. This period is called the contemporary research period. Jones et al (1997, 1999) suggested four levels of probabilistic thinking, i.e. subjective, transitional, informal quantitative, and numerical. Polaki (2002) developed the Jones’ probabilistic thinking level in more detail for several subjects or materials in probability theory
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