### Mathematical Probabilistic Thinking Process Stages in Problems Solving Probability

#### 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 9th 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.

#### Keywords

higher order thinking skills; probabilistic thinking stages; problem-solving

PDF

#### References

Aseeri, M. M. Y. (2020). Abstract thinking of practicum students at Najran University in light of Piaget's theory and its relation to their academic level. Journal of Curriculum and Teaching, 9(1), 63-72.

Borovcnik, M. (2016). Probabilistic thinking and probability literacy in the context of risk Pensamento probabilístico e alfabetização em probabilidade no contexto do risco. Educação Matemática Pesquisa: Revista do Programa de Estudos Pós-Graduados em Educação Matemática, 18(3).

Chernoff, E. J., & Sriraman, B. (2014). Probabilistic thinking: presenting plural perspectives. New York: Springer.

Creswell, J. W. (2014). Research Design: Qualitative, Quantitative, and Mixed Method Approaches. SAGE Publishing.

Facione, P. A., & Facione, N. C. (2013). Critical thinking for life: Valuing, measuring, and training critical thinking in all its forms. Inquiry: Critical Thinking Across the Disciplines, 28(1), 5-25.

Jan, I., & Amit, M. (2009). A four phase model for predicting the probabilistic situation of compound events. Beersheba: Ben Gurion University.

Jones, G. A., Langrall, C. W., Thornton, C. A., & Mogill, A. T. (1997). A framework for assessing and nurturing young children's thinking in probability. Educational Studies in Mathematics, 32(2), 101-125.

Jones, G. A., Langrall, C. W., Thornton, C. A., & Mogill, A. T. (1999). Students' probabilistic thinking in instruction. Journal for Research in Mathematics Education, 487-519.

Krulik, S., & Rudnick, J. A. (1996). The new sourcebook for teaching reasoning and problem solving in junior and senior high school. Allyn & Bacon.

Mason, J., Burton, L., & Stacey, K. (2010). Thinking mathematically. Pearson Education.

Moleong, L. J. (2015). Metodologi Penelitian Kualitatif. Bandung: Remaja Rosdakarya.

Nacarato, A. M., & Grando, R. C. (2014). The role of language in building probabilistic thinking. Statistics Education Research Journal, 13(2), 93-103.

Perkins, C., & Murphy, E. (2006). Identifying and measuring individual engagement in critical thinking in online discussions: An exploratory case study. Journal of Educational Technology & Society, 9(1), 298-307.

Polaki, M. V. (2002). Assessing and tracing the development of Basotho elementary students' growth in probabilistic thinking. In Proceedings of the Sixth International Conference on Teaching Statistics (ICOTS 6). Lesotho: National University of Lesotho.

Polya, G. (1971). How to Solve It: A New Aspect of Mathematics Method. New Jersey: Princeton University Press.

Sadler-Smith, E. (2015). Wallas four-stage model of the creative process: More than meets the eye? Creativity Research Journal, 27(4), 342-352.

Satchakett, N., & Art-in, S. (2014). Development of Heuristics Problem Solving, and learning achievement of grade 9 students by using learning management focusing on Heuristics Approach in Thailand. Procedia-Social and Behavioral Sciences, 116, 1011-1015.

Stacey, K., Burton, L., & Mason, J. (1982). Thinking mathematically. Addison-Wesley.

Sujadi, I. (2008). Rekonstruksi Tingkat-Tingkat Berpikir Probabilistik Siswa Sekolah Menengah Pertama. In Proceeding Seminar Matematika dan Pendidikan Matematika. FKIP UNS.

Watson, G. (1980). Watson-Glaser critical thinking appraisal. San Antonio, TX: Psychological Corporation.

DOI: http://dx.doi.org/10.12928/ijeme.v5i1.20005

### Refbacks

• There are currently no refbacks.

International Journal on Emerging Mathematics Education