Zamalia Mahmud, Anne Porter


Students’ understanding of probability concepts have been investigated from various different perspectives. This study was set out to investigate perceived understanding of probability concepts of forty-four students from the STAT131 Understanding Uncertainty and Variation course at the University of Wollongong, NSW. Rasch measurement which is based on a probabilistic model was used to identify concepts that students find easy, moderate and difficult to understand.  Data were captured from the e-learning Moodle platform where students provided their responses through an on-line quiz. As illustrated in the Rasch map, 96% of the students could understand about sample space, simple events, mutually exclusive events and tree diagram while 67% of the students found concepts of conditional and independent events rather easy to understand.

Keywords: Perceived Understanding, Probability Concepts, Rasch Measurement Model



Full Text:



Andrich, D. (1978). A Rating Formulation for Ordered Response Categories. Psychometrics, 43, 561-73.

Bond, T.G. & Fox, C.M. (2007). Applying The Rasch Model: Fundamental Measurement In The Human Sciences. New Jersey: Lawrence Erlbaum Associates.

delMas, R., Garfield, J., & Chance, B. (1999). A Model of Classroom Research In Action: Developing Simulation Activities To Improve Students’ Statistical Reasoning. Journal of Statistics Education, 7 (3).

delMas, R., Garfield, J., Ooms, A., & Chance, B. (2007). Assessing Students’ Conceptual Understanding After A First Course In Statistics. Statistics Education Research Journal, 6 (2), 28-58.

Garfield, J. & Ahlgren. (1988). Assessing Students’ Conceptual Understanding After A First Course In Statistics; Difficulties in Learning Basic Concepts in Probability and Statistics: An Implication for Research. Journal for Research in Mathematics Education, 19 (1), 44-63.

Garfield, J. & Ben-Zvi, D. (2004). Developing Students Statistical Reasoning: Connecting Research And Teaching Practice. Springer.

Garfield, J. (1995). How Students Learn Statistics. International Statistical Review, 63 (1), 25-34.

Garfield, J. (2003). The Challenge of Developing Statistical Reasoning. Journal of Statistics Education, 10, 3.

Garfield, J. & Chance, B. (2000). Assessment in Statistics Education: Issues and Challenges. Mathematics Thinking and Learning, 2, 99-125.

Jensen, D. & Kellogg, S. (2010). Improving Conceptual Understanding in Probability and Statistics. American Society for Engineering Education, 2-15.

Kolb, D.A. (1984). Experiential Learning: Experience As The Source of Learning And Development. Englewood Cliffs, NJ: Prentice Hall

Konold, C. (1989). Informal Conceptions of Probability. Cognition and Instruction, 6, 59-98.

Linacre, J.M. (2002). Understanding Rasch Measurement: Optimal Rating Scale Category Effectiveness. Journal of Applied Measurement, 3, 85-106.

Linacre, J.M. (2007). A User’s Guide to WINSTEPS. Chicago:

Reed-Rhoads, T., Murphy, T. J., & Terry, R. (2006). The Statistics Concept Inventory (SCI). Retrieved from

Sadler-Smith, E. (1996). Approaches to Studying: Age, Gender, and Academic Performance. Educational Studies, 22 (3), 367-379.

Saldanha, L.A. & Thompson, F.W. (2001). Students’ Reasoning about Sampling Distributions and Statistical Inference. In R. Speiser & C. Maher (Eds.), Proceedings of The Twenty-Third Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Snowbird, Utah. Columbus, Ohio: ERIC Clearinghouse, 449-454.

Shaughnessy, J.M. (1992). Research in probability and statistics: Reflections and directions. In Handbook of Research on Mathematics Teaching and Learning. D.A. Grouws (Ed.). pp. 465-494. New York: Macmillan

Tempelaar, D. (2006). A Structural Equation Model Analyzing The Relationship Students’ Statistical Reasoning Abilities, Their Attitudes Toward Statistics And Learning Approaches. Proceedings of The 7th International Conference on the Teaching of Statistics. ICOTS-7.

Tempelaar, D., Schim van der Loeff, S., & Gijselaers, W.H. (2007). A Structural Equation Model Analyzing the Relationship of Students’ Attitudes Toward Statistics, Prior Reasoning Abilities, and Course Performance. Statistics Education Research Journal, 6 (2), 78-102.

Zamalia, M., Porter, A., Nor Izzati, O., Masniyati, S., Az’lina, A. H., & Shamsiah, S. (2013). Understanding Probability Concepts and Learning Styles Among Students of the Malay Culture: A Rasch Analysis. Wulfenia Journal, 20 (1), 98-115.



  • There are currently no refbacks.

Journal on Mathematics Education
Doctoral Program on Mathematics Education
Faculty of Teacher Training and Education, Universitas Sriwijaya
Kampus FKIP Bukit Besar
Jl. Srijaya Negara, Bukit Besar
Palembang - 30139

p-ISSN: 2087-8885 | e-ISSN: 2407-0610

Creative Commons License
Journal on Mathematics Education (JME) is licensed under a Creative Commons Attribution 4.0 International License.

View My Stats