Many students exhibit some knowledge of probability before they have formally been taught. For example, in Taiwan, probability is not taught until the ninth grade, but Taiwan’s eighth graders perform above average in the probability category of the Trends in International Mathematics and Science Study. This fact inspired the authors to investigate ninth graders’ spontaneous conceptions of probability. In the present study, two activities were designed for data collection: a pop pretest and free problem posing. Two-dimensional analysis was employed to identity the spontaneous concepts demonstrated in the activities. Analysis was based on three probability types: subjective, classic, and frequentist. These three types encompassed four conceptual levels: single event, compounded events, independency, and conditionality. The results revealed that more than 70% of the students could solve single-event classic probability problems before they were formally taught relevant methods. Additionally, the students’ spontaneous concepts extended to all conceptual levels. We therefore suggested that the introductory probability curriculum can be implemented in grade eight, and independency and complementary-events could be taught in grade nine.
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Investigation of Ninth Graders’ Spontaneous Probabilistic Concepts in Pop Pretests and Problem Posing
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