Teaching Mathematics through Intuition as a Way of Enhancing Students’Probabilistic Conceptions
Author: Chien Chin(Department of Mathematics, National Taiwan Normal University), An-Lang Wang(Taipei First Girls High School)
Vol.&No.：Vol. 51, No.1&2
Date：October 2006
Pages：15-54
DOI：10.6300/JNTNU.2006.51.02
Abstract：
In order to develop a new, more intuitive approach to teaching probability in senior high school, this study employed an action research method with teaching experiment. Three classes of grade 12 students taught by the second author were investigated for one year: the focus was on the intuitive-probabilistic misconceptions of students and their influence on the students’ further steps of probabilistic thinking. In the first stage, the researchers utilized analogical comparison to study the cognitive conflicts students experienced on their way to acquiring scientific knowledge, followed by introducing Intuitive Rules and activating students’ meta-cognitive awareness. In the second stage, several formats for classroom discussion and focus-group investigation were employed separately. Based on the results of this 2-stage/3-cycle study, the authors argue that while some students are able to grasp intuitive-probabilistic misconceptions, they are still unable to fully utilize some primitively probabilistic intuitions. After having modified their original misconceptions, they either returned to the primitive misconceptions or reverted to their primary intuition where they encountered unfamiliar questions. This seems to suggest that the unique features of intuition influence not only students’ present learning of probabilistic concepts but also their future learning of the concepts; in other words, these primitive intuitions never completely disappear. Several students were not only able to amend their primitive misconceptions, but also able to transform these into second-level intuitions. The authors suggest that mathematics teachers should try to integrate students’ primitive probabilistic intuitions with mathematical logic.
Keywords：action research, intuition, intuitive rules, misconceptions, teaching experiment
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