高中機率概念的直觀教學

Teaching Mathematics through Intuition as a Way of Enhancing Students'Probabilistic Conceptions

結合行動研究和教學實驗，本文報導3班高三學生的原生機率直觀及1學年直觀教學的成效。全班教學階段以類推比較、認知衝突和科學性知識，引導學生察覺和驗證自己的原生直觀並以直觀法則引動後設認知，之後加入學生討論活動，再轉為小組晤談教學。結果發現，有些學生能察覺直觀的迷思卻無法抗拒或克服直觀；有些學生於修正直觀迷思之後又折返原迷思，或因不熟悉情境又再度使用原迷思。這些現象表明，直觀不但會影響高中生機率概念的學習，即使經過教學介入，原生直觀似乎很難完全消失也持續影響她們的機率思維。但是，有少數學生能夠察覺與修正原有迷思並轉換成二階直觀或修正直觀。我們認為：教師在教學時若能兼顧直觀與邏輯，並適當運用原生直觀和直觀法則，會有助高中生學習機率概念。

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.