| 摘要: | 1980年起，擬題活動逐漸受到國際間的重視。想出一個數學題目出來，即為數學擬題，而其中自由擬題的出題有著強烈的生活連結。針對近年來台灣學生數學學習成就高而興致低迷的情況，擬題活動可能作為改善學生態度的一種教學方法。另一方面，機率作為處理不確定性事件的數學基礎，也特別容易與生活連結產生。
本研究目的在以自由擬題為學習活動，提升學生學習數學的興趣，並了解機率概念的發展。因此，本研究將探討：1 )學生所擬的題目有何進展？2 )機率思維有何發展？3)面對超過國中範圍之問題，解題的能力為何？
本研究對台北市一所國中，兩個九年級班級共62名學生，進行自由擬題學習活動。在為期3個月，共10節課的活動歷程裡，讓學生進行機率方向的擬題。蒐集資料的工具有機率裸測試題、學生擬題單及擂台賽答題單三種。本研究方法採用內容分析法，以「機率自由擬題評量規準」為研究工具，量化學生擬題各向度表現，並使用成對樣本t檢定來分析擬題版本之間的變化。
根據研究結果顯示，第一，學生的擬題品質在可解性、可讀性、精緻性與機率概念層次有所進展，但生活性可能從一開始就具備良好的品質，所以沒有明顯的進步數據。第二，學生的機率思維，也可藉由一題多磨的擬題歷程得到提升與發展。第三，學生有能力解決超過國中課程的問題。最後再根據研究結果於自由擬題活動、未來機率課程提出若干建議。
;Since 1980, the problem-posing activities have gradually received international attention. Think of a math problem, which is the mathematical problem-posing, and particularly the free problem-posing has strong life link. In recent years, Taiwan students have high achievements and low attitudes for mathematics learning, the problem-posing activities may serve as a teaching method to improve students′ attitudes. On the other hand, Probability as the mathematical basis for dealing with uncertainty events. It is especially easy to link with life.
The purpose of this thesis in the free problem-posing, enhance students′ interest in learning mathematics, and understand the development of the concept of probability. Therefore, the two research questions are: 1) To what extend do student’s problem-posing improve? 2) What is the development of probability thinking? 3) When facing the problems exceeds the junior high school level, what is the ability to solve the problem?
The research is conducted to 62 ninth grade students from two classes of junior high school of Taipei City. In a period of 3 months, a total of 10 lessons in the course of activities, so that students in the direction of the probaility problem-posing. The following data are collected : the probability of naked test questions, problems between versions and answers of the probability challenge. The results were analyzed in a content analysis, evaluate the quality of the problems by posers, And use the paired sample t test to analyze the problem between versions.
The results show that: 1) The student-posed problems made significant progress throughout the three-version process of “solvability”, “readability”, “Exquisite”, “Probability level”. 2) The probability of students thinking can enhance and develop by the process of problem-posing of “one problem, many revised versions”. 3) Students have the ability to solve problems beyond the course of the junior high school.
Finally, the researcher offers some suggestions related to the free problem-posing, probability course in the future. |
