學生在學習遭遇困難的時候,最容易質疑學習數學的意義,甚至排斥學習,進而落入學習困難的惡性循環,一個好的教學者,要能觀察學生的學習情況,針對學生學習需要幫助的部分,特別強化,提供更多元且適合學生的教學。 本研究所討論的題目以高中二年級三角函數單元為基礎,整理利用三角函數解三角形的邊角關係之題型並分析解題策略。研究主題:(一) 學生在解三角函數題型時需要的解題策略和演算的知識有哪些。 (二) 希望學生可以透過較具體的三角形之邊角關係,幫助理解三角函數之概念,能熟悉公式操作並學習如何解證明題。 然本研究只有針對利用三角函數探討三角形之邊角關係的證明題提供解題策略,因此無法做為其它單元證明之參考。在教學上,準備更多元的教材、建立先備知識概念,來強化學習效果差的單元,教學生利用解題策略來解證明題,並訓練學生思考,來達到普通高級中學必修科目「數學」課程綱要上的核心能力之推理能力:「能認識證明,並進行推論。」
When students encounter difficulties in learning math, then the purpose of the learning will be questioned. Some students even fell into the vicious circle of learning difficulties. A good teacher observes the student's learning and provides more varied and also suitable teaching for student. Topic discussed in this study based on the high school sophomore trigonometric function unit. We collected the trigonometric function questions which discussing the relationship of sides angles in triangles and we also analyzed the problem solving strategies. This research purposes are: (a) to know how many problem solving strategies and calculating ability that a student needs to have; (b) to make students can learn this unit better and learn what proof is. This research only provides problem solving- strategies for solving the relationship between sides and angles in triangles by trigonometric functions. The strategies can’t suit for every unit.