私立高中數學課後學習輔導方案之個案研究

本研究旨在分析研究者任教之高三數學學習落後學生的學習困境，並針對學習困境實施有效教學及學習輔導策略，進而提出對本校高中數學學習落後學生的課後學習輔導方案。參與本研究的課後學習輔導學生共七位，本研究運用觀察、訪談與文件分析等方法，分析學生學習落後的成因，再進行每週一次的數學課後學習輔導，共10週。透過診斷學習問題、施以教學策略、評估成效的螺旋循環歷程，獲致研究結論如下：一、歸納數學學習落後學生的學習問題包括數學知識類型與非數學知識類型：數學知識類型有：概念不清楚，對所學的定義或性質未深入了解；粗心計算錯誤、看錯題目；忽視條件或考慮不周詳；無法從題意中獲得訊息，使用正確的定理，找到適當的解題策略；無法活用知識(類化)；無法理解文字所描述之抽象的空間圖形概念；看錯或忽略重要訊息，無法正確作答；邏輯錯誤；記錯公式；符號使用或表達不正確等十個類型。非數學知識類型的學習問題是在讀題時，對語文的理解發生問題，無法理解題目的文字的描述為何。二、對數學學習落後學生的有效學習輔導形式，在課堂採直接教學法，課後個別指導；有效的輔導策略有拋問、答問，圖示教學，課堂討論，作業、練習等。三、由於研究對象是高三下學期的學生，因為輔導時間短，所以成績不一定都有明顯的改善，但學生的數學理解能力有進步，觀念更清楚；解題方面也有改善，看到題目更有想法。四、適合數學學習落後學生的輔導方案執行步驟如下：首先透過學習動機、作業分析、課堂觀察診斷學生的數學學習問題。其次根據學生學習問題施以教學輔導策略，指定適當的課後練習，針對問題個別指導。最後確認是否達成學習目標，概念迷思是否獲得澄清，對未達學習成效的，繼續施以適當的教學策略，再評估。

關鍵字

學習輔導方案；數學學習落後；教學策略；學習成效；個案研究

並列摘要

This study aims to analyze the learning predicament of those 12th grade students who fell behind in learning mathematics in my teaching class and implement effective strategies of teaching and learning guidance. Moreover, a program of after school learning guidance is proposed for the students who fall behind in high school mathematics in my school. Seven students participated in the program of after school learning guidance under this study. Observation, interview and documentary analysis were utilize to analyze the causes of learning deficiency. Then the after school program was implemented for ten weeks. After running spiral process including problem diagnosis, teaching strategy implementation and effectiveness evaluation, the main conclusions are summarized below: 1. The predicaments of the students who fall behind in learning mathematics could be separated into two types. The “mathematical knowledge type” students do not have a clear concept and an in-depth understanding of learned definition. They calculate carelessly, misread questions, ignore conditions and are thoughtless. These students can’t get information from questions to apply right theorem to find appropriate solving methods. Besides, they can’t generalize knowledge, understand the text description of the abstract spatial graphics concepts, answer correctly due to misunderstanding or ignoring important information. Making logic errors, getting formula wrong, misusing symbols and expressing incorrectly are often found in these students. On the other side, the problem of "non-mathematical knowledge" is that the students have problem by reading. And they do not understand the text description. 2. The effective forms for guiding students falling behind in learning mathematics are direct instruction in class and personalized system of instruction after class. And effective methods include throwing questions, question and answer, diagraming Training, class discussion, homework and practices. 3. Some of the students did not improve their achievement dramatically because the students were in the second semester of 12th grade and the time was limited. However, their understanding ability has improved, they have a clearer concepts, their ability in solving problems has also improved and they have more ideas when solving problems. 4. The guidance program which is suitable for students falling behind in learning mathematics proceeds as follows. The students’ learning predicaments should be diagnosed through their learning motivation, homework doing and expression during class. Then the guidance program is implemented according to the diagnosis result. After school exercises are assigned to the students. Personalized instruction is also provided. Finally, it is to confirm whether the learning objectives are achieved and the students get clearer concept. For those who do not achieve learning objectives, a suitable teaching strategy should be implemented continuously. And effectiveness is evaluated.