本研究之主要目的：在於探討在現行的課程發展之下，針對最後一屆基測學生﹙現今九年級﹚，在函數的補救教學前後，其線型函數錯誤類型和迷思概念的變化情形。並歸納分析前測時學生作答的錯誤類型，藉此瞭解學生的迷思概念，施以補救教學。同時了解十二年國教學生與九年一貫學生的學習結果是否有任何差異性，可將此結論提供給以後任教此單元教師在教授十二年國教學生時做為參考，或做為教學的改進與建議。也希望將得到的研究結果能作為教師在教學上的參考，和發展以學校為本位的數學課程和編寫課程綱要時，也能提供適當的建議。 本研究以台北市某國民中學九年級全部學生為研究對象，樣本數為70名。主要是以Anna Sfard（1991）的概念發展理論和皮亞傑、布魯納等人的認知發展理論為依據，自編測驗卷，實施評測，輔以面談方式驗證其解題的策略和過程，然後依據所得資料進行統計分析，以探討國中學生在線型函數概念的學習狀況。 本研究之主要發現如下： 一、國中生對於線形函數概念的主要錯誤類型有：1. 對函數定義本身的誤解。2. 過於依賴線型函數。3. 文字敘述的表徵轉換到代數式的表徵發生錯誤。4. 表格表徵與函數概念間連結的困難。5. 函數圖形理解與繪製上的困難。6. 對數學名詞的不瞭解。 二、補救教學後的學習成效：1. 能由代數式完成表列進而畫出函數圖形。2. 能判斷線型函數的一次函數與常數函數的圖形。3. 能判斷出線型函數圖形間之平行關係。4. 能判斷出某點在直線上所對應的值與直線通過某點的函數值是相等關係。5. 能藉由兩個不同的函數值去求出線型函數。 以鑒於此面對現今十二國教的學生，所以教育部今年開始努力在推動「補救教學」，甚至於大動作的調訓國文、英文、數學三大領域的老師進行 8 小時的「補救教學」研習，期盼讓學生得以透過「補救教學」將學習效果能夠提升起來。 Abstract The main purpose of this study is to investigate the changes and the improvements of the linear function misconceptions of the students who will take the last Basic Competence Test (the present ninth graders). The students’ answers and errors are examined prior to analysis in order to understand the students’ misconceptions and to implement remedial instruction. Meanwhile, the study also investigates the difference in the learning outcomes between the students under the nine-year-curriculum and those under the new twelve-year-curriculum. The results will hopefully offer the teachers facing the new curriculum plan better references for teaching improvements. We also hope that the research results can be used as the reference of the development of school-based mathematics curriculum and the preparation of syllabuses. The subjects of this study are the ninth-grade students of a Taipei junior high school, a sample of seventy in total. Anna Sfard (1991) based her development theory on the theory of cognitive development of Piaget, Bruner et al. She developed self test paper, implemented evaluation to verify the problem-sloving strategies and processes supplemented by interviews to abstract the information of statistical analysis, thus to explore the concept of linear function of the junior high school students. The major findings of this study are as follows: First, the main error types of linear function of junior high school students are: 1. Misunderstanding the definition of the function. 2. Excessive dependence on the linear function. 3. Errors occur on the conversion of narrative characterization to the algebraic characterization. 4. Difficulties in linking the characterization of the tables and the concept of function. 5. Difficulties in function graph understanding and drawing. 6. The lack of understanding of the mathematical terms.
Second, outcomes of remedial teaching: 1. Students being able to complete the algebraic tables and then draw the graph of a function. 2. Able to analyze the graphics of the linear function and a constant function. 3. Able to judge the parallel relationship between the linear function graphs. 4. Able to determine the function corresponding to a point on a straight line and the straight line passing through a point. 5. Able to obtain a linear function from two different function values.
To prepare for the twelve-year-curriculum, the Ministry of Education, in the beginning of this year, has been working on the promotion of “remedial teaching,” and even recruit teachers of the three main areas: Chinese, English, and Mathematics for an eight hour “remedial teaching” workshop, looking forward to offering the students better remedial instruction in the future.