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  • 學位論文

國中二年級數學補救教學之行動研究

An Action Research of Remedial Teaching on Mathematics among the Eighth Graders

指導教授 : 鄭勝耀
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摘要


本研究採用行動研究法,旨在探討國民中學實施補救教學之歷程,同時分析學生在八年級下學期於等差數列與等差級數、簡單的幾何圖形及三角形的基本性質等數學課程中易犯的錯誤類型之探究,透過補償式的教學策略、補充式課程和加強基礎課程等類型來進行補救教學活動,研究時間為2014年2月到6月的每週四下午第一、二節,共6名學生。 本研究的主要研究發現為: 一、學生認為公差都是正數且在公差使用上有錯誤概念,教師可藉由學生生活經驗建立學生「數」的先備知識。 二、學生無法找出數列的規律,教師可透過撲克牌等小遊戲讓學生發現規律。 三、學生對於一等差數列經過同乘與同加後所產生的新的公差有所疑惑,教師可藉由實際操作一等差數列的同乘與 同加,讓學生自行理解。 四、學生對於等差數列與等差級數公式符號的不理解導致無法使用,教師先建立學生對於符號的定義,再藉由公式 的推導讓學生理解公式的由來。 五、學生對於線對稱的定義不清楚,教師可藉由摺紙或作圖的方式讓學生理解在不同對稱軸上的線對稱圖形該如何 呈現。 六、學生於線段概念僅用想像並未畫出來比較長短,教師可實際畫出線段作大小的比較讓學生理解。 七、學生對於各種角的定義不清楚,在幾何圖形中,國小概念已有銳角、直角與鈍角,在國中階段,多了平角、餘角、補角與對頂角,故在教學上教師可藉由畫出圖形引導學生理解各種角的定義。 八、學生將體積與底面積公式混淆,教師可先複習國小所學之圖形面積與體積,再讓學生觀察出柱體體積僅是將底 面積乘上高即得。 九、學生對於內角與外角定理的定義與應用不清楚,教師可先複習國小所學之三角形的內角和,並應用簡單的幾何 圖形中所學各種角的定義來講解外角,最後推論至多邊形的內角與外角。 十、學生對於三角形的全等性質定義及應用不清楚,教師可先讓學生釐清全等性質中符號的意義為何,再透過實際 圖形或教具講解各種全等性質,其中需要注意全等性質中沒有SSA全等性質。 十一、學生在三角形的邊角關係中不會比較大小,教師可直接透過角度和邊長不同的三角形讓學生理解,並可歸納 出三角形大邊對大角,小邊對小角之性質,反之亦然。 教師於補救教學中,應先了解學生的學習情形,著重於學生易犯錯之錯誤概念進行教學設計,並且透過讓學生動手實際操作,建立學生的心像,有利於日後的學習。 關鍵字:補救教學、等差數列與等差級數、簡單的幾何圖形、三角形的基本性質

並列摘要


Adopting action research as the research method, this research aims to investigate the process of the implementation of remedial teaching in junior high school. Also, the misconception which are easily made by eighth-grade students, such as arithmetic sequence and arithmetic series, simple geometric pattern and basic properties of triangles, are analyzed. In this research, the implementation of remedial teaching refers to the teaching strategies of compensation, supplementary curriculum and the enhancement of basic curriculum. This research was conducted in the first two classes in every Thursday afternoon, from February to June, 2014, and there were six students involved. The main findings of this study are: 1. Students easily misunderstand that common difference is positive and misuse the concept of common difference. Teachers could help students to acquire prior knowledge about “number” through their daily experiences. 2. Students are unable to figure out the patterns of the sequence; teachers could apply some games – such as poker – to help students to learn the concept of “regular pattern”. 3. Students get confused at the outcome of multiplication or repeated addition on an arithmetic sequence; teachers could help students by demonstrating an equation. 4. The lack of proper knowledge about the formula and the symbols of arithmetic sequence and arithmetic series results in the misuse of these concepts; it would be helpful if teachers could define the symbols first, and then help to reason the formula. 5. While students feel uncertain about the definition of line symmetry, teachers could take paper folding or drawing as a strategy for demonstration. 6. It could be difficult for students to compare the length of line segments by imagination only; to draw some line segments could be useful for making a comparison. 7. The definitions of angles are somehow ambiguous for students. The concepts of acute angle, right angle and obtuse angle are taught in elementary school, and the concepts of straight angle, complementary angle, supplementary angle and vertical angle are added in junior high school. Visualizing these concepts could help for clarification. 8. It is easy for students to confuse the formula of cubature formula and the basis of quadrature formula. A recall of the ideas concerning square measure and volume taught in elementary school could be the first step for students, and then move on to the understanding of cubature formula to be the height multiplied by square aera. 9. The definition and the application of interior and exterior angle theorems are difficult for students. The course arrangement could start at the review of the sum of the internal angles of a simple triangle. Also, familiarity of angles could be helpful for the understanding of external angles. The knowledge of interior and exterior angles of a polygon could be left to the final stage of learning. 10. Students find it difficult to figure out the definition and the application about the congruence property between two triangles. In this respect, teachers could make a commencement by clarifying the definitions of symbols of congruence, and further explaining the concepts by demonstrating real figures. One thing is for sure: SSA is not one of the congruence property between two triangles. 11. Students may fail in making comparisons of a triangle’s lengths or angles. Through directly comparing different triangles, students could learn better, even to conclude the facts that the longest length of sides is opposites to the biggest interior angle and the shortest length of sides is always opposites to the smallest interior angle, and vice versa. To have better understandings of students’ learning conditions could be the beginning point for a teacher to implement remedial teaching. The focal point of pedagogical design could be emphasized on students’ misconception or myths. Practical exercises and the establishment of new mindsets could be helpful for the future learning. Keywords:Remedial teaching, Arithmetic sequence and arithmetic series, Simple geometric pattern, Basic properties of triangles

參考文獻


李源順(2004a):國小數學專家教師在教學實務中的角色。國教新知,51,1-18。
李源順(2014)。數學這樣教:國小數學感教育。五南。
黃德華、羅家健(2009)。數學學習障礙與數學輔導教學。台灣數學教師電子期刊,18,3-17。
洪儷瑜(2001)。義務教育階段之弱勢學生的補救教育之調查研究。師大學報:教育類,46,45-65。
林怡如、何信助、廖年淼(2004)。提升數學學習動機的教學策略。 師友月刊,440,43-47。

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