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【繁體】國中數學滿分心法:引爆中學生數學能力的奧義

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KingStone

【繁體】國中數學滿分心法:引爆中學生數學能力的奧義

Name: 【繁體】國中數學滿分心法:引爆中學生數學能力的奧義
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SKU: 3136161611
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1.深化數學觀念
本書第一章依國中學習數學的順序，精選100題最優質的基測考題，以深化觀念的方式帶出國中生必備的數學知識，並同步加入100題延伸性思考題。

2.透析數學本質
心法解析部份以互動教學的方式書寫，它不僅只是解答，更帶領同學一起思考與解決問題，讓閱讀與演練的同學如同上了一堂數學課，從而建立並深化數學觀念。

3.強化數學能力
本書第二章是介紹「極端化、簡單化、特殊化、平移、對稱、旋轉」六個數學能力，讓看似複雜的資優競賽試題，經過「以簡馭繁」的轉化後，就能輕鬆容易的處理了。

4.鍛鍊數學思維
奧義解析部份以貼近教學的方式書寫，帶領同學同步思考與解決問題，建立數學課本知識以外的數學能力與思維。

近十年來，國中升高中的升學考試「國中基本學力測驗」改以單一選擇題命題，導致很多學生雖然是選對了答案，其實對題目想傳達的數學觀念並不了解。數學題目雖不會重複命題，但想測驗學生理解與否的數學觀念卻會一考再考，若同學沒能深度的理解其中的數學觀念，命題老師將題目做個轉換或是改以問答式的命題，同學就無法回答了。

在我十多年的教學經驗中，經常見到中學生這方面的問題，同學看到選擇題，沒先能理解題意就想猜答案，答對了就好，至於答案為什麼是這個選項，他們一點也不在乎。我想，同學要能考好國中基測考試或會考，首要就是要能真正深度了解題目想傳達的數學觀念，也唯有真正明白這些數學觀念，方能在日後的考試中輕鬆答題，取得高分。

國中基測考試的數學題目雖然靈活多變，但其實中學生所必須學習與具備的數學觀念並不多。如果同學能將一些優質的數學考題確實弄通，就足以具備與建立這些數學觀念。事實上，要建立同學的數學觀念是必須由思考題目與解決題目而來的，而非記憶冗長的數學定義與數學公式。在下面的內容裡，我將以100 個優質的基測數學題目與變化，帶領同學真正深度理解中學生所必須具備的數學觀念。

在國中數學課程內容裡，同學增加了許多小學所沒學過的數學知識。在「數」的方面，學習了「正負數」、「有理數」與「無理數」以及「實數」等概念。在「代數」的方面，學習了「一次與二次方程式」的解法、「多項式」的四則運算。在「解析幾何」的方面，學習了「直角座標系」、「一次與二次函數」等圖形概念。在「幾何」的方面，學習了「三角形」的邊角關係、「畢氏定理」、「四邊形」、「相似形」以及「圓」與「三心」等概念。

然而，同學數學上的知識雖然增加了許多，但數學的能力卻並沒有隨之而提升，遇到稍為靈活一點的題目，往往就沒有能力能將題目解出。本章內容就是我特別設計來訓練增強同學的數學能力，鍛鍊同學的數學思維，真正做到所謂的「以簡馭繁」。

第一章深化數學觀念
1-1 數論
1-2 代數與座標系
1-3 數列與級數
1-4 三角形與多邊形
1-5 圓與三心
1-6 機率與統計

第二章強化數學能力
2-1 極端化
2-2 簡單化
2-3 特殊化
2-4 平移思考
2-5 對稱思考
2-6 旋轉思考

內容試閱

從事數學教育工作已經歷了十五個寒暑，師大數學系畢業後，因為是公費生，必須先在中學教兩年書，隨後就在讀研究所期間，開啟了我的補教生涯。

這十多年來網路與通訊科技快速的普及與蔓延，平板電腦、電子書等科技教學工具也在這幾年間逐漸的興起，當然在各領域學科的教學與學習上會有一些改變與影響，但是在數學這門學科上，兩千多年前幾何原本的作者歐幾里得在為托勒密國王講授幾何學時，國王就曾問他：「學幾何有沒有快速的捷徑。」歐幾里得回答他說：「學幾何無王者之路。」兩千多年後科技快速的演進，但我還是必須要說：「學數學無快速的捷徑。」而紙筆運算與分析，更是無法全面的以現今任何科技產品取代，數學的教材也無法僅以閱讀的方式就能完全的吸收與學習。

中學生必修的學科中，數學這門學科和其他學科有著很大的不同，我們想了解學生是否已學會某學科，通常是看學生能否記得學程中的內容，但在數學上卻並非只是記憶與背誦這麼的單純。我們想了解學生是否具備數學觀念的方式，就是測驗學生能否運用這些數學觀念，解出一個數學問題。然而，我們要如何才能具備這些數學觀念呢？就像是一個循環，我們當然還是必須從思考與解出數學問題中學習，才能具備這些數學觀念，因此「數學解題」就是學習數學的關鍵。

早年數學試題的變化較少，因此許多同學的數學學習方法，就是不斷的演練僅改變些數據的類似題，甚至有些補教老師為因應某些題目，就發明一些速解公式與方法，這些當然對數學的學習都是負面的。這十多年來國中升高中的升學考試「基本學力測驗」改以選擇式的命題，使得許多學生常在不了解題意的情況下就想猜答案，加上頻繁且無完善規劃的教改，造成了學生的數學學習變的不夠扎實，我在教授高中課程時，經常會發覺學生有著這方面的問題。然而，雖說選擇式的命題不易測驗出學生真正的數學程度，但這十多年來，基測考試在數學科上，卻已累積了許多相當優質的試題。作為一位數學教育工作者，可以看出數學試題的進化，也肯定命題老師們的努力，它不再只是像過去的試題般呆版單調，而多了許多的巧思。若是能將這些優質的基測試題真正理解，數學的學習就必定能有長足的成長與進步。

早在兩千多年前柏拉圖的「對話錄」中，就記載了其師蘇格拉底以「產婆式」導引的教學法，讓沒受過教育的童僕美諾學習與解決了現今我們國二學生才會學習的數學觀念與問題。在中學生的數學教育與學習方法上，「互動與引導」早已是先哲所認同最好的學習方式。五年前的夏天，我懷抱著對教育的熱情，實現了自己的理想，創立了「林群數學補習班」。在這裡，沒有商業的包裝，只有質樸的關懷與陪伴；沒有冰冷的臉孔，只有溫馨的教學與輔導。我陪伴著同學一起成長，帶領著同學一起向上提升。我實現了自己對教育的理念與想法，也培育了許許多多優秀的學生。

承蒙五南圖書的邀請，希望我能分享自己的教學經驗與方法，為中學生寫一本有效學習國中數學的書，「國中數學滿分心法－引爆中學生數學能力的奧義」因此而誕生。我將本書分為兩個部份。第一章，我特別精選了一百題最優質的基測試題與相同觀念的模考題，深化同學國中必備的數學觀念。在心法解析的部份，更特別以我平日與學生互動教學的方式來書寫，讓它不儘只是試題的解答，更讓閱讀與演練的同學如同上了一堂數學課。第二章，是我訓練資優學生，強化數學能力的課程內容，讓閱讀演練本書的同學，除了能完整的建構國中數學觀念外，還能強化數學能力。但由於書本篇幅的限制，我先挑選「極端化、簡單化、特殊化、平移、對稱、旋轉」這六個重要的數學能力來介紹。希望將來有機會能再寫一本強化數學能力的專書，完整的介紹思考型試題與競賽試題。

最後，我要感謝我的父母親這些年給我的照顧與協助，更要感激我的學生與工作夥伴，因為有你們的陪伴，讓我的人生更加的精采。

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