北京市重點中學未出先火的複習紅寶書，數學家顧沛高度讚賞的數學文化典範之作！中國科學院院士陳佳洱、王大中聯袂誠意推薦
基本介紹
- 書名：高考中的數學文化
- 作者：齊龍新
- ISBN：9787121316371
- 類別：教育
- 頁數：360頁
- 定價：68
- 出版社：電子工業出版社
- 出版時間：2017年8月
- 裝幀：平裝
- 開本：170mm×240mm
內容簡介,作者簡介,編輯推薦,數學家顧沛推薦語,目錄,自序,
內容簡介
教育部考試中心以正式檔案明確提出在高考數學考題中要體現數學文化，這是一個明顯的信號：要求學生加強對數學文化知識的學習，自覺地、有針對性地重視對數學文化修養的提升。
本書創新性地從“以數化人”與“人數學化”兩個角度來談數學文化，對數學文化在數學歷史、數學精神、數學套用、數學之美、數學語言、交匯拓展、數學遊戲等各個主題上都作出了全面透徹的剖析和論述。除此之外，作者還結合曆年高考數學試題進行具體的案例分析，以此讓高考生能夠精準消化吸收高考中的各種數學文化知識。
對高中生而言，這是一部讓他們明確數學文化“是什麼”“怎么考”“怎么練”，為備考數學文化提供清晰學習方向的紅寶書；對數學教學工作者或研究者而言，這是一部系統揭示命制背景、展示解題過程、凸顯數學文化價值的寶貴內參書；對於廣大的數學文化愛好者而言，這又是一部讓人崇尚真理，淨化心靈，提升文化修養和文化品格的數學美書。
作者簡介
齊龍新，北京市數學特級教師，山東省教學能手，山東省新課程研修團隊專家，山東省基礎教育教師培訓專家，山東省優質課一等獎、教育部一師一優課一等獎獲得者，現為北京市育英學校經濟學實驗班班主任。作者致力於“新數學自學輔導教學法”的實踐與研究，所編自學教材曾獲得山東省優秀課程資源一等獎，在日常教學實踐中也取得了非常顯著的教學效果。其微信個人公眾號“龍新數學(zxfd66)”曾經獲得2016年數學文化雜誌社主辦的攜手北大數學文化節最紅公眾號評選全國第二名。
“把數學教得通俗易懂，讓學生學得幸福有趣”是作者一以貫之的精緻追求，其教學風格獨特，教法細膩、技巧純熟，教學成績突出，與學生之間亦師亦友，深得學生的喜愛。作者教學之餘寫出了數十篇教育教學論文，撰寫了《初高中數學銜接教材》等多部教研論著。
編輯推薦
★為什麼要學習數學文化？其實這個問題也等同於為什麼要學習數學。數學本身就是一種文化，所以這本書旨在幫助學生形成良好的數學思維能力，掌握解決問題的方法，培養理性精神。
★現在的高考試題越來越注重考生解決問題的能力，倘若只會刷題而不能理解題中真意將會寸步難行。本書以文化為核心，將理論、方法、歷史、文化融為一體，知識性、趣味性和實操性完美結合。
★數學家顧沛高度讚賞的數學文化典範之作，中國科學院院士陳佳洱、王大中聯袂誠意推薦，適合高中生及教學工作者使用。
數學家顧沛推薦語
數學是人類文化的重要組成部分，數學是人類文明進步的產物，也是推動社會發展的動力。通過對本書數學文化的學習，學生可以初步了解數學的思想精神，了解數學科學與人類社會發展之間的相互作用，體會數學的科學價值、套用價值、人文價值和審美價值，開闊視野，感受數學家治學的嚴謹，尋求數學發展的歷史軌跡，探索數學發展的不同階段，激發對數學的興趣和對數學創新的認識，從而提高自身的文化素養、思想素養和創新意識。
目錄
第一章數學文化總論··················································································· 1
第一節什麼是數學文化········································································ 1
第二節數學文化的四個層面································································· 3
一、知識系統······················································································· 4
二、工具系統······················································································· 4
三、價值系統······················································································· 5
四、史實系統······················································································· 7
第三節數學文化的人本特性································································· 7
一、精神特性······················································································· 8
二、物質特性······················································································· 8
三、行為特性······················································································· 9
四、審美特性······················································································· 9
第二章數學歷史························································································ 11
第一節數學名著················································································ 11
一、《九章算術》················································································ 12
二、《數書九章》················································································ 19
三、《算數書》··················································································· 24
第二節數學故事················································································ 27
一、畢達哥拉斯的故事········································································· 27
二、高斯的故事·················································································· 36
三、哥德巴赫的故事············································································ 41
第三節數學名題················································································ 44
一、米勒問題····················································································· 45
二、斐波那契數列··············································································· 57
三、阿基米德窮竭法············································································ 66
四、柯西不等式·················································································· 73
五、角谷猜想····················································································· 80
六、阿波羅尼奧斯圓············································································ 85
七、迴文數························································································ 93
八、勾股數························································································ 98
九、平均數······················································································· 101
十、皮克定理···················································································· 108
十一、數字黑洞················································································· 114
十二、伯努利不等式··········································································· 119
十三、正整數方冪和··········································································· 124
十四、切比雪夫多項式········································································ 130
十五、馬爾科夫定理··········································································· 135
十六、四色問題················································································· 143
十七、萊布尼茨三角形········································································ 146
十八、黃金分割比·············································································· 151
第三章數學精神······················································································· 155
第一節理性求真··············································································· 155
第二節創新意識··············································································· 167
第四章數學套用······················································································· 177
第一節行銷決策類············································································ 178
第二節金融經濟類············································································ 183
第三節環境保護類············································································ 188
第四節建設工程類············································································ 195
第五節交通運輸類············································································ 204
第六節機率統計類············································································ 209
第七節日常民生類············································································ 218
第五章數學之美······················································································· 227
第一節和諧美··················································································· 227
一、結構形式的和諧統一····································································· 228
二、項、項數、次數的和諧統一···························································· 235
三、轉換的和諧統一··········································································· 239
第二節簡潔美··················································································· 242
第三節對稱美··················································································· 248
第四節奇異美··················································································· 253
一、解法多樣的奇異美········································································ 254
二、解法之巧的奇異美········································································ 259
第六章數學語言······················································································· 264
第七章交匯拓展······················································································· 272
第八章數學遊戲······················································································· 276
附錄一本書習題參考答案········································································· 285
附錄二高考數學文化最新動態································································· 325
參考文獻···································································································· 344
自序
2016 年10 月8 日，教育部考試中心下發《關於2017 年普通高考考試大綱修訂內容的通知》（教試中心函〔2016〕179 號），增加了數學文化的要求。這一檔案的公布，引發了社會對數學文化的極大關注，成為教育界的熱門話題。
事實上，當人們不滿足於對數學本身的研究，開始從外部審視數學的價值時，對數學文化的研究就開始了。人們開始思考“數學是什麼”與“數學的價值是什麼”，並逐漸認識到數學已經成為人類文化的重要組成部分，在過去已經對人類文明做出了巨大的貢獻，在未來也必將做出更大的貢獻。
把數學作為文化來進行研究，國外要比我們早很多，比較有代表性的是美國的數學家懷爾德與數學史專家莫里斯·克萊因。懷爾德認為數學是一個由內在力量與外在力量共同作用，而處於不斷發展和變化之中的文化系統。數學文化是由文化傳統和數學本身所組成。這些觀點在他的兩部著作《數學概念的演化》和《作為一種文化系統的數學》中得以充分體現。莫里斯·克萊因在他的著作《西方文化中的數學》《數學：一種文化探索》《數學與知識的探求》中則系統論述了數學對西方文化、理性精神、現代人類思想發展所產生的影響。他側重於數學與各種文化以及社會因素之間相互作用的分析。我國開展數學文化研究是近二三十年的事情，時間雖短，但是相關研究也取得了極大進展。徐利治探討數學一般意義上存在的某些相同或不同的方法，開創了“數學方法論”的研究與教學；鄭毓信教授在他的《數學文化學》中基於數學哲學觀點構建數學文化學的理論體系，嘗試從理論層面論述數學作為文化的內涵；齊民友在《數學與文化》一書中則論述了中西數學文化的差異。
我國教育主管部門對數學文化也很重視。早在2003 年，教育部頒布的《普通高中數學課程標準（實驗）》中就突出強調了數學的文化價值——數學是人類文化的重要組成部分，對數學文化給予了特別重視，要求數學文化貫穿整個高中數學課程並融入教學中。這次教育部考試中心又再次以發布正式檔案的方式對數學文化重點提及，明確提出要在高考試題中考查數學文化，足以看出國家對數學文化的重視。
以往提及數學文化，大多停留在理論的層面，而且很多研究僅僅把史實、案例、故事等稍作整理，將數學史等同於數學文化。這種做法不過是給數學文化穿了件“數學史”外衣而已。類似的研究總給人以不接地氣之嫌，沒有引起人們的觸動。但這次之所以引發對數學文化思考與研究的熱潮，主要原因是考試主管部門從考試命題的角度提出了要求，第一次正式地明確要求把數學文化滲入數學試題，所以未來高考數學命題肯定會遵照執行。雖然我們提了很久的數學文化，但如何在數學試題中體現出來，對很多人來說還是比較陌生的。數學文化本來是個籠統的概念，傳統意義上“文化”在文科中出現得較為普遍，在文科類的命題中是很容易做到的。而數學是邏輯的科學、思維的科學，如何把“文化”滲透其中，是一個擺在廣大數學教育工作者面前的新課題。正是在這樣的背景下，我根據多年積累的豐富資料和大量的研究工作，捉筆成書，對相關問題作出了系統的回答。
《數學文化與高考》一書共分八章。第一章為數學文化總論，主要闡述了數學文化的含義、內容和基本特性等問題；後面七章分別為數學歷史、數學精神、數學套用、數學之美、數學語言、交匯拓展、數學遊戲，遴選近十五年高考數學中涉及數學文化的試題進行分類賞析，系統揭示命制背景，展示解題過程，凸顯數學文化價值。全書儘可能把數學文化出題的方向一網打盡，讓讀者明確數學文化“是什麼”“怎么考”“怎么練”，為備考數學文化提供清晰的複習方向。同時每個主題後面提供與主題相關的數學文化練習題，方便讀者練習鞏
固使用，從而更有針對性地複習。本書的編寫具有實用性、針對性和時效性三個鮮明特點，密切結合當下學生、教師對數學文化試題認識相對陌生的客觀實際，對高考中曾經出現的數學文化試題進行分類賞析，系統闡述“最新考綱”考查數學文化的內涵，同時為學生備考提供科學性的建議。
我國對數學文化的系統研究時間不長，尤其是數學文化與試題的結合研究更是不成熟。此書儘管對數學文化的理論探討與套用研究取得了較大突破，然而也不免出現不完善或者紕漏之處。但我相信，此書的問世將會受到廣大同行的重視和學生的歡迎。在此，我也懇請讀者批評雅正。
