【全新改版】美国数学(小学卷)(套装13册)

基本信息

出版社:天津社会科学院出版社;第1版((咨询特价)年9月1日)

正文语种:英文

开本:16

ISBN:42

定价：(咨询特价)

   这套《美国数学（小学卷·套装1~3册）》与麦加菲编写的《美国语文》，应该说对美国教育产生了很大影响。两套教材自19世纪以来，被10000多所学校使用，累计销量分别高达1.22亿册，至今仍作为“家庭学校”（Homeschooling）的推荐教材。雷伊数学课本，是一套系统完整的中小学数学教材，从简单的算术开始，到高级的代数与解析几何。在近50年里，雷伊数学课本一直被作为美国标准数学教材，10000多所学校采用,超过一亿的美国孩子用此套数学教材接受教育。直到现在仍作为学生学习和备考AST的参考用书。
　　对中国学生来说，这套系列教材，能帮助学生用英语学习数学，既提高他们的英语水片也帮助他们将来更好地适应西方学科考试。

    呈现于您眼前的这套《美国数学（小学卷@套装1~3册）》，是一套在西方流行了近半个世纪、至今仍在使用的经典教材。编者约瑟夫@雷伊教授，1807年出生于美国弗吉尼亚俄亥俄县，从小在当地学校接受教育，成绩优秀。16岁时开始其教师职业生涯。18岁,雷伊来到富兰克林学院跟随乔尔@教授学习医学，此后又进入俄亥俄医学院学习。大学毕业后，他在辛辛那提伍德沃德中学任教，讲授数学。1836年，伍德沃德中学由高中升格为辛辛那提伍德学院，雷伊成为该学院教授。1851年，该校又变为一所公立高中，雷伊一直在此担任校长，直至去世。雷伊一生杰出的成就是他倾心编写的系列数学教材，并以此闻名。这套数学课本与他在伍德学院的同事威廉@麦加菲编写的《美国语文读本》，同时被美国近万所学校作为教材，累计销量均超过1.22亿册，对几代美国人的教育产生了很大影响。直至今日，这两套书仍被当作美国家庭教育(Homeschooling)的推荐教材，也是美国学生准备SAT考试的参考用书。
与其他数学书相比，雷伊数学教材至少有以下几个明显特点：
　　第一，强调在“学”中掌握“数”。例如，《小学数学》不完全按难度分册，而是根据其实际应用范围分为四册：初级算术、智力算术、实用算术与高级算术。让学生从对数的认知、运算法则的掌握，延伸到数学在实际生活中的广泛应用，如购物、记账、存款、利息等，并向更高的学术层次过渡。
　　第二，将数学问题融于文字题（WordProblem）之中。即便最简单的加减运算，它也通过讲故事的方式呈现出来。这样孩子们在学习数学时，不仅可以训练其数学思维，语言能力也可以同步提高。
　　第三，将抽象思维具体化。书中的数学题大都结合现实事物表述出来，让孩子们理解他们所学的数学在现实生活中是如何加以应用的。这对低年级学生来说，尤其帮助很大，他们能更快更清楚地理解那些对其年龄来讲过于抽象的数学概念。
　　第四，将不同学科知识融入数学问题中。这种编写方法能让学生从数学应用的不同领域来掌握数学科学，帮助学生从低年级数学步入更复杂的数学应用领域，如几何学与会计学等。孩子们在学习数学的同时，又能接受其他学科知识。如书中有这样一道题：“华盛顿将军出生于公1732年，他活了67岁，那么他是于哪一年去世？”这么一道简单的计算题,便将历史知识与数学结合起来，一举多得。
　　对于中国孩子来讲，这套数学课本不仅能教孩子学习数学，更是学习英语的很好途径，让他们换个思维学英语。与阅读文学读本相比，这是另一种不同的感觉，或许更能激发孩子学习英语的兴趣。数学的词汇含义固定，也易于理解记忆，孩子在解题的同时也能提高英语水片可谓一举多得。对于那些将来准备参加出国英语考试的学生来讲，这套书意义更大，对他们将来的求学之路应该大有帮助。

约瑟夫·雷伊教授于1807年出生于美国弗吉尼亚俄亥俄县，小时在地方学校接受教育，学业优秀。16岁时，他就开始步入其教师生涯，1825年到富兰克林学院求学，跟随乔尔·教授学习医学。1828年毕业后进入俄亥俄医学院学习，1831年毕业。大学毕业后，他在辛辛那提的伍德沃德中学找了份当教师的工作，开始教数学。1836年，俄亥俄司法当局准许伍德沃德中学由高中升格为辛辛那提伍德学院，雷伊成为该学院的一名教授。1851年，该校以变为一所公立高中，雷伊一直在此担任校长，直至去世。
　　雷伊最杰出的贡献是他编写的系列数学教材，并以此闻名。这套数学课本与他在伍德学院的同事麦加菲编写的《美国语文读本》，一同被作为美国学校的语文和数学教材，近50年内，美国上万学校使用这两套教材，累计销量均超过1.22亿册，对美国教育产生了极大影响。
　　雷伊教授对俄亥俄州的教师职业培训也发挥了很大作用，他帮助建立西部文化中心与职业教师学院，将好的教学技术与经验传授给老师。他加入俄亥俄州教师协会成员，并于1853年任其会长，此外还担任《俄亥俄教育》杂志社的副总编。

第一册

第二册

THE ARABIC SYSTEM OF NOTATION  

ADDITION  

SUBTRACTION  

MULTIPLICATION  

DIVISION  

COMPOUND NUMBERS  

FACTORING  

FRACTIONS  

PRACTICE  

DECIMAL FRACTIONS  

THE METRIC SYSTEM  

PERCENTACE  

INTEREST  

DISCOUNT  

EXCHANGE  

INSURANCE  

TAXES  

RATIO  

PROPORTION  

INVOLUTION  

EVOLUTION  

MENSURATION  

PROGRESSIONS  

第三册

CHAPTER I. INTRODUCTION  

CHAPTER II. NUMERATION AND NOTATION  

CHAPTER III. ADDITION  

CHAPTER IV. SUBTRACTION  

CHAPTER V. MULTIPLICATION  

CHAPTER VI. DIVISION  

CHAPTER VII. PROPERTIES OF NUMBERS  

CHAPTER VIII. COMMON FRACTIONS  

CHAPTER IX. DECIMAL FRACTIONS  

CHAPTER X. COMPOUND DENOMINATE NUMBERS  

CHAPTER XI. RATIO  

CHAPTER XII. PROPORTION  

CHAPTER XIII. PERCENTAGE  

CHAPTER XIV. PERCENTAGE. —APPLICATIONS  

CHAPTER XV. PERCENTAGE. —APPLICATIONS  

CHAPTER XVI. PARTNERSHIP  

CHAPTER XVII. ALLIGATION  

CHAPTER XVIII. INVOLUTION  

CHAPTER XIX. EVOLUTION  

CHAPTER XX. SERIES  

CHAPTER XXI. MENSURATION  

CHAPTER XXII. MISCELLANEOUS EXERCISES  

显示部分信息

Ⅰ. INTRODUCTION

Article 1. A definition is a concise description of any objectof thought, and must be of such a nature as to distinguish theobject described from all other objects.

2. Quantity is anything which can be increased or diminished;it embraces number and magnitude. Number answers the question, “Howmany@”Magnitude, “How much@”

3. Science is knowledge properly classified.

4. The primary truths of a science are called Principles.

5. Art is the practical application of a principle or theprinciples of science.

6. Mathematics is the science of quantity.

7. The elementary branches of mathematics are Arithmetic,Algebra, and Geometry.

8. Arithmetic is the introductory branch of the science ofnumbers. Arithmetic as a science is composed of definitions,principles, and processes of calculation; as an art, it teaches howto apply numbers to theoretical and practical purposes.

9. A Proposition is the statement of a principle, or ofsomething proposed to be done.

10. Propositions are of two kinds, demonstrable andindemonstrable. Demonstrable propositions can be proved by the aidof reason. Indemonstrable propositions can not be made simpler byany attempt at proof.

11. An Axiom is a self-evident truth.

12. A Theorem is a truth to be proved.

13. A Problem is a question proposed for solution.

14. Axioms, theorems, and problems are propositions.

15. A process of reasoning proving the truth of a proposition,is called a Demonstration.

16. A Solution of a problem is an expressed statement showinghow the result is obtained.

17. The term Operation, as used in this book, is applied toillustrations of solutions.

18. A Rule is a general direction for solving all problems ofa particular kind.

19. A Formula is the expression of a general rule or principlein algebraic language; that is, by symbols.

20. A Unit is one thing, or one. One thing is a concrete unit;one is an abstract unit.

21. Number is the expression of a definite quantity. Numbersare either abstract or, concrete. An abstract number is one inwhich the kind of unit is not named; a concrete number is one inwhich the kind of unit is named. Concrete numbers are also calledDenominate Numbers.

22. Numbers are also divided into Integral, Fractional, andMixed. An Integral number, or Integer, is a whole number; aFractional number is an expression for one or more of the equalparts of a divided whole; a Mixed number is an Integer and Fractionunited.

23. A Sign is a character used to show a relation amongnumbers, or that an operation is to be performed.

24. The signs most used in Arithmetic are

+   -   ×  ÷   =  :  ::  ( )  ———  @@@@

25. The sign of Addition is [+], and is called plus. Thenumbers between which it is placed are to be added. Thus, 3+5equals 8.Plus is described as a perpendicular cross, in which thebisecting lines are equal.

26. The sign of Subtraction is [ -], and is called minus. Whenplaced between two numbers, the one that follows it is to be takenfrom the one that precedes it. Thus, 7-4 equals 3. Minus isdescribed as a short horizontal line. Plus and Minus are Latinwords. Plus means more; minus means less. Michael Steifel, a Germanmathematician, first introduced + and - in a work published in1544.

27. The sign of Multiplication is [×], and is read multipliedby, or times. Thus, 4×5 is to be read, 4 multiplied by 5, or 4times 5. The sign is described as an oblique cross. WilliamOughtred, an Englishman, born in 1573, first introduced the sign ofmultiplication.

28. The sign of Division is [÷], and is read divided by. Whenplaced

between two numbers, the one on the left is to be divided bythe one on

the right. Thus, 20÷4 equals 5.

The sign is described as a short horizontal line and two dots:one dot directly above the middle of the line, and the other justbeneath the middle of it. Dr. John Pell, an English analyst, bornin 1610, introduced the sign of division.

29. The Radical sign, [√], indicates that some root is to befound.

Thus, 36 indicates that the square root of 36 is required; 3125 , that the cube root of 125 is to be found; and 4 625 indicatesthat the fourth root of 625 is to be extracted. The root to befound is shown by the small figure placed between the branches ofthe Radical sign. The figure is called the index.

30. The signs, +, -, ×, ÷, √ , are symbols of operation.

31. The sign of Equality is [=], two short horizontal parallellines, and is read equals or is equal to, and signifies that thequantities between

which it is placed are equal. Thus, 3+5 =9-1. This is calledan equation, because the quantity 3+5 is equal to 9-1.

32. Ratio is the relation which one number bears to another ofthe same kind. The sign of Ratio is [：]. Ratio is expressed thus, 6：3 = 6 3 = 2, and is read, the ratio of 6 to 3 =2, or is 2. Thesign of ratio may be described as the sign of division with theline omitted. It has the same force as the sign of division, and isused in place of it by the French.

33. Proportion is an equality of ratios. The sign ofProportion is [∷], and is used thus, 3：6∷4：8; this may be read, 3is to 6 as 4 is to 8; another reading, the ratio of 3 to 6 is equalto the ratio of 4 to 8.

34. The signs [ (  ), ———], are signs of Aggregation—thefirst is the Parenthesis, the second the Vinculum. They are usedfor the same purpose; thus, 24-(8+7), or 24-8+7, means that the sumof 8+7 is to be subtracted from 24. The numbers within theparenthesis, or under the vinculum, are considered as onequantity.

35. The dots [. . . . ], used to guide the eye from words atthe left to the right, are called Leaders, or the sign ofContinuation, and are read, and so on.

36. The sign of Deduction is [∴], and is read therefore,hence, or consequently.

37. The signs, =, :, ::, (), —, . . . . , ∴, are symbols ofrelation.

38. Arithmetic depends upon this primary proposition: that anynumber may be increased or diminished. “Increased”comprehendsAddition, Multiplication, and Involution; “decreased”, Subtraction,Division, and Evolution.

39. The fundamental operations of Arithmetic in the order oftheir arrangement, are: Numeration and Notation, Addition,Subtraction, Multiplication, and Division.

……