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Understanding Numbers in Elementary School Mathematics
 
Hung-Hsi Wu University of California, Berkeley, CA
Understanding Numbers in Elementary School Mathematics
Hardcover ISBN:  978-0-8218-5260-6
Product Code:  MBK/79
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
eBook ISBN:  978-1-4704-1210-4
Product Code:  MBK/79.E
List Price: $95.00
MAA Member Price: $85.50
AMS Member Price: $76.00
Hardcover ISBN:  978-0-8218-5260-6
eBook: ISBN:  978-1-4704-1210-4
Product Code:  MBK/79.B
List Price: $194.00 $146.50
MAA Member Price: $174.60 $131.85
AMS Member Price: $155.20 $117.20
Understanding Numbers in Elementary School Mathematics
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Understanding Numbers in Elementary School Mathematics
Hung-Hsi Wu University of California, Berkeley, CA
Hardcover ISBN:  978-0-8218-5260-6
Product Code:  MBK/79
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
eBook ISBN:  978-1-4704-1210-4
Product Code:  MBK/79.E
List Price: $95.00
MAA Member Price: $85.50
AMS Member Price: $76.00
Hardcover ISBN:  978-0-8218-5260-6
eBook ISBN:  978-1-4704-1210-4
Product Code:  MBK/79.B
List Price: $194.00 $146.50
MAA Member Price: $174.60 $131.85
AMS Member Price: $155.20 $117.20
  • Book Details
     
     
    2011; 551 pp
    MSC: Primary 97; 00;

    This is a textbook for pre-service elementary school teachers and for current teachers who are taking professional development courses. By emphasizing the precision of mathematics, the exposition achieves a logical and coherent account of school mathematics at the appropriate level for the readership. Wu provides a comprehensive treatment of all the standard topics about numbers in the school mathematics curriculum: whole numbers, fractions, and rational numbers. Assuming no previous knowledge of mathematics, the presentation develops the basic facts about numbers from the beginning and thoroughly covers the subject matter for grades K through 7.

    Every single assertion is established in the context of elementary school mathematics in a manner that is completely consistent with the basic requirements of mathematics. While it is a textbook for pre-service elementary teachers, it is also a reference book that school teachers can refer to for explanations of well-known but hitherto unexplained facts. For example, the sometimes-puzzling concepts of percent, ratio, and rate are each given a treatment that is down to earth and devoid of mysticism. The fact that a negative times a negative is a positive is explained in a leisurely and comprehensible fashion.

    Ancillaries:

    Readership

    Pre-service elementary school teachers and current teachers interested in a logical and coherent account of school mathematics.

  • Table of Contents
     
     
    • Part 1. Whole numbers
    • Chapter 1. Place value
    • Chapter 2. The basic laws of operations
    • Chapter 3. The standard algorithms
    • Chapter 4. The addition algorithm
    • Chapter 5. The subtraction algorithm
    • Chapter 6. The multiplication algorithm
    • Chapter 7. The long division algorithm
    • Chapter 8. The number line and the four operations revisited
    • Chapter 9. What is a number?
    • Chapter 10. Some comments on estimation
    • Chapter 11. Numbers in base $b$
    • Part 2. Fractions
    • Chapter 12. Definitions of fraction and decimal
    • Chapter 13. Equivalent fractions and FFFP
    • Chapter 14. Addition of fractions and decimals
    • Chapter 15. Equivalent fractions: further applications
    • Chapter 16. Subtraction of fractions and decimals
    • Chapter 17. Multiplication of fractions and decimals
    • Chapter 18. Division of fractions
    • Chapter 19. Complex fractions
    • Chapter 20. Percent
    • Chapter 21. Fundamental Assumption of School Mathematics (FASM)
    • Chapter 22. Ratio and rate
    • Chapter 23. Some interesting word problems
    • Chapter 24. On the teaching of fractions in elementary school
    • Part 3. Rational numbers
    • Chapter 25. The (two-sided) number line
    • Chapter 26. A different view of rational numbers
    • Chapter 27. Adding and subtracting rational numbers
    • Chapter 28. Adding and subtracting rational numbers redux
    • Chapter 29. Multiplying rational numbers
    • Chapter 30. Dividing rational numbers
    • Chapter 31. Ordering rational numbers
    • Part 4. Number theory
    • Chapter 32. Divisibility rules
    • Chapter 33. Primes and divisors
    • Chapter 34. The Fundamental Theorem of Arithmetic (FTA)
    • Chapter 35. The Euclidean algorithm
    • Chapter 36. Applications
    • Chapter 37. Pythagorean triples
    • Part 5. More on decimals
    • Chapter 38. Why finite decimals are important
    • Chapter 39. Review of finite decimals
    • Chapter 40. Scientific notation
    • Chapter 41. Decimals
    • Chapter 42. Decimal expansions of fractions
  • Reviews
     
     
    • [This book] delivers the mathematical knowledge that elementary-grades teachers need.

      American Educator
    • The author has a published article related to this book entitled, "Phoenix Rising: Bringing the Common Core State Mathematics Standards to Life." To read the article, please go to the Fall 2011 issue of American Educator.

      The author has a published article related to this book entitled, "Phoenix Rising: Bringing the Common Core State Mathematics Standards to Life." To read the article, please go to the Fall 2011 issue of American Educator.

  • Requests
     
     
    Review Copy – for publishers of book reviews
    Instructor's Manual – for instructors who have adopted an AMS textbook for a course and need the instructor's manual
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
2011; 551 pp
MSC: Primary 97; 00;

This is a textbook for pre-service elementary school teachers and for current teachers who are taking professional development courses. By emphasizing the precision of mathematics, the exposition achieves a logical and coherent account of school mathematics at the appropriate level for the readership. Wu provides a comprehensive treatment of all the standard topics about numbers in the school mathematics curriculum: whole numbers, fractions, and rational numbers. Assuming no previous knowledge of mathematics, the presentation develops the basic facts about numbers from the beginning and thoroughly covers the subject matter for grades K through 7.

Every single assertion is established in the context of elementary school mathematics in a manner that is completely consistent with the basic requirements of mathematics. While it is a textbook for pre-service elementary teachers, it is also a reference book that school teachers can refer to for explanations of well-known but hitherto unexplained facts. For example, the sometimes-puzzling concepts of percent, ratio, and rate are each given a treatment that is down to earth and devoid of mysticism. The fact that a negative times a negative is a positive is explained in a leisurely and comprehensible fashion.

Ancillaries:

Readership

Pre-service elementary school teachers and current teachers interested in a logical and coherent account of school mathematics.

  • Part 1. Whole numbers
  • Chapter 1. Place value
  • Chapter 2. The basic laws of operations
  • Chapter 3. The standard algorithms
  • Chapter 4. The addition algorithm
  • Chapter 5. The subtraction algorithm
  • Chapter 6. The multiplication algorithm
  • Chapter 7. The long division algorithm
  • Chapter 8. The number line and the four operations revisited
  • Chapter 9. What is a number?
  • Chapter 10. Some comments on estimation
  • Chapter 11. Numbers in base $b$
  • Part 2. Fractions
  • Chapter 12. Definitions of fraction and decimal
  • Chapter 13. Equivalent fractions and FFFP
  • Chapter 14. Addition of fractions and decimals
  • Chapter 15. Equivalent fractions: further applications
  • Chapter 16. Subtraction of fractions and decimals
  • Chapter 17. Multiplication of fractions and decimals
  • Chapter 18. Division of fractions
  • Chapter 19. Complex fractions
  • Chapter 20. Percent
  • Chapter 21. Fundamental Assumption of School Mathematics (FASM)
  • Chapter 22. Ratio and rate
  • Chapter 23. Some interesting word problems
  • Chapter 24. On the teaching of fractions in elementary school
  • Part 3. Rational numbers
  • Chapter 25. The (two-sided) number line
  • Chapter 26. A different view of rational numbers
  • Chapter 27. Adding and subtracting rational numbers
  • Chapter 28. Adding and subtracting rational numbers redux
  • Chapter 29. Multiplying rational numbers
  • Chapter 30. Dividing rational numbers
  • Chapter 31. Ordering rational numbers
  • Part 4. Number theory
  • Chapter 32. Divisibility rules
  • Chapter 33. Primes and divisors
  • Chapter 34. The Fundamental Theorem of Arithmetic (FTA)
  • Chapter 35. The Euclidean algorithm
  • Chapter 36. Applications
  • Chapter 37. Pythagorean triples
  • Part 5. More on decimals
  • Chapter 38. Why finite decimals are important
  • Chapter 39. Review of finite decimals
  • Chapter 40. Scientific notation
  • Chapter 41. Decimals
  • Chapter 42. Decimal expansions of fractions
  • [This book] delivers the mathematical knowledge that elementary-grades teachers need.

    American Educator
  • The author has a published article related to this book entitled, "Phoenix Rising: Bringing the Common Core State Mathematics Standards to Life." To read the article, please go to the Fall 2011 issue of American Educator.

    The author has a published article related to this book entitled, "Phoenix Rising: Bringing the Common Core State Mathematics Standards to Life." To read the article, please go to the Fall 2011 issue of American Educator.

Review Copy – for publishers of book reviews
Instructor's Manual – for instructors who have adopted an AMS textbook for a course and need the instructor's manual
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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