Understanding Numbers in Elementary School Mathematics
豆瓣
Hung-Hsi Wu
简介
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.
Solutions to the activities are available electronically on the Supplemental Materials page.
Selected solutions are available electronically for instructors only. Please send email to textbooks@ams.org for more information.
contents
Cover 1
Title page 4
Contents 8
Preface 16
Acknowledgments 22
To the reader 26
Some conventions in this book 32
Part 1. Whole numbers 34
Place value38
The basic laws of operations72
The standard algorithms90
The addition algorithm94
The subtraction algorithm104
The multiplication algorithm118
The long division algorithm128
The number line and the four operations revisited160
What is a number?168
Some comments on estimation172
Numbers in base 𝑏188
Part 2. Fractions204
Definitions of fraction and decimal210
Equivalent fractions and FFFP236
Addition of fractions and decimals254
Equivalent fractions: further applications268
Subtraction of fractions and decimals286
Multiplication of fractions and decimals294
Division of fractions316
Complex fractions342
Percent352
Fundamental Assumption of School Mathematics (FASM)364
Ratio and rate368
Some interesting word problems390
On the teaching of fractions in elementary school400
Part 3. Rational numbers406
The (two-sided) number line408
A different view of rational numbers412
Adding and subtracting rational numbers414
Adding and subtracting rational numbers redux428
Multiplying rational numbers436
Dividing rational numbers446
Ordering rational numbers454
Part 4. Number theory464
Divisibility rules468
Primes and divisors478
The Fundamental Theorem of Arithmetic (FTA)488
The Euclidean algorithm496
Applications506
Pythagorean triples520
Part 5. More on decimals524
Why finite decimals are important528
Review of finite decimals530
Scientific notation538
Decimals544
Decimal expansions of fractions558
Bibliography574
Index 578
Back Cover586
Preview Material
Preface
Table of Contents
