Essentials of Elementary School Mathematics - 1st Edition - ISBN: 9780124386402, 9781483264882

Essentials of Elementary School Mathematics

1st Edition

Authors: Max D. Larsen James L. Fejfar
eBook ISBN: 9781483264882
Imprint: Academic Press
Published Date: 1st January 1974
Page Count: 430
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Essentials of Elementary School Mathematics is an introductory text on the essentials of mathematics taught in elementary schools. It presents a systematic development of the mathematics of arithmetic. A primary objective is to give students a background sufficient to understand and answer at an appropriate level the various quite penetrating questions asked by young students. Some examples and exercises are concerned primarily with pedagogical aspects of arithmetic.

Comprised of 14 chapters, this book begins with an overview of the language of mathematics, focusing on concepts such as the conjunction (and); negation (not); disjunction (or); and conditional (if...then...). The discussion then turns to the theory of sets; the concept of binary operations; and recognition and identification of properties of various relations. The next section deals with the number systems of arithmetic: whole numbers, integers, rational numbers, and real numbers. Number theory and clock arithmetic are also examined, along with counting techniques and probability. The final section is devoted to motion geometry and analytic geometry.

This monograph should be of interest to students and teachers of mathematicians at the elementary level.

Table of Contents


Note to the Instructor

Note to the Student

Part One Fundamentals

1 The Language of Mathematics

1 Conjunction (And); Negation (Not)

2 Disjunction (Or)

3 Conditional (If..., Then...)

4 Biconditional (If and Only If)

5 Quantifiers


2 Sets

1 Subset

2 Intersection and Union

3 Complement

4 Cartesian Product


3 Binary Operations

1 Definition of Binary Operation

2 Commutativity

3 Associativity

4 Distributivity

5 Identity Element

6 Inverses


4 Relations

1 Reflexive Relations

2 Symmetric Relations

3 Transitive Relations

4 Equivalence Relations

5 One-to-One Correspondence


Part Two The Theory of Arithmetic

5 The System of Whole Numbers

1 Definitions of Whole Numbers

2 Addition of Whole Numbers

3 Multiplication of Whole Numbers

4 Ordering of Whole Numbers


6 The System of Integers

1 Definition of Integers

2 Addition of Integers

3 Subtraction of Integers

4 Multiplication of Integers

5 Ordering of Integers


7 Place-Value Numeration Systems

1 The Nature of Our Decimal

2 Other Bases

3 Algorithms

4 Addition

5 Subtraction

6 Multiplication

7 Division


8 Systems of Rational and Real Numbers

1 Definition of Rational Numbers

2 Addition of Rational Numbers

3 Multiplication of Rational Numbers

4 Ordering of Rational Numbers

5 Division of Rational Numbers

6 Real Numbers


Part Three Expanding Mathematical Experiences

9 Number Theory

1 Divisors, Factors, and Primes

2 Division Algorithm

3 The Greatest Common Divisor


10 Clock Arithmetic

1 Introduction

2 An Equivalence Relation

3 Choosing Clocks


11 Counting Techniques and Probability

1 Permutations

2 Combinations

3 Probability


Part Four Geometry

12 Motion Geometry I

1 Congruence

2 Slides, Turns, and Flips

3 Successive Motions

4 Invariance

5 Angles

6 Symmetry


13 Motion Geometry II

1 Parallel Lines

2 Perpendicular Lines

3 Triangles

4 Quadrilaterals

5 Area

6 Similarity

7 Construction


14 Functions and Coordinate Geometry

1 Definition

2 Onto and One-To-One Functions

3 Graphing Functions

4 Graphing In R x R

5 Distance

6 Lines




Answers to Selected Exercises

Subject Index


No. of pages:
© Academic Press 1974
Academic Press
eBook ISBN:

About the Author

Max D. Larsen

James L. Fejfar

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