Mathematics content for elementary teachers

✍ Scribed by Douglas K. Brumbaugh, Peggy L. Moch, Mary E. Wilkinson

• Publisher: Routledge
• Year: 2005
• Tongue: English
• Leaves: 314
• Series: Lea Early Childhood Education
• Category: Library

✦ Synopsis

THE book for elementary education mathematics content courses! Designed to help prospective teachers of elementary school mathematics learn content beyond the rote level, this text stimulates readers to think beyond just getting the problem right and fosters their development into thoughtful, reflective, self-motivated, life-long learners. It stresses the what and why of elementary school mathematics content. Hints are provided about how to teach the content but this is mostly left to courses and texts that are dedicated to that purpose.The text is organized around the National Council for Teachers of Mathematics' Principles and Standards for School Mathematics. The Standards dictate the basic sections of the text. Within each section, appropriate specific topics are developed, intertwined with technology, problem solving, assessment, equity issues, planning, teaching skills, use of manipulatives, sequencing, and much more. In addition, major focal points of the Standards are emphasized throughout: effective teachers of mathematics should be able to motivate all students to learn, should understand the developmental levels of how children learn, should concentrate on what children need to become active participants in the learning environment, and should be engaged in ongoing investigations of new mathematical concepts and teaching strategies.Mathematics Content for Elementary Teachers is based on several fundamental premises:The focus of mathematics education should be on the process, not the answer.Elementary teachers should know the mathematics content they are teaching, know more than the content they are teaching, and teach from the overflow of knowledge.It is important for teachers to be flexible in allowing students to use different procedures--teaching from the "overflow of knowledge" implies knowing how to do a given operation more than one way and being willing to examine many different ways.Teachers need to learn to carefully cover the topics to be taught, to reflect upon them, and to be able to organize them. To help prospective elementary teachers concentrate on the mathematics content they will be expected to teach and begin to build the foundation for the methods they will use, this text includes only elementary mathematics content and does not address middle school concepts.Pedagogical features:The text is organized according to NCTM Standards.An informal writing style speaks directly to readers and is geared to pre-service teachers.Focus is given to multiple methods of problem solving at four developmental levels.Questions, exercises, and activities are interspersed throughout each section rather than gathered at the end of each chapter.*Complete solutions for exercises are provided.

✦ Table of Contents

Contents......Page 10
To the Student......Page 16
Focal Points......Page 17
To the Instructor......Page 18
Overview of Content......Page 19
References......Page 20
Personal Acknowledgments......Page 22
About the Authors......Page 24
1 Guiding Principles......Page 26
The Curriculum Principle......Page 27
The Teaching Principle......Page 28
The Learning Principle......Page 29
The Technology Principle......Page 30
The Challenge......Page 31
References for Guiding Principles......Page 33
Set Definitions......Page 34
Set Operations......Page 40
Venn Diagrams......Page 41
Properties......Page 43
Prime and Composite Numbers......Page 47
Sieve of Eratosthenes......Page 49
Divisibility Rules......Page 50
Greatest Common Factor and Least Common Multiple......Page 53
Whole Number Addition......Page 57
Standard Algorithm......Page 59
Partial Sum......Page 60
Horizontal and Vertical Writing......Page 61
Left to Right Addition......Page 62
Any Column First......Page 63
Low Stress Addition......Page 64
Whole Number Subtraction......Page 65
Terminology......Page 66
Concrete Subtraction......Page 67
Standard Algorithm......Page 69
Borrow Pay Back Method......Page 70
Scratch Method......Page 71
Integer Subtraction......Page 72
Terminology......Page 73
Standard Algorithm......Page 74
Partial Product Method......Page 75
Lattice Multiplication......Page 76
Horizontal and Vertical Writing......Page 78
Russian Peasant (Simple Halving/Doubling Method)......Page 79
Whole Number Division......Page 80
Terminology......Page 82
Repeated Subtraction Division......Page 83
Standard Division Algorithm......Page 85
Remainders......Page 86
Say What?......Page 87
Concrete Beginnings......Page 88
Equivalent Fractions......Page 89
Converting a Mixed Number to an Improper Fraction......Page 91
Converting an Improper Fraction to a Mixed Number......Page 92
Product of Whole Number and Mixed Number......Page 93
Product of Two Fractions......Page 94
Product of a Fraction and a Mixed Number......Page 95
Conclusions......Page 96
Adding Fractions When Denominators Are the Same......Page 97
Adding Fractions When the Denominators Are Related......Page 99
Adding Fractions When the Denominators Are Relatively Prime......Page 100
Adding Fractions When the Denominators Are Not Relatively Prime and One Is Not a Multiple of the Other......Page 101
Same Denominators......Page 102
Related Denominators......Page 103
Relatively Prime Denominators......Page 104
Mixed Numbers......Page 105
Division of Fractions......Page 106
Whole Number Divided by a Fraction......Page 107
Fraction Divided by a Fraction......Page 108
Common Denominator Division......Page 109
Conclusions......Page 110
Concrete Beginnings......Page 111
Adding With the Same Number of Places......Page 112
Lining up the Ones......Page 113
Subtraction of Decimals......Page 114
Subtracting With the Same Number of Places......Page 115
Concrete Beginnings......Page 116
Moving Beyond the Concrete......Page 117
Conclusions......Page 119
Concrete Beginnings......Page 120
Whole Number Divided by a Whole Number......Page 121
Decimal Divided by a Whole Number......Page 122
Conclusions......Page 123
Models......Page 124
Rules for Adding Integers......Page 126
Conclusions......Page 127
Models......Page 128
Multiplying Integers......Page 130
Division of Integers......Page 132
Signed Numbers in Inverse Operations......Page 133
Rational Numbers as Ratios......Page 134
Percents......Page 136
Proportions......Page 137
Solving Problems Using Proportions......Page 139
Conclusions......Page 141
3 Algebra......Page 142
Historic Underpinnings......Page 143
Having Fun With Algebra......Page 144
Integrating Algebra......Page 146
Patterning......Page 147
Representing Situations With Algebra......Page 148
Using Models......Page 149
Rate of Change......Page 151
Sequences......Page 153
Formulas......Page 155
Conclusions......Page 156
References......Page 157
Undefined Terms......Page 158
Angles......Page 161
Simple Closed Curves, Regions, and Polygons......Page 163
Polygons......Page 164
Circles......Page 167
Constructions......Page 168
Third Dimension......Page 169
Coordinate Geometry......Page 171
Transformations and Symmetry......Page 172
Conclusions......Page 174
5 Measurement......Page 176
Attributes......Page 177
Systems......Page 178
Linear Measure......Page 180
Area......Page 181
Volume......Page 186
Capacity......Page 189
Time......Page 190
Money......Page 191
Angle Measure......Page 192
Dimensional Analysis......Page 196
Conclusions......Page 197
Data and Where to Get It......Page 198
Representations of Data......Page 199
Circle Graph......Page 200
Bar Graph......Page 201
Line Graph......Page 202
Frequency Polygon......Page 203
Box and Whisker Plot......Page 204
Scatter Plot......Page 205
Stem and Leaf Plot......Page 206
Data Analysis and Statistics......Page 207
Measures of Central Tendency and Scatter......Page 208
Statistics......Page 214
Factorial......Page 216
Permutations......Page 218
Independent......Page 219
Dependent......Page 222
Lottery......Page 224
Odds......Page 225
Conclusions......Page 226
What Makes a Problem a Problem?......Page 228
Polya's Steps......Page 229
Strategies......Page 230
Collection of Problems......Page 232
Bibliography......Page 233
And......Page 234
Or......Page 235
If, Then......Page 236
Logical Equivalence......Page 237
Informal Proofs......Page 238
Beyond the Informal Proofs......Page 239
Two-Column Proof......Page 240
Conclusions......Page 242
9 Communication......Page 244
Independent or Interconnected Topics......Page 248
How Are Things Connected?......Page 249
Conclusions......Page 252
Different Ways of Saying the Same Thing......Page 254
Bibliography......Page 255
C......Page 256
E......Page 257
I......Page 258
N......Page 259
R......Page 260
U......Page 261
Z......Page 262
Solutions Manual......Page 264