Synopses & Reviews
Intended for the one- or two-semester course required of Education majors, MATHEMATICS FOR ELEMENTARY SCHOOL TEACHERS, 5E, offers future teachers a comprehensive mathematics course designed to foster concept development through examples, investigations, and explorations. Visual icons throughout the main text allow instructors to easily connect content to the hands-on activities in the corresponding Explorations Manual. Bassarear presents real-world problems, problems that require active learning in a method similar to how archaeologists explore an archaeological find: they carefully uncover the site, slowly revealing more and more of the structure. The author demonstrates that there are many paths to solving a problem, and that sometimes, problems have more than one solution. With this exposure, future teachers will be better able to assess student needs using diverse approaches.
About the Author
Tom Bassarear is a professor at Keene State College in New Hampshire. He received his BA from Claremont-McKenna College, his MA from Claremont Graduate School, and was awarded an Ed.D degree from the University of Massachusetts. Tom's complementary degrees in mathematics and educational psychology have strongly influenced his convictions about education--specifically, mathematics education. Before teaching at the college level, he taught both middle school and high school mathematics. Since arriving at Keene State College, Tom has spent many hours in elementary classrooms observing teachers and working with them in school and workshop settings, plus, he has taught 4th grade math every day for a semester at a local elementary school.
Table of Contents
1. FOUNDATIONS FOR LEARNING MATHEMATICS. 1.1 Getting Started and Problem Solving. Investigation 1.1a Pigs and Chickens. Investigation 1.1b A Coin Problem. 1.2 Patterns and Communication. Investigation 1.2a Sequences and Patterns. Investigation 1.2b Patterns in Multiplying by 11. Investigation 1.2c Pascal's Triangle. Investigation 1.2d Communicating Patterns in a Magic Square. 1.3 Reasoning and Proof. Investigation 1.3a Does Your Answer Make Sense? Investigation 1.3b Inductive Thinking With Fractions. Investigation 1.3c Deductive Reasoning and Venn Diagrams. Investigation 1.3d Why is the Sum of Two Even Numbers an Even Number. Investigation 1.3e Darts, Proof, and Communication. Investigation 1.3f The Nine Dots Problem. Investigation 1.3g How Many Games in the Tournament?. 1.4 Representation and Connections. Investigation 1.4a How Long Will it Take the Frog to Get Out of the Well?. Investigation 1.4b How Many Pieces of Wire?. Looking Back on Chapter 1. Chapter 1 Summary. Chapter 1 Review Exercises. 2. FUNDAMENTAL CONCEPTS. 2.1 Sets. Investigation 2.1a Classifying Quadrilaterals. Investigation 2.1b Describing Sets. Investigation 2.1c How Many Subsets?. Investigation 2.1d Translating Among Representations. Investigation 2.1e Finding Information from Venn Diagrams. 2.2 Algebraic Thinking. Investigation 2.2a A Variable by Any Other Name is Still a Variable. Investigation 2.2b Baby-sitting. Investigation 2.2c Choosing Between Functions. Investigation 2.2d Matching Graphs to Situations. Investigation 2.2e Developing "Graph Sense." . Investigation 2.2f Looking for Generalizations. Investigation 2.2g How Many Dots?. 2.3 Numeration. Investigation 2.3a Relative Magnitude of Numbers. Investigation 2.3b What if Our System was Based on One Hand?. Investigation 2.3c How Well do you Understand Base Five?. Investigation 2.3d Base Sixteen. Looking Back on Chapter 2. Chapter 2 Summary. Chapter 2 Review Exercises. 3. THE FOUR FUNDAMENTAL OPERATIONS OF ARITHMETIC. 3.1 Understanding Addition. Investigation 3.1a Pattern in the Addition Table. Investigation 3.1b Mental Addition. 3.1c Children's Strategirs for Adding Large Numbers. Investigations 3.1d An Alternative Algorithm. Investigation 3.1e Addition in Base Five. Investigation 3.1f Children's Mistakes. Investigation 3.1g What Was the Total Attendance?. Investigation 3.1h Estimating by Making Compatible Numbers. Investigation 3.1i Number Sense with Addition. 3.2 Understanding Subtraction. Investigation 3.2a Mental Subtraction. Investigation 3.2b Children's Strategies for Subtraction with Large Numbers. Investigation 3.2c An Alternative Algorithm. Investigation 3.2d Children's Mistakes in Subtraction. Investigation 3.2e Rough and Best Estimations with Subtraction. Investigation 3.2f Number Sense with Subtraction. 3.3 Understanding Multiplication. Investigation 3.3a A Pattern in the Multiplication Table. Investigation 3.3b Mental Multiplication. Investigation 3.3c An Alternative Algorithm. Investigation 3.3d Why Does the Trick for Multiplying by 11 Work?. Investigation 3.3e Multiplication in Base Five. Investigation 3.3f Children's Mistakes in Multiplication. Investigation 3.3g Developing Estimation Strategies for Multiplication. Investigation 3.3h Using Various Strategies in a Real-life Multiplication Situation. Investigation 3.3i Number Sense with Multiplication. 3.4 Understanding Division. Investigation 3.4a Mental Division. Investigation 3.4b Understanding Division Algorithms. Investigation 3.4c The Scaffolding Algorithm. Investigation 3.4d Children's Mistakes in Division. Investigation 3.4e Estimates with Division. Investigation 3.4f Number Sense with Division. Investigation 3.4g Applying Models to a Real-life Situation. Investigation 3.4h Operation Sense. Looking Back on Chapter 3. Chapter 3 Summary. Chapter 3 Review Exercises. 4. NUMBER THEORY. 4.1 Divisibility and Related Concepts. Investigation 4.1a Interesting Dates. Investigation 4.1b Patterns in Odd and Even Numbers. Investigation 4.1c Understanding Divisibility Relationships. Investigation 4.1d Determining the Truth of an Inverse Statement. Investigation 4.1e Understanding Why the Divisibility Rule for 3 Works. Investigation 4.1f Divisibility by 4 and 8. Investigation 4.1g Creating a Divisibility Rule for 12. 4.2 Prime and Composite Numbers. Investigation 4.2a The Sieve of Eratosthenes. Investigation 4.2b Numbers with Personalities: Perfect and Other Numbers. 4.3 Greatest Common Factor and Least Common Multiple. Investigation 4.3a Cutting Squares Using Number Theory Concepts. Investigation 4.3b Methods for Finding the GCF. Investigation 4.3c Relationships Between the GCF and the LCM. Investigation 4.3d Going Deeper into the GCF and LCM. Looking Back on Chapter 4. Chapter 4 Summary. Chapter 4 Review Exercises. 5. EXTENDING THE NUMBER SYSTEM. 5.1 Integers. Investigation 5.1a Subtraction with Integers. Investigation 5.1b The Product of a Positive and a Negative Number. 5.2 Fractions and Rational Numbers. Investigation 5.2a Rational Number Contexts: What Does 3/4 Mean?. Investigation 5.2b Wholes and Units: Sharing Brownies. Investigation 5.2c Unitizing. Investigation 5.2d Fund-Raising and Thermometers. Investigation 5.2e Partitioning with Number Line Models. Investigation 5.2f Partitioning with Area Models. Investigation 5.2g Partitioning with Discrete Models. Investigation 5.2h Determining an Appropriate Representation. Investigation 5.2i Sharing Cooking. Investigation 5.2j Ordering Rational Numbers. Investigation 5.2k Estimating with Fractions. 5.3 Understanding Operations with Fractions. Investigation 5.3a Using Fraction Models to Understand Addition of Fractions. Investigation 5.3b Connecting Improper Fractions and Mixed Numbers. Investigation 5.3c Estimation and Mental Arithmetic: Sums and Differences of Fractions. Investigation 5.3d Estimating sums and Differences with Fractions. Investigation 5.3e Understanding Multiplication of Rational Numbers. Investigation 5.3f Division of Rational Numbers. Investigation 5.3g Estimating Products and Quotients. Investigation 5.3h When Did He Run Out of Gas?. Investigation 5.3i They've Lost Their Faculty!. 5.4 Beyond Integers and Fractions: Decimals, Exponents, and Real Numbers. Investigation 5.4a Base 10 Blocks and Decimals. Investigation 5.4b When Two Decimals Are Equal. Investigation 5.4c When is the Zero Necessary and When is it Optional?. Investigation 5.4d Connecting Decimals and Fractions. Investigation 5.4e Ordering Decimals. Investigation 5.4f Rounding with Decimals. Investigation 5.4g Decimals and Language. Investigation 5.4h Decimal Sense: Grocery Store Estimates. Investigation 5.4i Decimal Sense: How Much Will the Project Cost?. Investigation 5.4j How Long Will She Run?. Investigation 5.4k Exponents and Bacteria. Investigation 5.4l Scientific Notation: How Far is a Light-Year?. Investigation 5.4m Square Roots. Looking Back on Chapter 5. Chapter 5 Summary. Chapter 5 Review Exercises. 6. PROPORTIONAL REASONING. 6.1 Ratio and Proportion. Investigation 6.1a Unit Pricing--Is Bigger Always Cheaper?. Investigation 6.1b How Many Trees Will be Saved?. Investigation 6.1c How Much Money Will the Trip Cost?. Investigation 6.1d Reinterpreting Old Problems. Investigation 6.1e Using Estimation with Ratios. Investigation 6.1f Comparing Rates. Investigation 6.1g Is the School on Target?. Investigation 6.1h Finding Information from Maps. Investigation 6.1i From Raw Numbers to Rates. Investigation 6.1j How Much Does That Extra Light Cost?. 6.2 Percents. Investigation 6.2a Who's the Better Free-Throw Shooter?. Investigation 6.2b Understanding a Newspaper Article. Investigation 6.2c Buying a House. Investigation 6.2d Sale?. Investigation 6.2e What is a Fair Reason?. Investigation 6.2f How Much Money Did the Bookstore Pay for the Textbook?. Investigation 6.2g The Copying Machine. Investigation 6.2h 132% Increase. Investigation 6.2i Saving for College. Investigation 6.2j How Much Does that Credit Card Cost You?. Looking Back on Chapter 6. Chapter 6 Summary. Chapter 6 Review Exercises. 7. UNCERTAINTY: DATA AND CHANCE. 7.1 The Process of Collecting and Analyzing Data. Investigation 7.1a What is Your Favorite Sport?. Investigation 7.1b How Many Siblings do you Have?. Investigation 7.1c Going Beyond a Computational Sense of Average. Investigation 7.1d How Many Peanuts Can You Hold in One Hand?. Investigation 7.1e How Long Does it Take Students to Finish the Final Exam? Investigation 7.1f Videocassette Recorders. Investigation 7.1g Fatal Crashes. Investigation 7.1h Hitting the Books. 7.2 Going Beyond the Basics. Investigation 7.2a How Many More Peanuts Can Adults Hold Than Children?. Investigation 7.2b Scores on a Test. Investigation 7.2c Which Battery do You Buy?. Investigation 7.2d Understanding Standard Deviation. Investigation 7.2e Analyzing Standardized Test Scores. Investigation 7.2f How Long Should the Tire be Guaranteed?. Investigation 7.2g Comparing Students in Three Countries. Investigation 7.2h Grade Point Average. Investigation 7.2i What Does Amy Need to Bring Her GPA up to 2.5?. 7.3 Concepts Related to Chance. Investigation 7.3a Probability of Having 2 Boys and 2 Girls. Investigation 7.3b Probability of Having 3 Boys and 2 Girls. Investigation 7.3c Probability of Having at Least 1 Girl. Investigation 7.3d 50-50 Chance of Passing. Investigation 7.3e What is the Probability of Rolling a 7?. Investigation 7.3f What is the Probability of Rolling a 13 with 3 Dice?. Investigation 7.3g "The Lady of the Tiger. Investigation 7.3h Gumballs. Investigation 7.3i Is this a Fair Game?. Investigation 7.3j What about this Game?. Investigation 7.3k Insurance Rates. 7.4 Counting and Chance. Investigation 7.4a How Many Ways to Take the Picture?. Investigation 7.4b How Many Different Election Outcomes?. Investigation 7.4c How Many Outcomes this Time?. Investigation 7.4d Pick a Card, Any Card!. Investigation 7.4e So You Think You're Going to Win the Lottery?. Looking Back on Chapter 7. Chapter 7 Summary. Chapter 7 Review Exercises. 8. GEOMETRY AS SHAPE. 8.1 Basic Ideas and Building Blocks. Investigation 8.1a Playing Tetris. Investigation 8.1b Different Objects and Their Functions. Investigation 8.1c Point, Line, and Plane. Investigation 8.1d Measuring Angles. 8.2 Two-Dimensional Figures. Investigation 8.2a Recreating Shapes from Memory. Investigation 8.2b All the Attributes. Investigation 8.2c Classifying Figures. Investigations 8.2d Why Triangles are so Important. Investigation 8.2e Classifying Triangles. Investigation 8.2f Triangles and Venn Diagrams. Investigation 8.2g Congruence with Triangles. Investigation 8.2h Quadrilaterals and Attributes. Investigation 8.2i Challenges. Investigation 8.2j Relationships Among Quadrilaterals. Investigation 8.2k Sum of Interior Angles of a Polygon. Investigation 8.2l What are my Coordinates?. Investigation 8.2m Understanding the Distance Formula. Investigation 8.2n The Opposite Sides of a Parallelogram are Congruent. Investigation 8.2o Midpoints of any Quadrilateral. 8.3 Three-Dimensional Figures. Investigation 8.3a What do you See?. Investigation 8.3b Connecting Polygons to Polyhedra. Investigation 8.3c Features of Three-Dimensional Objects. Investigation 8.3d Prisms and Pyramids. Investigation 8.3e Different Views of a Building. Investigation 8.3f Isometric Drawings. Investigation 8.3g Cross Sections. Investigation 8.3h Nets. Looking Back on Chapter 8. Chapter 8 Summary. Chapter 8 Review Exercises. 9. GEOMETRY AS TRANSFORMING SHAPES. 9.1 Congruence Transformations. Investigation 9.1a Understanding Translations. Investigation 9.1b Understanding Reflections. Investigation 9.1c Understanding Rotations. Investigation 9.1d Understanding Translations, Reflections, and Rotations. Investigation 9.1e Connecting Transformations. Investigation 9.1f Transformations and Art. 9.2 Symmetry and Tessellations. Investigation 9.2a Reflection and Rotation Symmetry in Triangles. Investigation 9.2b Reflection and Rotation Symmetry in Quadrilaterals. Investigation 9.2c Reflection and Rotation Symmetry in Other Figures. Investigation 9.2d Letters of the Alphabet and Symmetry. Investigation 9.2e Patterns. Investigation 9.2f Symmetries of Strip Patterns. Investigation 9.2g Analyzing Brick Patterns. Investigation 9.2h Which Triangles Tessellate?. Investigation 9.2i Which Regular Polygons Tessellate?. Investigation 9.2j Tessellating Trapezoids. Investigation 9.2k More Tessellating Polygons. Investigation 9.2l Generating Pictures Through Transformations. 9.3 Similarity. Investigation 9.3a Understanding Similarity. Investigation 9.3b Similarity Using an Artistic Perspective. Investigation 9.3c Using Coordinate Geometry to Understand Similarity. Looking Back on Chapter 9. Chapter 9 Summary. Chapter 9 Review Exercises. 10. GEOMETRY AS MEASUREMENT. 10.1 Systems of Measurement. Investigation 10.1a Developing Metric Sense. Investigation 10.1b Converting Among Units in the Metric System. 10.2 Perimeter and Area. Investigation 10.2a What is the Length of the Arc?. Investigation 10.2b Converting Units of Area. Investigation 10.2c Using the Pythagorean Theorem. Investigation 10.2d Understanding the Area Formulas for Circles. Investigation 10.2e A 16-Inch Pizza Versus an 8-Inch Pizza. Investigation 10.2f How Big in the Footprint?. Investigation 10.2g Making a Fence with Maximum Area. 10.3 Surface Area and Volume. Investigation 10.3a Are Their Picture Misleading?. Investigation 10.3b Finding the Volume of a Hollow Box. Investigation 10.3c Surface Area and Volume. Looking Back on Chapter 10. Chapter 10 Summary. Chapter 10 Review Exercises.