Mathematics for Elementary School Teachers

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.

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.

ntended for the one- or two-semester course required of Education majors, MATHEMATICS FOR ELEMENTARY SCHOOL TEACHERS, 5E, International Edition 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.

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