Math makes sense!: a constructivist approach to the teaching and learning of mathematics

Content: Preface
 Acknowledgments
 About the Authors
 Chapter 1 Fostering the Learning of Mathematics
 1.1 Introduction
 1.2 Problems in the Teaching of Mathematics Shared with Other Disciplines
 1.2.1 Teaching without understanding
 1.2.2 Teaching as information transfer
 1.2.3 Teaching without reflection
 1.2.4 Homogeneous instruction
 1.2.5 Teaching as an individual process
 1.2.6 Mathematics is a cold discipline
 1.3 Conclusion
 References
 Chapter 2 Construction of Concepts and Mathematical Interpretations
 2.1 Introduction
 2.2 Development by Following the Logic of Learning. 2.2.1 The cognitive development of concepts2.2.2 The internal organization of concepts in mathematical structures
 2.3 Slow and Steady Wins the Race
 2.4 Final Reflections
 References
 Chapter 3 Numbering
 3.1 Introduction
 3.2 Counting Numbers: The (Non-sensical) Number Sequence (Kindergarten to Six/Seven Years)
 3.2.1 Sequence as an order in space
 3.2.2 Sample activity
 3.2.3 Integrating metaphor: The number line
 3.3 Numbers as Quantity (Kindergarten to Six/Seven Years)
 3.3.1 Property of equivalence (1-1)
 3.4 Associating the Number Sequence with the Idea of Quantity. 3.5 Informal Arithmetic (Kindergarten to Eight Years)3.5.1 Examples of contexts to introduce addition and subtraction problems
 3.5.2 Examples of \" Counting-from\" Activities
 3.6 The Number System
 3.6.1 The idea of part-whole
 3.6.2 Examples
 3.6.3 Each place represents a different type of object
 3.6.4 Integrating metaphor
 3.6.5 Parallel forms to develop the idea of our number system
 References
 Chapter 4 Addition and Subtraction
 4.1 Introduction
 4.2 Stages in Teaching These Operations
 4.2.1 The part-whole idea
 4.2.2 Situations that model addition and subtraction. 4.2.3 Integrating models --
metaphors for learning4.2.4 Discussion and reflection on strategies
 4.2.5 Symbolism of addition and subtraction
 4.2.6 Properties of these operations
 4.3 Working with Numbers
 4.3.1 Basic combinations
 4.4 Situations that Model Addition and Subtraction
 4.4.1 Problem development by students
 4.5 Mental Arithmetic
 4.6 Addition and Subtraction Algorithms
 4.6.1 Jumping by tens
 4.6.2 Addition and subtraction with a two-digit number and a one-digit number
 4.6.3 Addition of two two-digit numbers
 4.6.4 Subtraction
 4.7 Estimation
 4.7.1 The path to estimating. 4.7.2 Uses of estimation4.8 Hand Calculators
 4.8.1 Support for calculations that take a long time
 4.8.2 Didactic tool
 4.8.3 Support in solving problems and identifying patterns
 4.8.4 Sample activities
 References
 ANNEX 1 ACTIVITY ANDCHALLENGE SHEETS
 ANNEX 2 ACTIVITIES WITH A CALCULATOR
 Chapter 5 Multiplication and Division
 5.1 Constructing the Meaning of the Operations
 5.1.1 Situations that model multiplication
 5.2 Basic Combinations
 5.2.1 Learning the multiplication tables by association
 5.2.2 Different rates of learning the tables.