Math Makes Sense!: A Constructivist Approach to the Teaching and Learning of Mathematics

✍ Scribed by Ana Helvia Quintero, Hector Rosario

• Publisher: Imperial College Press
• Year: 2016
• Tongue: English
• Leaves: 290
• Category: Library

✦ Synopsis

The methods for teaching mathematics usually follow the structure of mathematics. The problem with this is that the structure of mathematics took centuries of elaboration to develop and is not the same as how one originally experiences mathematics. Based on research of how mathematics is actually learned, this book presents an innovative approach for teaching mathematics that will engage pupils and can have lifelong benefits for how they take on board more advanced mathematical topics. Math Makes Sense! makes use of the realistic mathematics education (Rme) philosophy, which bridges the gap between informal mathematics learning (such as in day-to-day life) and more formal teaching in school. Many real-life situations as examples for learning are included, as well as different mathematical and logic puzzles that will stimulate learning and foster understanding. The ideas presented are not confined to one national curriculum and so can be helpful worldwide to teachers/ instructors (both in practice and those still in training), private tutors, homeschooling parents, and educational researchers

✦ Table of Contents

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.

✦ Subjects

Mathematics -- Study and teaching;MATHEMATICS -- Essays;MATHEMATICS -- Pre-Calculus;MATHEMATICS -- Reference