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Mathematical Models for Teaching
Reasoning without Memorization
By Ann Kajander, Tom Boland
Print ISBN: 9781551305561
Students of mathematics learn best when taught by a teacher with a deep and conceptual understanding of the fundamentals of mathematics. In Mathematical Models for Teaching, Ann Kajander and Tom Boland argue that teachers must be equipped with a knowledge of mathematics for teaching, which is grounded in modelling, reasoning, and problem-based learning. A comprehensive exploration of models and concepts, this book promotes an understanding of the material that goes beyond memorization and recitation, which begins with effective teaching.
This vital resource is divided into 15 chapters, each of which addresses a specific mathematical concept. Focusing on areas that have been identified as problematic for teachers and students, Mathematical Models for Teaching equips teachers with a different type of mathematical understanding—one that supports and encourages student development.Features:
- grounded in the most current research about teachers’ learning
- contains cross-chapter connections that identify common ideas
- includes chapter concluding discussion questions that encourage critical thinking
- incorporates figures and diagrams that simplify and solidify important mathematical concepts
- offers further reading suggestions for instructors seeking additional information
Table of Contents
PrefaceAcknowledgementsChapter 1: Introduction to Mathematics for TeachingChapter 2: Introduction to Mathematical ReasoningChapter 3: Introduction to NumbersChapter 4: Whole Number Addition and SubtractionChapter 5: Whole Number Multiplication and DivisionChapter 6: Fraction Representations and Additive OperationsChapter 7: Multiplicative Fraction Representations and OperationsChapter 8: Decimal and Percent Representations and OperationsChapter 9: Integer Representations and OperationsChapter 10: Beyond IntegersChapter 11: From Patterns to AlgebraChapter 12: Algebraic ConceptsChapter 13: GeometryChapter 14: MeasurementChapter 15: Data Management and ProbabilityReferencesGlossary