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.
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
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
Ann Kajander is an experienced classroom teacher who is currently an Associate Professor in the Faculty of Education at Lakehead University. She is the author of two previous books of creative mathematical activities for children. Her research interests include mathematics education, pre-service education, teacher mathematics knowledge, the development of mathematics for teaching, and teacher beliefs.
Tom Boland is currently a Special Education Facilitator for Lakehead Public Schools, where he has taught grades 3 to 8. He has also been a professional learning consultant in mathematics for school boards across Canada, a provincial math coach for the Ontario Ministry of Education, and an instructor in the Faculty of Education at Lakehead University.
"This book incorporates the latest research on how children learn mathematics. It fully embraces the idea that teachers learn mathematics best when framed in the context of their future role as teachers. It sends a strong message about the importance of developing conceptual understanding rather than encouraging rote memorization."— Susan Oesterle, Department of Mathematics, Douglas College
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