Are sequences functions? What can t the popular vertical line test be applied in some cases to determine if a relation is a function? How does the idea of rate of change connect with simpler ideas about proportionality as well as more advanced topics in calculus? How much do you know... and how much do you need to know? Helping your high school students develop a robust understanding of functions requires that you understand mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about functions. It is organized around five big ideas, supported by multiple smaller, interconnected ideas essential understandings. Taking you beyond a simple introduction to functions, this book will broaden and deepen your mathematical understanding of one of the most challenging topics for students and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing students understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently.

Developing Essential Understanding of Functions for Teaching Mathematics in Grades 9–12

Rose Mary Zbiek

Gwendolyn Lloyd

Sybilla Beckmann Kazez

NCTM

Why do some equations have one solution, other two or even more solutions, and some no solutions? Why do we sometimes need switch the direction of an inequality symbol in solving an inequality? What could you say if a student described a function as an equation? How much do you know...and how much do you need to know? Helping your students develop a robust understanding of expressions, equations, and functions requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about expressions, equations, and functions. It is organized around five big ideas, supported by multiple smaller, interconnected ideas essential understandings.Taking you beyond a simple introduction to expressions, equations, and functions, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing students' understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently.

Developing Essential Understanding of Expressions, Equations, and Functions for Teaching Mathematics in Grades 6–8

Beth Herbel-Eisenmann

Jon Star

This book gives teacher educators a collection of strategies and activities for using Standards-based curriculum materials in mathematics teacher education. In addition, the book offers personal accounts from mathematics teacher educators about how and why they use Standards-based curriculum materials in their teacher education work, as well as reflections about how their PTs learned through engagement with curriculum materials. An invaluable resource for all mathematics teacher educators, this book compiles the different ways the mathematics teacher educators at various universities have used Standards-based curriculum materials. The chapters show how both elementary and secondary prospective teachers can enhance their disposition toward, and understanding of, NCTM's Principles and Standards for School Mathematics from both their university coursework and their intern field experiences as they analyze and enact Standards-based curriculum materials. This book has More4U, which includes additional resources online. Download activities, classroom materials, and blackline masters. Look inside book for access code.

Curriculum-Based Activities and Resources for Preservice Math Teachers

Vanessa R. Pitts Bannister

National Council of Teachers of Mathematics

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Books by Gwendolyn Lloyd