Learning and Teaching K-8 Mathematics (with "Understanding Children's Mathematical Thinking" VideoWorkshop CD-ROM), MyLabSchool Edition

by Sharp, Janet M.; Hoiberg, Karen Bush

• ISBN13: 9780205464845
• ISBN10: 020546484X
• Edition: CD
• Format: Paperback
• Copyright: 2005-01-01
• Publisher: Allyn & Bacon

Summary

Try it! See it! Teach it! This hands-on, brief text takes an ACTIVE approach to teaching mathematics to future K-8 teachers. Several activities are embedded in each chapter for the adult learner to pause and complete to ensure that they are grasping the mathematics. Completing these activities provides future teachers with invaluable insight into how children think about and learn math, thereby equipping them with the skills to better make sound instructional decisions. Throughout the book and on the student CD, we see co-author Karen Bush Hoiberg in action. A practicing, presidential award-winning elementary teacher, Karen provides a multitude of practical applications and real-world examples to give preservice teachers the opportunity to connect chapter concepts with their own knowledge of teaching in the classroom. The text is divided into five parts based on four of the 5 major NCTM content standards. The fifth content standard (algebra) is integrated into each part . Each part begins with a problem that introduces the big ideas of that section. Chapters within each part are organized around four general themes: thinking about the mathematics, learning theories, the role of the teacher, and algebraic connections. Chapter one introduces the importance of assessment, an idea that is integrated throughout every part.

Table of Contents

The basics

Introduction

How We Learn

Theories

Features

Role of the Teacher

Algebra Connections

Middle School Connections

Before we get started

A bit about the NCTM and the NCTM Standards

Technology Connections The Basics

Classroom Connections

Classroom Connections (Video enhanced) Understanding How Children Learn Math

Instruction

Models of Teaching

Problem Solving

Lesson plan components

Classroom Connections Providing Interactive Instruction

Questioning

Assessment

Classroom Connections Using Assessment of Many Forms

Curriculum

Geometry and Spatial Thinking

Thinking about the Mathematics of Geometry and Spatial Thinking

Understanding The Mathematics--Mental Ideas v

Physical Models

Pulling Plane Knowledge from Solid Shapes

Accurate Descriptions

Analyzing a Circle

A Cylinder of a Circle?

Concentrating on the Concepts--Relationships among Shapes

Examples and Non-Examples

Rigid Motions

Symmetry

Classroom Connections Finding Symmetry in Nature

Practicing Spatial Visualizations

Middle School Connections The Net of a Solid Shape

Grasping the Procedures How to Build Shapes

Children Describe a Square

Drawing a Triangle

How We Learn About Geometry and Spatial Thinking

Using Relevant Learning Theory The Van Hiele Theory

(Visual)

(Analysis)

(Informal Deduction)

(Formal Deduction)

(Rigor)

Characteristics of the Theory

Promoting Development

Issues Specific to Spatial Visualization

Using Relevant Patterns Extending Pattern Starters

Repeating v

Growing

Recognizing Deep Structure

Using Teaching Aids Appropriately Concrete, Pictorial, Symbolic

Concrete Representations

Pictorial Representations

Symbolic Representations

Concrete Materials v

Types of Concrete Materials

Cubes

Pattern Blocks

Tangram

Assessment and the Use of Materials

A Chinese Legend

Explore Your Own Culture

Knitting

Literature Connections Developing Mathematical Imagery

Role of the Teacher in Geometry and Spatial Thinking Lessons

Analyzing One of The Teaching Models Discussion

Technology Connections Using Digital Technologies as Geometry Discussion Platforms

Cultural Connections Creating a Mosaic

Highlights of a Lesson Plan Component Creating Good Questions

Suggestions for Establishing Discourse Importance of Knowing the Mathematics

Mrs Hawthorne's Rhombus Lesson

Ms Steffen's Rectangle Lesson

Comparing Quadrilaterals

The Next Question

Middle School Connections Know the Math Well Enough to Ask Questions

Assessment To Make an Instructional Decision

Process of Assessment

Classroom Connections Usi

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