# Teaching Mathematics in Elementary and Middle School : Developing Mathematical Thinking

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## Description

For courses in undergraduate Elementary and Middle School Mathematics Education With an emphasis on inquiry and process, Teaching Mathematics in Elementary and Middle School embraces active mathematics instruction and the development of mathematical thinking through problem solving. The text challenges future teachers to prepare their K-8 students for a world that requires a higher level of mathematical literacy and enables them to compete in a global society. Teachers will develop their own mathematical abilities allowing them to help students discover a rich combination of thinking processes and problem-solving strategies, raising the learning expectations for all.

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## Product details

- Paperback | 432 pages
- 226.1 x 274.3 x 25.4mm | 975.23g
- 07 Aug 2006
- Pearson Education (US)
- Pearson
- United States
- English
- 0130549789
- 9780130549785

## Review quote

"...I feel that this text is indeed excellent. It does a very comprehensive job of blending theory and practice, and continually links its discussions to the classroom. It is indeed one of the better (if not the best) text that I have seen for this particular set of students. As a contrast to many texts on the market, it has some unique strengths in its conversational style and interactive approach, as well as its use of manipulatives and `real-world' activities. It also deals with topics in a very practical and interesting manner."Dr. Neal GrandgenettUniversity of Nebraska at Omaha"This text combines multiple classroom examples with excellent explanations of development of student understanding of mathematics concepts."Dr. Walter RyanIndiana University SouthEast"This text gives very specific learning struggles that are not addressed in general math texts. The examples paint real children with real struggles that are diagnosed with very clear and easy to understand how to resolve these struggles. I found the Tables at the end of each chapter very helpful in showing how to assist students in their struggles with specific concepts." Dr. Yolanda De La CruzArizona State University "I like a text book which integrates the theoretical and practical. The author truly does this with his/her numerous examples and lesson profiles. The lesson discussions truly added to the flavor of the text and enabled the author to make strong process points and support them with everyday examples of teaching to those processes. This section of the text is very strong and unique." Dr. John HintonHofstra University "The author's assertions are backed by sound research and presented in very reader-friendly formats. The classroom scenarios capture wonderful images of real classroom situations. The opportunities for reflection will help make the text and the course much richer for students." Dr. William O. Lacefield, IIIMercer University

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## Back cover copy

With an emphasis on inquiry and process, "Teaching Mathematics in Elementary and Middle School "embraces active mathematics instruction and the development of mathematical thinking through problem solving. The text challenges future teachers to prepare their K-8 students for a world that requires a higher level of mathematical literacy and enables them to compete in a global society.Teachers will develop their own mathematical abilities, allowing them to help students discover a rich combination of thinking processes and problem-solving strategies, raising the learning expectations for all. Unique text features "TIE-Thought, Investigation and Exploration "features ask pre-service teachers to develop their own thinking and learning abilities, preparing them to better challenge their students. "Mathematics in the Real World," "Idea Files," and "Teacher Profiles "model best practices and supply readers with concrete teaching tools and strategies. "Mathematical Thinking," "Mathematical Games" and "Mathematics and Technology" features detail activities to engage and develop students' mathematical thinking. Accompanying student artifacts illustrate the progression of students' conceptual understanding. [CD logo replaces bullet] "Math Activities CD-ROM" provides an outstanding text component containing more than 100 activities that use a three-step process-explore, invent, discover-to foster the development of mathematical thinking through guided inquiry. Aligned with the NCTM standards, each activity is integrated within the text and designed to help develop students' conceptual understanding of mathematics. "Mathematics in Literature" offers thoroughly developed ideas for using children's literature to create meaningful contexts for mathematics learning. An extensive bibliography that can be used for this purpose appears on the CD-Rom. "I think the text is an excellent resource for elementary and middle school methods courses. In particular, I like how the textbook handles the 'bigger issues' such as geometric reasoning rather than just 'geometry.' I also like the excellent foundation in educational research that the textbook provides, as well as some very careful attention and consistent referencing to the NCTM standards and principles. The incorporation of classroom vignettes, teacher illustrations, and samples of student work also all add to the excellent grounding of the text in real world classroom work." Dr. Neal Grandgenett, University of Nebraska at Omaha

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## Table of contents

CHAPTER 1 Teaching Mathematics in the 21st Century Being a Teacher in the 21st Century Beyond Shop-and-Yard Mathematics In Step with the New Mathematical Literacy Changing Views About Who should Learn Mathematics Tradition and Myths Equity ReformsChanging Views About What Should Be Learned Tying the Curriculum to Mental Age and Social Utility Responding to a Bigger WorldBuilding Consensus and Setting Standards National Standards for Mathematics Education State and Local StandardsMeeting the Challenges of the 21st Century Meeting the Challenges as a Nation Meeting the Challenges in the Classroom Questions for Discussion, Thought, and Further Research CHAPTER 2 Empowering Children to Learn MathematicsTeaching Important Mathematics to All Students Legislation for Equity and Excellence Important Mathematics Understanding How Students Learn Mathematics Changing Perspectives of Learning Matching Teaching to Learning: Modesl for Diversity Mastery Learning Inquiry-based Learning Universal Design for Learning Mathematics Questions for Thought, Discussion, and Further Research CHAPTER 3 Preparing Students to Think MathematicallyLearning to Think and Reason Mathematically The Importance of Mathematical Thinking The Processes of Mathematical Thinking Understanding Interactions That Affect Mathematical Thinking and Learning The Cognitive Domain The Affective Domain InteractionsApplying Mathematical Thinking in Problem Solving Polya's Four Steps to Problem Solving Problem-Solving Approach to Learning Multiple Solutions/New BeginningDeveloping a Mathematical World ViewDiversity in Learning and Thinking Mathematically Questions for Further Thought, Discussion, ResearchCHAPTER 4 Enhancing Mathematics Learning Through Instruction and AssessmentFlexible Mathematics Instruction Multiple Means of Engagement Multiple Means of Representation Multiple Means of Expression Multiple Means of AssessmentDiversity in Learning and Thinking Mathematically Questions for Further Thought, Discussion, and ResearchCHAPTER 5 Understanding NumbersUnderstanding the Mathematics of Young ChildrenLearning the Language of NumbersDeveloping Verbal and Nonverbal Mathematical Skills Concrete Mathematics and Nonverbal Skills Spoken and Written Mathematics and Verbal SkillsDiscovering Number in Patterns and Relationships What is more, less, or the same? Why is something more, less, the same?Counting and Number SenseUnderstanding Number Systems What is a number system? Why do we need number systems? Number Systems and Time Number Systems and Measurement Number Systems and Money The Decimal Number SystemDiversity in Learning and Thinking Mathematically Questions for Further Thought, Discussions, and Research CHAPTER 6 Working with Whole Numbers: Addition and SubtractionThe Changing Faces of Whole Numbers: Cardinal, Ordinal, Measurement Cardinal Numbers Ordinal Numbers MeasurementSingle-Digit Addition and Subtraction Children's Strategies for Adding Children's Strategies for Subtracting Fingermath Mental Addition and SubtractionMulti-digit Addition and Subtraction Building Concepts for Working with Multi-digit Numbers Adding and Subtracting Multi-digit Numbers Understanding Standard Algorithms Understanding Alternative AlgorithmsDiversity in Learning and Thinking Mathematically Questions for Further Thought, Discussion, and ResearchChapter 7 Working with Whole Numbers: Multiplying and DividingDiscovering Multiplication and Division in Early GradesUnderstanding Multiplication What is a multiplication algorithm? What kinds of multiplication algorithms do students invent? How might teachers introduce other multiplication algorithms?Understanding Division What kinds of division algorithms do students invent? How do students handle division problems with remainders? How can teachers help students understand other division algorithms?Diversity in Learning and Thinking Mathematically Questions for Further Thought, Discussion and Research CHAPTER 8 Geometric Thinking Across the Grades Geometry as the Mathematicas of Living Space and the Living World The Four Faces of GeometryGeometric Thinking from Level to Level Early Experiences with Shapes and SpaceLater Experiences with Shapes and Space Symmetry Transformations Symmetry, Transformations, and NCTM StandardsExplorations in Two and Three Dimensions: Plane and Solid Geometry The Early Grades The Middle Grades The Upper GradesDiversity in Learning and Thinking Mathematically Questions for Further Thought, Discussion, and ResearchCHAPTER 9 Understanding and Using Measurement ConceptsMeasurement Sense Early Stages in Understanding Measurement The Three Knowledge Bases of Measurement The Mental Tools of MeasurementMeasurement Systems Teaching the Metric System Measuring Time and TemperatureMeasurement and Geometry Plane Geometry Solid GeometryDiversity in Learning and Thinking Mathematically Questions for Further Thought, Discussion, and ResearchChapter 10 Algabraic Thinking Across the GradesChanging "Algebra for Some" to "Algebra for All"Understanding Algebraic Thinking Identifying Patterns in Algebraic Thinking Fostering Algebraic Thinking Problem Solving and Algebraic ThinkingUnderstanding the Big Ideas of Algebra Equality/Balance Variable Functions Representation ProportionBuilding Bridges from Arithmetic to Algebra Hands-on Algebra Real-life and Imaginative Contexts ConnectionsDiversity in Learning and Thinking Mathematically Questions for Further Thought, Discussion, and ResearchCHAPTER 11 Working with DataWorlds of DataThe Processes of Working with Data Collecting and Organizing Data Analyzing Data Displaying and Interpreting Data Understanding and Using DataProbability Talking about Probability Calculating ProbabilityThe Process Plus Probability: The M&Ms ProjectDiversity in Learning and Thinking Mathematically Questions for Further Thought, Discussion, and ResearchCHAPTER 12 Exploring Part-Whole Relationships: Fractions Students, Teachers, and Fractions--Complex Topic, Complex Relationship A Hands-on Pedagogy for Teaching Fractions: Connecting Constructed Knowledge and Instructed Knowledge Real-life Contexts Hands-on Explorations Multiple Representations Language ConnectionsBig Ideas of Fractions Properties of Fractions Operations with FractionsDiversity in Learning and Thinking Mathematically Questions for Further Thought, Discussion, and ResearchCHAPTER 13 Exploring Part-Whole Relationships: Decimals, Percents, Ratio, and ProportionUnderstanding Decimals and PercentsConnecting Fractons, Decimals, and PercentsExploring Decimals and Percents as Mathematical Concepts Decimals PercentsConverting Percents, Decimals, and FractionsPerforming Operations with Decimals and Percents Addition and Subtraction Multiplication and DivisionUnderstanding Decimals and Percents in Practical ApplicationsUnderstanding Ratio and Proportion Ratio Proportion Strategies for Developing Proportional Reasoning Diversity in Learning and Thinking Mathematically Questions for Further Thought, Discussion, and ResearchCHAPTER 14 Building BridgesMaking the Transition Reviewing the Research Identifying the GapsBuilding Affective and Conceptual Bridges Affective Bridges Cognitive BridgesDiversity in Learning and Thinking Mathematically Questions for Further Thought, Discussion, and ResearchAPPENDIX A: Make Your Own Manipulatives and Blackline MastersMake Your Own Manipulatives Fraction Strips Fraction Squares Fraction Circles Pattern Shapes Tangrams Geoboard Base-10 Blocks Counters Decimal Squares Multiplication Arrays Polygon Cut-outsBlackline Masters Modified Cartesian Coordinate Grid Geoboard Dot Paper One-Centimeter Grid Paper Triangular Grid Paper Classroom Observation Form Learning/Teaching Plan FormAPPENDIX B: Resources, Mathematics in Literature For Elementary and Middle SchoolNCTM Standard: Number and Operations Number Sense Counting Addition Subtraction Multiplication Decimals/Percentages Division/Fractions Ratio and/or Proportion Place Value Time Money Classification OrderNCTM Standard: AlgebraNCTM Standard: Geometry Geometric Progression Tangrams Geometric Shapes Area Perimeter DimensionalityNCTM Standard: MeasurementNCTM Standard: Data Analysis and ProbabilityOther Topics Multicultural Cartesian Coordinate System Code-Breaking (Problem Solving Involving Codes) Classic Literature Geography and Reading Maps Spanish Language Prime Numbers Multiples/FactorsReferences/Readings

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