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Description |
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In their series of professional books for teachers, Young Mathematicians at Work, Catherine Twomey Fosnot and Maarten Dolk described Mathematics in the City, an innovative project where teachers helped young children construct a deep understanding of number and operation in a math-workshop environment. Now they and two colleagues from the project have developed a flexible, video-based, digital context for inquiry into the teaching and learning of mathematics that will change how professional development is conducted.
Designed for you, the workshop leader or college instructor, the Working with the Array Resource Package enables your in- or preservice teachers to not only watch but interact with video that depicts classroom teachers as they listen to, question, and interpret students' thinking; develop connections between mathematical ideas and strategies; and, ultimately, develop vibrant mathematical communities in their classrooms.
The Resource Package includes three valuable components:
- A completely interactive CD-ROM, where your workshop participants can explore—independently or under your guidance—videos of instruction and assessment; sample children's work over time to analyze development; take and save notes on what they see; capture specific frames or footage; and then email their captured video clips and notes to other members of your professional development workshop. The context of the classroom will be at the fingertips of your participants for exploration.
- A Professional Development Overview Manual that provides general advice on how you can use the CD-ROM for staff development.
- A Facilitator's Guide whose field-tested content is specific to the CD-ROM and includes helpful suggestions for using video clips and student examples on the CD to design rich professional development experiences; sample dialogue to help you anticipate what your participants might say; tips for facilitating discussions among teachers; and descriptions of the mathematical ideas being explored.
In Working with the Array, your workshop participants will observe fourth graders as they construct some of the big ideas related to surface area and volume, making connections between multiplication's commutative and associative properties and uncovering landmark division strategies like halving and factoring. By studying the use of carefully crafted problems designed both to generate a range of solution strategies and to highlight the power of arrays and other models for multiplication and division, teachers will discover what a valuable tool real-life contexts are for building a solid foundation in mathematics.
System Requirements for CD-ROM
Windows/PC
Pentium II Processor
266Mhz (or higher)
Windows 98 (or higher)
64 MB RAM (more recommended)
SVGA Color Display (or better)
4X CD-ROM Drive (or faster)
Sound Card
16-bit Flash™ Player and Acrobat Reader®
Quicktime 6.0 (or higher)
MacIntosh
PowerPC Processor
G3/233Mhz (or higher)
System 9.2 (or higher)
64 MB RAM (more recommended)
SVGA Color Display (or better)
4X CD-ROM Drive (or faster)
Sound Card
16-bit Flash™ Player and Acrobat Reader®
Quicktime 6.0 (or higher)
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Table of Contents |
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| Journey 1 |
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The Class at Work |
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Math Congress |
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How to Continue |
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Growth and Development |
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| Journey 2 |
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The Role of Context |
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The Role of the Teacher |
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Developing a Community |
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| Epilogue |
| Appdendix A: Activity Sheet |
| Appdendix B: Student Work from Math Congress: Choldren Preparing for Math Congress |
| Appdendix C: Transcript of Math Congress: A Deeper Look |
| Appdendix D: A Handy Guide to the CD–ROM Clips |
| Appdendix E: Dialogue Boxes |
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Also Available From
Antonia Cameron
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Books
- YMAW Minilessons for Operations with Fractions, Decimals, and Percents, Grades 5-8 (Resource Package) (Paperback + CD)
- YMAW Fostering Children's Mathematical Development, Grades 5-8 (Resource Package): The Landscape of Learning (Resource Package)
- YMAW Exploring Playgrounds, Grades 5-8 (Resource Package): A Context for Multiplication of Fractions (Resource Package)
- Working with the Ratio Table, Grades 5-8 (Resource Package): Mathematical Models (Paperback)
- Sharing Submarine Sandwiches, Grades 5-8 (Resource Package): A Context for Fractions (Paperback + CD)
- Young Mathematicians at Work, Grades 3-5: Professional Development Materials Pack (Other)
- Fostering Children's Mathematical Development, Grades 3-5 (Resource Package): The Landscape of Learning (Paperback + CD)
- Working with the Array, Grades 3-5 (Resource Package): Mathematical Models (Paperback + CD)
- Young Mathematicians at Work, PreK-3: Professional Development Materials Facilitator's Pack (Resource Package)
- Multiplication and Division Minilessons, Grades 3-5 (Resource Package) (Paperback + CD-ROM)
- Turkey Investigations, Grades 3-5 (Resource Package): A Context for Multiplication (Paperback + CD-ROM)
- Exploring Soda Machines, Grades 3-5 (Resource Package): A Context for Division (Paperback + CD-ROM)
- Addition and Subtraction Minilessons, Grades PreK-3 (Resource Package) (Paperback + CD-ROM)
- Exploring Ages, PreK-3 (Resource Package): The Role of Context (Paperback + CD-ROM)
- Taking Inventory, PreK-3 (Resource Package): The Role of Context (paperback + cd rom)
- Working with the Number Line, Grades PreK-3 (Resource Package): Mathematical Models (paperback + cd rom)
- Fostering Children's Mathematical Development, Grades PreK-3 (Resource Package): The Landscape of Learning (paperback + cd rom)
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Also Available From
Maarten Dolk
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Books
- Organizing and Collecting: The Number System (Paperback)
- The Double-Decker Bus: Early Addition and Subtraction (Paperback)
- YMAW Minilessons for Operations with Fractions, Decimals, and Percents, Grades 5-8 (Resource Package) (Paperback + CD)
- YMAW Fostering Children's Mathematical Development, Grades 5-8 (Resource Package): The Landscape of Learning (Resource Package)
- YMAW Exploring Playgrounds, Grades 5-8 (Resource Package): A Context for Multiplication of Fractions (Resource Package)
- Minilessons for Operations with Fractions, Decimals, and Percents, Grades 5-8 (CD) (CD)
- Fostering Children's Mathematical Development, Grades 5-8 (CD): The Landscape of Learning (CD)
- Exploring Playgrounds, Grades 5-8 (CD): A Context for Multiplication of Fractions (CD)
- Working with the Ratio Table, Grades 5-8 (Resource Package): Mathematical Models (Paperback)
- Sharing Submarine Sandwiches, Grades 5-8 (Resource Package): A Context for Fractions (Paperback + CD)
- Sharing Submarine Sandwiches, Grades 5-8 (CD): A Context for Fractions (CD)
- Working with the Ratio Table, Grades 5-8 (CD): Mathematical Models (CD)
- Young Mathematicians at Work, Grades 3-5: Professional Development Materials Pack (Other)
- Fostering Children's Mathematical Development, Grades 3-5 (CD): The Landscape of Learning (CD-ROM)
- Working with the Array, Grades 3-5 (CD): Mathematical Models (CD-ROM)
- Working with the Array, Grades 3-5 (Resource Package): Mathematical Models (Paperback + CD)
- Fostering Children's Mathematical Development, Grades 3-5 (Resource Package): The Landscape of Learning (Paperback + CD)
- Young Mathematicians at Work, PreK-3: Professional Development Materials Facilitator's Pack (Resource Package)
- Multiplication and Division Minilessons, Grades 3-5 (Resource Package) (Paperback + CD-ROM)
- Turkey Investigations, Grades 3-5 (Resource Package): A Context for Multiplication (Paperback + CD-ROM)
- Exploring Soda Machines, Grades 3-5 (Resource Package): A Context for Division (Paperback + CD-ROM)
- Multiplication and Division Minilessons, Grades 3-5 (CDs) (CD-ROM)
- Turkey Investigations, Grades 3-5 (CD): A Context for Multiplication (CD-ROM)
- Exploring Soda Machines, Grades 3-5 (CD): A Context for Division (CD-ROM)
- Addition and Subtraction Minilessons, Grades PreK-3 (Resource Package) (Paperback + CD-ROM)
- Exploring Ages, PreK-3 (Resource Package): The Role of Context (Paperback + CD-ROM)
- Addition and Subtraction Minilessons, Grades PreK-3 (CD) (CD-ROM)
- Exploring Ages, PreK-3 (CD): The Role of Context (CD-ROM)
- Working with the Number Line, PreK-3 (CD): Mathematical Models (cd-rom)
- Fostering Children's Mathematical Development, Grades PreK-3 (CD): The Landscape of Learning (cd-rom)
- Taking Inventory, PreK-3 (CD): The Role of Context (CD-ROM)
- Working with the Number Line, Grades PreK-3 (Resource Package): Mathematical Models (paperback + cd rom)
- Fostering Children's Mathematical Development, Grades PreK-3 (Resource Package): The Landscape of Learning (paperback + cd rom)
- Taking Inventory, PreK-3 (Resource Package): The Role of Context (paperback + cd rom)
- Young Mathematicians at Work: Constructing Fractions, Decimals, and Percents (Paperback)
- Young Mathematicians at Work: Constructing Multiplication and Division (Paperback)
- Young Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction (Paperback)
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Also Available From
Catherine Twomey Fosnot
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Books
- Minilessons for Extending Addition and Subtraction: A Yearlong Resource (Paperback)
- Minilessons for Extending Multiplication and Division: A Yearlong Resource (Paperback)
- Minilessons for Operations with Fractions, Decimals, and Percents: A Yearlong Resource (Paperback)
- Minilessons for Early Addition and Subtraction: A Yearlong Resource (Paperback)
- Minilessons for Early Multiplication and Division: A Yearlong Resource (Paperback)
- Games for Early Number Sense: A Yearlong Resource (Paperback)
- Contexts for Learning Mathematics Teacher Pack 2-3 (Books)
- Contexts for Learning Mathematics Teacher Pack 3-4 (Books and Posters)
- Contexts for Learning Mathematics Teacher Pack 4-5 (Books and Posters)
- Contexts for Learning Mathematics Teacher Pack 5-6 (Books and Posters)
- Contexts for Learning Mathematics Teacher Pack 1-2 (Books and Posters)
- The Teachers' Lounge: Place Value and Division (Paperback)
- Field Trips and Fund-Raisers: Introducing Fractions (Paperback)
- The California Frog-Jumping Contest: Algebra (Paperback)
- Best Buys, Ratios, and Rates: Addition and Subtraction of Fractions (Paperback)
- The Mystery of the Meter: Decimals (Paperback)
- Exploring Parks and Playgrounds: Multiplication and Division of Fractions (Paperback)
- Ages and Timelines: Subtraction on the Open Number Line (Paperback)
- Trades, Jumps, and Stops: Early Algebra (Paperback)
- Groceries, Stamps, and Measuring Strips: Early Multiplication (Paperback)
- The Big Dinner: Multiplication with the Ratio Table (Paperback)
- Muffles' Truffles: Multiplication and Division with the Array (Paperback)
- The Box Factory: Extending Multiplication with the Array (Paperback)
- The T-Shirt Factory: Place Value, Addition, and Subtraction (Paperback)
- Measuring for the Art Show: Addition on the Open Number Line (Paperback)
- Organizing and Collecting: The Number System (Paperback)
- The Double-Decker Bus: Early Addition and Subtraction (Paperback)
- Bunk Beds and Apple Boxes: Early Number Sense (Paperback)
- Beads and Shoes, Making Twos: Extending Number Sense (Paperback)
- Contexts for Learning Mathematics : 3-level Bundle (Product Bundle)
- Contexts for Learning Mathematics, Level 3: Investigating Fractions, Decimals, and Percents (Books + CD-ROM)
- Contexts for Learning Mathematics Level 3 Posters (Posters)
- Contexts for Learning Mathematics, Level 2: Investigating Multiplication and Division (Books + CD-ROM)
- Contexts for Learning Mathematics Level 2 Posters (Posters)
- Contexts for Learning Mathematics, Level 1: Investigating Number Sense, Addition, and Subtraction (Books + CD-ROM)
- Contexts for Learning Mathematics Level 1 Read-Alouds (Paperback)
- YMAW Minilessons for Operations with Fractions, Decimals, and Percents, Grades 5-8 (Resource Package) (Paperback + CD)
- YMAW Fostering Children's Mathematical Development, Grades 5-8 (Resource Package): The Landscape of Learning (Resource Package)
- YMAW Exploring Playgrounds, Grades 5-8 (Resource Package): A Context for Multiplication of Fractions (Resource Package)
- Minilessons for Operations with Fractions, Decimals, and Percents, Grades 5-8 (CD) (CD)
- Fostering Children's Mathematical Development, Grades 5-8 (CD): The Landscape of Learning (CD)
- Exploring Playgrounds, Grades 5-8 (CD): A Context for Multiplication of Fractions (CD)
- Working with the Ratio Table, Grades 5-8 (Resource Package): Mathematical Models (Paperback)
- Sharing Submarine Sandwiches, Grades 5-8 (Resource Package): A Context for Fractions (Paperback + CD)
- Sharing Submarine Sandwiches, Grades 5-8 (CD): A Context for Fractions (CD)
- Working with the Ratio Table, Grades 5-8 (CD): Mathematical Models (CD)
- Young Mathematicians at Work, Grades 3-5: Professional Development Materials Pack (Other)
- Working with the Array, Grades 3-5 (CD): Mathematical Models (CD-ROM)
- Fostering Children's Mathematical Development, Grades 3-5 (CD): The Landscape of Learning (CD-ROM)
- Working with the Array, Grades 3-5 (Resource Package): Mathematical Models (Paperback + CD)
- Fostering Children's Mathematical Development, Grades 3-5 (Resource Package): The Landscape of Learning (Paperback + CD)
- Young Mathematicians at Work, PreK-3: Professional Development Materials Facilitator's Pack (Resource Package)
- Multiplication and Division Minilessons, Grades 3-5 (Resource Package) (Paperback + CD-ROM)
- Turkey Investigations, Grades 3-5 (Resource Package): A Context for Multiplication (Paperback + CD-ROM)
- Exploring Soda Machines, Grades 3-5 (Resource Package): A Context for Division (Paperback + CD-ROM)
- Multiplication and Division Minilessons, Grades 3-5 (CDs) (CD-ROM)
- Exploring Soda Machines, Grades 3-5 (CD): A Context for Division (CD-ROM)
- Turkey Investigations, Grades 3-5 (CD): A Context for Multiplication (CD-ROM)
- Addition and Subtraction Minilessons, Grades PreK-3 (Resource Package) (Paperback + CD-ROM)
- Exploring Ages, PreK-3 (Resource Package): The Role of Context (Paperback + CD-ROM)
- Addition and Subtraction Minilessons, Grades PreK-3 (CD) (CD-ROM)
- Exploring Ages, PreK-3 (CD): The Role of Context (CD-ROM)
- Fostering Children's Mathematical Development, Grades PreK-3 (CD): The Landscape of Learning (cd-rom)
- Working with the Number Line, PreK-3 (CD): Mathematical Models (cd-rom)
- Taking Inventory, PreK-3 (CD): The Role of Context (CD-ROM)
- Taking Inventory, PreK-3 (Resource Package): The Role of Context (paperback + cd rom)
- Working with the Number Line, Grades PreK-3 (Resource Package): Mathematical Models (paperback + cd rom)
- Fostering Children's Mathematical Development, Grades PreK-3 (Resource Package): The Landscape of Learning (paperback + cd rom)
- Young Mathematicians at Work: Constructing Fractions, Decimals, and Percents (Paperback)
- Young Mathematicians at Work: Constructing Multiplication and Division (Paperback)
- Young Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction (Paperback)
- Contexts for Learning Mathematics Teacher Pack K-1 (Paperback)
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Also Available From
Sherrin B. Hersch
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Books
- YMAW Minilessons for Operations with Fractions, Decimals, and Percents, Grades 5-8 (Resource Package) (Paperback + CD)
- YMAW Fostering Children's Mathematical Development, Grades 5-8 (Resource Package): The Landscape of Learning (Resource Package)
- YMAW Exploring Playgrounds, Grades 5-8 (Resource Package): A Context for Multiplication of Fractions (Resource Package)
- Working with the Ratio Table, Grades 5-8 (Resource Package): Mathematical Models (Paperback)
- Sharing Submarine Sandwiches, Grades 5-8 (Resource Package): A Context for Fractions (Paperback + CD)
- Young Mathematicians at Work, Grades 3-5: Professional Development Materials Pack (Other)
- Working with the Array, Grades 3-5 (Resource Package): Mathematical Models (Paperback + CD)
- Fostering Children's Mathematical Development, Grades 3-5 (Resource Package): The Landscape of Learning (Paperback + CD)
- Young Mathematicians at Work, PreK-3: Professional Development Materials Facilitator's Pack (Resource Package)
- Multiplication and Division Minilessons, Grades 3-5 (Resource Package) (Paperback + CD-ROM)
- Turkey Investigations, Grades 3-5 (Resource Package): A Context for Multiplication (Paperback + CD-ROM)
- Exploring Soda Machines, Grades 3-5 (Resource Package): A Context for Division (Paperback + CD-ROM)
- Exploring Ages, PreK-3 (Resource Package): The Role of Context (Paperback + CD-ROM)
- Addition and Subtraction Minilessons, Grades PreK-3 (Resource Package) (Paperback + CD-ROM)
- Taking Inventory, PreK-3 (Resource Package): The Role of Context (paperback + cd rom)
- Fostering Children's Mathematical Development, Grades PreK-3 (Resource Package): The Landscape of Learning (paperback + cd rom)
- Working with the Number Line, Grades PreK-3 (Resource Package): Mathematical Models (paperback + cd rom)
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