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Young Mathematicians At Work book and CDs

Young Mathematicians at Work Overview
Young Mathematician at Work 3–5 Resource Packages Overview
Contexts for Learning Mathematics and Young Mathematician at Work Resource Packages

Young Mathematicians at Work Overview

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In our efforts to reform mathematics education, we've learned a tremendous amount about young students' strategies and the ways they construct knowledge, without fully understanding how to support such development over time. The Dutch do. So, funded by the NSF and Exxon, Mathematics in the City was begun, a collaborative inservice project that pooled the best thinking from both countries. In Young Mathematicians at Work, Catherine Fosnot and Maarten Dolk reveal what they learned after several years of intensive study in numerous urban classrooms.

The first in a three-volume set, Young Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction (Grades PreK-3), focuses on young children between the ages of four and eight as they construct a deep understanding of number and the operations of addition and subtraction. Rather than offer unrelated activities, Fosnot and Dolk provide a concerted, unified description of development, with a focus on big ideas, progressive strategies, and emerging models. Drawing from the work of the Dutch mathematician Hans Freudenthal, they define mathematics as "mathematizing"—the activity of structuring, modeling, and interpreting one's "lived world" mathematically. And they describe teachers who use rich problematic situations to promote inquiry, problem solving, and construction, and children who raise and pursue their own mathematical ideas.

ISBN 978-0-325-00353-5 / 0-325-00353-X / 2001 / $23.50

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In Young Mathematicians at Work: Constructing Multiplication and Division (Grades 3-5), the second book in the three-volume series, Fosnot and Dolk focus on how to develop an understanding of multiplication and division. Their book:

  • describes and illustrates what it means to do and learn mathematics
  • provides strategies to help teachers turn their classrooms into math workshops that encourage and reflect mathematizing
  • examines several ways to engage and support children as they construct important strategies and big ideas related to multiplication
  • takes a close look at the strategies and big ideas related to division
  • defines modeling and provides examples of how learners construct models-with a discussion of the importance of context
  • discusses what it means to calculate using number sense and whether or not algorithms should still be the goal of computation instruction
  • describes how to strengthen performance and portfolio assessment
  • emphasizes teachers as learners by encouraging them to see themselves as mathematicians.

ISBN 978-0-325-00354-2 / 0-325-00354-8 / 2001 / $23.50

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In Young Mathematicians at Work: Constructing Fractions, Decimals, and Percents (Grades 5-8), the third book in the three-volume series, Fosnot and Dolk focus on how children construct their knowledge of fractions, decimals, and percents. Their book:

  • describes and illustrates what it means to do and learn mathematics.
  • contrasts word problems with true problematic situations which support and enhance investigation and inquiry.
  • provides strategies to help teachers turn their classrooms into math workshops.
  • explores the cultural and historical development of fractions, decimals, and their equivalents and the ways in which children develop similar ideas and strategies.
  • defines and gives examples of modeling, noting the importance of context.
  • discusses calculation using number sense and the role of algorithms in computation instruction.
  • describes how to strengthen performance and portfolio assessment.
  • focuses on teachers as learners by encouraging them to see themselves as mathematicians.

ISBN 978-0-325-00355-9 / 0-325-00355-6 / 2002 / 192pp / $23.50

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In contrast to other books on math reform the Young Mathematicians at Work series provides a new look at the teaching of computation. It moves beyond the current debate about algorithms to argue for deep number sense and the development of a repertoire of strategies based on landmark numbers and operations.

Young Mathematician at Work 3–5 Resource Packages Overview

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In their Young Mathematicians at Work series, 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 operations in a math workshop environment. Now they and two colleagues from the project have developed a 21st-century approach that provides pre- and inservice teachers with an interactive, video-based, digital context for inquiry into the teaching and learning of mathematics.

Designed for workshop leaders and college instructors, each Resource Package consists of three valuable components:

  • A CD-ROM (developed by Maarten Dolk and Catherine Twomey Fosnot) that offers users a multi-media learning environment for professional development on topics ranging from instruction to assessment, and that stimulates action, reflection, and discussion with dynamic video clips, children's work samples, and interviews with students and teachers
  • A Professional Development Overview Manual that provides general advice on teaching in a digital environment
  • A Facilitator's Guide (developed by Antonia Cameron, Sherrin B. Hersch, Lynn Tarlow, Suzanne Werner, Bill Jacob, Carol Teig, and Catherine Twomey Fosnot) specific to the CD-ROM that includes suggestions for using the video clips; sample dialogue from field-tested sites; facilitation tips; and more. System Requirements for CD-ROM

Through these resource packages users also are able to study teachers at work: designing rich contexts for problem solving; listening to, questioning, and interpreting students' thinking; drawing connections between mathematical ideas and strategies; and, ultimately, developing a vibrant mathematical community.

Multiplication and Division Minilessons
In Multiplication and Division Minilessons, clips of teachers conducting effective minilessons in real classrooms show you how these short, focused sessions can build big mathematical thinking in young learners. (2CD-ROMs)

These video clips support and extend the teaching throughout Contexts for Learning Mathematics' Investigating Multiplication and Division (3-5).

ISBN 978-0-325-00776-2 / 0-325-00776-4 / 2005 / $65.00

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Turkey Investigations: A Context for Multiplication
In Turkey Investigations, your workshop participants will observe third graders as they begin to construct ideas about multiplication. Exploring contexts of weights and measures over three days, the children invent strategies such as repeated addition on the number line, doubling and halving, and using ratio tables. Teachers will discover what a valuable tool real-life contexts are for building a solid foundation in multiplication.

These video clips show the teaching and investigations from Investigating Multiplication and Division's The Big Dinner: Multiplication with the Ratio Table.

ISBN 978-0-325-00774-8 / 0-325-00774-8 / 2005 / $49.50

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Exploring Soda Machines: A Context for Division
In Exploring Soda Machines, your workshop participants will observe fourth graders as they construct some of the big ideas related to division, including the connection between partitive and quotative division and the inverse relationship between multiplication and division. 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 division, teachers will discover what a valuable tool real-life contexts are for building a solid foundation in division.

These video clips show the teaching and investigations from Investigating Multiplication and Division's The Teacher's Lounge: Place Value and Division.

ISBN 978-0-325-00772-4 / 0-325-00772-1 / 2005 / $49.50

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Working with the Array: Mathematical Models
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.

These video clips support and extend the teaching throughout Contexts for Learning Mathematics' Investigating Multiplication and Division (3-5).

ISBN 978-0-325-00778-6 / 0-325-00778-0 / 2005 / $49.50

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Fostering Children's Mathematical Development: The Landscape of Learning
Fostering Children's Mathematical Development focuses on short video clips from interviews, routines, minilessons, games, and investigations. The clips provide opportunities for teachers to observe, analyze, and discuss critical moments in children's development, and then to build a landscape of the ideas, strategies, and models of multiplication and division. The Resource Package helps teachers examine children's thinking; investigate their strategies; and analyze how they model their world mathematically.

These video clips support and extend the learning and strategy development throughout Contexts for Learning Mathematics' Investigating Multiplication and Division (3-5).

ISBN 978-0-325-00780-9 / 0-325-00780-2 / 2005 / $49.50

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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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