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 Mobil, 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. In this second volume in a series of three, Fosnot and Dolk focus on how to develop an understanding of multiplication and division in grades 3-5. Their book: 
<ul>
<li>describes and illustrates what it means to do and learn mathematics </li>
<li>provides strategies to help teachers turn their classrooms into math workshops that encourage and reflect mathematizing </li>
<li>examines several ways to engage and support children as they construct important strategies and big ideas related to multiplication </li>
<li>takes a close look at the strategies and big ideas related to division </li>
<li>defines modeling and provides examples of how learners construct models - with a discussion of the importance of context </li>
<li>discusses what it means to calculate using number sense and whether or not algorithms should still be the goal of computation instruction </li>
<li>describes how to strengthen performance and portfolio assessment </li>
<li>emphasizes teachers as learners by encouraging them to see themselves as mathematicians. </li>
</ul>

Young Mathematicians at Work: Constructing Multiplication and Division

Education & Teaching

Fosnot, Catherine Twomey

Dolk, Maarten

Schools & Teaching

Heinemann

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 National Science Foundation and ExxonMobil, 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. In this third volume in a series of three, Fosnot and Dolk focus on how children in grades 5-8 construct their knowledge of fractions, decimals, and percents. Their book: <ul>
<li>describes and illustrates what it means to do and learn mathematics. </li>
<li>contrasts word problems with true problematic situations which support and enhance investigation and inquiry. </li>
<li>provides strategies to help teachers turn their classrooms into math workshops. </li>
<li>explores the cultural and historical development of fractions, decimals, and their equivalents and the ways in which children develop similar ideas and strategies. </li>
<li>defines and gives examples of modeling, noting the importance of context. </li>
<li>discusses calculation using number sense and the role of algorithms in computation instruction. </li>
<li>describes how to strengthen performance and portfolio assessment. </li>
<li>focuses on teachers as learners by encouraging them to see themselves as mathematicians. </li>
</ul>

Young Mathematicians at Work: Constructing Fractions, Decimals, and Percents

Science & Math

Mathematics

Recommended by the Ontario Ministry of Education 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.

Exploring Soda Machines, Grades 3-5 (Resource Package): A Context for Division (Young Mathematicians at Work)

Hersch, Sherrin B

Recommended by the Ontario Ministry of Education      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.

Multiplication and Division Minilessons, Grades 3-5 (Resource Package) (Young Mathematicians at Work)

Recommended by the Ontario Ministry of Education 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.

Fostering Children's Mathematical Development, Grades 3-5 (Resource Package): The Landscape of Learning (Young Mathematicians at Work)

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 Ratio Table 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: <ul>
<li>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. </li> <li>A Professional Development Overview Manual that provides general advice on how you can use the CD-ROM for staff development. </li> <li>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. </li> </ul> In Working with the Ratio Table, your workshop participants will observe sixth graders as they construct some of the big ideas related to fractions, making connections between ratios and equivalence and uncovering landmark division strategies like comparison through common denominators. By studying the use of carefully crafted problems designed both to generate a range of solution strategies and to highlight the power of ratio tables and other models for 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(TM) Player and Acrobat Reader(R) Quicktime 6.0 (or higher) Mac PowerPC Processor G3/233MHz (or higher) System 9.2 or 10.2 (or higher) 64 MB RAM (more recommended) SVGA Color Display (or better) 4x CD-ROM Drive (or faster) Sound Card 16-bit Flash(TM) Player and Acrobat Reader(R) Quicktime 6.0 (or higher) *Please note CD-ROM is not compatible with Mac OS X 10.7

Working with the Ratio Table, Grades 5-8 (Resource Package): Mathematical Models (Young Mathematicians at Work)

Jacob, William

In Working with the Ratio Table, participants can interact with footage of sixth graders:  solving carefully crafted problems that highlight ratio tables and other division models constructing big ideas related to fractions making connections between ratios and equivalence uncovering division strategies like comparison through common denominators.   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(tm) Player and Acrobat Reader Quicktime 6.0 (or higher)   Mac PowerPC Processor G3/233MHz (or higher) System 9.2 or 10.2 (or higher) 64 MB RAM (more recommended) SVGA Color Display (or better) 4x CD-ROM Drive (or faster) Sound Card 16-bit Flash(tm) Player and Acrobat Reader Quicktime 6.0 (or higher)

Working with the Ratio Table, Grades 5-8 (CD): Mathematical Models (Young Mathematicians at Work)

Recommended by the Ontario Ministry of Education Fostering Children’s Mathematical Development focuses on short video clips from classroom situations, providing opportunities to observe, analyze, and discuss critical moments in children’s development, and then to build a landscape of the ideas, strategies, and models of operations with fractions, decimals, and percents.

YMAW Fostering Children's Mathematical Development, Grades 5-8 (Resource Package): The Landscape of Learning (Young Mathematicians at Work)

Cameron, Antonia

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 Fostering Children's Mathematical Development 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.   Fostering Children's Mathematical Development focuses on short video clips from classroom situations, providing opportunities to observe, analyze, and discuss critical moments in children's development, and then to build a landscape of the ideas, strategies, and models of operations with fractions, decimals, and percents. The Resource Package helps teachers examine children's thinking; investigate their strategies; and analyze how they model their world mathematically.  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(TM) Player and Acrobat Reader(R)  Quicktime 6.0 (or higher)  MacIntosh PowerPC Processor G3/233MHz (or higher) System 9.2 or 10.2 (or higher) 64 MB RAM (more recommended) SVGA Color Display (or better) 4x CD-ROM Drive (or faster) Sound Card 16-bit Flash(TM) Player and Acrobat Reader(R) Quicktime 6.0 (or higher) *Please note CD-ROM is not compatible with Mac OS X 10.7

Fostering Children's Mathematical Development, Grades 5-8 (CD): The Landscape of Learning (Young Mathematicians at Work)

Recommended by the Ontario Ministry of Education      This title offers structured series of computation problems or strings, used to build and highlight number relationships and operations and to develop efficient mental math computations

YMAW Minilessons for Operations with Fractions, Decimals, and Percents, Grades 5-8 (Resource Package (Young Mathematicians at Work)

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Books by Fosnot, Catherine Twomey