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

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)

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)

The Double Decker Bus: Early Addition and Subtractionis one of eight units in the Contexts for Learning Mathematics' Investigating Number Sense, Addition, and Subtraction (K-3) This unit begins with the story of a double-decker bus-a bus that has two decks with ten seats on each. Five seats on each deck are red and five seats are white. The bus goes by quickly and the little girl in the story, sitting at her bedroom window and watching, works out ways to use the colors of the seats to calculate quickly how many people are on the bus. Her father drives a double-decker bus and she helps him figure out a way to know how many empty seats there are on the top deck even though he can't see them. The unit introduces the arithmetic rack as a powerful model and tool to act out the story. The arithmetic rack is a calculating frame consisting of two rows of ten beads-two sets of five (one red and one white) in each row. (Instructions for creating or buying your own arithmetic racks are included.) Cognitive psychologists, such as Susan Carey and Stanislas Dehaene (1999), have shown that even toddlers can recognize small amounts, such as two or three, as a unit and that this ability (known as "subitizing") is probably innate. Children can even do addition and subtraction with amounts of this size because they use this innate perceptual ability to see that three is one more than two. Using the arithmetic rack allows kindergarteners and first graders to build on their natural ability and see five as a unit. When five can be subitized as a whole, it can be used to support understanding of 6 as 5 + 1, 8 as 5 + 3, or 4 as 5 - 1. The arithmetic rack also supports the strategies of doubles and near doubles, 6 + 7 = 6 + 6 + 1, and making tens, 9 + 6 = 10 + 5. In this unit, children move the beads on the arithmetic rack to represent passengers going from one deck on the bus to the other, and sitting in various combinations in the red and white seats. This context supports the development of the understanding that numbers can be named in many ways, for example 10 as 6 + 4, 7 + 3, or 5 + 5. The unit also includes minilessons with quick images, and strings of related addition and subtraction problems solved with the arithmetic rack to help automatize the basic facts. Several games-Passenger Pairs, Rack Pairs, and Passenger Combos-are also included in this unit. They can be played throughout the year as a way for children to extend composing and decomposing strategies as they establish equivalence-for example, representing 7 as 5 + 2, 3 + 4, or 1 + 6 (Treffers, 1991). To learn more visit http://www.contextsforlearning.com

The Double-Decker Bus: Early Addition and Subtraction (Context for Learning Math)

Liu, Nina

FirstHand

Organizing and Collecting: The Number Systemis one of eight units in the Contexts for Learning Mathematics' Investigating Number Sense, Addition, and Subtraction (K-3) This unit begins with the story of the Masloppy family-an endearing, large family that finds it difficult to keep track of things. Everyone is forever losing, misplacing, and looking for things. One of the children, Nicholas, decides to sort, organize, and take inventory of things in the house. He counts and bundles materials and labels containers and baskets, and life in the Masloppy household is smoother thereafter. The idea of taking inventory is brought to the classroom, where children work to count and label baskets of supplies and materials. The discussion focuses on organizing in groups and skip counting, then specifically on groups of ten. The concept of place value is developed as the children pack objects into groups of ten and study patterns in the data. There are opportunities to deepen their understanding by packing in fives and playing games that focus on groups of ten, and there are minilessons that use the ten-frame as a visual model of five and ten. (The structure of the ten-frame is similar to that of the arithmetic rack, which is discussed in The Double-Decker Bus (previous unit).Both units use five and ten as landmark numbers: the arithmetic rack has four groups of five arranged in two rows of ten, the ten frame has two groups of five. The ten-frame is used in this unit because it resembles the context of packing more closely.) In the second week the inventory context is extended to include ordering more classroom supplies as a way to develop and support addition strategies, which include jumping to friendly numbers (multiples of ten) and jumping by ten. As children pack and count groups of items, they begin to unitize-to count groups and objects at the same time. Children develop an understanding of place value as they construct the idea that the number of packs and loose items is related to the total number of objects and that the numbers change when items are added to make full packs or when a pack of ten is added. The game Collecting Stamps and its variations are included in this unit. These can be played throughout the year as a way for children to develop place value and addition strategies. The game and its variations extend composing and decomposing strategies while promoting understanding of equivalence-for example, representing 26 + 8 as equal to 26 + 4 + 4. To learn more visit http://www.contextsforlearning.com

Organizing and Collecting: The Number System (Context for Learning Math)

In their Young Mathematicians at Work series, Catherine Twomey Fosnot, Maarten Dolk, and Bill Jacob describe an innovative approach to mathematics instruction where teachers help young children construct a deep understanding of numeracy and operations in a math workshop environment that supports the Common Core Standards for Mathematical Practice.    The hallmarks of their approach include:       Supporting children as they construct mathematical strategies and big ideas         Creating realistic contexts and mathematical models that develop children’s capacity to mathematize their world

The Complete Young Mathematicians at Work Series

Jacob, William

"Our digital-lab environment provides an active, more meaningful professional development experience, which empowers teachers to integrate theory and practice. We offer teachers the opportunity to embark upon their own landscape of learning journey." --Catherine Twomey Fosnot The bestselling Young Mathematicians at Work series has helped tens of thousands of teachers inspire deep mathematical understanding in students with its signature workshop approach. The Contexts for Learning Mathematics series has helped even more teachers bring that approach into their classrooms to align their math program to the Standards of Practice in the Common Core. Now Cathy Fosnot and her colleagues have developed an invaluable resource that gives teachers ownership of the core ideas and essential understandings of early algebra. Learning to Support Young Mathematicians at Work offers Professional Development providers interactive, meaningful tools to help teachers deepen their algebraic thinking within a unique digital environment. Two DVDs feature classroom sessions that show students exploring the sequence of investigations and activities found in the popular Contexts for Learning Mathematics algebra unit books Trades, Jumps, and Stops and The California Frog-Jumping Contest. Extensive classroom video footage allows participants to study children over time, and examine and analyze their development as well as the teacher's pedagogy. The user can respond to prompts, create video clips and presentations, and explore related materials all from the DVD, either alone at home or in a workshop setting. The PD facilitator's guide features a flexible menu of workshops, ranging from two-hour sessions that focus on a particular topic to comprehensive 5-day institutes. As participants engage in the investigations, they build their own conceptual and pedagogical understanding of algebra and proof, questioning and conferring, observing children at work in mathematics, and using the powerful tools of context and representations. These learning experiences foster teachers' algebraic thinking and set the stage for robust and active classroom practice that promotes students' deep understanding. The DVDs are also available individually without the facilitator guide for teachers who may prefer to study the material outside of a workshop setting. Trades, Jumps and Stops DVD California Frog Jumping Contest DVD NOTE: The DVD-ROMs are compatible with Windows XP, Vista, Windows 7, and Mac OS X up to 10.6. They are not compatible with Mac OS X 10.7 (Lion) or above.

Learning to Support Young Mathematicians at Work: An Early Algebra Resource for Professional Development (Context for Learning Mathematics)

Imm, Kara

Stylianou, Despina

See the best price to sell, buy, or rent books by Dolk, Maarten. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Dolk, Maarten