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Explains how children between the ages of four and eight construct a deep understanding of numbers and the operations of addition and subtraction.
Explains how children between the ages of four and eight construct a deep understanding of numbers and the operations of addition and subtraction.
Questioning has become one of the biggest challenges of teachers everywhere as they rise to the challenge of transforming their classrooms into communities of mathematicians. The CCSS Standards of Mathematical Practice require that children engage in problem solving with tenacity and confidence, use models as tools for thinking, and read and write viable arguments. This mandate demands that teachers foster a climate conducive to the generating of mathematics rather than the explanation of it. This book sets the bar for providing suggestions on how to question and confer--how to teach and mentor young mathematicians in elementary classrooms. Written by a leading author in the field, the book describes characteristics of powerful conferrals, and shows how to make the moments matter. Developmental frameworks, ways of assessing in the moment, and tips on how to help children get started and overcome math anxiety are all described as well as several example conferrals. Video clips of the author and several exemplary teachers conferring with students are provided throughout as illustrations.
Explains how children between the ages of four and eight construct a deep understanding of numbers and the operations of addition and subtraction.
"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.
Vladimir Arnold (1937-2010) was one of the great mathematical minds of the late 20th century. He did significant work in many areas of the field. On another level, he was keeping with a strong tradition in Russian mathematics to write for and to directly teach younger students interested in mathematics. This book contains some examples of Arnold's contributions to the genre. "Continued Fractions" takes a common enrichment topic in high school math and pulls it in directions that only a master of mathematics could envision. "Euler Groups" treats a similar enrichment topic, but it is rarely treated with the depth and imagination lavished on it in Arnold's text. He sets it in a mathematical context, bringing to bear numerous tools of the trade and expanding the topic way beyond its usual treatment. In "Complex Numbers" the context is physics, yet Arnold artfully extracts the mathematical aspects of the discussion in a way that students can understand long before they master the field of quantum mechanics. "Problems for Children 5 to 15 Years Old" must be read as a collection of the author's favorite intellectual morsels. Many are not original, but all are worth thinking about, and each requires the solver to think out of his or her box. Dmitry Fuchs, a long-term friend and collaborator of Arnold, provided solutions to some of the problems. Readers are of course invited to select their own favorites and construct their own favorite solutions. In reading these essays, one has the sensation of walking along a path that is found to ascend a mountain peak and then being shown a vista whose existence one could never suspect from the ground. Arnold's style of exposition is unforgiving. The reader--even a professional mathematician--will find paragraphs that require hours of thought to unscramble, and he or she must have patience with the ellipses of thought and the leaps of reason. These are all part of Arnold's intent. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.
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 participants and preservice teachers, the Working with the Number Line CD-ROM offers users a multi-media learning environment for professional development on topics ranging from instruction to assessment, that stimulates action, reflection, and discussion with dynamic video clips, children's work samples, and interviews with students and teachers. In Working with the Number Line, students construct a number line, initially as a model to represent a measurement situation, then as a model to represent their computational strategies, and, finally, as a tool for thinking. The CD-ROM helps teachers examine children's numeric thinking; investigate their strategies; and analyze how they model their world mathematically. Users also study teachers at work: designing rich contexts for problem-solving; drawing connections between mathematical ideas and strategies; and developing a vibrant mathematical community. 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 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)
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 participants and preservice teachers, the Exploring Ages CD-ROM 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. In Exploring Ages, students explore addition and subtraction through the lens of ages, building new understandings and strategies and learning concepts like removal, missing addends, and constant difference as they solve problems that reflect their natural curiosity. Users also study teachers at work: designing rich contexts for problem-solving, drawing connections between mathematical ideas and strategies, and developing a vibrant mathematical community. 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 FlashTM 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 FlashTM Player and Acrobat Reader Quicktime 6.0 (or higher)
The DVD features classroom sessions that show students exploring the sequence of investigations and activities found in the popular Contexts for Learning Mathematics algebra unit book Trades, Jumps, and Stops. 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. NOTE: This DVD-ROM is compatible with Windows XP, Vista, Windows 7, and Mac OS X up to 10.6. It is not compatible with Mac OS X 10.7 (Lion) or above.
