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Do your students have the incorrect idea that addition “makes
numbers bigger” and subtraction “makes numbers smaller”? Do
they believe that subtraction is always “taking away”? What
tasks can you offer - what questions can you ask - to determine
what your students know or don’t know - and move them forward in
their thinking? This book focuses on the specialized pedagogical
content knowledge that you need to teach addition and subtraction
effectively in prekindergarten–grade 2. The authors demonstrate
how to use this multifaceted knowledge to address the big ideas and
essential understandings that students must develop for success
with these computations - not only in their current work, but also
in higher-level mathematics and a myriad of real-world contexts.
Explore rich, research-based strategies and tasks that show how
students are reasoning about and making sense of addition and
subtraction. Use the opportunities that these and similar tasks
provide to build on their understanding while identifying and
correcting misunderstandings that may be keeping them from taking
the next steps in learning. You have essential understanding.
It’s time to put it into practice in your teaching. The Putting
Essential Understanding into Practice Series moves NCTM’s
Essential Understanding Series into the classroom. The new series
details and explores best practices for teaching the essential
ideas that students must grasp about fundamental topics in
mathematics - topics that are challenging to learn and teach but
are critical to the development of mathematical understanding.
Classroom vignettes and samples of student work bring each topic to
life, and questions for reader reaction open it up for hands-on
exploration. Each volume underscores connections with the Common
Core State Standards for Mathematics while highlighting the
knowledge of learners, curriculum, instructional strategies, and
assessment that pedagogical content knowledge entails. Resources
and tasks are available at nctm.org/more4U.
Unpacking"" the ideas related to multiplication and division is a
critical step in developing a deeper understanding. To those
without specialised training, many of these ideas might appear to
be easy to teach. But those who teach in grades 3-5 are aware of
their subtleties and complexities. This book identifies and
examines two big ideas and related essential understandings for
teaching multiplication and division in grades 3-5. Big Idea 1
captures the notion that multiplication is usefully defined as a
scalar operation. Problem situations modelled by multiplication
have an element that represents the scalar and an element that
represents the quantity to which the scalar applies. Big Idea 2
relates to the algorithms that problem solvers have invented - some
of which have become "standard" - for multiplying and dividing. The
authors examine the ways in which counting, adding and subtracting
lead to multiplication and division, as well as the role that these
operations play in algebraic expressions and other advanced topics.
The book examines challenges in teaching, learning and assessment
and is interspersed with questions for teachers' reflection.
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