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Do your students suppose that 1/3 is greater than 1/2, since 3 is
greater than 2? Do they believe that having "halves" means having
two, and only two, congruent "pieces" of a whole? 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 specialised pedagogical content
knowledge that you need to teach fractions effectively in grades
3-5. The authors demonstrate how to use this multifaceted knowledge
to address the big ideas and essential understandings that students
must develop for success with fractions-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 fractions. 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.
Do your students believe that division "doesn't make sense" if the
divisor is greater than the dividend? Explore rich,
researched-based strategies and tasks that show how students are
reasoning about and making sense of mulitplication and division.
This book focuses on the specialised pedagogical content knowledge
that you need to teach multiplication and division effectively in
grades 3-5. 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 maths 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 multiplication and division. 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.
About the Series: You have essential understanding. It's time to
put it into practise 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 practises 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 reflection 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, understanding into practise, instructional strategies
and assessment that pedagogical content knowledge entails. Maximise
the potential of student-centred learning and teaching by putting
essential understanding into practise.
Do your students have “concept images” that limit their ideas
of shapes to specific examples, oriented in particular ways? Do
they confuse the size of an angle with the length of the rays in a
drawing of an angle? When solving problems, do they mix up the
concepts of perimeter—the distance around a shape, measured in
linear units—and area—the region within the shape, measured in
square units? What tasks can you offer—what questions can you
ask—to determine what they 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 geometry and
measurement effectively in grades 3–5. The authors demonstrate
how to use this multifaceted knowledge to address the big ideas and
essential understandings that students must develop for success
with geometry and measurement—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 geometry
and measurement. 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. Putting Essential Understanding of
Geometry and Measurement into Practice in Grades 3–5 is the
eighth title in NCTM’s highly useful and very readable Putting
Essential Understanding into Practice Series, edited by Barbara J.
Dougherty. Each volume in the series builds on the companion volume
in the earlier Essential Understanding Series to show teachers how
to implement their understanding of mathematics in the classroom.
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