But Why Does It Work

Author: Susan Jo Russell
Publisher: Heinemann Educational Books
ISBN: 9780325081144
Size: 58.80 MB
Format: PDF, Mobi
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Designed for individuals as well as study groups, this book includes access to classroom-ready instructional sequences, each built on a model supporting students in: noticing relationships across sets of problems, equations, or expressions ...

Teachers Professional Development And The Elementary Mathematics Classroom

Author: Sophia Cohen
Publisher: Routledge
ISBN: 113563226X
Size: 23.41 MB
Format: PDF, Mobi
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Abby talks about an activity that she does with her students daily. ... In Abby's
class, she was finding that children tended to stick to the several methods of
generating these equations that had come first to mind and had been discussed
in class. ... This ability and willingness to take on the work of evaluating what is
and is not a valid mathematical argument, or what is and is not a valid
mathematical proposition, is an important step in a child's development—
mathematically, as well as ...

Proving In The Elementary Mathematics Classroom

Author: Andreas J. Stylianides
Publisher: Oxford University Press
ISBN: 019103472X
Size: 14.43 MB
Format: PDF, Mobi
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To conclude, given how large a part calculation work occupies in the elementary
mathematics curriculum of different countries, and also the powerful aspect of
mathematical sense-making that proving can bring to this work, one may talk
about a transformative ... The definition of proof that I discussed in Chapter 2
breaks a mathematical argument down into three components: the set of
accepted statements, the modes of argumentation, and the modes of argument

Best Practices For Elementary Classrooms

Author: Randi Stone
Publisher: Skyhorse Publishing, Inc.
ISBN: 1632209594
Size: 48.56 MB
Format: PDF
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What Award-Winning Teachers Do Randi Stone. percentage of student work. The
child should be in charge of his own learning. By investigating one standard in a
variety of ways, each child is able to find a medium that “talks” to him or her. ... My
hope is that with the conclusion of this lesson, it seems we are well on our way to
six-year-olds being fluent in analyzing characteristics and properties of 2-D and 3
-D geometric shapes and developing mathematical arguments about geometric ...

Mathematics For Elementary School Teachers A Process Approach

Author: Mark A. Freitag
Publisher: Cengage Learning
ISBN: 128552876X
Size: 15.66 MB
Format: PDF, Mobi
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Initially, we limited the discussion to segments and angles, but we can extend the
idea of congruence to other two- and three-dimensional shapes. Of these,
congruent ... In the elementary classroom, children come to an intuitive
understanding of congruence and similarity by manipulating physical shapes. ...
Once students have a solid understanding of congruence and similarity, they use
the ideas to identify geometric properties, develop mathematical arguments, and
solve problems.

Teaching And Learning Proof Across The Grades

Author: Despina A. Stylianou
Publisher: Routledge
ISBN: 1135856753
Size: 28.40 MB
Format: PDF
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the. Elementary. Grades. Proving is a human activity that extends beyond formal
mathematics. While there are rules of logic that govern a rigorous notion of
mathematical proof, the idea of proof has its genesis in human activity, in the
need to establish certainty. Even young children, without formal training in logic
and deduction, exhibit an innate curiosity to know why things work as they do, to
understand why things are as they are, to be convinced. Indeed, as toddlers
begin to acquire ...

Geometry As Objective Science In Elementary School Classrooms

Author: Wolff-Michael Roth
Publisher: Routledge
ISBN: 1136732209
Size: 66.37 MB
Format: PDF, ePub, Mobi
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Thatis,a central aspectofprotogeometry hasbeen theact of measuring —though
subsequently,once the Greeks were doing geometry scientifically, measurement
does not appear to have playeda major role. Historically, however, geometry as
mathematical science arose from the prescientific, intuitively given world, from the
“first very primitively and then artistically exercised method of determination by
surveying and measuringin general” (Husserl, 1997a, p. 26, original emphasis).

Effects Of State Level Reform Of Elementary School Mathematics Curriculum On Classroom Practice

Author: David K. Cohen
Size: 12.87 MB
Format: PDF, Kindle
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Her teaching does reflect the new Framework in many ways. For instance, she ...
She has revised the curriculum to help students understand math, but she
conducts the class in ways that discourage exploration of students'
understanding. From the ... From one angle, the curriculum and instructional
materials in this class were just what the new Framework ordered. For instance,
Mrs. O regularly asked her second graders to work on "number sentences." In
one class that I observed, ...

Mathematical Olympiad Challenges

Author: Titu Andreescu
Publisher: Springer Science & Business Media
ISBN: 9780817646110
Size: 57.68 MB
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As Paul Halmos said, “problems are the heart of mathematics,” so we should “
emphasize them more and more in the classroom, in seminars, and in the books
and articles we write, to train our students to be better problem-posers and
problem-solvers than we are. ... work. Whereas by a problem, we mean a more
intricate question for which at first one has probably no clue to how to approach it,
but by perseverance and inspired effort, one can transform it into a sequence of

A Few Of Our Favorite Things

Author: Patricia D. Morrell
Publisher: Springer
ISBN: 9462097798
Size: 74.46 MB
Format: PDF, Kindle
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We may work hard to prepare preservice teachers to craft standards-based
inquiry science lessons in our methods classes, but when preservice teachers
arrive in the classroom, they often quickly find that the pressure is on for
language arts and mathematics, but science (and social ... As many of us have
learned, integration with other content areas such as language arts (e.g., Akerson
, 2001; Young & Akerson, 2005) is a way that we can 'sneak' science into the
elementary classroom.