But Why Does It Work

Author: Susan Jo Russell
Publisher: Heinemann Educational Books
ISBN: 9780325081144
Size: 17.92 MB
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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 ...

Proving In The Elementary Mathematics Classroom

Author: Andreas J. Stylianides
Publisher: Oxford University Press
ISBN: 0191034738
Size: 18.72 MB
Format: PDF, Docs
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why they occur, become attuned to looking for regularities in mathematics (cf.
Russell et al., 2011a). Without prompting from the teacher, they come up with
ideas about what might be true and offer their own conjectures. That is, they
become curious about how mathematics works and develop tools they need to
test and prove their ideas. As Stylianides points out in the concluding chapter, “
once classroom norms that support argumentation and proof have been
established, students ...

The Mathematical Education Of Teachers

Publisher: American Mathematical Soc.
ISBN: 9780821828991
Size: 21.74 MB
Format: PDF, Kindle
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More abstractly, how does the source of Josh's error connect to additive
procedures, the distributive property, multiplication algorithms, multiplication of
binomials, and so on? ... The key to turning even poorly prepared prospective
elementary teachers into mathematical thinkers is to work from what they do
know — the mathematical ideas they hold, the skills they possess, and the
contexts in which these are understood — so they can move from where they are
to where they need to go.

Teachers Professional Development And The Elementary Mathematics Classroom

Author: Sophia Cohen
Publisher: Routledge
ISBN: 113563226X
Size: 29.74 MB
Format: PDF
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This kind of seminar community is the hub of the teachers' professional world.
The character of a DMI seminar community—its supportiveness, agenda, and
rigor—owes a good deal to the three core aspects of the semi- nar set out in
chapter 1: (a) the solidity and complexity of the mathematics, (b) the concurrent
study of teachers' and students' mathematics, and (c) the parallel between the
seminar's pedagogy and envisioned elementary classroom pedagogy. In that first
chapter, ...

The Construction Of New Mathematical Knowledge In Classroom Interaction

Author: Heinz Steinbring
Publisher: Springer Science & Business Media
ISBN: 0387242538
Size: 73.17 MB
Format: PDF
View: 5037
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221), one can still assume that, when working on a mathematical argument, the
individual mathematician cannot do without such idealized object conceptions in
his consciousness or private world of ideas (Heintz, 2000, p. 220ff). As a
consequence it can be stated that in professional mathematical communication,
the contradiction-free conceptual structures and relations dominate and
determine the ideal objects which are not interpreted any further. In contrast to
content related ...

Mathematical Models For Teaching

Author: Ann Kajander
Publisher: Canadian Scholars’ Press
ISBN: 1551305569
Size: 52.23 MB
Format: PDF, ePub, Docs
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This knowledge is indeed mathematical; Ball, Thames, and Phelps (2008) claim
that “deciding whether a method or procedure would work in general[,] ...
determining the validity of a mathematical argument, or selecting a
mathematically appropriate representation ... requires mathematical knowledge
and skill, not knowledge of students or teaching” (p. 398). Such specialized
mathe- matical knowledge helps teachers construct good classroom problems
while antici- pating students' ...

Mathematics Education

Author: Jacqueline Dewar
Publisher: Springer
ISBN: 3319449508
Size: 25.75 MB
Format: PDF, Mobi
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Following a carefully designed sequence of tasks rather than a textbook, students
construct, analyze, and critique mathematical arguments. Their ideas and
explanations define and drive progress through the curriculum. In class, students
present and discuss solutions alone at the board or via structured small-group
work, while instructors guide and monitor this process (p. ... I did my practicum for
the elementary licensure in a 4th grade class that was taught using methods of

Moving Into The Classroom

Author: Stacia C Miller
Publisher: Springer
ISBN: 9811064245
Size: 56.85 MB
Format: PDF, Docs
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Once the starter has found the missing sum or addend, ask them to identify a
classmate whose card has the solution on it and throw the ball to them. ...
Students could work in small groups to create additional sets of cards for the
activity. ... Principles and Standards for School Mathematics (NCTM, 2000)
identifies five major themes for the geometry strand at the elementary level: (1)
analyzing characteristics and properties of two-dimensional and three-
dimensional geometric shapes; ...

Connecting Arithmetic To Algebra

Author: Susan Jo Russell
Publisher: Heinemann Educational Books
ISBN: 9780325041919
Size: 59.57 MB
Format: PDF, Mobi
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PLCs and book-study groups! Save $47.25 when you purchase 15 copies with the Book Study Bundle.

Teaching Children Mathematics

Size: 65.95 MB
Format: PDF
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However, teachers who have a firm understanding of logical necessity are better
equipped to help young students reflect on their reasoning skills and transition
toward increasingly formal reasoning as they progress through the grades.
Literature review Researchers who have noted the importance of argumentation
in elementary school have also noted that teacher candidates often struggle
when evaluating mathematical arguments (Martin and Harel 1989; Morris 2007).
Particularly ...