A Research Companion to
Principles and Standards for
School Mathematics
Chapter 16
Communication and
Language
tension between
Acquisition
and
Participation
metaphors for learning
How do we distinguish between
the two?
Mathematics is something
students are to
ACQUIRE
…
The activities of instruction are
treatment and outcomes are
increased student knowledge
of mathematics
[including learning mathematical
communication]
Mathematics is something that
students
PARTICIPATE
in
[to inherit
–
mathematical
practices developed over time.
]
Communication is one aspect
of this participation view
–
and
is not separate from
instruction
Types of communication are
constrained or developed and tied to
mathematical understandings
Acquiring Knowledge of
Mathematical Communication
page 238
Instruction in Communication
Small groups/Peers
Teacher and Individual
Teacher and Whole Class
Review research by Webb about
correlations between the level of
communication and achievement
Partic
ipating in Mathematical
Communication to Learn
page 238
–
240
Talking about Mathematics
Talking about Talking about
Mathematics
Apprenticeship
Mathematics Register
What is Taught and Learned in
Mathematical Communication?
page 240
–
244
Mathematizing
Reflective Discourse
Concrete to Iconic to Abstract
How is Mathematics Taught and
Learned in Classroom
Communication?
page 244
–
245
What has happened in your
classroom(s) this week?
Does it connect to the studies
discussed?
Can you continue the
pattern?
2, 3, 5, 5, 8, 7, 11,
,
,
, 17, …
What do you see?
Can you share your thinking
with a partner?
Teaching Mathematical
Communication to All Students
page 245
–
246
What is
silencing
?
m
arginalizing
?
What do we need to be
concerned
about?
MATH 381
PROBLEM OF THE WEEK #
Grading Rubric
Name
I.
The
answer(s)
to this week’s problem is/are:
INCORRECT SOLUTION
PARTIAL SOLUTION
CORRECT SOLUTION(S)
(1 points)
(2 point)
(3 points)
II.
My
work
to support my answers is attached or shown here:
NO WORK SHOWN
INCOMPLETE WORK
ALL WORK
(0 points) SOLUTION NOT SUPPORTED
SUPPORTS SOLUTION
(1 point)
(2 points)
III. My explanation
, which clearly states the problem

solving s
trategy (or strategies)
used, explains my thinking and problem solving process to support the work shown
:
[LOOK BACK!]
CLEARLY STATES STRATEGY USED?
YES
NO
(1 point)
(0 points)
Overall Quality
and
Completeness
of explanation:
BELOW
MEETS
EXCEEDS
EXPECTATIONS
EXPECTATIONS
EXPECTATIONS
(2 points)
(3 points)
(4 points)
TOTAL
(10)
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