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Topic: Professional Standards IX (11/27)
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Ronald A Ward

Posts: 298
Registered: 12/4/04
Professional Standards IX (11/27)
Posted: Nov 27, 1995 7:54 PM
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This is the ninth in a series of questions, concerns, & issues concerning
the 1991 NCTM publication "Professional Standards for Teaching Mathematics."
We are currently reading the third set of Standards within that
document;namely, the "Standards for the Professional Development of
Teachers of Mathematics." Today, we will focus on pages 132-143, a
fairly lengthy Standard 2: Knowing Mathematics and School Mathematics.
[If you have missed any of the previous eight postings, just e-mail me
directly and I will send you whatever you want.] Because all questions in
this series have been numbered consecutively for reference purposes, and
because I have felt like Martin Luther all week, I'll begin today with
question number 96.

Ron Ward/Western Washington U/Bellingham, WA 98225

96. I'm sure everyone knows what is meant by saying that the education
of teachers should develop their knowledge of the CONTENT of
mathematics. But what does it mean to you when the authors say that the
education of teachers should develop their knowledge of the "discourse of
mathematics"? In other words, what IS the "discourse of mathematics"?

97. How does your professional development program prepare teachers to
"communicate mathematics effectively at DIFFERENT LEVELS OF FORMALITY"?
Where in your professional development program do teachers develop [or
revisit] their knowledge of SCHOOL mathematics, and how does SCHOOL
mathematics fit within the discipline of mathematics generally?

98. Could readers recommend good resources concerning the "role of
mathematics in culture and society"? This is, I believe, something
different from the "contributions of different cultures toward the
development of mathematics."

99. Do teachers-as-learners experience "the struggles, the false starts,
and the informal investigations that lead to an elegant proof" rather
than just "experience the record of others' constructions"? Do teachers
ever see their PROFESSORS OR SUPERVISORS engaging in such struggles and
false starts?

100. Do teachers ever get to see the "Big" picture of mathematics across
the elementary, middle, and high school years? If so, when and where
does this happen?

101. Starting on page 135, the authors identify by level the mathematics
that all teachers should experience. I'll just recommend here
that this information be compared to the recommendations contained in the
MAA's "Call For A Change."

102. Note that the 5-8 teachers are ALSO supposed to have studied the
mathematics studied by the K-4 teachers [plus some additional material], and
that the 9-12 teachers are supposed to have ALSO studied the mathematics
studied by the K-8 teachers [plus some additional material]. Does this
really happen in practice?

103. Do your K-4 teachers take AT LEAST NINE semester hours of content
mathematics in college? Do your 5-8 teachers take at least FIFTEEN
semester hours of content mathematics in college? Do these math courses
really assume as a prerequisite FOUR years of MATHEMATICS

104. In vignette 2.2, one of the tools discussed is technology such as
the use of computers in geometry [probably the reference is to something
like Sketchpad]. Something encouraged is its use in open-ended
exploration and discovery. But the authors say "At times, many teachers
have felt their own knowledge of geometry inadequate to deal with
questions and conjectures that arise from open-ended explorations." Is
this true in your experience? How can this be overcome?

Well, for the first day back after Thanksgiving, that's enough, don't you
think? Please feel free to respond to the listserv on any one of these
items--you need not reply to them all. Or ask a different question
related to this particular standard. As usual, our purpose is to
encourage the subscribers to work their way thru the Professional
Standards, and to offer a forum for discussion.

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