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Topic: Professional Standards II (9/29)
Replies: 1   Last Post: Oct 7, 1995 7:46 PM

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Ronald A Ward

Posts: 298
Registered: 12/4/04
Professional Standards II (9/29)
Posted: Sep 29, 1995 9:47 AM
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Here is the second set of questions, issues, concerns about the NCTM's
1991 publication "Professional Standards for Teaching Mathematics."
[Please note that this is a different document from the 1989 "Curriculum
and Evaluation Standards."] This week's focus is on pages 19-32.
Because all items in this series are numbered consecutively for future
reference, I'll begin with #8. [If you missed the first set, those
questions were posted last Friday (9/22), but I will be happy to forward
them to individuals upon request]

Ron Ward/Western Washington U/Bellingham, WA 98225

8. What does it mean to be "mathematically literate"? Does this differ
from having "mathematical power"? Although a partial definition is given
on page 19, you might want to compare that to the discussion of literacy
in the MSEB's "Everybody Counts."

9. What do you see as the connection or relation between the 1989 C&E
Standards and the 1991 Professional Standards?

10. Although there are six standards in the initial section of the
document, they are grouped under four major arenas of teachers' work.
Some of these have familiar rings to them (e.g., tasks or environment).
But "discourse" may sound new to many readers. What does it mean, e.g.,
to say that the classroom discourse "embeds fundamental values about
knowledge and authority"?

11. Because analysis requires "systematic reflection" by teachers, do you
have a time set aside for such reflection? Is there an opportunity for
you to share your thoughts with other teachers?

12. The authors say that professional standards for mathematics teaching
should "represent values about what contributes to good practice without
prescribing it. Such standards should offer a vision, not a recipe."
Why do you think they say this?

13. How do you foster in students "the disposition to use and engage in
mathematics"? An "appreciation of its beauty and utility"? A "tolerance
for getting stuck or sidetracked"?

14. If you have any question about the complexity of teaching, read
Assumption 4 on page 22! [It is also related to question 12 above :) ]

15. Standard 1: Worthwhile Mathematical Tasks lists a super collection of
criteria. How would you ensure that all these are being met as you
select or create tasks throughout the year? A checklist? A Kaplan-style
matrix? Please share your ideas. It is also worth reflecting on each
criterion separately. For example, what does it mean to "engage students'
intellect"? How do you know if you've done that? Also please feel free
to choose any one of these criteria from page 25 and share your views on it.

16. Where do you personally get your best tasks? Do you create them? Do
they grow out of your students' conjectures or questions? Do you find
them in resource materials? The authors correctly point out the wide
range of materials available, but do you think most teachers are aware of
them? If so, do they have ready access to them?

17. On pages 26-27, the authors discuss some considerations regarding the
mathematical content of a task, the students performing the task, and the
ways in which those students learn mathematics. Although there are many
questions that could be raised, I'll ask just a few: How do you
personally use the history of mathematics to foster students' sense that
mathematics "is a changing and evolving domain, one in which ideas grow
and develop over time and to which many cultural groups have
contributed"? Are you able to "create contexts that foster skill
development even as students engage in problem solving and reasoning"?
[This reminded me of the Bob Wirtz CDA materials on drill and practice at
the problem-solving level, which I still find useful with my students]
How well do you really know your students? Do you consider their
interests as you develop or select tasks? Do you find yourself taking
into account what you know generally about students from "psychological,
cultural, sociological, and political perspectives" as you select tasks?
How are teachers' understandings about how students learn mathematics
"informed by research"? Do you read "Research Within Reach"? "What We
Know About Mathematics Teaching and Learning"? Other suggestions?

18. There are three vignettes on pages 28-32. As usual, please react to
any of these.

Well, I think that's enough for this week. I invite you to share with
the listserv your comments concerning any of these items, or to raise
additional questions, concerns, issues about this material. Last week,
although I received several private communiques, there were only a couple
of public postings. You need not wait until you have something to say
about all the items--just respond to whatever interests you. I know it
takes time to read the material first, but that's one of the objectives
of this discussion series. Cheers :)

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