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Topic: Professional Standards III (10/6)
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Ronald A Ward

Posts: 298
Registered: 12/4/04
Professional Standards III (10/6)
Posted: Oct 6, 1995 6:19 PM
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Here is the third in the series of questions, comments, concerns, and
issues related to NCTM's 1991 "Professional Standards for Teaching
Mathematics." The focus this week will be on pages 34-54, Standards 2-4
on Discourse. [If you missed the posting on either 9/22 or 9/29, let me
know personally, and I will send you a copy]. Because all questions in the
entire series will be numbered consecutively, I will start today with # 19.

Ron Ward/Western Washington U/Bellingham, WA 98225
ronaward@henson.cc.wwu.edu

19. In the statement "Discourse is both the way ideas are exchanged and
what the ideas entail," does the inclusion of the second phrase sound
novel to you? Do you think of discourse as "what the ideas entail"? In
what way? I found it a useful exercise, as I read thru the three related
standards, to note every illustration of this phrase.

20. There are any number of really good questions in this material,
whose answers would be beneficial to us all, I think. Here are just a few:
a. What makes something true or reasonable in mathematics?
b. How do we figure out whether or not something "makes sense"?
c. Why is it so important for classroom discourse to be founded
on mathematical evidence?

21. There is a statement here which ties this commentary to an earlier
question [# 3] about mathematical communities: "When students make public
conjectures and reason with others about mathematics, ideas and knowledge
are developed collaboratively, revealing mathematics as constructed by
human beings within an intellectual community." Perhaps some of you
could share how you develop your classroom into such a community.

22. Standard 2: "The Teacher's Role in Discourse" lists a number of
skills that teachers must possess. I was particularly struck by the
number of critical decisions that teachers must be able to make "on the
spot"--How do teachers learn to do this? What kind of knowledge must
they have to make the right decisions?

23. It seems to me that many experienced teachers will find it difficult
to break some old habits;e.g., following a student statement with "Why?"
only if the statement is wrong, or endorsing or dismissing student
suggestions. What other habits must be broken in order to embrace the
vision of teacher's role presented here?

24. The authors correctly point out that some students, "particularly
those who have been successful in more traditional mathematics
classrooms, may be resistent to talking, writing, and reasoning together
about mathematics." How do you overcome such resistance?

25. This standard identifies at least three aspects of the teacher's
role [to provoke students' reasoning about mathematics;to encourage and
expect students to do virtually all the talking, modeling, and explaining
themselves;and to monitor and organize students' participation]. I
believe it would be helpful for teachers to share their techniques for
addressing these aspects.

26. Now, as a teacher who resists "covering ground," and who tends to
move rather slowly thru material, milking it for all it's worth, I hate
myself for even asking this next question: Doesn't it seem that taking
the approaches suggested here will drastically reduce the amount of material
that will be learned? Isn't there a point where the "less is more" idea
really does translate into too little?

27. When you think about ways that students can contribute to the
classroom discourse, other than by talking or writing, what comes to mind?

28. When there is an emphasis on students "constructing" their own
understanding, when a teacher remains neutral about the correctness of
what is being said, is there a danger that kids will construct incorrect
concepts? Have to subsequently unlearn an incorrect procedure?

29. As usual, I encourage readers to react to the four vignettes
included in this standard.

30. One of the things I noticed as I read the vignettes, is that there
are several places where some form of assessment is occurring. I would
certainly invite readers to comment on any of these in light of the 1995
Assessment Standards;however, I will refrain from posing related
questions myself since it is challenging enough just to get subscribers
to read one of these documents, much less two or three at once! :)

31. Standard 3: "Student's Role in Discourse" makes it quite clear that
students have a responsibility in the classroom. But do they accept it?
If not, how can you as a teacher encourage it?

32. It would be worthwhile, I think, to take any one of the bulleted
responsibilities (skills) required of students and discuss it. For
example, one statement mentions a "variety of tools" that students should use
to reason, make connections, solve problems, and communicate. They don't
initially identify any of these, so you might ask yourself what "tools"
are appropriate for this purpose. Later, as you read the various
vignettes, you will encounter a number of them, but they are not labeled
as such. [You can find a pretty complete checklist, though, when you get
to Standard 4 :) ]

33. There are three more vignettes in this standard to which I invite
reader reaction. I was particularly struck by illustrations
of the teacher's role as a "facilitator" of learning. What are the
hallmarks of a good facilitator?

34. Standard 4: "Tools for Enhancing Discourse" presents a rather
extensive list of tools for student use. It occurred to me that it would
be helpful to have some way of continuously reminding students of all the
tools to which they have access. Any suggestions? Visual possibilities?

35. Once again, please feel free to react to the vignettes in this
standard. I will just say that as I have read thru all the vignettes up
to this point, I have occassionally found mathematical errors. I am
assuming that these should be fairly apparent to the readership and am
not pointing them out. But you should read carefully!

Well, that's it for another Friday. Once again, I have received
several responses directly to me that were not posted to the listserv.
At the end of the first set of standards, I will summarize all of these.
But I also note that individuals are now starting more focused
discussions centered around specific items mentioned in these standards.
For example, Jason Sustarsic's "Model Teacher" heading touches on a
question raised back in Question 2: Do teachers teach as they were taught
or as they were taught to teach? Ted Panitz has introduced a discussion
related to "Getting Students to take Responsibility." This extends
nicely the question in Question 4 about getting students to take charge
of their own learning. And it dovetails beautifully with the current
issue raised in Question 31. So I encourage others among you to select
issues which interest you and participate similarly. It is my feeling
that we can benefit greatly from the real-life experiences of the
teachers on this listserv to augment, supplement, and complement the
written material in the Professional Standards.








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