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 email@example.com
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 :)