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 email@example.com
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 FOR COLLEGE-INTENDING students?
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.