Sometimes a look backwards can produce interesting insights. Cogitating on the two major chunks of content for this newsletter got me thinking about the context in which I began writing these newsletters -- thirteen years ago already! I did it because I felt research mathematicians were being overprotected to the point of missing out on some really interesting stuff. There is no question that a certain amount of shielding is essential to the maintaining of a clear space for deep thinking, but around that shielding had grown a culture of shutting out many interesting and relevant things that carried no risk of soaking up great dollops of time. I suspected that a number of my colleagues -- faculty members and graduate students both -- would enjoy learning about them, and it turned out I was right.
That was then. Since that time both the local and the national scene have undergone some major changes. On the local front, efforts to collaborate with community colleges and reach out to the K-12 systems have steadily increased and have taken many forms. One is the first of my aforementioned chunks of content:
As I have worked with high school teachers over the past decade and a half, one theme that was guaranteed to recur was the dread Math Placement Test. While giving my (generally inadequate) responses to their questions, I arrived gradually at the realization that the real question was "What do youall need my students to know?", with the Placement Test being the language in which the answer was read. With the institution of the 10th grade WASL test, the question took on a whole new set of layers, including an assumption on the part of many students that succeeding with what was designed to represent the bare mathematical necessities for high school graduation constitutes college readiness. Fortunately, this caught the attention of many, including the Gates Foundation, and the Transition Math Project was born. I wrote about its early phases in Newsletter 121 . Since then it has published the College Readiness Standards (you can find them at http://www.transitionmathproject.org/) and begun a campaign to get them into not just the hands but the minds of teachers and parents and students throughout the state. This winter a new player entered the scene: the state legislature decreed that a placement test was to be put in place that would be used by all of the state's universities and community colleges, and that furthermore a version of that test was to be made available to all juniors at all public high schools by autumn of 2008. The Office of Educational Assessment at UW went into instant high gear and convened a bunch of mathematics folks from universities, community colleges and K-12 schools all over the state to address this task. We have so far met twice and I think we have made pretty respectable progress. Characteristically for such a meeting (for a good one, anyway), while I enjoyed the progress, I enjoyed the discussion even more. One complicating factor had a consequence that nicely offsets a major concern of mine: with my eye on the scene I know best, I have been seeing the placement test as something to distinguish whether a student is ready for calculus, precalculus or neither. Given my personal view that calculus is the Godzilla that has stomped the Bambi of lots of really nice general mathematics out of the college and high school curricula, I was concerned that the new placement test and its planned use might push that trend yet farther. As it turns out, the community colleges and at least some of the other universities offer a considerable array of entry level mathematics courses not geared to calculus. It's hard to give a really nuanced message with a 50 minute multiple choice test, but at least we won't be conveying the information that all that statistics, geometry, probability, etc. is a waste of time in the view of colleges and universities.
That was one of my chunks of news. The other provides evidence that the broadening of the horizons of research mathematicians is not just a local phenomenon. The Mathematical Sciences Research Institute (MSRI), which is the West Coast version of Princeton's Institute for Advanced Studies, albeit a trifle younger, decided a few years ago that it needed to be making a contribution to mathematics education. The contribution took the form of annual conferences on Critical Issues in Education, organized and run by a number of the major players in the field. This year's was on Teaching Teachers Mathematics, and for the first time I got there. As I expected, it was exciting. Plenary sessions addressed a range of relevant issues, from the need for a coherent vision on how we educate teachers to a study on very specific aspects of the requirements and course offerings in two particular states. They also included examples of a number of things people are doing that enrich their teaching, such as a couple of partnerships between university and K-12 faculty members in teaching courses for future teachers. Parallel sessions at other times presented a wide variety of programs and experiments and ideas, some of them novel and inspiring and others comfortably close to being familiar. By the end I was afraid that I had taken so much on board that I might never be able to retrieve any of it, but I find a fair amount did stick with me.
One final benefit of the conference came as a sort of post script. It needs a little background: in the two courses the mathematics department teaches for future elementary school teachers I have been having some reservations about the textbooks for one and completely unable to find a textbook I could use for the other. Consequently when I read in the MER Newsletter last spring of some course materials developed by an outstanding bunch of folks at San Diego State University and covering exactly what I wanted to cover, I hastened to have a look. As it turned out, they were just in the process of turning the materials over to a publisher. The upshot was that we got to field test both modules by downloading various PDF files. There were references to video-clips on "the accompanying CD" but I figured they were not yet available. At the MSRI conference one of the parallel sessions was by Judith Sowder, a lead author on the series in question, describing the books and various of their features. One thing she emphasized was the importance of the video clips. After the talk I asked her how to get them, and she very kindly sent me a CD the following week. The second one I watched had me practically jumping out of my seat, because it crystalizes perfectly something I have been trying for years to articulate. Again some background: one of the single most polarizing issues in the current debate on mathematics education is that of algorithms. At the extreme of one camp we have the folks who maintain that since algorithms have been honed by centuries of mathematicians, children shouldn't have to mess with inefficiency, but should rather be given the directions for using the algorithms and lots of practice using them. At the other extreme we have the folks who say that the use of standard algorithms interferes with a child's understanding of the mathematical context and they should never even turn up in the classroom. By and large, anybody in one camp tends to assume that everyone in the other camp espouses that camp's most extreme position, which is the polarization factor. Me, I am a notch short of the never-let-an-algorithm-cross-the-threshold stance, but very firmly feel that spending the time to develop their understanding first is neither a luxury nor an addition to the total length of time needed to get children making fluent use of some good algorithm, which may well be one of the standard ones. The video clip in question illustrates why. It consists of two interviews with a fifth grade teacher and one of her students, the first one after, at the request of the researchers, the teacher taught a lesson on fractions by adhering strictly to a traditional teacher's manual, and the second some weeks later after she re-taught it by her accustomed inquiry tactics. It can be found by going to http://sdmp-server.sdsu.edu/nickerson and clicking on the second clip (Rachel).
I'm not going to risk an anti-climax by attempting to follow up after Rachel!