I have just had a highly educational trip. Not only did I survive several days in a city where walk signs are advisory and the honking of horns is mandatory, but I found out a lot about what strikes me as a highly impressive education program for elementary teachers. The occasion was a visit with Ros Tischler Welchman, whom I met first at a meeting of PME (= Psychology of Mathematics Education) and subsequently at two meetings of MER (= Mathematicians and Educational Reform.) This is called networking, no? Ros is on the faculty of Brooklyn College and has written quite a number of books for the use of elementary school teachers and/or those who teach them. Currently she is also experiencing the joys of assistant deanship--I arrived to find her in the throes of deciding whether it was worthwhile moving around the walls in a conference hall and left her dealing with the doorknob which had fallen off the inside of the faculty lounge door (the last person in before Thanksgiving vacation just may still be in there.) In between, I found out about lots of things. Most spectacular was their elementary education major, which has a requirement of 25 credits of mathematics and a similar number of credits in mathematics education. Furthermore, within the mathematics courses links are built with education by tactics like having the data for study in the statistics course be those gathered in an elementary classroom by a student working on a Masters in Elementary Education. Mind you (a little reality check here) the links don't always work out--among other things they are dealing with a constant flow of adjunct faculty in the math department-- but the existence of the theory carries in itself a huge message. Students who complete the degree get a provisional teaching certificate, with which they can teach for up to six years while completing a masters degree (which explains the scheduling of the graduate classes--though even at that my mind boggled at one that meets from 9 to 11 PM!)

I suspect that by this time a number of you are thinking "Er...what do we require?" Well, we do not have an undergraduate program which provides certification, provisional or un-. The Teacher Education Program, which is in the College of Education, is a graduate program and requires its applicants to have completed a degree with a regular Arts and Science major. That has some definite virtues in terms of breadth of background. The downside is that a humanities major requires darned little in the way of math and science, and the College of Education is limited in how much more it can realistically hold out for. One thing it does explicitly require is Math 170 (Mathematics for Elementary School Teachers), which is why I consider that course to be colossally important.

Back to Ros: the other area where we exchanged information (and here I managed not to be exclusively on the receiving end) was NSF Grants. Ros is a PI for an Urban Systemic Initiative which is just getting up and running. Theirs focuses on Excellence in Teacher Preparation while ours (assuming we are funded!) will help us to work with in-service teachers, but the benefits of exchanging information are clear.

And that brings me cleverly up to the next topic, which has been gathering dust for an alarming length of time: a synopsis of the last couple of Brown Bags. The first was a report on the NSF proposal Ramesh Gangolli and I, together with Jack Beal from the College of Education , Gini Stimson from Mercer Island High School, and Rosemary Sheffield from Extension, submitted in September. If our proposal is accepted, all manner of interesting possibilities will open up for us--and that "us" refers to both ends of these e-waves. We are hoping to run a five year project building a community of mathematics learners which includes kindergarten teachers, us, and many people in between from each of five local school districts. Teachers will participate in summer workshops two or three weeks long, with several one or two day follow-up workshops during the school year. They will go through these in cohorts, with each district's cohort members to include teachers from kindergarten through 12th grade in a single feeder pattern (if possible) so as to increase their connection with each other and the coherence of their students' experience. As a lead-in, we ran a one week pilot workshop last summer, which was a blast. The follow-up to that workshop is coming up this Saturday--if you'd like to be part of it, let Ramesh or me know! Meanwhile, in terms of the proposal itself crossed fingers, charms, incantations and anything else you suspect might be helpful will be gratefully accepted.

A thumbnail version of the remaining Brown Bag: Fred Holt took on the subject of graphing calculators, and in particular their role in teaching. Since I have maintained a state of almost total ignorance on the subject, I started in on a really steep learning curve. Eventually, however, it (or I) crashed, which strikes me as illustrating one of the hazards of the field. I did not, however, crash so hard that I failed to enjoy the discussion Fred led on the calculator's merits (with grundgy computations cleared away, a student can focus far better on the conceptual content of a problem; with no need to worry about keeping computations easy, a teacher is far freer in choice of examples and problems) and dangers (how do you deal with differences in level of sophistication of the students' equipment? how much time should you allocate to teaching the students calculator technique?) Many interesting points arose, but (needless to say) without any overall solutions.

I shall finish with a Teaching Tidbit that turned up in the course of that discussion. It arose from the question of how to tell students working with calculators just how much they need to put on paper, but it applies across the board: tell them to write enough so that a bright classmate who knows as much as they do BUT NO MORE would be able to follow their reasoning. I think that's neat!

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