Date: Jul 20, 1995 12:39 PM Author: LPETERSON@bnk1.bnkst.edu Subject: Better math teachers:Long post I recently posted a reply to Clara Einfeldt's comments on the need to teach

college math courses in a manner consistent with the Standards so that

teachers become constructivist learners as well as constructivist teachers.

I was very pleased that I received many letters through personal e-mail that

indicated that more of a dialogue on this matter would be helpful. Rather

than try to answer them all individually, which I truly cannot find the time

to do (I am teaching the July summer session courses which are a bit

time-intensive), I would like to thank everyone who sent me e-mail and

acknowledge the questions in the letters by commenting a bit further.

I think of myself as a teacher, having been in the classroom for more than

30 years--both as an elementary teacher and later as a high school math

teacher. My degree is in mathematics, very traditionally taught, and I

worked in engineering before becoming a teacher. Now I work with teachers

in our graduate program in Math Leadership and visit teachers in their

classrooms and also teach Math for Teachers courses at the college. I do

not have a doctorate. I still am *just a teacher*. That has been, and

still is, my raison d'etre.

The course I talked about is not a course of Math for Teachers or how to

teach math to children. My students still have to take that course.

Topics in Math is a course for my students to learn math for themselves- as

adults. While there is some overlap in the goals of the Math for Teachers

and the Topics in Math, the emphasis is quite different. We don't talk

about teaching issues. We talk only about math. When I said I emphasized

definition, algorithm and all those traditional sounding mathy ideas, I mean

that I try to give them the experience of what it is to define a

mathematical term with just the right amount of information--not too much,

not too little. I try to give them the chance to build an algorithm for

themselves so they can see what the role of algorithm is in mathematics. In

one of my classes this semester the students discussed the differences

between an algorithm and a formula. The discussion came from them. That's

important I feel. I didn't have written in my course description two months

before I met my students that on day such and such we will discuss the

difference between an algorithm and a formula. I feel really strongly that

timing is crucial. The time to discuss an idea is when it comes up from the

students. I guess this comes from my elementary experience. They also

discover patterns and express them as functions--Tower of Hanoi type of

experiences.

This course is 3 and 1/2 hours per session twice a week for the month of

July. The sessions are mostly cooperative learning. Some students are

nervous at first working with any one else. They don't want to appear

stupid and are easily discouraged if someone else is perceived as "catching

on" faster than they are. So there is a flexibility allowed for going in

and out of group work at will--as the need dictates. As trust builds, that

seems to change. There is sharing at the end of each session as we

celebrate what we have learned and that is different for different people.

Everyone doesn't learn the same thing on the same night. But we hear each

other and stimulate each other to go on in different directions. One

person's findings encourage another person to go on in a similar direction.

I guess this makes me nervous too, as I mentioned in my earlier post. The

idea of everyone learning the same thing in the same way at the same time is

so deeply embedded in me that I somehow have to deal with the guilts of not

providing that kind of experience for them---EVEN THOUGH I REALLY BELIEVE

that math is not learned in that factory oriented manner. It's hard to

shake those demons from the past.

The first night of this course is the hardest for me. I put out about 30

activity cards that are related in some way to triangles. They use

materials, problems, geometry, number...Sierpinski is in there too.

Geoboards to see what happens to the area when you double the height of a

triangle, the base, both. Problems like how can you divide a triangle in

half so that each half has the same area. Geo-sticks to investigate the

relationships of the lengths of the sides of triangles, piles of triangles

to categorize as they see fit, triangles made of foamcore to try to find the

point at which they will balance on the point of a pencil and why, distance

across the river problems, heights of trees, patterns of triangular numbers,

Pascal's triangle. triangles to tessellate, How many degrees in the

angles--in the exterior angles...I watch as the students select activities

and begin to engage with each other. Later as a group they define a

triangle. They bring up many old theorems from hs geometry that they want

to check out. From this opening experience I learn alot about each student

(they also write a personal math biography) as I watch and interact with

them. So far, students have been able to find something to get interested

in. It starts the ball rolling. Lots of words come up, lots of questions

about their understandings of this common shape...Ican do alot of one on

one interactions and teaching.

My goal in this course is to give them a math learning experience that

empowers them as adults to learn math, to continue being interested in

learning more math and dissipating some of the phobic behavior associated

with math, to see the need for math literacy in the healthy functioning of

our society. I don't want them to need handholding for learning math in the

future.

Lucille Peterson

Lucille L. Peterson

Math Leadership Program

Bank Street Graduate School of Education Tel: 212-875-4665

610 West 112th Street Fax: 212-875-4753

New York, NY 10025 E-mail: lpeterson@bnk1.bnkst.edu