# Math for freshmen who want to do extra (status report)

I have an extra class, one period each week, totally voluntary, for freshmen who want to do extra math. I solicited your input on how to start it, and wanted to provide an update.

Here is the background:

This year I am teaching all of our freshmen – half in two sections of algebra, and half in two sections of… hmm… we started the year by finishing algebra, really redoing the second half, but at depth, and have now moved on towards algebra.

A word about my teaching. I go off topic. In many directions. Usually once each period (it provides a planned break, a chance to refocus. The kids just think I am a little scattered. Most of them never realize why it is so easy to move me off topic once, and so hard to do it a second time in the same period. No problem.)

I also will stall a class to look at something interesting that’s shown up in the math. Especially in those advanced classes, where we are often reviewing material they have seen before, going for mastery, going for depth, it is easy to justify taking extra time on an unexpected question. I started the year by asking if all odd perfect squares had a remainder of 1 when divided by 4. But it was in November that Noah, looking at the unexceptional parallel lines y = x + 2 and y = x + 3, and hearing a classmate say that the distance between parallel lines is constant, wanted to know what that distance was. (Try it yourself, they are not one unit apart).

Out of the parallel lines discussion came the suggestion that some kids would really like a math team. Or a math club. I polled them a few times over the next few weeks – I am reluctant to commit to afterschool activities – would they do it on one of their lunch periods (one of my preps), and consistently five or six from that class said yes.

In January I asked the other advanced class. Only one clear yes, but half a dozen maybes. I was envisioning 6 – 10 kids. I ran it by the principal (trading a one-period/week elective for this freshman math thing). He was good. I thought hard, and ran it by one regular class. A lot of interest, but only 2 or 3 who looked likely. And as it looked like it would become a reality, I ran it by the last class.

They were going to have to eat lunch in a math classroom, away from their friends. I thought to send home a permission slip (to keep it down to the more serious). Little did I expect to receive signed consent/request forms from 20 freshmen out of a class of 100, with a few more forgetting the forms but begging to be allowed to submit them late (of course). It’s more boys than girls, but not lop-sided, and a mix from all four classes.

Next: Materials and the opening weeks

Last (for now): What the students have chosen as their first study projects

>I also will stall a class to look at something interesting that’s shown up in the math.

Yeah! Today in precalc, I wondered (as I have before) what a factor of x^2+1 does to the graph of a degree 6 polynomial that it’s part of. Some day I’ll play with that enough to really see it.

Also today, I found a really cool bit of symmetry in a problem we were working on. (“No class, you don’t have to do this part.”) It was (after we used synthetic division to find factors) y=(x-1)(x+2)(x^2+x-1), with x-intercepts at 1,-2, and -1+or- sqrt(5)/2 (about 0.6, -1,6). I noticed that the roots came in pairs, and figured the y-value at -1 would be the same as the y-value at 0 if there were symmetry. Those values were the same. (!) So I knew the graph was symmetrical across x= -1/2. I found it delightful. My students, not so much.

But some days I see a few eyes light up when I’m sharing my math enthusiasms. So I keep it up.