# Math for freshmen who want to do extra – What did we do? What are they doing?

Some freshmen liked my mathematical digressions, and wished out loud we could work on them instead of regular math. And we ended up with a one period/week math – hmm – not club, really class – where kids could pick their subject, and I would guide them. And instead of a half dozen kids, two dozen signed up, with a range of skills.

No one, on the first day, knew where to start. I told them that they would pick a topic, they would team up or decide to stay individual, I would provide resources, and they would work on that topic until they decided to stop. At that point they would have to submit something in writing to show me what they had done, and they would also make a short presentation to the class.

But it was meaningless until I got the gears moving.

So the first classes I taught them to count in base 4. Then to add. Subtract (ouch ouch!). Multiply. Then I used slightly watered down modular arithmetic to “clearly demonstrate how our rule for divisibility by 9 works” (that was a proof they watched, and semi-participated in). And then I nudged them. And if they could not find something that appealed, they could kill a few days on base 6, or base 8, or maybe extending base 4 beyond the decimal point….

And now we are a few weeks in, here’s what they are attacking:

- Predicate Logic (with quantifiers) Two groups of two, reading a text, and doing exercises. One will continue, one is ready to move on.
- Pascal’s triangle. One kid, playing with patterns.
- GCDs. A group of three playing with, understanding, applying Euclid’s Algorithm. They are done, and ready for something new.
- Modular arithmetic. A group of three trying to understand how to solve equations involving congruence classes Mod Z. They will present what they have, and then decide whether to continue, or to turn to something new.
- A group of four playing with base 6 arithmetic. They are using long division to transition to decimals. Not done yet.
- Three boys had their fancy caught by “derangements” – they are doing background work on permutations, building up to their desired goal. Not there yet.
- Prime number conjectures. One boy played with Goldbach and a few others. He is ready to present, then try something else.
- There is a girl trying another base (8?) on her own.
- There is a girl playing with Fibonacci and nature. It looks like she has made good use of more of a variety of resources .

Amazing? No. But very good. Walk in on any given Tuesday, and you’d see a small class (22) of freshmen, quietly, and without pressure, reading and discussing math that for them is novel. But I wish I saw more things like this…

What next? Presentations start April 9, as some students move on to new topics. I’ll look over their submissions. And I think we will try to arrange a trip to the Museum of the Mathematics when the weathers nicens.

Is it great fun for you? (Or do you sometimes feel lost, with nothing to do?) Or…?

It is great fun. I float, impromptu conferences, formal conferences. Show me what you figured out. Can you make up an example? Do you have questions? Do you want to keep going with this, or switch to something new?

I have slowed a few down. Suggested some shifts. But mostly, I get to watch kids learn stuff that they would not normally learn, because I suggested it, and made the space for them. This self-selected group is quiet and focused, and would not have come to teach themselves these things without me setting it up. And so even when I am not helping, I take pleasure and pride in watching.

Looks like your students are exhibiting good mathematical taste :). (Though I always worry with Fibonacci and nature — there’s a lot of beautiful Fibonacci math, but the connections to other areas can be pretty dubious, and there are a lot of garbage sources on this topic.) Looking forward to hearing more!

This sounds really neat! Do you think you would do anything differently if you were to do this again? And how much does it take to set something like this up (e.g. choosing and getting books)? I think it’s amazing that you had such motivated students.

I mentioned it to two classes, determined, with ten expressing interest, that I would safely have more than five. Mentioned it as a possibility to principal, got a tentative ok. Came here and on facebook, took suggestions, bought some of the books, thought through more ideas. In January I actually pitched it to kids, and got some almost-commitments – more than I expected. And class started in February. I’d say it was about two months putting it together (but not a lot of work).

I wouldn’t change much. I think I’d need to see it run for two or three terms before I would tinker. The Museum of Mathematics didn’t work, but given their unapologetically abysmal communications, I’ll just drop that idea. Permanently.

I’ve got ideas for a “student math conference” – but not sure that it should tie into this.

And I’d like to see our freshmen and sophomores, who don’t have elective room in their schedules, get more options like this, not just math, for lunchtime “selectives” or whatever. Some kids really got to dig at interesting stuff.

I also like that in some cases quiet kids and their friends got to be quiet friends together, away from the noisy cafe. Math was quiet socialization. Maybe it could have been poetry or knitting or astronomy, but I helped make them a nice space.

Makes me think of the book Math Girls.