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.