A little over a year ago, someone on Living Math Forum asked for advice. She wanted to start a math circle. I was in a hurry, and gave her some quick thoughts. Here are her questions and my replies:
Rodi wrote: Some homeschool families in our community are hoping to start a math club, or even a math circle. I was hoping that some of you with experience could help with some start-up advice, such as:We did end up talking on the phone, and Rodi decided to attend the Math Circle Institute. I didn't find out until recently that one of her cohorts at Talking Stick Learning Center had already urged her to attend it, having just heard Bob & Ellen Kaplan being interviewed on NPR - talking about their math circles and their philosophy.
1. What's the widest age spread a math club or circle can handle? (We have kids from 6-13 right now who might be interested.)
Your format will determine how wide an age and skill-level spread you can handle.
2. Can someone lead a math circle without formal training and have it still be great? (More than anything, we don't want an unsuccessful attempt to turn kids off to math)
Definitely. Collect some good math materials and let kids browse, if you want to see what they find enticing. (I recommend Polydrons, Set, Blink, Blokus, pentominoes, tangrams, graph paper, Math Without Words, by James Tanton, ...)
3. Are there any math clubs or circles we could visit within reasonable driving distance from Philadelphia?
Penn State seems to have one. (I found it here.)
4. What training do you recommend (formal or informal), and how would we access that?
Second week of July, Math Circle Institute. It's fabulous. I went 3 years in a row. It's at Notre Dame.
5. What kind of support is out there in terms of finding topics to cover with the kids?
Lots. I can point you to bunches this weekend if you don't get enough pointers here. Start with joining the NaturalMath google group that Maria Droujkova runs, to watch what she does in her NC group. Follow my blog, Math Mama Writes, for ideas, although I blog about other math stuff too. Follow Math for Love - Dan's doing great work in the Seattle area. There's also a free book online called Circle in a Box. You are welcome to email me (suevanhattum on hotmail) for more ideas, and I'd be happy to talk on the phone with you.
Rodi knew exactly what she wanted. She figured she could learn the math anywhere. What she wanted was to figure out how Bob & Ellen did their magic. So she took copious notes whenever Bob was presenting. (She didn't get as many chances to see Ellen in action.) She and Bob have graciously allowed me to share those here. Think of this as ways to lead without giving away too much.
Bits of Bob
(collected during the math circles held at the 2011 Math Circle Institute)
Imagine that an "accessible mystery" has been posed - an intriguing math problem that will have the participants scratching their heads for the next hour. Bob is up front, but eager to disappear. Here are a few things he said last summer in service to that goal:
- By the the way, “obviously” means “I don’t know what the heck I’m talking about.”
- I’m going to put something on the board. Raise your hand but don’t say anything if you recognize the pattern.
- When we said “the pattern” we made a mistake; we should have said “a pattern.”
- Most of math is unknown – like a big piece of cheese and we’re a little mouse nibbling at it.
- What a good way to put it!
- I don’t know, I’m just the secretary.
- Math is freedom. ... I don’t know.
- Let’s play function machines. What sound do you want it to make?
- (If kids want to do their own function machine) Do you have a rule in mind? Can you handle all the numbers they might give you? (“I guess the machine needs oiling” if something doesn’t work out.)
- (If kids don’t get it, give hints, rearrange inputs, if necessary, deform the machine.) What do you think is going on with the machine?
- Do you see….
- Why is/are….
- What an interesting idea. Why?
- That’s great, but are you really sure about that? Is 19 really less than 18?
- Sounds good, sounds right, it could work with this, but how could you convince a martian or a skeptic….
- Always simplify to something your intuition can glom onto.
- Math is an art – the art of choosing the best… (i.e. circle of inversion in inversive geometry)
- Can we make this simpler?
- This may not work, but it might!
- (“I’m confused” said someone) I sympathize.
- I have a terrible memory for these things so I’m going to put them on the board.
- Take a wild guess: 17? 3 1/2?
- That’s a good point.
- That’s a good thing you’re doing.
- Hey, that’s terrific!
- I’m bothered that this is an odd number.
- This is great thinking, by the way.
- What would a harder problem be?
- Are they the same? Anyone think no?
- Take a risk. You can guess or take a risk and be wrong. Sometimes it’s fun to be wrong.
- I’m getting confused – we have too many examples up here.
- S, what’s your guess, same or different? (to girl not participating)
- That’s a good clarification – thanks. (to a question)
- I’m in complete doubt – let’s do it out.
- Guesses about the answer? I’ll guess 204.
- That’s an interesting discovery: you can’t have….
- Yes! Terrific!
- I’m convinced we’ve done everything we can with….
- I’m not convinced….
- Wait, can I just check?
- Wait, you’re going too fast for me.
- What do you think?
- What’s a way to be systematic in exploring this?
- That is great work since it just got so much harder.
- Exactly. Give us the argument again. Why?
- I have a feeling that gamblers know this kind of thing. Why would they?
- I’ve got a weird question. What if you had?
- You’ve found an economical way of thinking about it?
- Oh, nice idea.
- Why? I’m sure you’re right, I just don’t see it.
- 12 and 24 are both in the same family, so they’re both good guesses.
- I’m not sure I understand why….. I get it.
- (time’s up) You’ve done an incredible amount. I think leaving it with thinking about…. Email us with what you get.
- This is puzzling to me. What’s the area under here? Figure it out and email me. (to student after class, wanting more challenge)
- That’s not the game we’re playing here.
- You may be right, but that isn’t really interesting. What’s interesting is that we’re working together. The problem is what’s important.
- Intellectual activity isn’t a competitive sport.
- That’s probably what many others are thinking, but it’s not important.
- Math is an art, not a sport.
- I want to hear a new voice this time.
- Wait wait wait, first what do YOU think. ('wait's to boy dominating, rest to the others)
Talking Stick Learning Center
I found out about this wonderful collection of quotes when I asked Rodi if I could interview her about her experience. She went from asking generic math circle advice to running an amazing math circle and blogging about it, all within well under a year. I love her reports about her math circle, and how she integrated her "mindfulness practices" into her math circle.
Rodi's concept of how a math circle begins, as she learned about them from Bob, Ellen, and Amanda:
- Ask an interesting question.
- Throw out the history behind it.
- Bring in other aspects of life that are related.
Some kids were getting distractingly physical with some of the math manipulatives on the table, so we engaged in an attention- focusing activity: the Bobble-Head doll.And this, from two weeks later:
The Bobble-Head doll (who is “a distant relative of the man who owns the zoo”) sat in the middle of the table. I tapped his head, which is on a spring, and told the kids that they had to watch until it stopped moving, then put their own heads down. The doll never stopped; with every fidget (and possibly truck passing outside) the bobbling/vibrations increased. At this point, attentions were sharpened, and we decided to put him away and try him on the floor next time. I told the kids that the doll is somehow related to math, and with that, we were ready to return to our story.
Enjoy more of her math circle reports at her Talking Stick Learning Center math circle blog. (Talking Stick is a learning center for homeschoolers, offering a number of different classes. Rodi's math circles are only one part of their offerings.)“Something is in the air today,” said Talking Stick co-director Angie. The kids came in brimming with energy, and most came early. As we waited for the last child to arrive (still early), four of the kids were at the table writing newspaper articles. Soon I asked them to put their papers on the windowsill. They complied a bit reluctantly, and I pulled out a small musical instrument in the shape of a triangle. I asked, “Who knows the name of this instrument?” “A wind chime!” guessed J. No one knew for sure so I gave the hint that its name is a shape name. “Triangle” called the group in unison.I instructed, “When I strike this and you think the sound has ended, it will not have and you’ll be wrong. Listen harder. Then put your head down when it’s really done.” I struck it, heads went partially down, back up, and then down again. M asked whether eyes should be open or closed, and I said “whatever you think – you could even try both ways.” O said “You mean like this?” and closed one eye. N said “I can’t do that,” so I suggested covering an eye with a hand like a pirate’s eye patch. We focused our attention with three triangle chimes before I asked them to recall what was happening in our zoo story last week.
After less than a year of leading her math circle, Rodi was invited to present at the Circle on the Road conference hosted by MSRI (Mathematical Sciences Research Institute). She shared these bits of her presentation with me:
Eight Things I Try to Remember
- Practice detachment. (Don’t try to hold on to your agenda. Let it go if the kids are moving in another direction that is still math.)
- Approach things with a “Beginner’s Mind.” (Don’t always know the answer. It’s okay not to be a mathematician. Pick topics that interest you and that you don’t know a lot about. )
- Listen more. (When in doubt about what to say, shut up.)
- Include relevant history, arts, philosophy, and fictional narratives.
- Let kids move. (If J wants to stand on her head while pondering an interesting or difficult mathematical question, it’s okay as long as she’s not interfering with anyone else’s productivity.)
- Remind kids that math is not equivalent to arithmetic. Remind them repeatedly.
- Appreciate and encourage different avenues of engagement: graphic/geometric, numeric, algebraic, logical, etc. Different kids will approach the same problem with different styles.
- Have fun. Enjoy seeing things from a child’s perspective. (At my April 10 Math Circle, 12-year-old M was quite surprised to learn that Sonya Kovalevsky was not paid in hot dogs. Turns out francs and franks are two different things.)
If you'd like to meet Rodi and me, Bob & Ellen Kaplan, Amanda Serenvey, and more math enthusiasts than you thought possible, come to the Math Circle Institute, July 8-14, at Notre Dame. If you haven't seen my previous posts about how fabulous it is, read this one and this one.