Math On A Stick, Part II: Stepping Stones, Parent Talk, Teacher Lessons Learned & Mathematical Depth

Part I here.

After the phenomenal time I spent last weekend at Math on a Stick, I signed up for 2 more slots this week – making a total of 4 for this year. Here are some more stories about why it’s so great and then some teacher musings.

The Stepping Stones

Math on a Stick is blessed to have Max Ray-Riek and Annie Fetter as volunteers, and while I have sadly missed working with Annie this year, I have gotten to spend a fair amount of time there with Max. He is extraordinarily awesome.

 

‘Twas Wednesday evening when Max came over to tell me he’d just had a great experience at the stepping stones with a mom and daughter. I hope he’ll write up his version of events, because I came in only halfway through. Anyhow, he told me this girl was so excited about them that he’d exhausted the problems he usually uses (count by 2s; 23 minus 24, etc.). They even counted PRIME NUMBERS on the stepping stones. They also did it in an awesome way. They figured out which stones they would not step on if they were skip counting, and stepped on those! (Mom did a lot of carrying her daughter between stepping stones that were too far apart.) Awesome!

For those who know me well, PRIME NUMBERS ARE MY JAM. I love them. One of my Achilles heel’s as a teacher is that my students can always get me off topic by asking questions about prime numbers. I fall into that trap EVERY. DARN. TIME. I even do it willingly because primes are just so flipping neat. Needless to say, I nearly knocked people over in my haste to reach this mom-daughter pair. They kindly indulged me while I pestered them with questions about how they thought about prime numbers and explained about the infinite-ness of primes. They were duly impressed (or faked it well enough for the sake of my enthusiasm) that there were numbers with billions of digits that can’t be put into equal groups. We used the really handy wood chips Math on a Stick is covered in as a model for splitting numbers into equal groups.

The girl, however, wanted more problems, so I wracked my brain and came up with the sum of odd numbers. If you’ve never done it, stop reading, and go figure out what happens when you add consecutive odd numbers starting at 1. It. Is. Bananas.

Turned out this problem was a bit of a doozy on the stepping stones. We got 1+3=4 easily, and she leapt from 1 to 4. Then 1+3+5=9 wasn’t too bad, but we had a bit of a time keeping the numbers in our heads and had to frequently remind ourselves what we were adding to what. After mom graciously carried her daughter from 9 to 16 we saw that we would exceed our number line in the next leap, so we paused to figure out what we’d decided. The stepping stones we’d landed on were 1, 4, 9, and 16. The girl wasn’t quite sure what to make of this, so I brought her over to the eggs, and asked her to put 1 egg on a tray. Then I asked her to describe it, which wasn’t too exciting. Then I had her put another 3, for a total of 4 on the tray. I had to nudge her in the direction of making a square, but we got there, and she noticed that. Then when I had her add 5, she added them along the outside of her 4 square, and found that it was still a square! WHAT?! She was into it. I assured her that when she added 7 more it couldn’t possibly be a square again, and boy did she prove me wrong. She was all grins, and I was probably scaring the other visitors I was so excited. We then conjectured that if we had been able to continue, we would have landed on 25. So cool.

BUT WE’RE NOT DONE YET! Because Max, being the super creative genius that he is, had a new problem for us. We were going to need our muscles. He brought us back to the stepping stones, and suggested what many of you may recognize as the “locker problem”. He was going to flip over every single stone from 1-10. Then the girl was to flip over every other stone. I flipped every 3rd stone. Mom flipped every 4th stone, and Larry Luck (yeah! he was there, too!) flipped every 5th. We continued like that until we’d flipped up to 10. Guess what we were left with?!? 1, 4, and 9 were upside down and the rest were upside-up. When we connected this to my adding odd numbers problem my math teacher joy could barely contain itself. It didn’t in fact.

As a last joyful thing, the girl and her mom said they were going to try to get stepping stones at her school, and when we gave her a blue ribbon – originally intended for the Number Game – the girl asked for a sharpie so she could cross out “Number Game” and write in “Stepping Stones”. My face hurt from smiling.

Parent Talk

I find myself often explaining that as a volunteer, my job is partially to get in between the parents and their child so the kid has long enough to get their idea out. If I’m successful, the kid gets the space and time to create share their ideas, and parents then get rewarded with seeing their kids doing cool stuff.

I was working at the entrance, where we offer up “The Number Game”, when some very excited young kids came running up. I explained the number game to them, and they were off to the races. For those not in the know, the number game is very simple. You get a card with the number 1-20 on it, and your job is to go out and notice groups of things. “Can you find 7 of something?” I thought it was a silly game, but kids are SUPER into it. And if you get over yourself enough to play it, you realize it’s actually lots of fun. It’s very satisfying when you find 17 of something. Over and over again, I saw kids come running up, smiles covering their whole face, declaring that they’d done it! They’d finally done it and they were so proud. They had earned their blue ribbon. Yay!

Back to this family. The kids came up and I got them started, but Mom & Dad were hanging out outside the Math on a Stick space. I told them they were welcome inside, but Dad meekly asked if it was okay that they just took a quick break? They both looked exhausted after many hours with excited children at the fair. I laughed and assured him that was fine. They were clearlystill keeping an eye on the kids. Again and again their kids came back to me to ask some question, to which I often replied, “What do you think?” or “Tell me how you found it.” It is a conscious decision of mine as a teacher to do as little explaining as I can, as much eliciting of ideas as possible.

Dad, having caught his breath, approached me after a while and commented that he was really curious listening to how I talked to his kids. He noticed that I never explicitly answered questions that they could answer themselves, and he was really impressed by what his kids said and did.

This thoughtful questioning – seeking what the kids think as opposed to confirming for the kids that adults have the answer – is a skill I learned from great teachers like Terry Wyberg, Christy Pettis, Sara Van Der Werf, and Annie Fetter’s ignite talk. I mention the last because when I told Sara about this talk later, she said it reminded her of the ignite talk, and of course, that’s one of the places I learned it.

Math on a Stick is so cool because parents get to witness this. It’s so much more powerful for them to see it than to have me explain it at parent-teacher conferences.

Teacher Lessons Learned

This brings me to the teacher moves I’m taking away from Math on a Stick. It would be foolish of me to say that I’m not trying to be on my A-game teacher-wise while at Math on a Stick. I’m constantly surrounded by name-drop-worthy teachers: Larry Luck, Sara Van Der Werf, Kassie Benjamin…Christopher Danielson, and SO, SO many more.

Seriously, if this Key and Peele sketch were real, the volunteer list for Math on a Stick could be first round draft picks. So while there, I feel a bit like I’m on display – am I asking the right questions? Am I giving enough wait time? Am I noticing who needs to be engaged more?

It’s not intimidating, necessarily, just pushing me to do well. And of course, it’s not like I don’t try to do well in my classroom all the time, I do. I’m just hyper vigilant about it at Math on a Stick. This is excellent for 2 reasons:

1. Being around excellent teachers, I get to see and steal all of their good teacher moves. I listen to their questions, I see what they notice, I get to talk to them about their decisions. It’s like classroom observations on steroids, but the mood is light and welcoming. I learn a lot.
2. Since I am trying really hard to be on my A-game, I get to notice what that looks like in myself.

I experience the awkwardly long wait time which I might not have held quite as long if Christopher wasn’t 5 feet away. And because I held it that long, the kid got out an idea she might not have, had I cut her off.

I refrain from pointing out a solution. It’s easier to do this at Math on a Stick because the stakes are very low. I don’t have to get these kids to pass a test. I just want them to have fun and learn. I mess this up in my classroom far too often, and it was great to feel the opposite. I’m hoping I’ll take more of that back to my classroom this year.

I see the power of a variety of manipulatives. I was so excited when working with the stepping-stones-girl that the eggs were right there for me to make use of. In my classroom, I would very likely have gone straight to paper and pencil. The lack of that at Math on a Stick makes me get more creative. I have to use what’s around me, and luckily, what’s around me is awesome. The eggs were perfect for creating squares. And they were right there! I have to figure out how to set my room up such that those types of manipulatives are always there. Paper and pencil are great, but they’re not perfect.

Mathematical Depth

I also love the mathematical depth one can go into at Math on a Stick. It is the ULTIMATE low floor, high ceiling. ANYONE can come play with tiles. Anyone can do the stepping stones. Anyone can play with large circles. Yes, most of it is what we might think of as elementary math. But not all of it.

Sara wanted to take pictures of people interacting with everything, so she asked me to get down and pretend to be interacting with this:

I got down to “pretend” and was immediately struck that this was a paraboloid. Right?  But there were 2 layers of each size, so I could make this into a sphere.

Wait a second. They have the same volume. They have the same height. So how the heck is a paraboloid’s equation related to the equation for the volume of a sphere?! Someone pointed out that maybe it’s not a paraboloid, but rather half of an ellipse. Can those be the same? What the WHAT?! This problem is now in my “Problems for me” notebook, and I can’t wait until I have time to dive in. (School starts tomorrow, I should probably be getting ready for that…)

I hope I’ve already explained the versatility of the stepping stones, but another of my favorite things was that there was a blank stone in front of zero. Asking kids what they thought should go there is FASCINATING. Adults insist it should be -1, but kids, being far more creative, think most often (in my questioning, at least) that it should be “double zero”, with reasons ranging from “that’s more zero” to “it’s twice as big as zero”. FASCINATING.

On the spiral machine, I was trying to create a straight line by drawing a circle at the same rate.. backwards? Then another volunteer, Stephanie, came along with a different method: She made a mark on the outside and drew an arc from the center to that mark. So cool.

This is more than 2000 words at this point, so I’m going to stop. I could go on forever. Math on a Stick is the greatest thing ever. I love it. My nephews came yesterday and I was SOOOOO excited to have them there. They loved it.

If you haven’t gone, go. If you have gone, YAY! Go back! Come hang out with me!