Monday, July 31, 2017


(Have to read that post title Sixth Sense style.)

First do I write about: #iteachmath or Twitter Math Camp 17? ...  have to get the hashtag stuff off my chest.

I love that Dan is thinking about inclusivity, and it befits his problem solving orientation that he's willing to rethink any aspect of the situation.

I started blogging April 2009 with a 50 word post, just sharing a resource I liked. I thought I would use the blog to share the stuff I found around the web that I like or was thinking about how to use in my class. Ten posts later I finally shared an first activity that I did back then. A math game, of course.

This was a long time ago in internet years, and I understand that the world is different. I was inspired by what I was finding, and just wanted to join in.

First tweet, 2010.  (Find yours.)

I was at Maria Anderson's tech camp (@busynessgirl) and she suggested Twitter as a way to connect with student teachers. That's been great, but I wound up liking the math twitter/community plenty for myself.

When it was time, 2013, the community wondered how to refer to itself. They came up with Math-Twitter-Blog-o-Sphere, and I liked the silliness of it right off.

Is #MTBoS a barrier now? People are hurt by this suggestion, because they work like hell to make the community inviting and inclusive. And are always looking for more ways to do that better.

From where do the hard feelings come, then? I have theories. Basically this list is the consequence of people new to twitter don't know how it works yet.

  • some of the most followed people are friends. They take math with anyone, but also talk real life to each other. There's shared experiences, so they refer to things that not everyone was a part of. But because of the way Twitter is, we see some of those relationships. That could make you feel like (Justin Aion analogy) being at a party by yourself. As Justin says, at a party, they'd see you standing alone and approach you, but on Twitter, you can be invisible if you want.
    Remedy: new users can let people know they are there. 
  • People say 'Include #MTBoS and get your questions answered.' Sometimes? More people watch that tag and respond to new people than I think would ever happen in most communities, but not everyone gets responded to.
    Remedy: tweet @someone. If I see someone asking for a resource, I may not have a response, or know others who have better. But if you tweet @mathhombre, I reply. (I think?) I challenge you to find a community with a higher response rate.
  • #MTBoS is a community. We have relationships, shared values, and even meet when we can. If there's an in, there's an out.
    Remedy: come on in!
What I notice about these problems is that the remedies are all putting the burden on the people who feel outside, which is usually the hallmark of an exclusion problem. But that's where we need to see and popularize the efforts of Tina Cardone, Sam Shah, Lisa Henry et al. There wasn't an intention to brand anything, but having a name is part of making you a group, a tribe or a family. I would rather reassure people that this family wants you and is inviting you in, than worry about what the name connotes. 

It did feel autocratic, and like a dictate, but that's probably mostly because of his position in the community. He is the introduction to the MTBoS for most math teachers. He is going to hear the complaints the most, maybe? 

The timing was really unfortunate, as it distracted from the amazing keynote by Grace Chen. (Pts 1 and 2) (Which I will talk more about in the next post.) 

Dan is trying to connect people with #iteachmath. Great! I don't see how that solves any of the three bullet points above. Hopefully, the new tag will be successful. If it is, within a couple years people will feel like it's cliquish or there are rockstars and arguing for #mathlearnersunite. Great! 

I don't think of this as particularly important - or coherent - post, but this is a blog. I can work out my thinking here, and live long enough to be embarrassed of it. I can give a first take. No one else may read it or maybe it becomes the rare post that gets a comment. One of my Twitter Math Camp take aways, from Carl Oliver's sweet keynote (Pts 1, 2 and 3), is that it's important to push send. 

If you hear about the #MTBoS, my guess is that you will be curious enough to investigate. If you do investigate, you'll find things that will help your learners. If you value that, I encourage you to join in. The more you participate, the more you'll feel a part. If you can get to a Twitter Math Camp, you'll be stunned at the welcome. But nobody's going to make you.

Monday, July 24, 2017

Same Game, Different Grade

I love working with people. Given the choice of math together or apart, or teaching together or apart, I would pretty much always take together.

So I was thrilled when Joe Schwartz was willing to work with me for Twitter Math Camp this year. Among many shared math interests, we both love math games. I've learned a lot from Joe's math game posts, and his Twitter Math Camp 16 presentation on them blew my mind. Such great learning potential the way he approaches games with students.

E.H. Shephard illustrating A.A. Milne
One game with which we had both already done things was Fill the Stairs, which has been around for a while in many variations. I had done a version with Esther Billings and David Coffey in an inservice, that involved having cut up bags of numbers. Joe had done a version with digit cards 0 to 9 where students fill in a staircase with 10 on the bottom stair
and 100 on the top stair. Joe and I had connected on a version I came up with earlier called Decimal Pickle. As we talked about it, the spirit of Tracy Zager began again. She's been haunting me all year from her TMC16 keynote, where she challenged us to do cross-grade collaboration. "What if we did variations of the game across grades?" Joe wondered. So we were in.

Necessary references: Joe's first post about it, and the redux.

The idea for Decimal Pickle came from a need for comparing decimal numbers of different length. Why would we flip different numbers of cards? The colors are pretty intuitive there. Black? Flip again! It added a lot of excitement to the game, almost a black jack feel. For the mathematics, it was perfect for the 5th graders to compare tenths, hundredths and thousandths.

Talking with Joe got me thinking about the big topic. How does order show up across the grades? When I think about number sense, I see a few components. First, number as quantity. Or the numbers in context. But second only to that is comparison. Well, second is representation. But third only to those two is comparison. And comparison before computation, which is right out. But this idea of order is really an up and down the curriculum issue. As numbers grow more complex, how to order them is very relevant. It's the experiential aspect of number that we often ignore as we get farther up the curriculum. One of the strengths of this game is that it requires comparing more than two numbers. I think ordering a set is more complex and challenging task. There may be a component of number sense I haven't thought about at play, a kind of sense of distribution.

I like games to use easily accessible materials, so playing cards are great. I often use J as 0. (And if the kids are old enough, "You know what you have if you've got Jack?")  I'm not sure why I first tried having students make their own gameboard, but I love it, now. There are students for whom that's their in for the game. (Deep game design - there's probably a whole player psychographic aspect to this.)

The first step for me on this generalize the game journey was to fit it for 3rd graders. I wanted single digit and 2 digit (teachers asked for no three digit), but thought that half and half was a weird balance. I settled on turn over a card. On a diamond you stop, otherwise turn over another.

Kids are not as familiar with playing cards as they used to be, so we started with something halfway between notice and wonder and Which One Doesn't Belong.  Then, as I often introduce games, I played vs the entire class. Then they break up and play in 2 vs 2 teams. One of Joe's great ideas was to have students make a number line with their results. Great task, ripe for discussion, strong in representation, awesome assessment.

Thinking about how to go even younger, I was thinking about sorting single digit cards. But how to make a game out of it? First came the first grade variation. Fill five spaces. Flip cards like War to start in the the middle space. Higher goes first (advantage) but their card is probably too big for the middle space (disadvantage). Every flip you place in a spot. If it's the same as a card you have, cover that card. Cards have to stay in order. So if you have 3 __ 4  6  __   __ and you turn over a 5, you can cover the 4 or the 6, but not the blank between 3 & 4.

That requirement to not move cards was too much for Kindergarten, so they could move their cards around. That generated plenty of discussion, too.

Thinking about how to extend the game past high school was a challenge. I kept thinking about order of operations. One of my pet peeves is PEMDAS, as I want students to think about 4 levels, grouping - exponents - multiplication/division - addiition/subtraction. (GEMS if we need an acronym.) So I thought about doing the red/black for more cards. 2 cards minimum, you can add or subtract. Three cards, have to join with add/subtract and multiply/divide. Four cards, have to do an exponent or root. Five cards you have to use a grouping structure, parentheses, radical, fraction bar. I think this could work, but haven't got a chance to test it yet. The class in which I was going to get to test was a college algebra class working on exponents, so this became the variation.

Marcel Duchamp
It was great. The students were constantly surprised by their results, got a lot out of comparing these extreme numbers, and became more efficient at arranging the numbers to get the effect they wanted even in the course of an hour playing the game. Older students also need these play experiences, I think they just abstract from them more quickly than younger students.

We'll be talking about this at Twitter Math Camp 17, so I hope you can join us if you're there. Here's a page with downloads and resources:, regardless. If you have ideas for more variations or get to try one of these, let me know!

What games do you use that connect to a big idea in math?