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Archive for April, 2013

Christopher Danielson posts a video of Good Teaching:

My eyes tear up watching this sequence. I am neither kidding nor exaggerating. It gives me hope for quality classroom instruction in elementary mathematics. Be sure to notice the transition to a new task at the 4-minute mark, and how the teacher deals with the struggle that occurs at the 6-minute mark. Also please look in the kids’ eyes. Watch their body language and their waving hands. Watch them think.

You cannot flip the first instructional activity because it involves adapting instruction in response to student ideas, and it involves students justifying their thinking to the teacher and to each other.

You can’t flip that.

Leave your comments at Danielson's blog.

Tiny Math Games

Jason Dyer writes a very important post highlighting Tiny Games, a listing of games you can play quickly, almost anywhere, with only limited materials. He then pivots to ask about tiny math games.

Could one make an all-mathematics variant — mathematical scrimmages, so to speak?

His post, and Tiny Games, are important because they reject an article of faith of the blended learning and flipped classroom movements, that students must learn and practice the basic skills of mathematics before they can do anything interesting with them.

For example, here's John Sipe, senior vice president of sales at Houghton Mifflin Harcourt, talking about Fuse, their iPad textbook:

So teachers don’t have to “waste their time” on some of these things that they’ve always had to do. They can spend much more time on individualized learning, identifying specific student needs. Let students cover the basics, if you will, on their own, and let teachers delve into enrichment and individualized learning. That’s what the good teachers are telling me.

This is a bad idea. People don't mind practicing a sport because playing the sport is fun. It's easy to tell a tennis player to practice 100 serves from the ad side of the court, for instance, because the tennis player has mentally connected the acts of practicing tennis and playing tennis. The blended learning movement, at its worst, disconnects practice and play.

Take multiplication of one- and two-digit numbers for instance.

If you need to learn multiplication facts, one option is to watch a video and then drill away. Or we can queue up all that practice in a tiny math game that'll have students playing as they practice:

Pick a number. Say 25. Now break it up into as many pieces as you want. 10, 10, and 5, maybe. Or 2 and 23. Twenty-five ones would work. Now multiply all those pieces together. What's the biggest product you can make? Pick another. What's your strategy? Will it always work? [Malcolm Swan]

Easy money says the student who's practicing math while playing it will practice more multiplication and enjoy that practice more than the student who is assigned to drill practice alone.

Jason Dyer helpfully highlights two examples of tiny math games, Nim and Fizz-Buzz, but he and I are both struggling to define a "tiny math game." The success of the Tiny Game Kickstarter project indicates serious interest in these tiny games. I'd like to see a similar collection of tiny math games. Here's how you can help with that.

1. Offer Examples of Tiny Math Games

This may be tricky. We all have games we play in math class. What distinguishes those games from "tiny math games?"

2. Help Us Define "Tiny Math Games"

This may be a better starting point. I'll add your suggestions to this list. Here are some seeds:

  • The point of the game should be concise and intuitive. You can summarize the point of these games in a few seconds or a couple of sentences. It may be complicated to continue playing the game or to win it, but it isn't hard to start.
  • They require few materials. That's part and parcel of being "tiny." These games don't require a laptop or iPhone.
  • They're social, or at least they're better when people play together.
  • They offer quick, useful feedback. With the multiplication game, you know you don't have the highest product because someone else hollers out one that's higher than yours. With Fizz-Buzz, your fellow players give you feedback when you blow it.
  • They benefit from repetition. You may access some kind of mathematical insight on individual turns but you access even greater insight over the course of the game. With Fizz-Buzz, for instance, players might count five turns and then say "Buzz," but over time they may realize that you'll always say "Buzz" on numbers that end in 5 or 0. That extra understanding (what we could call the "strategy" of these tiny math games) is important.
  • The math should only be incidental to the larger, more fun purpose of the game. I think this may be setting the bar higher than we need to, but Jason Dyer points out that people play Fizz-Buzz as a drinking game. [Jason Dyer]

What can you add to our understanding of tiny math games?

2013 Apr 17. Nobody wanted to tackle the qualities of tiny math games, which is fine since you all threw down a number of interesting games. I'll be compiling those on a separate domain at some point soon.

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Jason Dyer elaborates on his contribution above.

Other teachers go in on the lie that students need basic skills before they can do anything interesting in their disciplines:

2013 Apr 24. Jason Dyer elaborates in another post.

If the deluge of interesting problem-based material on the Internet overwhelms you, as it does Jonathan Claydon, Geoff Krall's curriculum maps are a great place to start. He's taken the Common Core's scope and sequence documents and combed the Internet for items that fit. He's included a few of my own items, some items from the Shell Centre, along with a lot of great lesson ideas I'd completely forgotten. Bookmark it. Throw him some love in the comments.

NCTM 2013 Schedule

  • My own talk is at 11:00AM on Saturday.
  • I'll be cohosting a happy hour with Team Desmos and Team Mathalicious on Thursday from 5:00 to 8:00PM at Blake Street Vault. I'll be emceeing the trivia competition and, if y'all are lucky, I'll preview a few songs off my upcoming album. (RSVP!)
  • We could still use volunteers over at MathRecap if you'd like to write up a few words about sessions you attend.

Then there is the conference itself. Here are several sessions that interested me. (The usual biases against exclamation points and dead technology apply.)





BTW. Ihor Charischak has helpfully located the hidden technology strand in the NCTM program.

SAL KHAN: You're in tenth grade Algebra class. The teacher asks the student to do like six problems. "Oh my god." They're groaning. "This is the meanest guy on the planet." And then three hours later we're in wrestling practice and the coach says, "I want you to do fifty pushups followed by running three miles followed by another fifty pushups." And they're like, "Yes, sir. Yes, sir. Push me harder. I want to collapse." I mean, literally, sometimes people would collapse, they were willing to work so hard.

CHARLIE ROSE: So what's the difference?

It goes without saying that if you're Sal Khan or anybody else in the drill-based math proficiency software business, you should give Charlie Rose's question a lot of thought. Kids generally like sports practice a lot more than math practice so there's huge risk and huge reward here.

I don't think Khan's answer is wrong exactly but it's as though Charlie Rose asked him about the appeal of ice cream on a hot summer day and Khan enthused for a few minutes about the taste of the sugar cone. Sugar cones are tasty but there's a lot more to say there.

So let me load the question up on a tee and invite you all to swing away:

What makes sports practice satisfying and how is sports practice different from math practice?

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In short: Do quadratics for 3 hours a day and you are a nerd with no life. Hit batting practice for 3 hours a day and get the girl and go to the party on the weekend.

Pete Welter:

Sports practice leads to an actual game – a chance for the results of that hard work to be put to use. And that game will probably happen next week. The payoff for school math is far enough off – years – for most students to be forever. See what happens if you have a wrestler doing just pushups for 5 or 10 years without using it.


Speaking as a track coach / math teacher, I really think the biggest difference is that the kids signed up for it in sports. they knew what they were getting into, and if they want to quit, they are totally able to do so. Ask gym teachers if they have 100% participation in their classes.

Chris Robinson:

A lot of us grow up watching sports with our friends and families. Not a lot of us grow up talking and doing math. For better or worse, sports holds a significant place in our culture.

Dan Anderson:

Immediate and clear feedback. I can make that fade away basket now because I tried it 50 times from the same spot and have hit the last 10 in a row.

Mandy Jansen:

Sports — The practice gets put to use, and there is a real payoff or outcome to work toward.

Kelly O'Shea:

First, there are plenty of kids who feel the inverse (love math practice, hate sports practice). Why do we not think that’s true? Math is required, sports are not.


Recently, in a polynomial unit, my kids had to multiply a binomial by a trinomial a few times (like three times). There was also a problem of a 7-term polynomial being multiplied by a trinomial. I told my students that this problem was “challenge by choice” but that I really wanted them to try it – because it was kind of fun in an algebra geeky sort of way. It was really my subversive way to get them to understand the distributive property and that “FOIL” isn’t the best acronym. About 90% of my students tried the hard (or tedious) problem; a bunch did it correctly and most of them came really close.

Ultimately, it’s about a sense of accomplishment – whatever the practice is for.

Nathan Kraft:

We try much harder in sports practice because we’re preparing for a game. In most math classrooms, there is no “game”. There’s just practice.

Justin Lanier:

Hard-nosed and repetitive skills work in sports is essential and beneficial. In math, it’s a chore if you “get it” and unhelpful if you don’t.




Sorry. This sounds like a typical US American discussion to me.


I think another angle would be “growth mindset”. Students believe that they will get better at a sport with that kind of focused practice.

Santosh Zachariah:

Try running a season’s worth of sports practice without a “scrimmage” and see what happens.

Gary Stager:

A trumpet player, actor, cellist, dancer who is improving, does so not just through repetitive button pushing or by being yelled at by a coach/math teacher. Productive practice requires intrinsic motivation, reflective ability, attention to detail and a cognitive clarity that connects often the tiniest of personal goals to prior knowledge and past experiences. Understanding results from such clarity. Also, one cannot discount the value of relevance in this equation.

People do not get “good” at something by doing it 10,000 times without caring about it, finding personal value in the activity or by making connections to something bigger than yourself.

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