Hello, reader! If you intend to post a link to this blog on Twitter, be aware that for utterly mysterious reasons, Twitter thinks this blog is spam, and will prevent you from linking to it. Here's a workaround: change the .com in the address to .ca. I call it the "Maple Leaf Loophole." And thanks for sharing!

Monday, May 31, 2010

Do Not Be Discouraged

f(t) didn't have many readers for a long time, either.

What happened in March 2009? I think it was Math Teachers at Play #3 and Logarithm War.

Sunday, May 30, 2010

Love, Your Fairy Blogmother

[update: Sam Shah disagrees with half of what I say here, but in very compelling ways. Highly recommended reading there, too.]  [Also, Elissa has awesome and high-larious wisdom on the matter.]

So you want to start a blog.

What you should not do: Email me. I mean, I don't mind, but I'm just going to be generically encouraging. I've been getting deluged lately, so this post is a public service. "Start a blog" must be a popular summer project for teachers this year. I'm sure commenters will add many helpful suggestions I didn't think of, so be sure to check them out, too. Also note: I violate these pointers all the time! They're just suggestions.

What you should do before you start:
  • Start reading. Set up Google Reader, subscribe to every blog you can find that's like the one you want to start. Check your reader at least once a week. You don't have to read every word. Read the posts that interest you.
  • Start commenting. Don't just use your first name if it's common. Especially if it's "Dan" "Dave" or "Matt." Use your last name or make up a hilarious or distinctive nom de plume. Also, don't just comment to comment. Say intelligent things. Add to the conversation. Point to good resources or tell a helpful anecdote. 
  • Pick a title that stands out, that people will see the title and think, "Oh yeah. That guy." Don't choose a title with "Math" in it. Don't choose a title that only differs by one word or letter than someone else's blog. It might take you a while to think of a good name. It's ok. Take your time. You're going to be stuck with it.
  • Write a tagline that concisely describes your purpose.
  • Optional: Get on Twitter. Contribute to the conversation there.
When you start writing:
  • Add your link to the comments you write, so people can follow it and get to your blog.
  • Some people publish several times a day, some a few times a week, some go months between posts. I don't think it really matters, as long as what you do publish is worth reading.
  • Give each post a title that makes the reader wonder what it's about and want to read on.
  • Don't be afraid to post about your failures as well as your successes.
  • Tell a story. Give it a beginning, middle, and end. Include an illustrative anecdote about how it went down in your class. Dialog helps, which you can totally make up if you need to.
  • Avoid posting fodder just for the sake of posting, such as : embedded videos without commentary that adds to its viewing, lists of links to other blogs, etc.
  • Stick to the topic. Don't badmouth anyone. Try not to complain too much.
  • Credit and link back to ideas you got from and references you make to other people's work.
Realizing I May Have Buried the Lede:
  • Be generous. This community is a gift culture - sharing is how reputations are built and respect is earned. If you have worked hard on a successful lesson, it's worth writing up. Share your presentation files, handouts, dynamic geometry sketches. There are many sites that allow you to share documents for free, and BetterLesson has a nice platform for this now. 
Some suggestions for getting more readers:
  • Don't be too focused on hit counts or number of subscribers. Are you learning from your written reflections? Are you having worthwhile conversations? Isn't that why you're doing this?
  • The best way to get people to read you is to write original content worth reading.
  • Volunteer to curate and host a carnival like Math Teachers at Play.
  • Keep commenting elsewhere, and including the link back to you.
How to manage comments:
  • Acknowledge insightful comments and keep the conversation going for as long as it makes sense.
  • Respond to direct questions to you.
  • Learn to tell the difference between commenters who want to discuss legitimate differences in opinion and issues raised by your post, and the ones who just want to drag you into a pointless holy war. Engage the former.
I hope that helps. Good luck!

Drumroll, Please

After careful consideration, my esteemed colleague Mr. Shah and I have declared a victor in the Binomial Expansion video contest: Jason Dyer! Woo! High fives! Crowd going wild!

Jason, in a moment of genius, chose a winner of a concrete basis for developing the structure of binomial expansion: the game Q-Bert. There's an outside chance he gamed the judging based on my non-secret, unabashed enthusiasm for all things with a high score and a controller, but I'm ok with that! Here was Sam's take:
Not only for the fact that students can use it to count out things, and really engage hands on with figuring out the numbers -- really get intimate with what's going on instead of just noticing patterns -- but there is something powerful about the physicality of it. I kept on imagining Qbert jumping, instead of seeing things in some abstract algebraic framework. It also, merrily, explains why the pattern we use to draw Pascal's triangle works (why the two numbers above it add to form the next). Jason too saw the power in it, because he kept on referring back to Qbert as the base structure on which he built his lesson, instead of saying "here's a cool thing" and then going into the world of abstraction never drawing the abstract back to the concrete.
All of the entries had their own strengths and deserve recognition, including:

Eric Buffington - Who produced a much better-looking, cleaner version of the type of lesson I presented in the original post.

John Scammell - I thought the mathemagic angle was effective for this topic, and well-presented to a live class in his video - a breathtaking act of bravery for a teacher.

James Tanton - Whose approach shared the appealing physical basis of Jason's Q-Bert lesson. 

Any of these would make an effective lesson, and made for a competitive field and a difficult decision. Congratulations to Jason, who will be receiving a brand-new Factorial! t-shirt, courtesy me, who decided not to be a cheapskate and send him a hand-me-down, and a lovely book, courtesy of Sam - I think he has his choice of a few

This was fun! Should we do it again sometime? Maybe better-timed than the end of spring when everyone is super busy? What tough-nut-to-crack topics are begging for the mathedublogsphere treatment? Anyone else want to host the next one?

Saturday, May 29, 2010

Get Your Hot Fresh SBG Checklists

For the uninitiated, SBG stands for Basing the Grades On Making Sure the Children Get What They Are Supposed to Get. People who are smarter than me have already described it extensively.

All of these were only really tried one time for real because of curricular changes and my-schedule changes. I anticipate people will object to their length. I agree that in some cases, two concepts could be pared down to one. Either I need to do that for next year, or I had a reason. Some of it is just the reality of our curricula - overloaded. Sometime when I was training to be a teacher I was told, "A good teacher is one who knows what to cut." But, I don't know, I wrestle with cutting anything. I have an overdeveloped sense of duty.

The Lists
Algebra 1
Algebra 2 with Trigonometry

More Details
I do about one quiz a week. Sometimes it takes the whole (43 minute) period but usually it doesn't. They see a question about each concept on two separate quizzes. I score them out of five. I give them one point even if they leave a question blank. It makes it easier for me to tell later if they were absent and didn't take the quiz (zeroes) or they just did really badly. So it's like
0 - Didn't take it
1 - Left it blank or wrote absolutely nothing redeeming
2 - Wrote something correct or in the right direction but is essentially clueless
3 - The cluebird has landed, but major conceptual error
4 - Minor conceptual or major computational error
4.5 - Minor computational error
5 - Knows what's up, no kidding.
Our grades are calculated by 1/5s: four marking periods and a regents exam. I tend to cut off remediation opportunities at the end of the marking period for all the concepts up to that point. It just makes sense for us.

The best modification this year was: require that if you are staying after school with me, you are either there to get help, or you are there to re-test. Never both. If you want my help, great, but you have to come back to re-test. Retesting is a no kidding, materials put away, sitting at a desk by yourself with a pencil and a calculator situation. It was a good change because: they are more likely to at least try to do some preparation on their own, and their grade is a better reflection of what they've learned as opposed to what they just stored in their short term memory.

Plans, Big Plans
Be more proactive about insisting students come for remediation. Like, the instant their average goes below 70%, assign them detention if need be. Most kids, once they come in once, they realize how much it helps their grade, and then they take it upon themselves.

Be more insistent that everyone have a place to keep their checklist and graded quizzes from the current marking period. How to do this, I don't know. The worst ones keep all their subjects in a huge spiral notebook, and stuff handouts in the insubstantial pockets in the dividers. What a terrible solution. Pretty soon they can't find their checklist, and they have quizzes everywhere. One step up, but still pretty bad, is a sturdy pocket folder. It's impossible to keep stuff in order. The best would be a binder but I think that's a pipe dream. Kids hate binders. They are that awkward triangle shape, and you can't quickly deal with paper that's not hole-punched. In Geometry this year, I tried individual file folders, kept in the classroom. Organization was better, but they didn't have their old quizzes with them for studying. Major flaw.

That's all for now... I will probably add more to this as I think of it.

Thursday, May 27, 2010

Just How Long Is That Quarter Mile Track Anyway?

This morning I got up early and came to school to run around the track. (I know, right? Nobody was chasing me or anything.) And I know it's a quarter-mile track, but of course the inside lane is much shorter than the outside lane. So I started wondering, what is a quarter mile? The inside, the outside, somewhere in the middle? I'm getting this down now so I remember to revisit it in Geometry next year when we do all those composite perimeters and areas.

Here is our track from Google Earth:

I'll ask the kids to decide what to measure.

If you try to measure in miles, the diameters of the semicircular ends only differ by a hundredth of a mile. So I measured in feet for more precision.

I'd love to give the kids a printout and have them do the measuring, but measuring in centimeters or inches and scaling it up might be more trouble than its worth. Maybe if I find a few more interesting questions like this, we can have a computer day and they can use the GE measuring tools. Times like these I envy you 1:1 schools.

For the outside track, rounding to the nearest foot I get 1444 feet or 0.273 miles and for the inside track, I get 1320 feet which is exactly 0.25 miles. Can anyone verify that? Track stars?

Friday, May 21, 2010


Straight-edge hack:


Paper-saving hack (Thanks to Sarah Cannon):

The document camera doesn't do video hack (Thanks to Maria Anderson):

Floppy compass hack (Or just order these. They are the bomb.):

End-of-May Motivation Hack: Make something cool

Saturday, May 15, 2010

Teach Us Something

I continue to be frustrated with kids afraid to try something because they're afraid of being wrong or admitting they are confused - you know, the nodders, the silent ones... They hate taking a risk in front of peers like a terrorist hates freedom. I know it's totally normal and human. I'm just frustrated by my "What do you think? What ideas do you have?" being met with "Can you check if it's right first? What if I'm wrong?" I often give a friendly "So what if you're wrong?" and then some crack about how I won't let M.I.A. take them away on a prison bus even though they have red hair.

Does anyone else do something like this in the first few days of school? Get in a group of 2-4 and tomorrow, your group is going to teach the rest of us something that you are good at. It just has to be something that we can do here in school, that we will be able to try a few times within about 10 minutes. If you need any special equipment, you'll need to bring it.

There are plenty of things that these kids like to do that I'm sure I would be comically awful at. And maybe it will show that it's safe to take a risk and/or admit that you're clueless - that it's really sort of essential if you want to learn from another person. But I also wonder if this is a terrible idea, because I want them to feel safe with me, and throwing them in front of the class within the first few days of school will freak them out.

Has anyone tried something like this? Did it work? Was it a waste of time? Was it awesome or horrible in unexpected ways? Please let me know.

Thursday, May 6, 2010


is the country with the most amusing name.

But The Booty, on The Challenge, has just gotten better! So if you're thinking maybe you got the goods that will bring the kids along for the ride, well, you know what I'm hoping you'll do. (Bring it.)

Monday, May 3, 2010

It's About That Time

At lunch today (provided by our fantastically supportive STPA - it's such a nice thing they do for us every year) we were talking about how soon the year is going to end. It's only a few weeks until Memorial Day. After that, we just have two four-day weeks of classes, a week of exams, and then a week of sitting around and twiddling our thumbs because we already took all of our personal days. Ok that's maybe just me.

I am not quite sure yet about this year, but in other years I have used this Survivor-themed review game to help review for final exams. I was going to write up a whole big thing about it, but then I realized that the original description was pretty darn close to what I ended up doing. So I am just formally endorsing it. Check it out.

I made a few minor modifications:

  • I score each challenge out of 10, but there are only 5 points available on it. So their score is never lower than 50%. This prevents all these scores from really killing their quarter grade if they bomb a few. Or more than a few. Reviewing a whole year can be rough.
  • I can't exempt anyone from Regents exams, so I work "immunity" thusly (I've been watching a bunch of Alton Brown, can you tell?): The winning tribe for each challenge automatically gets a perfect score on the next challenge. However, they still take it and try hard on it, because they could always get immunity a second time!
  • To up the joy quotient, I gave some incentive for the tribes that made beautiful signage of their tribe name to hang above their work area.
  • One year I gave $5 Amazon gift cards to each winner of the winning tribes, and another year I had t-shirts made. The t-shirts were the far more popular prize. They wore them to the exam and took pictures. You want to see a bunch of regents kids act like math nerds? Give em a free t-shirt.
  • The first few days of the game, and more if you feel like it, you MUST blare the survivor theme song in your room as class starts, and you MUST wear a safari jacket and bush hat. NO EXCEPTIONS, buddy.

Saturday, May 1, 2010

Negative Numbers are Hard

Go read, especially if you teach math in grades 6-9, but really, go read it anyway. Ben Blum-Smith is performing a public service, reporting on primary sources you should read but are too-hard-a-slog and when-do-you-have-the-time and teasing out recommendations you can use in any classroom. The post is lengthy but well worth your time if you've ever watched a student struggle with negative numbers, and who hasn't.

I won't give away the punchline because Ben lays it out much more elegantly than I can summarize, but here's as good an analogy for a typical clumsy, contrived introduction of algebra as any:
The way I learned it was the opposite of “natural” or “meaningful.” Very cool, but only in an after-the-fact sort of a way. Like you came to the show at the very end and only saw the climactic scene, and everybody in the audience gasped and shrieked, except you because you didn’t care about any of the people in the show because you just walked in one second ago. And then after it was over your friend explained to you what had been going on and you understood why the other audience members cared, and were kind of mad you hadn’t gotten to watch the rest of the play first.