Monday, June 2, 2014

#TMWYK: Number Development

If you've even read this blog, you probably know that I have a two year old daughter. He's another picture of Callista from the guy who shamelessly posts pictures of his daughter on his math teaching blog.

I can remember the first time Callie came up to me with two balls and said, "two!" That was a big deal for me and I logged into twitter for the first time in weeks just to brag about it.

I later learned that for her, "two" meant more than one. For example when I put one cracker out she'd say "one," two crackers were "two," but three crackers were also "two." Four crackers were "two."

About two months ago she picked up "three." Instead of asking for two crackers, she'd request three. She knows that three fingers is "three." When asked how many she is very reliable with 1, 2, 3, and 5. 4 seems to be foggier for her and I believe we are having the same issue of three sometimes meaning "more than two."

For example, when she goes to bed, she'll request three blankets. But she has five or six in her crib. Really what she wants is ALL of the blankets, yet she requests three. She seems a little puzzled when I stop at three. She'll then request another blanket and I'll keep counting.

Is this the typical way children pick up numbers and begin to develop number sense?

Monday, April 21, 2014

The Graveyard

How many great ideas have we had that fall away because they didn't work or are unsustainable? How many have you had personally? Here's a couple of mine:

Moodle Testing. Turns out it is a lot of work learning the coding, making the tests, and chasing down kids when they don't take them. I also get the sense that there are better test mechanisms out there.

Forums. It worked great the first year when I emphasized it and gave students credit for it. I guess I thought the next year it would simply take hold organically without credit or emphasis this year. It didn't. Complicating matters, I didn't know whether it'd be best to keep the old posts up or have kids start fresh. I suppose it depends upon my goals, which I did not articulate.

Those are two, and I'm sure there's more. Do you have any ideas in the #mathgraveyard you'd like to share?

Tuesday, April 15, 2014

Speed Teaching

My buddy and colleague Matthew Sauter calls this "Speed Teaching," which I think is a bit of a misnomer, but it was his idea so he gets to name it.

 The traditional classroom might look something like this:

"Speed teaching" looks like this:



test up

The thought is that we test faster and differentiate sooner. We have leveled practice based on test scores and put keys up around the room for the different levels. It seems to work well since students practice at their level rather than painting everyone with the same fat (or skinny) brush.

Tuesday, April 8, 2014


I have something to talk about. WeVideo.

 I had to edit a video recently and although I am by no means an expert, I am capable. The new Windows Movie Maker has been driving me bonkers since it came out a few years ago. I don't do it enough to buy Adobe After Effects or anything really sophisticated. Just a few basic edits like the sweet videos of my daughter that I made last year:

(And of course there's this one too.)

WeVideo makes it easy to edit videos. It's user friendly and has enough basic features to do the job. It will charge you a dollar to export large videos but in my opinion it's $1 well spent. It also exports directly to google drive, youtube, et cetera.

I added as an app in google drive. It's terrific.

Wednesday, December 11, 2013

Nothing to Say

I gone a clear month and a half without writing anything here. I just haven't had anything profound to say.

This is certainly not an original blog post. Bloggers fall in and out of writing spurts all the time. But I'm trying to figure out why. Why have I had a general disinterest lately in reading twitter and checking my reader? What changed? What's going on with me that I'm just not finding the value that I used to?

Perhaps if I articulate a few reasons I'll find my way to something useful. If not, I apologize. I need to write something to try to move my energy in a positive and productive direction. Because right now, when it comes to math education, I am truly bored.

Reason #1: Family
My daughter is the cutest and sweetest thing ever and I'd rather be hanging with her than you. Sorry. Can you blame me?

Reason #2: General contentment with my practice
I feel like all of our hard work over the past few years is paying off. We have a good system and good assessments. And while we can always get better, seems like it might be time to reap the fruits of our many years of refinement.

It's also nice that my district isn't screwing things up as much as they used to.  It's been a good year for them. But it's been bad for my blog and twitter account: my readers do enjoy it when I go off the deep end and rail publicly against my district. I just haven't been as pissed off as I've been in the past.

Reason #3: An eye on the bigger picture
I've been doing math for years now and other things are exciting me. For some reason literacy and behavior are turning my crank. Questioning tactics and intervention strategies interest me. My classroom management is certainly at the best it has been in my career despite a tougher than usual class of sophomores coming into our school.

I recently completed my masters in Educational Leadership and Administration and perhaps will look that direction. I am also a negotiator for our teachers contract and I feel like this is in the wheelhouse of my skill set.  These things above and beyond my classroom practice excite me more and more.

An aside: I was a state speech champion in the category of discussion. If you don't know how it works, 5-8 of us sit at a table and are given a task. The person who should win is the person who contributes the most to the completion of the task, in whatever form.  For example, a task might go something like
Recently, President Obama relaxed Cuban travel and money restrictions. As members of the House Foreign Affairs Committee, you should identify the ramifications of the eased policy, including impacts on Americans, Cubans, and relationships between countries in the region.
The competition is bizarre. You are simultaneously competing against and collaborating with the others at the table. At the time I thought there was absolutely nothing like it. I was wrong. Negotiations is exactly like it.

Reason #4: Overload
I'm pretty sure I have overloaded my twitter feed and reader. Too many superfluous and extraneous tweets and posts that overwhelm me. I need to weed in a BIG way. Sorry all.

All that combines into a rather uninspired and uninteresting web presence. I wish I could do better. But for today, this is what you get.

Thursday, October 24, 2013

Tennis Balls

Along with coaching, I captain two men's tennis teams.  It's pretty cool.  We have a team of 12-16 guys and on any given night we play eight: three doubles matches and two singles matches.  We have a fun team and we (surprise, surprise) pretty much always go out and celebrate afterward, win or lose.

And by celebrate I mean go out and drink beer.  Our latest favorite watering hole is the Groveland Tap. Excellent beer selection and a good happy hour menu.

If you're counting, we have five tennis matches per night.  Our home courts are at Fred Wells Tennis & Education Center in St. Paul and they are great hosts.  There are five tennis courts in the back bubble and those are the ones we play on.  Here's an overhead view of the facility in the summer when the bubble isn't up.

(As an aside, it's odd that they aren't oriented north-south, as is the convention in the U.S.)

Put this information about the courts in your back pocket for a minute while I introduce the other part of the story.

As a home captain, I have to provide balls for all five matches. My favorite ball is the Pro Penn.

When we play a match, we need to keep track of our balls. Every match gets a can of three balls and we don't want them to get mixed up with those on adjacent courts. To this end, Penn (and every other ball manufacturer) is helpful. They put numbers on their balls so that they don't get mixed up.

The problem is, Penn only numbers balls 1-4 and we have 5 courts. So two matches will have the same numbers on their ball. I need to keep those balls away from each other.  One possible favorable distribution of balls would look like this:

And this would be an unfavorable distribution of balls, because the 1's on the adjacent courts could get mixed up:

Because it is desirable to let the players open the cans (there's a certain thrill to it, even if you've opened thousands in your life), I as captain have to shake the cans and rotate the balls to see the numbers through the wrapper. It's kind of a pain and the other night as I was rotating the balls so that I could give the right numbers to the right players, I thought,

"Is it worth it? How likely is it really that two consecutive courts will end up with the same ball if I do it completely at random?"

And this is how I introduced combinatorics to my HL Math class.

Wednesday, October 16, 2013

Playing Games, Part 2

I recently blogged about how my Higher Level Mathematics class went to the Brunswick Zone to explore functions. The idea was to have the kids take down information about their transactions.  Step one was putting money onto a card. Step two was using the money on the card to play games and get points (tickets). Step three was redeeming those points for prizes.

On the surface it seemed like a great way to explore composition of functions until I realized...STEPS 2 & 3 ARE NOT FUNCTIONS!


After a few deep breaths I concluded that it didn't really matter. Truly, who really cares if anything is a function. The refinement from relation to function seems like something we do for mathematical convenience.

The Lesson

Step 1: Putting money on the card.

Prompt: Name the domain, range, and rule of assignment.

Pretty cool conversation about piecewise functions here.  Also, the range is anything but trivial.  I divided the class into two groups: half assumed they had the cards already. The other half assumed they needed to buy the card.

Please excuse any clumsy notation.

Step 2: Play games and win points.

We explored the games we all played by watching a few videos we took and looking at the pictures we all contributed to our lensmob album. BTW, thanks to Frank Noschese for the great lensmob suggestion!

Prompt: Pick a game and name the domain, range, and rule of assignment.

The only actual functions were from those games that did not distribute tickets.

Because you pay a flat fee and you can get a variable amount of tickets, it complicated my original idea about a explicit conversation about function composition. It is possible, however, that the conceptual gains were greater because they were not functions.

There were a couple of really interesting games. Take, for example, what we called "Ball Drop."

The fact that you can get bonus plays makes the range very tricky to figure out!  (Or maybe not? Think about it.)

Step 3: Turn tickets in for prizes.

The nice thing about this step is that the range no longer includes numbers.

Not much to this part; the heavy lifting has already been done.

All-in-all, it was a fun lesson with the potential to increase students' conceptual understanding of relations and functions.  I was very happy with how it turned out, and will do it again!