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!

Mequals and Hats

I write this with complete deference to www.nixthetricks.com. I will rationalize my use of these dirty, horrible tricks by saying that this notation is completely arbitrary and does little for mathematical conception. I'm a math teacher so I like it, but for the average 10 grade Geometer, I'm not sure these subtle differences in notation have much real meaning.


How do you get a kid to recognize that measures are equal and angles are congruent?  MEQUALS!  If you use an EQUALS sign, you need to put an M on the front.  MEQUALS.

Shameless, I know.


If one of them wears a hat, they all wear hats.  BOOM.

Friday, September 20, 2013

Playing Games, Part 1

I was really in awe earlier this week when local hero Christopher Danielson posted about sameness in his college algebra class.

Vending machines as functions is really intuitive.  And neat.  Easy to talk about their domains and ranges.  Easy to talk about their rules of assignments.

I was less excited about whether or not the change machine is a true identity function.  That's the topic that took over the comments, and frankly I'm getting bored writing about it.  Perhaps that's a personal shortcoming.

But as an IB Higher Level Math teacher about to put formal definitions on functions and then embark upon compositions and inverses, I thought, "I wonder if it's worth trying to relate vending machines to functions?"  "How can I bring this into my class?"  "Is there anything to be gained?" And, "How could we relate this in a way that's efficient, engaging, and relevant?"

And then the Brunswick Zone walked into my brain.
Turns out the BZ doesn't give out tokens tickets anymore.  (That's very 1995.)  They use a card now.

I had four days to turn this crackpot idea into something meaningful.

So today when we went over there to win points (the e-equivalent of tickets) and then prizes, I gave them this e-worksheet:

(This form is live, by the way, so feel free to contribute if you live near a Brunswick Zone.)

My verbal instructions were probably a bit simpler.

We want to build our collective intelligence about the transactions that occur at the BZ.  (Money to card, card to points, points to prize.)  Take as many pictures or videos as you can of the possibilities of each transaction so that we can collectively begin to understand them.

Well, maybe that wasn't simpler, not sure.

Bottom line is, we got a lot of cool information that will be useful, relevant, and enhance student understanding of functions.  Take this for example:

A lot of possibilities when it comes to putting money on a card.  A new card, by the way, costs $1.  So if I went with the $5 option, really I'd have to spend $6.

Ok, got my card and ready to go.

Off to the games.  I really rocked this one:


40 tickets is a good haul, that spin alone could have gotten me a Spongebob Squarepants ball.

All in all, I'm hoping we can pool our experiences to come up with some really cool questions.

What would a function look like for putting money onto a card?  The domain?  Range?  Rule of assignment?
What would the functions look like for getting points onto your card?
What about for turning points into prizes?
And then we have games like this?  You win the prize straight up, no points at all!  (I lost $4 trying to get a giant husky.)

And then there's this one...no points, no prize!


If you're curious to see what images we've captured, check out our photo gallery.

I haven't written the lesson plan for Monday yet, but I believe I have plenty of raw materials.  Stay tuned for part 2.