This was an hour and fifteen minute breakout session with Dan Meyer titled Capturing Perplexity. Dan delivered the opening keynote yesterday. Within one minute (I am not kidding) of the dismissal from the Panel Discussion, this session was standing room only. NCTM personnel kicked anyone out without a seat, but not before announcing that Dan had graciously agreed to do this session again in the afternoon in place of a session that had to be cancelled. He later tweeted that the afternoon session was almost full in spite of it only being announced by people on twitter and word of mouth.
My notes are a little more sketchy here at times because I was being an active participant in the session. I did really like that Dan had us engaged and we weren't all looking at packets of problems as I am accustomed to at a workshop.
Dan began with a worksheet involving census data that a teacher had emailed him that used U.S. census data. There were two columns – one for your county, one for neighboring county. It was three pages of questions (2 of them pretty full of stuff) and the verbalization of the question is on the last line of page 3. He then proceeds to tell us that the biggest thing to do is to get the verbalization away from the end of the problem and move it to the beginning. Then do the abstraction – start looking for what information you need.
The session was broken down into three parts.
Part One: Look at Textbook Problems and Make Them Over
He put 4 problems in front of us and we were to determine “where’s the hook?” and "what's the hook?" I'm not going to bore you with all the details. After all, I really think that you need to go see him and experience all the Dan Meyer goodness in person. So I can't tell you everything or it will be spoiled for you when you have the opportunity yourself. Here are some of the issues/bad points of these problems:
"Let’s word these things like human beings." The problems aren't worded well and in some cases they are downright awkwardly worded. In one problem I think he counted 15 words to the question that we/he worded in 4 words.
In the textbook world, you get the info before the question. Not that way in the real world.
Once you have the hook, students have to know who we’re talking about. We want a visual that asks the question and lets us do work on it/with it.
Don’t have the abstraction already on the image – doesn’t let kids wonder.
Keep in mind that the information you are presenting is the starting point, not the ending point.
Part Two: Look at Video and the Internet
**Note - You can find the slides and videos referenced here. **
Dan shares with us that the first year he taught at the bottom of the warm ups, he would have some fact. At the end of the year, it dawned on him that he had it all wrong - it didn't engage the students. So the second year, he flipped it around into a question. Instead of telling students that Oman is the only country that starts with "O," he would put on the warm up "What is the only country that starts with 'O'?" Or "How many letters in the Hawaiian alpabet?" Or "What is the longest one-syllable word?"1 If we bring in the image and look at it with all the information given to them and move on, this is equivalent to giving the students the fun fact. Students don't really engage with the material. When you take an impage and use it for motivation of the question, students engage with the material and all sorts of great things happen.
We then proceed to work with a graph (see Everybody Flushes on the referenced website). We had a great discussion about it. We talked about how to work with the graph since it wasn't our original graph - and this was really great because Dan modified it right there and talked about what to do. Now, granted, people who are more comfortable with technology would have recognized that he created some white rectangles to cover the labels, but if you haven't ever done this before, it is powerful to see it done. I thought this was great. This way, you can have two graphs - the original one that you captured from the website and the one you obscured. The idea here is to look at what is interesting, whatever it is that gets your adrenaline going with the picture or video, obscure it and make that the question you are going for. Then you can reveal the information to answer the question. Keep in mind that there are different levels of obscuring you can use depending on your students. Seeing this in action - watching someone go through the process helped clarify this even more for me. In addition, it has given me even more confidence to proceed on my own. Now to find those things to use...
Part Three: Turn Your Own Lives Into Mathematical Inspiration
A lot of this gets to the heart of the #anyqs challenge - find one photo or one minute or less of video and ask "any questions?" Your video or photo should strongly evoke the same question from your audience.
We finished the session by looking at several photos and videos and trying to decide "What makes a good photo or video?" You can go to the earlier referenced website Dan set up to see the photos and videos. Most of these I had seen as they came through #anyqs but it was still a valuable exercise to ask yourself what question you have and rate how strongly you want to know the answer to the question. Here was the list we generated as a group:
What makes a perplexing photo / video?
Snickers bar video: (most perplexing of the group)
- you can relate to it
- knew it was going to be a math question – suspense
- aesthetic video quality
We also talked about the two faucet examples that Dan had gotten in Grand Forks and why we felt one was better than the other. This also helped to see what *not* to do when creating these images.
This session was everything I hoped, and then some. Probably the biggest thing for me personally to take away from it is the confidence that I can do this. I truly feel armed and ready for the next image or video that strikes me as relevant to the mathematics we encounter in my classes. It has also encouraged me to stop and think more as I plan - what would be an engaging "real world" example to illustrate what I want students to learn and then see what I can find and create. Having been a "traditional" teacher for my 19 years of teaching to this point, this is huge for me. I can't say that I have felt this confident about working through the three acts/four tasks that Dan has brought to our attention until today. I feel empowered and ready to tackle this even though this represents a radical shift in my classroom. Having the opportunity to see the process first hand and work through the key questions made it very clear for me. I think it's like many things we encounter in life - reading it is good, but experiencing it is so much better. If you have not had the opportunity to see Dan Meyer present and/or participate in a workshop he is doing, find one and go. It should be on every math teacher's "Math Teacher Bucket List" - see Dan Meyer present. I am confident that you will not regret it.
1 12 letters; screeched or strengths