This past Saturday I attended the BCAMT New Teacher Conference for 2012. I’m not as new as I used to be, but I’d heard good things about past conferences and felt like I could use a boost of inspiration and ideas after last semester.
The open ing keynote was by Ray Appel, a consultant and Faculty Advisor in SFU’s education program. His focus seemed to be elementary and middle school teaching, but his message about students’ sense-making ability in math class applies across the board. The opening example:
Kyla is inviting 8 people to her birthday party. The party takes place in 4 days.
How old will Kyla be on her birthday?
What would your students do if you gave them this question? Apparently in the average grade 3 class, over 40% of kids will grab the numbers and try to solve this somehow. (What’s even more depressing is how unsurprised I was to hear that.)
The top suggestion I picked out of the keynote was a simple one: give students “word problem” style questions that don’t make sense and ask them to explain why. His worksheet example used a t-chart with two questions on the left, space to fill in why it’s crazy on the right, and he specifically said he found this necessary. Putting the question into a box makes it visually distinctive from the usual format of a word problem, highlighting that you *aren’t* just supposed to read it and “solve”, I guess. But presumably you could make this a discussion question as well.
An example of a linear rate nonsense question that was closer to secondary curriculum:
Ray eats two hot dogs in ten minutes. How many hot dogs will he eat in an hour?
(Apparently he doesn’t really like hot dogs, and wouldn’t eat any more after that.)
One of his student teachers took over the last third of the keynote, which was impressive (both that a student teacher was brave enough to do so, and that he gave that opportunity). The big Stealable Idea was a structured approach to having students teach each other by integrating it into a “Homework Wheel”. Every day kids spin a wheel to see which additional homework questions are assigned (above and beyond a core set of q’s), with a 1/3ish chance of getting a blue/red mix option. At the start of class students have already dragged their name on the smartboard into either a red or blue group; if the blue/red thing comes up, then one group makes up some number (five?) of new questions on that day’s topic and then works with the other group on solving them. The question-writers play the part of the expert, assisting where the students are having trouble. I’ve been too clumsy or unstructured when I’ve tried to have students teach each other, and this looked like one good solution to that problem.
Fred Harwood put on an excellent session in the morning, demonstrating his Top 10 List of things that have improved his teaching. And he authentically demonstrated them, rather than just talking about them – step one was moving desks around into small groups, giving us a discussion question around what education means and giving us space to talk to each other. I dunno, call me crazy but the moment we started moving desks out of rows I knew I’d found the right workshop.
Highlights of his list:
Discovery learning. His example of a rich space for this was giving expansions of fractions like 1/7, 1/49, and a few other 1-over-denominator examples. He set them in front of us and simply asked us to look for patterns and generate questions. Each expansion had at least 3-4 lines of digits printed, and his last example (1/999081 or something) was a full page long – like staring at a sea of digits.
But these digits were PACKED with patterns I had never noticed before. Take this one here:
1/49 = 0.020408163265306122448979591836734693877551020…
Just start reading across … 2, 4, 8, 16, 32, 65…okay, powers of two until it breaks at 65 so I guess it’s a coincidence, right? But what would the next number have been? 128? What if the 1 carried over onto the 64?
I’ll be honest, I’m still not feeling awake enough to have followed all of the ideas that came out of this. But I’m hooked enough that I want to come back to it.
Which led to the next highlight concept: named student discoveries. As in, he has had students discover patterns that he hadn’t known before, and which he couldn’t find any reference of anywhere. When this happens, he names that discovery after the student.
One of his first examples came out of Pascal’s Triangle. A student discovered a really quick way to generate powers of 11 out of Pascal’s Triangle. It’s similar to the above pattern in that it looks like it breaks after a few early steps, until you start carrying digits and realize it just keeps going all the way down. I won’t spoil it beyond that – go take a look and spot it yourself. A student by the last name of Wong discovered it, so Fred named this technique “The Wong Way”.
His website has a list of other student discoveries (possibly not up to date, but still lots of great stuff). Fred gave one small anecdote of a student who was struggling with math coming into grade 9, but after having a discovery named after him he turned around and within a few years was in an honors math class.
The other key highlight was group problem-solving, and we practiced this rather than talking about it. I think we got sucked in for a good 20 min at least, but to be honest I was so absorbed in this annoyingly hard problem (the first one on the page) that I don’t know for sure. All I know is a bunch of us kept working on it over lunch, and swapped emails after in case one of us figures it out later. (I think I’m close but not there yet – no spoilers please.)
Oh, also great tip: Fred was very deliberate in our session about referring to us by name as soon as he could – in this case we had conference nametags to go by – and it really made the room feel more inclusive. His classes don’t have nametags, so his approach to opening day seating plans is a preprinted sign for each four-person group, and groups are deliberately of mixed gender, mixed race – narrowing the problem for the teacher of knowing which name on the sign goes with which face at the table. (Race guessed at by last name, which obviously doesn’t always work, but it works often enough to be helpful.)
One thing that he practiced but didn’t mention was that he had some relaxed instrumental music playing at a background-sound volume throughout the first half of the session; it set a nice tone to the room without being obvious or cheesy. Something I’ve tried but usually made it a little too obvious; it worked really well here, so I’ll keep it in mind next time I’m starting a course.
I attended Marc Garneau’s “Secondary Math Concepts Across The Grades” workshop for the afternoon. He opened up with a slightly modified version of Dan Meyer shooting a basketball (and gave credit), and then transitioned into a few more examples of rich activities that can be used at different levels across the grades.
Activity #1 was taking a piece of twine, measuring it, and then tying knots and measuring it to fill in a table connecting rope length to number of knots. Collected data, plotted it, and then we looked at a set of questions with some explanation as to how the questions asked afterwards can scale this to anywhere from grade 4 to grade 9 linear relations.
(My partner and I ended up rabbit-trailing into adding excessive amounts of knots to find out if it would go non-linear, and creating uber-knots on top of each other to see if that breaks linearity.)
Second one we worked on was a set of three diagrams made of colored tiles with a growth pattern. Fill in the table, recognize a growth pattern, predict what the next two will look like, generalize. I’ve done one like this before where students create their own growth patterns (with tile “creatures”). One thing this activity had which the tile-creature one doesn’t is that you can highlight how many ways there are to interpret visual patterns; we had about half a dozen different ways of connecting the visual pattern to a generalized algebra expression.
There were a few more activities we didn’t have time to dive into for long; the afternoon felt to me like a natural continuation of the morning, working on math in a setting where discussion and question-generation was a norm.
Coming off of a long, overwhelming semester back into a semester of on-call teaching, it was good to see examples of how things can, and do, get better. When you’re new at teaching plus trying “new” things that aren’t the norm, the usual newbie flaws and mistakes end up being pinned by others onto your “new” techniques. It’s relieving to see experienced, skilled teachers who have taken the ideas I want to explore – collaborative group work, discovery / inquiry work, and other techniques to emphasize real comprehension – and see that yes, they can work, and can work really really well.
Like most things worth learning, it’s just going to take a lot of practice.