Standing and Talking: a first attempt

Note: Google Camp 5.0 will be Saturday, Nov. 4. Registration is open for TDSB teachers on K2L. This event always sells out, so register soon! If you're interested in presenting, submissions are open until Monday, Oct. 2. The TDSB's Renewing Math Summit will be Friday, Dec. 1; you can still submit a proposal until Sept. 30. Yes, that's today. Hurry!

When I did my physics honours specialist with John Caranci way back when, he told us that one of the easiest ways to become a great teacher is to try or adopt one new technique per month. Well, I'm still working on that (I probably average 3-4 a year), but this year I'm going to really make the effort to try them several times per month.

I've already made the first change by getting the students used to grouped tables -- a bit challenging in one of my classrooms which has fixed benches, but I'm trying to make it work -- and I started my October technique a bit early because I couldn't wait.

I was inspired by this blog post by Sara Van Der Werf to try a Stand and Talk with my grade 11 mixed math students last week. To summarize, the old-style "share with your neighbour/elbow-partner/TPS" doesn't really work most of the time. Sara has found that getting the students to stand up and walk across the room to talk to another person and giving each pair a paper with something to look at with the instruction "notice 10/20/50 things about this" really increases student engagement. Her post is excellent, with specific instructions on how to make it successful and a lot of math examples to use.

(By the way, the link to the "rumors" group learning routine at the end of Sara's blog post would be great for the prediction part of POE or for review.)

I thought mapping diagrams would be a good place to try this. We'd looked at domain and range and function/NAF. I prepared this picture for them to look at and notice at least 10 things (yes, it's supposed to be a big number).

This is my revised version

Did it work? Mostly. I wound up grabbing the wrong folder and left the students' copies of the diagrams in my office, but I did put them up on the screen. Not ideal, because on my original version the arrow heads were not as obvious and I used too small a font for the sets of points and the labels, so they were a bit hard to read from the back of the room. There was a bit of "I don't know what she wants, do you know what she wants?" at the beginning, but after I encouraged them to go for the obvious first and used Sara's prompts ("I should see you pointing," "What do you wonder?" "Everything on the screen is there for a reason. What else to you notice?"),  I heard some good discussions. And once we were talking as a class, I had volunteered suggestions right away instead of the usual silence.

Some of the suggestions:

• there are circles on the page
• there are numbers in the circles
• the numbers go from negative to positive in both of the left circles
• there are no negative numbers in the right circles
• the numbers go in order
• there are 4 numbers in one left circle and 3 in the other
• both right circles have 3 numbers

I was a bit surprised that nobody mentioned the arrows, but that could be because the arrow heads wee small and didn't really register, but when I pointed out that there were arrows, more suggestions came in thick and fast:

• an arrow goes from the -3 to the 3
• another arrow goes from the -2 to the 1 (etc)
• two arrows go to the 3 in both right circles
• there are two arrows going from the -1 in one circle, but all the rest have only one arrow

Nobody noticed the connection to the coordinate pairs above the diagrams, but I think that is because the font was too small and they didn't really notice it. Once I asked "do you see a -3 anywhere else on the page?" the penny dropped.

• Oh! The arrow goes from -3 to 3, and there's a -3 and 3 together above. 
• Same with the -2 and 1.
• That first circle is all the first numbers and the second is all the second numbers

At this point I switched to Socratic questioning, and we established that the left circles were the x's, or domain, and the right circles were the y's, or range; none of the numbers were repeated and were in order from most negative to most positive; that one was a function and the other wasn't; and that you could tell whether it was a function or not by the number of arrows coming from each of the points in the domain. I then told them these were called mapping diagrams and had them create some from sets of points.

We stood the whole time we did this, and nobody complained. This was very surprising to me because there are a few students in that class who complain as a matter of principle, but who were actually mostly engaged in the activity and even offered a suggestion or two.

So will I be using stand and talks again? You bet. I'm already scheming my next picture. I love the way I could work concept attainment^* into the notice and wonder. I need to make I also focus on the "what do you wonder" questions. The diagrams do require a bit of thought first, so I'm aiming to do two per month in my math classes to begin with and work up to once a week in all classes. I'm already planning on trying this as a way to introduce B-R diagrams, chemical formulas, and circuit diagrams later on in grade 9 science; and more immediately, rational vs irrational numbers, polynomials,  like vs unlike terms in grade 9 math; standing waves in physics; and different forms of the quadratic function in the mixed math. That will do to start with, I think!

^*I did my math honours specialist final project on concept attainment, and I keep meaning to work it into lessons whenever I can. Perhaps I'll do a blog post about it so I will remember to use it.

Group multiple choice tests and DIY scratch cards

Last year while on leave I had the opportunity to watch a live webinar with Eric Mazur on assessment as a silent killer of learning, and I got really excited by one of the ideas he presented. Here's a video of that same lecture; the pertinent section starts at around 41 m 44 s and it's only about 6 minutes long. I recommend watching the whole video some time.

I love this idea. It's like test corrections, but without my having to grade the test first. Because of the nature of the test, the question level should be such that it should be difficult for any one student to get 80% by themselves. Lots of higher-order thinking skills, not so much of the recall.

I was hoping to try this method out with my pre-AP physics class several times this year, but I only got a chance to do it once right at the end in the electromagnetism unit. I opted to go the scratch card route, since coding a trouble-free non-mc group test would take more time and energy than I usually have in May and I also already have a nice bunch of conceptual mc questions (plus some shamelessly pulled from previous OAPT physics contests for extra oomph).

My test was 15 questions long. The students sat around trapezoidal tables in groups of 3-4 more or less based on their (self-chosen) lab groups -- the class is pretty homogeneous so that worked out fairly well grade-wise. I gave them 25 minutes to solve the questions on their own, then put the scratch cards on the tables. I also gave them individual white boards and let them use the blackboards if they wished. [One of my students is mute, and since I didn't let them use their phones, having a personal whiteboard for communicating was crucial.] They had the rest of the period (45 minutes) to redo the test as a group. Difficulty-wise, I tried to err on the side of the test being too easy since it was our first try (and I always tend to think questions are too easy when in reality, not so much).

I have to say, it was a lot of fun to watch. There was cheering. There were groans of agony. Most importantly, there was immediate feedback and learning... and I didn't have to mark it myself. Marks-wise, we went from high 50s to mid-90s, with most marks in the 70s. The marks are a bit lower than this class is used to, but I'm putting that down to it being the last test of the year and having rushed through teaching some of the material. I wound up just adding their individual marks to the group marks and making the whole thing out of 70 (one of the questions was a bit too confusing, so I made it a bonus).

Weirdly, not many of them used the whiteboards. I need to get the students using the whiteboards early and often in class so they are used to thinking things through visually.

I wish I had done this for the post-friction lab quiz. I am thinking that I will adopt this for the multiple-choice sections of future tests; since I'm considering moving to standards-based grading for the calculations/written explanations, I might get the best of both worlds.

On to the slightly more crafty section of the post.

I used 4x6" matte photo cards because I have a huge number of them at home, but you could probably use construction or even regular paper. There is also the online IF-AT test maker, but that is geared towards (very) large groups (minimum 125 cards). To send the cards through the "no, I really only want to print on letter-sized paper and maybe legal if you really insist" school laser printer, I used loops of masking tape to tape the wrong side of the photo card to a scrap piece of letter-sized paper and send it through. Using masking tape is important because it doesn't form an immediate permanent bond like clear tape does; you're less likely to tear the card when you remove it. Painter's tape would be even better for this. I had to experiment to see which side tore less.

Once you've printed your cards and answered them (I used a red checkmark), you make them into scratch cards. How to DIY: some quick Googling brought me to this site. Essentially, you need some clear tape, acrylic paint, dish soap, and a brush.



























You tape over the bubbles, then mix 2 parts paint to 1 part dish soap, and apply. Ideally, you'd apply thin coats so you don't get a lumpy paint job, but frankly the bubbles are so small I don't think it matters. I started by using gold paint but it was taking too long to become opaque -- I got up to 5 coats on my tester cards and you could still see through the paint (on both sides if you held it up to the light), although it's possible I originally had too high a ratio of soap to paint. I added a large dollop of grey paint and presto! I only needed 2 coats to cover my bubbles.

You could make a stencil if you wanted to get really finicky and avoid overpainting; I just scraped off the worst of the excess paint where I could.

I also made scratching tools by cutting up an old plastic membership card. The flat edge was pretty much the size of a bubble, so they wouldn't "accidentally" scratch off part of the wrong bubble. The kids loved scratching off the answers; this would be fun to do as a vocabulary lottery card-type thing or a fun take on a homework pass. And it's reusable!

I'm also going to explore doing this as a computer exercise because multiple choice is great for conceptual questions, but a bit of a pain for calculation exercises. I like that in Mazur's version, the group members' answers come up and that's what they discuss. I'm sure Mazur got someone to code specialty software, but I think it could be done with GAFE tools using a combination of Forms, Sheets, my self-grading quiz tutorial, and the FormRanger add-on. The one difficulty I see is getting the students to write exactly what I put in as an answer, and how to let them know that they need to fix a small issue (say, sig figs or direction) as opposed to having completely the wrong answer.

What other ways could we use scratch cards (physical or computer-based) in class?