Saturday 10 June 2017

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).

action shot of group mc test


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.

required materials for scratch card

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.

printing the cardsbubble cards printed
























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.

one coat of gold paint
tape over the bubbles
























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.

painting in the bubbles on the scratch cards


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!

scratch cards completed

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?

Sunday 4 June 2017

Updated: Fidget spinner math


Update: I've added a link to the data in Desmos and TI lists below.
Yes, I jumped on board the "if you can't beat 'em, join 'em" boat.

Inspired mostly by Harry O'Malley's site, I brought a fidget spinner* and my phone to grade 11U math class one day and the students modelled the spin. The above graph is the one of my student's results. It's a bit wonky because in the two days since I had bought it, one of the end caps had fallen off, which made the central bearing ring shift off centre. This made it slow down a lot; the above graph shows a few tries at spinning. The student at the top of the post took an average of the cycles while other students just looked at the first.


To make a good video, mark one of the edges of the spinner so you have a reference point to track. The app I used is VidAnalysis Free for Android (for Apple fans, Vernier has an app for LoggerPro that lets you do the same stuff, if not more). Don't spin it too quickly unless you have much better equipment than I do -- I tried to analyse that lovely first video and got goobledeegook because it's spinning too fast for the video to capture properly.

You then pick reference points (known length and origin of coordinate system) and track your mark. You can skip forward and backward in time to get to the section you want to analyse. I goofed because I forgot that I had made a spin without my finger in the way; by the time I remembered, I had already invested too much time getting the other data. Hence the starts and stops.

I didn't want to take up class time getting the analysis ready, so we discussed what equation we were likely to see, and then worked on other problems. Before the next class, I made the analysis and turned the data into graphs in Google Sheets. The next class, I put the x-distance graph up on the screen and got the students to figure out the model. When they had an equation, I graphed it against the data (if you do this, remember that spreadsheets do trig with radians, not degrees).

It was a really good exercise, considering it's the first time I've officially used the VidAnalysis in class. We had some great discussions about the vertical translation (did I deliberately make the coordinate system off-centre? no, but I will next time because that led to interesting math); how to deal with the increasing period; how the amplitude of our function compared with the actual measured distance.





I've since shifted the centre bearings back and made another, better video analysis. The screen shots are below:
What I like about this, mathematically, is a) how it shows the spinner slowing down; b) how it shows that I didn't hold the camera completely still -- notice that the "zero line" of the equation shifts up (nice for composition of functions!); and c) the x- and y-distances are essentially translations of each other (sin vs cos). I could have really expanded on this activity and got them to break the functions into different domains.

The velocities show the same math effects as the distances; this could be used to show that the derivative of sinusoidal functions are still sinusoidal (and how). If only Google Sheets would get their act together and let us connect points in scatter plots.

More screenshots. What I really like is that you can upload the data as a csv file to Drive.
Copy-paste makes it simple to create a spreadsheet.

Note that the Free part of the app means ads. I was still giving it a trial run, but I think I will upgrade to the premium version because it's a great little app.


I started the trig functions section by creating a periodic wave using a salt-shaker pendulum (an idea I cribbed from someone on Twitter -- I can't remember who it was, but I'd love to give her the credit). I now wish we had filmed the pendulum at the same time so we could compare our rough model to the data. Future ideas!

I have a graphing calculator assignment that grabs tuning fork data from a microphone; I get the students to model the function and work backwards to determine the frequency of the fork. We didn't get to it this year, but it would go well with this exercise.

If you'd like to use my data, feel free to make a copy of fidget spinner 2, or download the csv file. I'm going to import this into a Desmos activity and graphing calculator lists at some point; when I do, I'll update this post with links. Update:Here are links to the data in Desmos and as TI lists.

*I meant to use one of the students' spinners in my MCF3M class, but ran into difficulties because that student wasn't in class the day we were supposed to do the model. Since I wanted a permanent mark on the spinner, I decided to not buy trouble and get my own. Plus, they're fun.

I did this exercise with the 11M students as well, but we wound up doing it as a class instead of individually.