I'm writing this on the train back from the OAPT conference hosted at the University of Western Ontario, and it was, of course, amazing. I have so many thoughts and new great ideas to put into practice. Some quick takeaways:
thinking about using improv techniques in class to overcome my (and students') implicit bias, especially "Yes, and?"
"We use mathematics to help us make the physics more precise."
"Just because I don't have a 'math brain' doesn't mean I don't have something useful to contribute."
"You're not part of a group, you're part of a team."
Yes, the students do really need to draw a picture
Why haven't we been using the rotunda at Jarvis to make super-long pendula?
I think I'm going to have to wait until June to do the write-up justice. I will share my presentation on Tweaking the Traditional Lab below; a link to various files and resources is posted in the resources section of this blog.
(Incidentally, one of the things I always like to mention when I'm introducing myself at presentations is how amazing the PD is on Twitter. The chart on the first slide is a perfect example. Elizabeth Houwen (a math teacher, incidentally) posted it last June, and I thought it would be a great way to get the students to practice unit conversions as well as estimation, and we also got a nice little lab out of it and an anchor chart so they have "reasonable" speeds to compare their answers to. All from one small tweet!)
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I've been busy converting my drill sheets practice sheets, which I mentioned in my last post) into Google sheets, as well as creating new ones. I'm fairly proud of the chemical nomenclature one (in part because I just found out how to write superscript and subscript numbers in Sheets, so the clunky ^3 _4 notation is mostly gone), but I really want to share the electromagnetic right-hand rules ones.
I made these using the =image() function, which allows you to put an image directly into a cell (and not just overlay the image on top). Unfortunately, you can't use the shared url of images on your Google drive (which is odd and annoying).
I'll probably refine the mixed version so that it's a little more clear what you need to find in each question; I'm not sure a student would recognize immediately that they need to find the direction of the action of the magnet for 1 and the location of the north pole for 6.
You can find these and a lot more randomized practice sheets at my course website; click on the practice sheets link under Resources.
Incidentally, sometime between last December and April, Google changed the formatting of "publish to pdf" for Sheets so that it's landscape instead of portrait. There doesn't seem to be a way to modify this, and it's really mucked up my formatting. Everything is spread over two pages, and don't get me started about what it did to my spectroscopy sheets.
I'm still trying to put together my blogs for the fall PD I've been doing, but for now I wanted to share a few things I'm really excited that I figured out how to do.
Inspired by Robert Prior many years ago, I started coding a lot of Excel spreadsheets as randomized drill sheets on many topics. My goal for this year is to get most of them up as Google Sheets so I can publish them to the web and students can go straight to my website to print out an infinite number of sheets.
Anyway, I've also been working on adding new, richer sheets to my catalogue. In particular, I was very jazzed last year when I figured out how to get a spreadsheet to draw spectrographs (hint: error bars). And last night I spent far too long working on how to get a Hertzsprung-Russel diagram (yay for the Bubble chart, boo for the fact that the labels are arbitrarily hidden when you go to a larger font).
Behold, I give you my Spectrograph and HR diagram drills for the grade 9 space unit (and Earth and Space science, too).
I'm still working on the HR diagram answers; I have to figure out how best to get it to choose whether it's on the main sequence or not. Also, I think I need more white dwarf stars, because that area is looking pretty sparse.
However:
If you'd like to see my other drill sheets, head on over to the drill sheet section of my course webpage. It's very much a work in progress. I have a lot more sheets than I've listed there.
I have completely fallen down on my plan to blog at least once biweekly. I'm going to catch up on blogging all the PD I've been doing though, and I'm going to try to get them done before the break.Consider it a pre-holiday present. For TDSB teachers, make sure to sign up for the Technology-Enabled Learning sessions (aka the after school workshops) on K2L. For LN24, there are a number of sessions you can still attend this and next month. Note the change to the Virtual Library session. Sign up now!
Wednesday night I attended York U's open-house night for high school physics teachers. hosted by the Physics and Astronomy Department. It's a great evening of PD, not just because they serve dinner with wine, but also it's a chance to learn about some of the ground-breaking research taking place right now. The topic this year was "How large is the proton? ̶ the proton size puzzle".
During dinner, there were three 15-minute talks, which is an excellent length. The first was from Dr. Randy Lewis. He talked about how my previous 3-quark understanding of the proton (seen below in the basic Wikipedia image)...
...is incomplete; the masses of the three quarks make up less than 1% of the mass of the proton. In reality, at least as far as we currently understand, what we have is much more complicated: at any given time, uncountable pairs of quarks and anti-quarks are appearing and disappearing (along with the associated gluons), and the whole thing somehow makes sure that three valence quarks are always unpaired, as in the picture below, grabbed from phys.org
The blue circle isn't really there. As with everything, protons are mostly empty space. The green circles represent quarks, the orange antiquarks, and the springs are gluons.
Because of this hurricane of energy, current theoretical attempts to calculate the size of the proton aren't there yet, so we need to turn to experiment (the subject of the next two talks).
Dr. Eric Hessels firstly blew our minds by telling us that because of this – We can determine the size using atoms – but atoms with electrons and atoms with muons give different answers.
Dr. Marko Horbatsch – Maybe scattering electrons off of protons can determine the size – but maybe it can’t.
There are some fantastic PD opportunities coming up in the next few weeks.
Google Camp 5.0 will be on November 4; sadly it has already sold out, but you can put your name on the waiting list and some of the sessions will be simulcast on Twitter. I'm thrilled to be joining some amazing speakers; I'll be presenting a follow-up session to my Flipping Your Classroom session from March -- I'm going to try modelling a flipped lesson! There will be pre-session homework (if you so choose)! I'm very excited to be talking about EquatIO and Desmos, which are two really amazing ways to take math and STEM digital. As usual during the day there will be a room with helpful helpers available if you've been running into difficulties with GAFE and need someone to walk you through the solution.
The TDSB's Renewing Math Summit on the Friday, December 1 PD day is offered to secondary teachers. The focus is on Teaching/Leading in an Equitable Classroom and 21st Century Global Competencies. I'll be giving a session called Rope-a-Slope: Inquiry in Grade 9 Math where a simple piece of rope and a measuring tape and guided inquiry can lead to learning about relationships between variables, slope, direct and indirect variation, and more. The other sessions look amazing as well -- I'd love to be able to attend them all. There might also be a drop-in room to learn more about digital math tools like Knowledgehook, Desmos, Geogebra, etc.
Registration for TDSB secondary teachers is on K2L until November 23, or they reach capacity.
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.
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?
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.
