Saturday, 27 July 2013

MAT: TMC 2013 Day 2 - Rapid Fire

I blogged previously about arriving on Wednesday. I then blogged about Day 1, aka what happened on Thursday. Today is Friday, and Day 2 of Twitter Math Camp 2013.

I woke up before 7am again because my brain hates me. Didn't crawl out of bed until after 7:30. As mentioned yesterday, since the in-house restaurant allows social networking or ease of billing, but not both, I explored elsewhere. Namely the Wawa convenience store across the street. (That's the name of a town in Ontario, so I am amused.) Bought an egg sandwich thing, walked over to the presentation site via Sansom St., to have a look at the fare there.

At the building early, so I end up stopping outside to observe Tina Cardone (@crstn85), Matt Lane (@mmmaaatttttt), Chris Lusto (@Lustomatical) and Kate Nowak (@k8nowak). Oh, so that's a k8, with a professional looking business card holder and everything. Eventually I go inside and schedule starts.

My Favourites Session:
1) Justin Lanier (@j_lanier) talks Math Munch. A weekly digest which "curates the Mathematical Internet", with middle schoolers in mind; has it's own twitter account (@MathMunch). Justin references Dan Meyer's post about things needing to be Easy, Fun and Free... and how a year ago it didn't seem to be "Easy". So redesigns were done including a Getting Started page (OMG, I should do that!), and newsletter, plus comparing Easy with Important.

A very nice analogy made in that there may be a "common core" but with "uncommon extremities", likening math teaching to similar apple cores/tree trunks but with extremities that make each of us unique. I also liked the "raise your hand if you have a hand" to check the system comment, as a way to immediately engage everyone. ONTARIO TEACHERS: I'm reminded of David Petro (@davidpetro314) who runs a weekly summary of web links blog geared to our math courses.

2) Nicole Paris (@solvingforx) talks orangemellows. If you put 2 marshmellows and 3 marshmellows in a bag, you have 5 marshmellows. If you put 2 oranges in a bag and 3 marshmellows in a bag, you do not suddenly have 5 orangemellows. Actually physically doing this is helpful, and I liked her calling us out on "you didn't look [in the bag]". It's a concrete way of demonstrating like terms.

Cal tweeted this picture of me and group
3) Me again! I dialed up the Stargate to demonstrate the Unit Circle of Trig - total credit goes to Esmeralda Fernandes, a teacher at my school. I'm mostly demonstrating her work. Basic idea: Instead of just showing 'sin' and 'cos' in a generic circle, actually have a unit circle with scales, then when you draw a line out at 25 degrees, use the point on the circle to drop down to the scales, thus estimating values for trig. (With thanks to Michael Pershan for checking my work on his calculator.)

Then use both values to estimate tangent (rise over run). Then go backwards given a trig value, and hey, you can see there's two angle points, no messing about to find the second answer your calculator won't tell you. Also works with radians, visually. Don't teach trig? Use the slope part only, or adapt for proportions; 40% of the way around a circle is what amount of the circumference?

Later Anthony (@aanthonya) told me he liked this because you have to understand for it to work, but it's easy enough that students can explain to each other; Sam Shah (@samjshah) also said it was useful for the inverse element in PreCalc. So yay.


From 9:30 to 11:30 as yesterday. Stats lost Ashli, Sean and Ginny, but gained David Price (@compactspaces) who I actually met last night early on at Karaoke. The more Nik Doran (@nik_d_maths) talked, the more I feel like Ontario is aligned more to England than the US.

Statistics is one strand out of some maths courses? Check. (11 college level for an Ontario example.) We teach Standard Deviation but not variance? Check. We don't make a deal out of 'n' or 'n-1' in terms of degrees of freedom? Check. No use of 'hats' to indicate predictions? Check. Nothing about Central Limit Theorem? Check.

It's "globe"al math!
So Glenn (@gwaddellnvhs) started things out by explaining the Central Limit Theorem, which is: Regardless of the shape of a population, if enough random samples of large enough size are taken with replacement, you will end up with a normal distribution. He illustrated the point with pennies, which is slightly more problematic in Canada these days, but I'll continue regardless.

From a bucket of pennies, remove one, record date by marking an 'x' in on a graph, return. Do this LOTS. The distribution will likely be skewed (not many really old, lots in very recent years). Next, remove a group of five pennies and average them, record by marking an 'x bar'. Do this NOT lots, like maybe 40 times. The mean of the first graph will match the mean of the second - and the second will be a normal distribution.

Glenn then extended this to categorical data, such that you remove 5 pennies and determine the proportion in the 2000s. (For instance, if 3 of the 5 are, you record 0.6 on the graph.) This will also make a normal distribution around the average number of 2000s pennies for the whole population. You can also just take 15 samples of 20, rather than 40 samples of 5.

A bit mind blowing, but put forth here very simply and concretely. Related to this, Anthony showed a clip from "The Code" (Wisdom of the Crowd) to show that if a lot of people gave their estimates for an answer, averaging them will put you close to the true value, as high/low errors cancel each other out.

We talked more about the normal distribution at this point. For instance, the idea of there being '1' under the normal curve is a problem. Nik indicated that calculations outside of straight percentiles are an issue, and I'll back him up on that, though we still really don't know why. Nik also plugged the book "Developing thinking in ... Statistics", one of a math series that he's reading. It was mentioned that you CAN add variances, but you cannot add standard deviations. So why use standard deviation? Because it's units will then match the mean for the scale.

Hedge then pulled us back in to demonstrate some activities. Legal cases were mentioned, one about a chair breaking in a Macdonalds, and I referenced the Sally Clark trial. She tossed a globe around, where the left index finger being on water or land could ultimately model the percentage of land mass on Earth. Stu Schwartz ( was mentioned as a resource - he has some stuff for other courses too. Also, avoiding pronouns in examples is recommended. There was also a marshmellow cannon, not fired off. Stats wiki page was updated.


For lunch I bypassed the food trucks, partly still guarding my cash, but also wanted refillable water, I'm not drinking enough. Looked for "Sabrina's", ended up at train station, so went to "Slainte Pub" instead. Leaving I ran into Kate (@fourkatie), Pam (@pamjwilson) and Roxanne (@justagurl24) who is a fellow Canadian. She teaches at a school in Saskatchewan with under 200 people, if memory serves.

Ok, actual #globalmath tweeps
Was back at the building early, so Jaclyn (@JMorr417) showed me how to fold some pinwheels for the origami project. Did a few while observing the global math people having a discussion (#GlobalMath Department meets Tuesday evenings). Then time for another round of My Favourites.

1) Michelle (@park_star) talked Representations. Represent any pattern using five forms - Graph, Table, Concrete/Picture, Verbal scenario. Given one, create the others.

2) David Wees (@davidwees) talked Questioning. As the teacher, make sure you wait after asking something, no matter how uncomfortable it feels. Then when students ask questions, see if they are "Stop Thinking Questions" (Is this right?), "Proximity Questions" (So long as you're here, is this right?) or "Start Thinking (Curiosity) Questions". Only answer the last type of question.

3) Adrienne (@shlagteach) talked Do You Need A Ref. Having students be able to not only identify errors, but explain HOW the mistakes are errors.

4) April (@GooberSpeaks) talked Trig Murder Mystery. A 'Clue' style setup where every correct response eliminates an option, until you are left with the murder. She offered a handout based on law of Sine/Cosine, noted that it's a nice activity to leave with a substitute as well.

5) Jonathan (@rawrdimus) talked the Points Game. Randomly assign groups, then give them points for things - don't tell them the rules. You can make those up as you go. "There's no real reason why you're winning, but you're winning." It's a classroom management strategy; point totals can be reset every six weeks.

6) Jenn (@crasejd) talked "4 to 1". Put up four questions on a topic, make groups of four. The teacher only needs to check '1' result from each group, for instance the sum. Go around and if "Not right", leave it to them to figure out which problem has the error. Can also assign numbers 1-4 and, for instance, make the fourth problem more difficult.

7) Chris Lusto (@Lustomatical) talked What Is. It came from starting conics with the question 'What is... a circle?' We all know, but can we EXPLAIN it? Apparently not well. He then challenged students to come up with an example that fit their offered definition but was NOT a circle. This narrowed the options down, or resulted in a frustrated description of just how to draw it. Which then led to the interesting question... if a circle is defined only to be a series of points from a focus, how can it have area?

At 1:30pm Team Mathalicious presented "Still Keeping it Real" with founder Karim (@karimkai) as spokesperson. Many here apparently already know about the mathalicious website, which looks at:  How does math manifest itself, and how to use tools to understand it. Seems they'll be shifting their multimedia component to be something more dynamic, as well as (in 2014) rolling out project extensions, to cover more than a two day lesson plan.

Karim's shows a task that combines inverses,
inequalities, and teenage relationship angst
We were taken through two activities, one on Datelines and the Romance Cone (or RoCo). Nik Doran tweeted out a link to this xkcd strip that offers up the math for the Creepiness Rule. Their second activity is new - and OMG, it's AWESOME. It looks at the sets of Dangerous People as compared to PRISM Flagged People, then asks the question - given you are flagged, what is the probability you are actually not dangerous?

Effectively the old question about "this test is 99% reliable, what is the chance you have the disease" updated to be more immediately relevant. But it also clicked tree diagrams into place for me - for while the tree diagram shows the conditional probabilities, the venn diagram gives the FINAL state once you have worked out all the probabilities and where they overlap. I'm not sure WHY this never clicked before. Derp.

During the session, I was comparing notes with David Price next to me. After the session, I was talking with Mark Sanford (@hfxmark), and learned that his godson actually goes to the same school in Ontario where I teach. Small world.


Back in separate sessions again, I went to Elizabeth Statmore's (@cheesemonkeysf) presentation on adding "Stickiness" to Rich Tasks and Math Projects. I recall when she first blogged about this in March. In brief, the book 'Made To Stick' (follow prior link for authors) looks at what makes anything MEMORABLE. It postulates you need: Simple (find the core), Unexpected (curiosity gap), Concrete (activate senses), Credible (testable), Emotional (a gatekeeper) and a Story (good or bad). Which is a lousy acronym.

Sticky situations also involve projectors
Why do we want to do this? Two reasons. One, yourself, in that sometimes you're f***ed, having to include some standard that doesn't link in very nicely. Two, for students, a matter of inclusion. Apparently 65% of the population are visual learners, but this still leaves several million others who need more. Here you map in multiple ranges. Elizabeth is also left handed, and suggests even just using your non-dominant hand can pull from your subconscious.

We split into groups here to play a number line game where the cards drawn involved doing some of these alternative style tasks. Such as describe something while back to back with another person, or while on one foot, or suggest how to incorporate the sense of smell into a mathematical concept. I was with Sadie (@wahedahbug), Megan (@mgolding), Marsha (@MarshaFoshee) and Eric (@mrbenzel).

Then went to the "Organization" session by Tina Cardone and friends. In transit I was identified as 'the cartoonist' by someone. I admit I was thrown for a loop, I definitely do NOT see myself as being known for my personification of math drawings within the math community itself. But cool.

Tina talked DropBox and sending emails to yourself as a way to save things for later. Also using a physical cabinet with tabs to organize materials, and Simplenote for organizing remarks on pedagogy. Sam Shah talked Virtual Filing Cabinet, which is not something he recommends, but being web based other people can (and do!) use what he links together. Anna (@BorschtwithAnna) talked Evernote, where you can annotate - it requires a bit more processing beyond 'star it for later' - then LiveBinders which is a method you can ask @Fouss about.

Fawn Nguyen (@fawnpnguyen) offered the filing system of someone who's been teaching for a while - you cannot keep everything, that's crazy. Start with the math standard. Look for tasks, settle on 5. If you find a 6th, it replaces one of those 5. Then create Standards Based Grading assessments and retakes. Also "Print everything out. Because when you need it most, technology fails." Be that the wireless, the printer, what have you. In closing remarks, Nicole Paris also offered up wikis, and showed one that her colleagues have used.

This brings us to 5pm and I was mentally crashing, though I still spent an hour cruising through Twitter to see what was up. Cal Armstrong (@sig225) and Michael Pershan (@mpershan) independently brought up an interesting point. At the camp we're reasonably well split male/female, but not in other facets of diversity. Is this an issue in the profession? In the use of technology? And regardless, how do we grapple with this problem?

Also learned that Cal teaches at an independent school down in Southern Ontario, near where I used to live.


I fell asleep for over an hour, then when I got up, started crafting this post, as I had done yesterday. (These take me over two hours to do, by the way. Yeah.) Before I realized, it was kind of late, and there was a gathering scheduled for 9:30pm at Jolly's Duelling Piano Bar; not on the schedule, just something proposed at lunch.

Don't look too closely at the phrase of the night.
I showed up a little before 9:30, many teachers had been there a while and eaten dinner previously. Not too long after my arrival, all math teachers were called up to the front - the half of the crowd still seated mostly had 'what the hell' looks - and the piano men sang... "Baby Got Back". Okay, full disclosure, I do NOT like this song, and yet this is the third time I've heard it in as many nights. The heck?

So that didn't make me any more comfortable, and I pretty much ended up standing off to the side for the next hour. Spoke briefly with Edmund (@Gelada) as I seem to do at these things, sparking the remark of doing "Anti-Social properly, in company of others". Meanwhile other math teachers had song requests and dance events, and someone got the piano man to sing "Tweet Me Maybe". So fun in the general sense.

Eventually I left to have some dinner (I never really saw any waitresses, and you could barely hear someone standing in front of you anyway). Got back to the hotel about 11:30pm once again, then immediately back to this post. Which I finished just after 2am and am going to put up now at about 3am. Enjoy?

New business cards reciprocated:
Kate Nowak


  1. If nothing else (and it looks like you got a ton of useful ideas just reading the above), I see at least two plot lines for the Math-tans - The "Trig Murder Mystery" and the Romance Con[ic]. Combine the two and someone tries to murder Hypotenuse (

    1. Heh, thanks. (There's even going to be an unintentional connection with the serial this Wednesday.) Weirdly enough, I don't see the Conics being very date-able... but I should keep that in mind given the ParaB-QT romance happening in the background.

  2. Thanks for the shout out Gregory! I can do a full writeup on my blog of anyone is interested with more detail and pictures. Also, just in case anyone wants to contact me, there is a typo in my twitter handle. It is @gwaddellnvhs.

    Thank you!

    1. Fixed the typo, thanks for being observant. I'd be interested in the full writeup! In fact I was quickly browsing your blog as I did for several 'My Fave' presenters... oh, so much stats goodness. I'm going to plug your Stats Teacher Twitter list in this comment too: