Wednesday, 31 July 2013

ETC: About Introverts and Conferences

Max Ray (@maxmathforum) posted a comment to my TMC (Twitter Math Camp) Day 3 blog where he remarked on my "introvert perspective". Mary Bourassa also made a TMC post referring to her "lack of outgoiness". I want to expand a bit on these ideas, and possibly debunk two things I've seen online:
1) An introvert "hates being around people".
2) An introvert "is fine when around friends".

Note that I'm not trying to put words into anyone's mouth, so definitely call me out if you think I'm representing the introvert situation inaccurately, or unfairly. You can do it through email if you'd prefer to be anonymous, I promise I'll call myself out in the comments.

It's not that you're against me. It's that you're so different from me.


First, let's be clear that there is a sliding scale involved. While people CAN be "all introvert" or "all extrovert", it's more likely that you simply identify more with one category than the other. Bearing in mind that I'm speaking from experience, not research, here's my test:

You are at a conference. You walk into a room where there are a bunch of like minded people you know, and would call friends. Do you:
a) Keep quiet UNLESS spoken to?
b) Keep quiet UNTIL spoken to?
c) Speak up because you know THEM?
d) Speak up because you know THEIR INTERESTS?

Notice the full introvert might not walk into the room, and the full extrovert would probably speak up regardless. So where are you on the scale?

I am firmly in category (B), leaning (A) if anything. If you want my opinion, or you want me to tag along, you will ask me. At that point, and ONLY at that point, I'll jump in and join in with whatever. Otherwise, you've got a thing happening, that's cool, I'll be over here. Note that I tend to do this even with friends and colleagues I HAVE KNOWN FOR YEARS. Acquaintance time is a very negligible variable. Moreover, even after I have jumped in, after 2-3 hours, I just... can't anymore. I'll start subtly watching the clock.

My wife, incidentally, identifies in category (C). If she walks into a room full of strangers, she will keep quiet. But if she walks into a room of friends, she's fine, because she knows them. She can also carry on a conversation with them for over 2 hours, again, because she KNOWS them. Now, I love my wife to pieces, but I don't understand her ability to do that.

Similarly, I think a number of people out there who would put themselves in category (C) or above do not understand me. Or worse, you think you do, but you don't.

I really take the cake.
Reaching for a metaphor, it's sort of like the difference between being invited to a birthday party, and simply crashing one. No one "invites" you to a conference (unless you're a guest speaker), so I don't want to crash in and start talking to people unless there's an opening. It doesn't matter if I've known everyone there for 5 minutes or 5 years. I NEED that opening, so that I'm certain that I'm not intruding. I CAN'T just "GET OVER IT"... at least, not without effort on EVERY interaction!

But, you protest, you KNOW these people, you've met them online and in person, or you've been teaching in their department for five years, or you've been drinking beer with them EVERY Monday for ten years, and it's this big birthday celebration, just say 'hi'! AGH. That's SO incredibly awkward.

I've seen some tweeting recently about how some people have no trouble conversing, but they have trouble writing. Like that, EXACTLY like that, but my problem is the TALKING. I can write easily, because you can choose not to read. It's much harder for you to choose not to hear me! The opening, the "Hey there, so what's your opinion about..." makes all the difference. I try to offer it up to others whenever I can, because I'm usually on the opposite side of it.


The other thing about writing, and online things in general, is that it's easier because it's implied "public". I agree with the logic that if you wanted a private conversation, it wouldn't be, say, on Twitter. Now, two caveats. First, that all changes at a conference in person, where pocket conversations still feel "private", even if they're in the lobby. So I will only speak up if I feel I have something to contribute. Second, throwing oneself into an online conversation - even during a Play-By-Email Roleplay session - STILL feels awkward to me.

Someone at TMC (possibly Sean Sweeney) mentioned they tend to accept an invitation the second time it's offered, not the first time. I can totally see the logic in that. You want to make sure someone is actually interested and dedicated, not just tossing something out offhandedly. I mean, you don't want to give a person a job to do, then have them flake out on you when you need them most. Right?

I will not offer a second time.

If you ignore (or reject, or miss) my first request, I will assume that either you've got things well in hand and do not need my help, or more likely that you recognize I do not have the necessary skills (eg. interpersonal skills) and thus DO NOT WANT my help. In fact, I'm almost the complete REVERSE of the above, in that if you come to me first, I may not ACCEPT until the second request. Because surely there's other people you could ask who are not only more qualified, but who, you know, can actually talk to people. Have you asked one of them? (Me? Really? Huh. Okay then.)

Now, with the baseline established, are you ready for the exception to all this? It's the great leveler.


Passion is what makes an introvert stand up and present. At a conference, or anywhere really.

It might be passion for a specific subject. At my brother in-law's wedding, I hung out on the sidelines for well over an hour until someone came up and asked me about the Ontario teaching system. Boom, half hour conversation. It might be passion for a specific person. Last year, at ConBravo, I went up to Lewis "Linkara" Lovhaug and asked for a picture with him because damn it, I KNEW I would regret it if I didn't. Or it might be passion for a specific event. I dare say that this is what made some people stand up at TMC and deliver their "My Favourite", in order to give back to the conference.

Getting this picture wasn't so hard, was it? Well, actually...

But the passion tends to be specific. If a bunch of friends are talking in general about their personal lives, or their dinner plans, well... I'm just not that passionate about dinner. There is no opening there. I won't speak up unless maybe there is a pause of at least three seconds in the conversation, so that I feel I'm not interrupting. Which doesn't happen so often if the other people are type (C) and above.

I also regret to inform you that passion can be bled out of a person over time, if it seems like no one else wants to hear from them.

It's like how someone who's written a great novel, then had it rejected by many publishers, and seen their requests for beta reading go ignored, can reread it themselves and go "yeah, guess it wasn't so great after all, I suck".


First, it's a two-way street. So, any introverts who have been reading this and nodding all the way through - sorry, while you don't necessarily have to "Get Over It" you DO have to MAKE ADJUSTMENTS. I know, I know, it does take effort EVERY. SINGLE. DAMN. TIME. I feel your pain, REALLY I do, but if you don't make the effort, you'll regret it. Worse than that, we're not going to see your passion, and WE WANT TO SEE IT!!

Try to find a coping strategy, if you can. Make like you're not talking to the whole group, but just one individual, to bring you in. Max Ray has said that when he writes, he writes with a particular person in mind, kind of like it's an email to them. I think that's brilliant. After that, when you post something up, if there's no response... send it out a second time! Fire it @ someone, even. Fire it @ me if you want to. I can't promise I'll comment, but I'll read, and if I RT, it increases your chances of it being seen.

As to the second direction on that street, those definitively above category (C), be aware of the issue. As the story goes: LISTEN, SHUT UP. Ask the guy sitting quietly at the table if he wants to split an appetizer with you. Or maybe try to hook two introverts together, which I suspect at least one person tried to do with me at TMC Karaoke. In fact, in terms of conference planning, I think a number of things are going right already:

1) Scheduled evening events. There is no doubt in my mind that if there had been no scheduled events at TMC, I would have ended up in my room every single night. Hating myself for doing it. (Okay, maybe not every night, David Wees called me out at one point.) The one dinner I did go to was in part due to the fire alarm, thus we were all hanging around in the lobby anyway. Sidebar: Quieter venues are nice too. Given the amount of effort an introvert needs merely to speak, having to shout to be heard tends to induce silence.

2) Long breaks. Having fifteen minutes between sessions is a good thing not just for travel time but for decompression. Likewise for extended lunch, and time before the evening events.

3) No forced groups. Occasional pairing is fine, and some sessions did involve group work, but I think four was the largest group, and I joined by choice. Groups make my stomach twist in knots.

One possible improvement that occurs as I write? Signup sheets. For sessions, for dinners, whatever. This not only allows introverts to feel like they're not "intruding", it can allow extroverts to notice "that name on the list I haven't spoken to yet" or "that person presenting to an empty room".

At this point, you're probably wondering why I'm even a teacher, given the number of students I have to talk to. I'll simply point you at my post "Why I Teach". For more reading on introverts, you can look here in comic form, or here for an amusing video.

Oh, just one more thing! I've noticed a media trend lately of comparing "Extroverts" not to "Introverts" but to "Neurotics". Seriously. Not helping.

Okay, thanks for reading to the end, flame away in the comments below!

Tuesday, 30 July 2013

MAT: TrigGate r=1

The unit circle can be used to estimate trigonometry, in place of a calculator. First, total credit for this idea goes to a colleague of mine, Esmeralda Fernandes. All I did was jazz it up, and present it as a Favourite idea at Twitter Math Camp 2013.

With that said, there is now a calculator that requires the user to enter a mental estimate; if the estimate is reasonable, you get the precise answer. It's the QAMA (Quick Approximate Mental Arithmetic) calculator. But even if you do not have one of those calculators, perhaps at some point you'll find yourself trapped on an alien world, with no power for your electronics, and to escape, you need to do some trigonometry. (Use your imagination.)

Fortunately, you can make yourself a unit circle:


Now, you've probably seen trig labelled in the unit circle before, but in a very generic way, as I've done below. I've even used that image myself, as part of my web serial, in Series 3. But what's with that generic triangle in Quadrant 1? Consider using a more specific triangle. One showing an actual angle.



Pick an angle. Start dialing from (1, 0) - that is, spin your angle around the unit circle until you've located it's position. For instance, let's encode 125 degrees. (The 45 degree markers can help make an estimate, we know we need to be 10 degrees off of that.) Now simply drop perpendiculars to the axes! You can get a two decimal approximation, and check it on the calculator. Notice the sign of the trig comes right off of the axis, no need for that silly "CAST" rule.

Tangent is a little more interesting. Instead of actually drawing a tangent to the circle though, we can recognize it's merely slope. Rise over run. Sine over cosine. 0.82/-0.57, or simply -82/57. Which is somewhere around 1.5, in decimal. You don't even need to use the circle endpoint for this one, if you see it going through a grid square.

This can be done just as easily with radians; in fact the visual might make it easier. What's 5pi/6? Recognize pi is half the circle, and subdivide that into six parts. Now you've got your dialing point. Proceed exactly as above.


Time to work in reverse. Need to know what point to dial such that you get a result where sine is 0.8192? Sine: Start on the y-axis. Hopefully you can immediately see that there are two possible coordinates within 360 degrees. The first one is 55 degrees. Play around with the angles however you like to get that second measure of 125 - hopefully you can recognize that 90+55 is not a reasonable possibility.


Oh, you wanted radians? Well, the upper semicircle is already split into four equal parts. So we need a bit more than pi/4; how about pi/3? In other words, a bit more than one? (Ok, my calculator says pi/3.272, which is 0.96 or a bit less than one - but we're estimating here.) If I was really keen I could subdivide the half circle more accurately.

Oh, you were given sine as a negative? You're just working in the lower quadrants now. Oh, you were given tangent? That's dead easy! Rise by the decimal, and run by 1. Draw in the line. Or rise by half the amount and run by 0.5, if you're running out of space.


Personally, I've only had the opportunity to show a class how it works, and they get a unit circle to use on their unit test. Possible other (better) extensions for you:
-Give them some of the basics (like sine), and see if they can extend (to figuring out tangent, for instance). Or to using the reciprocal ratios!
-Special angles also come into play, what do those triangles look like?
-You could turn this into a game, and see who can come up with the closest approximations.
-Even if you don't teach trig at all, you could use proportional reasoning to see how much of the circumference (~6.28) you cover if you only encode an angle of 80 degrees.

And one more Stargate connection: A Stargate is made up of 9 chevrons, each one equidistant from the others. The last chevron is positioned at the very top of the gate, 90 degrees. So what are the trig measures for the FIRST chevron, to it's right?


Click here for: Other TMC (Twitter Math Camp) Presentations
 (Additional 'My Favourites' are at the bottom)
Click here for: My TMC presentation on Musical Mathematics

Monday, 29 July 2013

MAT: TMC 2013 Day 4 - Growth

So this isn't exactly live blogging any more, as it's a day late. Well, nothing's perfect. Note that there is no need to read the accounts for Day 1, for Day 2, or for Day 3 in order to read this entry! That said, this is Day 4 of Twitter Math Camp 2013.

One Drexel Plaza features this device. Fully functional?

Ever experience something that feels wrong, and annoying, and you wish you could change it? Hold on. Consider that the event itself might not be wrong, what might be wrong is the circumstances surrounding it. For instance, a lesson which dies a horrible death in front of one class - maybe it would work with another? Or if you keep waking up before your alarm clock - maybe that's a good thing if you set your alarm wrong?

So yes, after posting up my Day3 blog after 3am, like a sleep deprived fool I set my alarm for 8pm, instead of 8am. Ergo, when I randomly woke up before I'd had 6 hours of sleep... it was 8:45. Oh, snap. So I'm NOT complaining about that today, as the mental bug has turned into a feature. Not sure I would have forgiven myself for just sleeping through what happened next.


Many people still present and conscious!
I get to Paul Peck a bit after 9am (obviously not having eaten), in time for a few early announcements... there's a place to upload photos (on Shutterfly), there's a place to log TMC blogs, sessions can be updated on the TMC13 Wiki and ideally My Favourites people should add info there as well (even link to a post, if they have done one!). Unofficial attendance tweet, by the way, was 107. Up from 37 in 2012.

My Favourites Sessions:
1) Terrell Stevens (@ladyt316) talks Factoring Frenzy. She presents a two by two grid, called a 'Tic-Tac' (no Toe) where the left column was made using the product and the sum of the two numbers in the right column. Students, what do you notice? What is the pattern? She then presents boards with only the left column, asking to fill in the full Tic Tac. The left column is naturally made up of 'ac' and 'b' from a standard form quadratic; this method was so successful with students, the PreCalc teacher adopted it as well.

2) Sandra Miller (@sandramiller_tx) talks My Favourite Multiple Choice. If you use MC questions for AP prep or test prep, allows you to print your own scantrons. You can then use your document camera or iPhone app to scan and grade them on the spot! This allows the teacher to circle the ones a student got wrong and give it back before the end of the period so they can retry. The free version only allows 10 question tests. Sandra has paid the $10/month version, which also gives her access to recording analysis tools (see how many people answered which letter).

3) Chris Lusto (@Lustomatical) defends the Romance Cone as discussed by Mathalicious on Day 2. How can it be a cone in 2-space? Consider a circle. Take any non-coplanar point as the apex, and draw lines from there to the boundary, and you have a cone. But there is no reason for it to be finite; we use infinite double napped cones to define conics. There is also no reason we have to stick with 3 dimensions, we can see it in 4D or 5D... or 2D. To take it further, consider topology of Euclidean space. For a challenge, think of something else for which you have a good understanding, and then try to generalize it.

4) Jennifer Silverman (@jensilvermath) talks Geogebra. She points out there's 40,000 applets for Geogebra 2, and that it's entirely dynamic with sliders. She demonstrates some of her GeoGebra tube, including Quadratic-Palooza, Multiplying integers in "Cartesian Plane" (axes 1st factor, second factor) and a rolling out of a radian protractor she's designed to demonstrate central angle of 1 rad. (A physical proradian was included for all attendees, see that web link if you want one.) She also mentioned a GeoGebra conference next week (Aug 3), in Ohio, organized by Steve Phelps (@giohio). For another source of GeoGebra, follow John Golden (@mathhombre), and Bowman Dickson (@bowmanimal) has some materials from TMC12 as well.

5) Cal Armstrong (@sig225) talks PCMI (Park City Mathematics Institute), while noting his Microsoft Surface electronic has no adaptors. There's a gathering for 3 weeks in Park City, Utah, involving 4000 math people from high school students through grad students and professors. In the morning, they do math problems, and in the afternoon, they do projects. Some are available on the web, though they are hidden behind a firewall. Talk to Cal for more information; there's also an E-Table in Texas that participates.

6) Glenn Waddell (@gwaddellnvhs) talks about the linear vertex form. In particular Algebra 1 doesn't use common vocabulary with later courses, yet you can have y=a(x-h)+k for a line, in addition to the parabola, absvalue, trig, et cetera. The only difference is that the point for the line doesn't matter, whereas it does for the others. When Glenn said this at a dept leaders meeting, some said "it's forbidden to discuss it like that!" but he proved it with sliders in Geogebra. Using the "linear vertex form", even low speed kids were able to write equations for parallel and perpendicular lines. Jennifer Silverman has since put together a GeoGebra demo here.

7) Jasmine Walker (@jaz_math) talks about teaching programming even if you can't do it yourself. Be "authentically unhelpful". This is something that came out of David Wees' presentation Saturday morning. With her Grade 9 class, they start by doing linear models, then shapes and attributes of diagonals using an investigative process. She then offers two different assignments, where one of them is programming: Given an input of four coordinates, produce an output stating the type of quadrilateral. She makes a point of suspending practice work outside of class so that they can focus on this.

Word of mouth has spread in her school, such that older kids encourage others to give the programming a try, and they are willing to help out. Jasmine's help is often in the form of seeing if anyone else is having similar problems, or checking websites along with the students for information. The final product also needs to have documentation, which allows her to mark it. To get a high A-level, students need to additionally explain why their method is particularly elegant and/or provide a bibliography of sites for future students given the assignment. As she concludes, Michael Pershan throws in a plug for 'Scratch' as a language.

8) Mark Dittmer (@MisterDittmer) talks about a book, "The Choice in Teaching and Education". It's only 100 pages, and is good for reflection. He came across it after reading another book by the same authors, "Leadership and Self Deception". Picture someone you know who is a problem, believing that the people around them are threats or somehow less important. Moreover, they doesn't KNOW their attitude is a problem, and may argue against it if challenged. In such cases the self-deception has become a larger problem. Now ask yourself, do you see students as threats who will misbehave? Or is there greatness there? Mark read a snippet from the book too.

9) Roxanne Mah (@justagurl24) talks division hugs and kisses. Consider that when you divide fractions, the "rule" says invert and multiply. (But we all know students get confused about where they're inverting.) Now picture 'xoxo', as representing kisses and hugs. You "Kiss and Flip" to divide fractions.

10) Edmund Harriss (@Gelada) talks Mathematical Play. How can we make it easier for students to play with mathematics, such that they can find something cool... even if they may not understand it until they see it again in a later course. (Or at his level; he's a university professor.) He illustrated this by hacking Desmos to produce the following graph; it's a function in two variables, cos(x-r)/[x^2+1]. Sliders produce interesting results. Edmund actually makes physical cards with designs like this on them, which he will put on the wiki. Note also that the answer to a student question is allowed to be "That is a reason to take Calc3 in college."

That concluded the scheduled favourites, at which point Lisa Henry opened the floor for anyone else to toss something up.


11) James Cleveland (@jacehan) talks Blogging Motivation. For those who are motivated by deadlines (or who constantly revise), schedule your post to go out sometime within the next week. Better finish your writing before it posts!

12) Anthony (@aanthonya) talks Google Voice. It's a free account, and gives him a phone number for school related help. It can be set to ring on all his phones at the same time (home, cell, etc) and if he doesn't answer, service will transcribe the message left and send as a text (sometimes humourously).

13) Max Ray (@maxmathforum) talks, run by Gordon Hamilton, a Canadian Mathematician. He's currently compiling 13 gaming analogies to unsolved problems in mathematics, and raising 13 million dollars so there is money available to those who solve them; half a million to whoever discovers it, other half to a teacher who inspired them. Max illustrated one of these games with the group.

Red team picks a composite number. Blue team picks a prime number. Red team picks a prime number and multiplies by their first. Blue team picks a composite number such that their own product is EQUAL to Reds' - if they can, they win, if they can't, red wins. Who has the harder job here? The unsolved question: Is there a strategy such that blue can ALWAYS win? The connection: Factoring products of very large prime numbers; solve this and you can hack secure transactions.

At this point there were a few rapid announcements that I couldn't shorthand fast enough. I do recall Justin Lanier (@j_lanier) talking about "Exploring the MathTwitterBlogosphere", a new Blogging Initiative for October 2013. Watch for info in September.

Paper? Sheet music? What's that?
From there, Sean Sweeney and his band came up to present a song for TMC13, which was to the tune of "Tik Tok", and includes a cents symbol. Michael Pershan recorded it and you can watch here on YouTube. Video includes bonus reprise of last year's "Tweet Me Maybe".

At this point, Lisa Henry (@lmhenry9) came back up. There were acknowledgements of the rest of the committee (Shelli, Anthony, James, Jessica, Max). Lisa then mentioned how it was a freshman English teacher who inspired her, and she left us with two thoughts. "Can miles truly separate you from friends?" (If you love someone, aren't you already there?) & "Don't be dismayed at goodbyes. Farewells are necessary so you can meet again." (Be that in a few minutes or a few years.)

She got a standing ovation. And at 10:45am, that was it.

Feedback forms were filled out, the origami dragon logo was torn down, and people said their individual goodbyes. I was thinking of acknowledging a few people here, but on second thought, no - don't want to miss a mention, and everyone was great anyway.

Michael Pershan's got 99... origami birds? Wait.


After 11:15, I went back to the hotel to check out by noon. Think the last person I talked to was Glenn in the elevator, which I remember because he told me that the digits of Pi actually produce a scannable bar code (which he had on his shirt). Incidentally, I'm hyper organized, so the fact that I didn't check out until 11:55am is a testament to how much this conference threw me for a loop. Feel free to skip the next italicized paragraphs, as I wander Philadelphia.

This has a familiar ring
In brief: Sheraton people were very good about making change for me. First stop, Institute for Contemporary Art, literally a block from hotel. Whoever made the green and pink guide sheets, I read those. Then thank goodness for maps in subway system, made me less worried; remember I'm flying blind, no net access to online maps. Liberty Bell Center. Washington Square. Penn's Landing. My only food of the day about 3pm (aside from a muffin at TMC). Then rain as I head to Town Hall. Hide out there.

Dominos game: Rained out

Rain mostly clears, I go to "Your Move" game artwork (1997) that Max told me about. Monopoly pieces near Pennsylvania railroad, funny! Next JFK Plaza and love statue; I miss my wife. Walk down Benjamin Franklin Parkway. Pours rain again, so I'm pulling a Rocky, running up stairs to Philadelphia Museum of Art to find shelter. Carrying all my stuff. Trying to protect my laptop. Wait there, but soon it's 5pm, no choice, must get to train station. Fifteen minute walk to 30th St. is wet. Train down to Airport, arriving just before 6pm.
It was a Rocky Road

MANY math teachers had troubles at the airport, as the rain apparently knocked out power in some terminals. It was the most rain Philadelphia has seen in a day for over 140 years. I had to wait a half hour as US Airways computers were down. When I did go through security, they had to pat me down because I was so wet the machine gave them odd readings. Shuttlebus to Terminal F involved 3 second dash through pouring rain (did see a rainbow too). Couldn't get WiFi signal. Then flight systems went down again.

At 9:15pm, was announced that they would be doing a "manual boarding" of my 8:45pm flight. (I'm picturing manual dialing of a Stargate, because that's what I do.) They actually tore that perforated part of my ticket off. Left gate about 9:45pm, but taxied around for a good half hour. Out window, amazing visual of a plane taking off with lightning strikes in the background made me think "take your time". Back to Ottawa for 11:30pm, my wife is there. Local busses not running to my house anymore, took a taxi home.

And that's day 4. In all I've apparently earned 19.5 professional development hours (according to my certificate). So I guess that's all my work hours for July; don't expect an analysis as I did for June! Do expect some further reflections after this experience though.

Sunday, 28 July 2013

MAT: TMC 2013 Day 3 - Enlightenment

Previously: A blurb about arriving on Day 0. Then full out postings for Day 1 and Day 2 - in same-day fashion, for those of you following after the fact. Let's keep at it. Welcome, blog readers, to Day 3 of Twitter Math Camp 2013.

I woke up about 8am, before my alarm, I don't know how to fix this. Headed out after 8:30. I'd noticed a campus coffee shop yesterday - but not that they were closed on weekends, so no breakfast. Whatever, math is my food. Got to the main room in time to see people putting finishing touches on the origami Dragon Curve.

Measure once, fold twice
I'm aware of at least the following people helping out Ashli (@Mythagon) with the specifics of it: Tina (@crstn85), Glenn (@gwaddellnvhs), Megan (@mgolding), Elizabeth (@cheesemonkeysf), Max (@maxmathforum), Edmund (@Gelada), Mary (@MaryBourassa). And of course congrats to all the people who were wing and pinwheel folders. If I missed giving someone credit, let me know.

My Favourites Session:
1) Heather Kohn (@heather_kohn) talks Texting Olympics. She gets students to bring a phone to class, two events: Sprint (straight texting) and Hurdles (includes odd syntax and punctuation). Used for scatterplots and lines of fit as students are timed. They must fix mistakes for it to count. It's a way to collect data they're invested in (and to show how including punctuation isn't a huge time difference?).

2) Megan Hayes-Golding (@mgolding) talks Global Math, which presents Tuesday at 9pm EST. Straw poll shows only about a dozen in room have never been to one. This Tuesday, plan is to recap the TMC conference, so if you found something compelling, let her know, you can talk for 5 min. Just avoid in-jokes, idea is to bring this experience out.

Jennifer's helping Sean with his
Lion King impressions.
3) Jennifer Silverman (@jensilvermath) talks Liu Hui, a third century Chinese mathematician. He split the cube, eg. one third is a Yangma, and Jen has nets for his solids. Held together with magnets, which she tossed out into the crowd. Math Munch (see also Justin yesterday) talked rhombic dodecahedrons lately, so she had solids for that too, and referenced tetrahedral numbers.

4) Greg Hitt (@sarcasymptote) talked dogs doing archery. Wait, no, he talked about playing his ukulele in class. Read his post for more details (don't be uku-lazy), but in brief, the idea is to put a psychological barrier in place. Students will be more inclined to talk to each other if Greg is "busy playing his ukulele", yet not tune out entirely as if he's on the other side of the room. Question cards also came up, the idea that you can only ask a certain number in a day or week? Anyway, in conclusion, noted that accordion music doesn't work for this.

Announcements followed about flex sessions and room changes, then we headed out for morning sessions. Ended up chatting briefly with Lisa Henry (@lmhenry9) in transit, about "making the leap" to talking with people. Which has to be on one's own terms. First, one needs a comfort level with themselves, and what they might have to offer. More on this later.


9:30-11:30am but morning sessions today weren't for subjects. I was hesitating between the High School Mathalicious session and David Wees presenting Powerful Ideas via Programming. Went to the latter for two reasons: Wees did a great 'My Favourite' yesterday, and he tweeted out a link to his slides this morning, which I had a chance to glance at, and was further intrigued. Was there with Raj Shah (@drrajshah), Cal Armstrong (@sig225), Ilana Horn (@tchmathculture), Jasmine Walker (@jaz_math) and Justin Lanier (@j_lanier).

David started with the big question of "Why do we teach mathematics?" Skills are forgotten. Moreover, supermarket math, when turned into quizzes, causes a drop in responses by 60%. He then posits eight big ideas, noting how math is to see structure, as well as to network and make connections. Referenced the image of "This is Not a Pipe" - because it's only a photo, AND because it's a single item out of a million we would classify as "pipe". (For smoking or plumbing, for instance?)

From there, an online program called Blockly. Has a turtle, sort of like Logo, but others likened it to Scratch. Noted Scratch is more object based, this is more procedural. "The algorithm is where the precision is, not the language." The first program we see - David says he has taught to kindergarden students. He walks the code out for them, and how often can a kid of that age tell an adult what to do, and the adult DOES it? Upshot: Students can code before they read.

Can Wees do it? Yes, we can!
Then another program, session gradually stepped up the complexity, which was good, as earlier material became procedures. The middle was just difficult enough to get me to play around with the interface, and the "cheat" documents for the harder stuff as we ran out of time were useful. Each program also related back to a "why" concept. One program calculated out the root of 200 with increasingly accurate predictions; David showed graphically why, and Raj suggested incorporating that visual too.

Jasmine brought up something she does with students. Outside of class time, she has them program a TI-83 calculator to, given four points, return the type of quadrilateral. A common bug is when the program divides by zero (on a vertical line), which she doesn't help them with. A number gain an interest in computer science.

I end up talking a bit with David after it ends, as he wonders about feedback; think I said what I just posted above. One element not raised was student ACCESS to computers; guessing it wasn't a problem for attendees as it wasn't raised, but might bear scrutiny. He also shows me how computers draw a parabola, namely using acceleration and velocity - and so how is an exponential drawn? Something to think about.

I get a message from Sean (@SweenWSweens) about song discussions, so that's where I go to talk at lunch. Only one food truck in the immediate vicinity is open, so I go there - egg and sausage sandwich works as brunch. Briefly overhear Sam Shah (@samjshah) and Chris Robinson (@absvalteaching) talking about Mathalicious lesson planning. The group starts not with the standard but with an idea, then whittle it down to a standard... hardest thing can be to "leave some elements on the table" if they don't fit. Also, saw a very brave rabbit.


1pm, My Favourites Session:
1) Peg Cagle (@pegcagle) was going to talk Origami 101 but the Michael Pershan (@mpershan) Mistakes session yesterday gave her another thought towards truly building exponential concepts. She handed out tissue paper, and did a table for #folds & #layers... but ALSO #folds & top area. The top area was defined as 1 first, then as folds occurred, modeled exponential DECAY. Peg (btw, also on the board of NCTM) demonstrated she could get folds down to 10, said student minds can be blown when they realize they're holding over 1,000 layers, and noted analogies can be done with the height.
Addendum 1: In Japan, only babies fold on surfaces.
Addendum 2: The origami Dragon Curve on the wall is related to folds, but they are 90 degree folds, not 180.

2) Anthony (@aanthonya) demonstrated a writing pad, which connects to the Smartboard. You can hand it to a student, have them write on it, and the work will appear at the front of the class. Available for $50 on Second part was mention of Remind101, a method for texting students which doesn't involve account info sharing and can post texted homework right to a website.

Warning: Graphic content
This was followed by Eli Luberoff (@eluberoff) the founder and CEO of Desmos, a graphing calculator app. He started the presentation with an ode to everyone, flashing up tweets and blog notes, saying they print those at the company to post in their office. They don't have a single sales or advertising person. They get other companies coming to talk with them since teachers are advocating their product instead of texts. He introduced others at Desmos too.

The app itself is constantly being upgraded. Eli says they never add a button to the interface unless they think really hard about it, so that newcomers don't see it as complicated. It also works even if you're not connected to the internet (with HTML5), so as long as you went to the site (and don't refresh), you're good to go.

Eli first demonstrated the problem of a $5 coupon and a 25% off coupon. If you apply each to a $36 item, order matters - but is it the item cost, or the size of the percent, or... "This actually raises way more questions than it answers." So input two functions, then demonstrate f(g(x)) and g((f(x)), which gives a couple parallel lines. Change the constants (like $5) to be slider values, and - animate! This is a feature coming before mid-August. He actually hit play then went to sit down to watch with us.

Second activity. Balloons and measuring tape, recording data for # breaths & circumference. I was in a group with John B and Judy. Once points were made, question of what model to use: Root? Log? Spoiler: f(x) turns out to be the cube root. Demonstrated how a third column could be added, y-f(x) to show the residuals of the data points. Desmos has also recently added an 'nth root' feature.

To close, there were some quickies, such as making draggable points on a curve, (a, f(a)); parametric graphs like (sin t, cos t); and the favourite graphs section as made by users at In questions, Geogebra and GeoSketchpad were raised... for now, those apps create equations given a drawing, while Desmos creates drawings given equations, though lines could be blurred in future.

After things wrapped up, talked to John Berray (@johnberray) a bit more about some things I'd tweeted previous night. Kind of agreed that atmosphere is very Give and Take, which can lead one to worry "what did I bring?" and not wanting to be all take. But what does the individual offer? I know unless I'm addressed individually, I rarely step forwards, just stand there awkwardly. Part of the "leap" referred to with Lisa above.

There may be more introverts here than anyone realizes. If you're one, particularly one who has concerns, and maybe isn't comfortable speaking up given the atmosphere of OMG YAY, feel free to use me your voice, anonymous or otherwise. Just mail.


On to the next session, and like the morning, I was waffling between a couple of them. (Curiously, didn't do much of this previous days, one always felt ahead of others.) I decided on "Copernican Mathematics" by Sandra Miller (@sandramiller_tx) mostly because a lot of people already seemed to be going to "Effective Group Tasks". Hence I figured I could ask those others about it later.

And then I was the only person in this session.

Yes, in a stunning reversal of my situation from Thursday, I was Sandra's entire audience. Which prompts two reactions. First, enlightenment as to the fact that this can happen to anyone. And second, concern over whether other tweeps would even have been aware of these couple instances if it weren't for me blogging about them. I think there's an issue here. Personally, I believe that if you're passionate about something, and the appearance is that 100 other like-minded people aren't, it's a bit soul crushing.

That's just me though, back to Copernicus. I got to do an activity that Sandra runs in her Geometry class in the last few weeks of school after testing concludes. She often scaffolds it a lot, and had removed that element to see what could be figured out without it. It involves finding distances using old school (and circular) methods. Quick pre-test for you: Which planet is roughly halfway between the Earth and "Pluto", aka the limits of the solar system? Probably not what you think.

Two key things struck me here, the first is that there's a lot of proportional reasoning involved, and second that tracking units turns out to be really important. Both elements that seem straightforward when you know what you're doing, but I didn't, and was having trouble parsing Earth days and Mars days. (I blame lack of sleep, but students also suffer from that.) Sandra was very patient with me. Overall it was cool, and quadrature is a fun phenomenon.

We wrapped it up at the end with a brief mention of escape velocity, and I learned that astronomy isn't in the US curriculum. I'm trying to remember if they kept it in the Ontario Grade 9 when it was switched over several years back. Sandra also mentioned there is a southern conference in February, the SEEC (Space Exploration Educators Conference). She has been to it, and it tends to be more science and middle school teachers, despite the fact that you get to go to NASA and see things like them detonating explosive bolts. Needs more math! I found an article here. And did you know there was an all astronaut band, the MAX Q? Yeah.

Can anyone drive standards?
The last session of the day was a "flex session", only generated during the conference. I attended Jasmine Walker's talk on Standards Based Grading (SBG). It apparently blossomed out of the talk "Using Google to Manage your SBG workflow" with Jamie Ryske and Ashli Black on Thursday... the idea of Hybrid Plans. This session also served to enlighten the Canadian on what goes on in the US. When I asked, "What constitutes a pass?" I got answers ranging from 60% to 67% to 70%: It's not consistent!

Jasmine started by having everyone answer three questions, 'What do you do now?'; 'What works well?'; 'What would you like to improve?'. The main issues that came out of the first half were: 1) Spiraling how; 2) Overwhelmed by number of options/systems; 3) Creation of retakes and tests vs skills; 4) Too much grading; 5) How to communicate system to kids/parents; 6) External constraints; 7) How to align to common core; 8) Students who don't retest or count on the system.

These were addressed in the second part. Bowman Dickson (@bowmanimal) apparently has a good Prezi explaining things. (Someone want to link that in comments?) Was thought Daniel (@MathyMcMatherso) had some discussion of synthesis. The "I'll just retake" attitude often not a problem once it's realized it's more work, or can make 10% of mark pegged to it and unchangeable. Retesting can be tracked easily with mark of 70.1 then 75.2 instead of 65. When an Online Gradebook is required, can keep two books. ActiveGrade is a good SBG markbook (behind a small paywall).

Don't allow granularity, just assign 3 (on 0-4 scale), since retakes will happen anyway. Don't allow "tutor" on a topic the same day as an evaluation. Create a bank of quizzes on the standards (use random index cards?) then a culminating project or task. To ensure reassessment, make 90% the highest grade until second evaluation. Build in "quiz time" and each student can just take whatever quiz they're ready for at that time. Other tweeps with posts about this: Frank Noschese (@fnoschese), Shawn Cornally (@ThinkThankThunk) and Kelly O'Shea, who teaches physics but has a good explanation.

That wrapped up, from there, back to the hotel - and a fire alarm that apparently went off about 5:30pm, just before I arrived to hang out in the lobby. Once firemen had wandered about and given an all clear, I headed out for dinner with tweeps who were there.


Dinner was at "Salento" as recommended by Max Ray; in fact of the 11 of us, me and him were the only guys. Though in Jasmine's session, Matt Owen had also been the only other guy in the room, so - par for the course? I learned the meaning of the "double factorial!!", some behind the scenes on "Infinite Tangents" and "Global Math", and I posit that approaching a group of a few people in person is harder than just tweeting something. Artichokes were had, and plates were served semi-symmetrically.

Elizabeth also had a thought about the diversity problem I mentioned in my blog yesterday. Perhaps some sort of kickstarter, to raise money to ensure that people can come to TMC who might not otherwise be able to. One other item that came up is how the hour long afternoon kickoff slot seemed to be a "promoted" one, as it was filled by: Our host, then Mathalicious, and then Desmos, but this vibe was probably not intentional.

Spent most of my cash this evening. Chatted with Max a bit about writing on the walk back. Then, back in the hotel lobby, from Glenn and Raj, heard the story of math tweeps who ate at a pizza place, were advised by a server there to have their gelatos at a place where his girlfriend worked, and then who proceeded to do some singing telegrams back and forth. Sweet?

Came up to my room about 9:30pm or something, and started in on this post. Which has taken me four hours. Derp. Sooo, has this been useful to anyone who couldn't attend? Or for that matter, who could?

New business cards reciprocated:
David Wees, Raj Shah

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