Thursday, 21 July 2016

TMC 2016 Entry 4: Connections

Here's the last half day of "Twitter Math Camp". Previously there was Entry 0 (Descon), Entry 1 (So It Resumes), Entry 2 (Getting Personal) and Entry 3 (Breathe). Now, the rest of the story. Which begins with these quotes from Glenn Waddell, Tom Hall, and Lisa Henry - but do you know who said what? Read on.
  • "'That' wasn't the best, but I'm trying here - and here's what I'm going to do to make sure 'that' doesn't happen again."
  • "You are great, and you inspire me, and everybody in this room, and in the MTBoS community, and don't you ever forget it."
  • "Fears are what keep ourselves from reaching the potentials we can reach."


I had a choice to make on Tuesday, except it wasn't really a choice. Sean asked me if I wanted to help with singing the final song, that more people involved would be helpful. I'd also been speaking with John Golden, about doing a math comic together. Both of these things would be happening at 8am, before the sessions.
The question becomes, which would I regret more: Not being part of a community group and event that would be talked about for days and weeks to come? Or, not being able share something that has been so personal to me for the last five years with a friend? For me, not really a choice.

Why even bring it up here? On the off chance that anyone actually wondered why I didn't participate, and got the wrong idea. I don't want people to think they can't talk to me about music. It's just I've been personifying math for longer than I've been writing math song parodies, and I care more about it. Anyway.

I had breakfast at another new place, namely Einstein Bagels right on campus, because convenience. Triangleman later joined the table where me and John were drawing, and there was some playing around with turtles. At 9am, everything got going.

#17: "Plickers" by Jonathan (@jschool0218). Yes, schoolcraft is his last name. He learned about these from a history teacher back in Tenessee. Go to, sign in as teacher (vs student). Create classes and add students, you can copy and paste, it took him only 10 minutes to set everything up.

The site then provides cards, and each student gets a unique one. He writes the student's name on their card. Then students hold up their "QR card", and depending on the orientation it registers as A, B, C or D. Download the app, scan device across the room, click on computer, and it pulls up the data of how many chose each option.

Jonathan uses it as a simple exit ticket, a way to get immediate data (like on bell curve understanding), or "Which One Doesn't Belong" Wednesdays. His senior students are so eager they start while he's still doing attendance - "Put 'em down, I'm not ready yet, your arm'll fall off." It's also a quick way of seeing how a geometry class perhaps thought differently from an algebra class. If a student loses a card, it can be reprinted. Any questions, feel free to contact Jonathan.

#18: "" by Tom (@trigoTOMetry). His fave thing is saying that a lesson sucked - to students. Not just in the teachers' lounge. Tom is going into his third year, teaching 6th grade math, and there were days that felt terrible. He wasn't sure where to go with that, so would write about it in his personal journal, talk to other teachers and pick up the pieces, making tweaks along the way.

In early November of year one, a percentages lesson was going nowhere, and so he stopped what he was doing, saying: "I know this sucks right now. I'm going to come back to it tomorrow, I can make this better.". The students gave him a look like 'Is that okay? I don't think a teacher is supposed to do that.' The following day, he elaborated, saying it while that might have been hard to hear, it was harder to say. But he didn't want to do a disservice to them, not admitting when modification is needed.

Afterwards, even on a mediocre lesson, the following day Tom would start by saying "I know that wasn't the best", partly to find out if it was really as bad as he'd thought. And in the months that followed, students got to see his humanity. Failure is built into the learning process, but how often are we not okay with it? How often do we blame the students, or an activity, or time, instead of taking a moment to say, "That wasn't the best, but I'm trying here - and here's what I'm going to do to make sure that doesn't happen again."

Or if it does happen again, forgive yourself - how often have people made an error on a concept they knew four months ago? Own your failure, but don't let it stop you, and be honest with students. It adds another layer of accountability to your practice.

#19: "Break the Ice" by Amy (@zimmerdiamonds). She has an activity with a hidden agenda, done at the start of the year (1st or 2nd day). Get table groups, usually four students, figure out who is the oldest to youngest. After that's known, say that youngest is the scribe, next is timekeeper, next makes sure all have input, and eldest is the reporter/speaker at the end.

Timed task - you have 3 minutes to collectively come up with a favourite book, movie and game that you can all agree on. After this, give 90 seconds for them to list all the ways they came to a final decision as a team. Then "popcorn" the list, getting the reporter to explain, "massaging" the answer to fit our hidden agenda.

Amy started by suggesting "strong arming". Other items that came up were something everyone had in common. Voting (which Amy "massaged" to imply majority rules). Modifying the prompt (like narrowing to kids books). Noted that the pickiest person isn't necessarily the loudest person. Sometimes "Hamlet" is the favourite book because it's the only one they've all read.

The hidden agenda is how you can work as a group. You can't always pick your team in real life, so know team dynamics, and how to work as a group so that it's effective, and everyone's ideas are heard.

#20: "Triangle Congruence Art" by Max (@maxmathforum). Max, with some other teachers, got to go to where NCTM is, and make some art. Resources were scattered, they made a collection, and 'Triangle congruence' was especially fun because Common Core said "don't do it the way all texts do except this one - show congruence with transformations". Derive SSS, SAS, AAS from transformations.

The pieces: (1) Congruent Halves. (2) Standard introduction to triangle congruence. (3) A game: You try to draw a triangle based on given features, to get one that matches. Then one that would not match. Then ask for three pieces of information to draw. (4) The proving of triangle congruence shortcuts. All we have is that point A is congruent to D, et cetera, with measured side lengths. One person has no triangles, and they tell their partners how to transform, for instance "Do a translation left so that A is on top of D."

Is that enough for the triangles to line up? Maybe not - is there a rotation or reflection that is needed? A transformation proof means that there EXISTS a transformation, even one without me seeing it. This is a sneak preview, not on the website yet, send Max a message to know when it goes online.

#21: "Guided Visualization" by Sue (@suevanhattum). Who has heard "I knew the material but I freaked out"? I was tired of that and thought it was true, so looked into test anxiety. Your subconscious (like dogs) doesn't understand the word "NO". If you tell yourself "do NOT be nervous, do NOT be anxious" all your body hears is "nervous! anxious!".

We have to frame things in a positive way, so that we focus. Hence her "Math Relax" audio track (to avoid saying "anxiety") - see that link. She has students get it on their phones. Credit to Wayne for the flute music. The more often you listen, the more effect it will have.

Sue also mentioned her book, "Playing With Math", started in 2008 - and she got to meet a number of people here who contributed, for the first time in person. She asks, how many people love to lecture aside from me? (Interesting response; some, like me, not sure about committing.) The teacher can be a facilitator, leading discussion. Some good ways of becoming invisible, "Holding your cards close" and "Vague thinking prompts".

For the former, responses like "That's a good way to put it, why does that work?" or "I don't know, I'm just the secretary." For the latter, responses like "Can we make this simpler?" or "Do you see what the previous speaker was saying?". See Sue's blog for more; her book is also available at whatever price you can pay, on pdf, because Creative Commons.

#22: "Integrating Computer Science" by Jeremy (@greenbloch). He is an 8th grade math teacher who was asked to include coding in his math class. Jeremy felt he didn't know computer science and was not in a position to do that - but about a year ago, he went to a workshop led by Bootstrap computer coding (see

They do algebraic video game programming and are having a conference in Colorado this week. The coding works in "WeScheme", with hooks into embedding functions, domain and range; Jeremy has access to Chromebooks. You take a math expression, to a circle of evaluation, then Racket code. Jeremy had his class make world flags - some associated with their own heritage.

He showed a number of examples, including a set of personal flags. "Zoe was off the hook." Finally, there were video games. Each had these components: The player, the danger, and the target. The students were so creative in picking the images and theme, and he tried to show one: "In Shock cuz of Mr. Bloch", where he's the danger. There were loading issues.

You can relate function based thinking and link function tables to this work. It's one of those decisions where we'll do something interesting/fun versus more traditional curriculum. Check it out.


#23: "Facing Your Fears" by Glenn (@gwaddellnvhs). He began by saying he almost didn't speak here. What he has to say is very meta, very introspective. He's had a very challenging weekend; he found out Friday that his grandma was passing away, and then she passed on Saturday morning. In a place with friends but no family, it makes you think about who you are.

What keeps people from going out and talking to other people is your fears, and where your comfort zone is, which Glenn got from the keynote sessions. Regarding growth and fears, "Four years ago, my fear was you. No joke." He is an incredible introvert who cannot stand to be in a room with other people, and you may laugh, but it's true.

Four years ago, he decided he had to do something. With the people on the internet that he could communicate with because it wasn't in the same room, he made the decision the face this fear. He got on his motorcycle. He didn't fly, because it means when you're there, you're STUCK, but on a motorcycle, you can give up and escape at any time. His map said 1,800 miles and with a 1 gallon tank, that's a lot of stopping for gas.

Every time Glenn stopped, he sat on his motorcycle and thought, "you can turn around, and no one will ever care, and no one will ever know". (Lisa Henry interjects, I would know!) Each time, Glenn would hit the button to turn on the cycle, and keep going. And every morning when leaving the next hotel, he said "you can turn around right now, and no one will ever care, and no one will ever know". And he kept going, having that conversation with himself 50 times over those 1,800 miles.

You have to face your fears REGULARLY to beat them.

When Glenn at last drove into the parking lot, he sat there, and not even his wife knows that he sat there for five minutes. Because he could turn around right now, and no one would ever care, and no one would ever know. Then, instead of leaving, he did the most courageous thing he'd ever done his entire life. He walked through the doors into the hotel lobby.

You hear courageous things others do, "this was mine". And it connects to those keynotes, because it's always fear that keeps us from doing things. "But when I met people, with the personal touch, the fear evaporated." And when he got home afterwards, he thought about his local colleagues. And that no one was going to listen to him.

And then he thought, WHO CARES, because he walked through those doors! And pretty soon, there was an email going out, and people were saying, to talk math, go to Glenn. And then universities were considering him for a class, and he didn't need to teach that, but SCREW that because he walked THROUGH those doors. And a PhD became an option, and that seemed scary, but SCREW THAT because HE WALKED THROUGH THOSE DOORS.

"Fears are what keep ourselves from reaching the potentials we can reach." And so his personal challenge to everyone is to find your fear, and do what you can to overcome it. Even if it's a three day motorcycle ride, DO it. ... But don't do it in July.

After Glenn spoke, Lisa added, that is why you do a My Favourite. If you're not sure, it's these types of things that we need to remember.

#24: "Nominations" by Kathryn (@iisanumber). Some students were only giving the bare minimum in assignments, while others were putting in more effort - and she wanted to encourage those doing less to up their work. So that open ended assignments weren't something they did in three minutes on the bus.

Her solution was a gallery walk, and nominations. Since work was in notebooks, and couldn't be hung on the wall, she had everyone walk around the room to see it. And they got two post-it notes, being asked to write two positive or challenging comments, feedback to push their peers a little further.

The work could be a lesson, a word web, or defining terms. One student rewrote "All Star" by Smashmouth to be about quadratics. Many students were impressed but didn't know the song, so Kathryn found a karaoke version on the internet. The next day, that student said they hadn't had time to do the whole song, and felt bad about that, "so is it okay that I went back and finished it last night?" (Yup!)

The "nominations" are work displayed on the room's document camera. A nominator must give a reason, and a nominee may accept or decline. (To avoid people trying to get friends in trouble or the like.) Now those who had spent 5 minutes were spending 20 minutes. And if someone didn't do something, they wouldn't get to do the gallery walk. It's great because the kids define what is best, peer feedback is valuable, and they get attention with creative freedom.

#25: "Clever Spiral Title" by Megan (@veganmathbeagle). Megan felt like Tracy's talk really hit home for her - she'd spent the last week in Baltimore at training for teachers, learning about connections with elementary. Many elementary educators are very, very hard on themselves about their math abilities, in part due to high school teachers being hard on them. So one commitment is to being more aware of how she talks about math with elementary teachers.

Which has nothing to do with spirals. Here's the thing, Megan's degree is accounting and math education, so she never thought of herself as a mathematician. But she thought, what if I took the numbers 1-100 and wrote them in a spiral, and then marked all the multiples of four. (During a meeting.) And it was interesting, so she made a copy from 1-1024, and then shaded in squared numbers. All on the diagonal. So what does x^2 + x look like? Or x^2 + 2x?

She made an animated gif out of it, and Christopher Danielson said "that's really cool", which gave Megan the confidence to explore a little further. Triangular numbers, hexagonal numbers, and pentagonal numbers are her favourite, because positive values for x give a different result from negatives. It became a spiral explosion. "I don't even remember what I was doing here, some variation." The coolest was the double spiral.

And then the thrill of her life was being asked to be the visiting mathematician for one day at "Math on a Stick" at the Minnesota State Fair. She's thrilled to have the opportunity, looks forward to getting to know the other guests, and wanted to share somehow. Final aside, thanks for coming to Minneapolis, this place that I tolerate, and now realize is not that bad.

#26: "Birthdays + Function" by Hannah (@girl_got_range). The inspiration comes from a tweet by Rebecka Peterson (who introduced Friday Letters at TMC13), asking if any secondary teachers have ways of celebrating student birthdays. Many did, from birthday stickers to a chair cover you can put on a seat. Hannah's "birthday board" is her way to build student relationships, which is simple and cheap.

She makes a spreadsheet of dates at the beginning of the year, highlighting and tracking, weekly updating that section of the whiteboard. It's the last thing she does before leaving on Friday, so she feels good about it too. She teaches all freshmen, but they bought into it, warning her "miss, my birthday is coming up in two months and five days!". And it's also her favourite analogy for teaching functions!

In the beginning, she lists name and birthday. Then as they learn input/output and domain/range, she'd list in tables. And with mapping diagrams, because they don't connect as well to the toaster or machine analogies. Here, students can have the same birthday, but Andy cannot have two birthdays. Students will eventually catch it - sometimes right away, sometimes later.

That concludes the "My Favourites", which had some announcements between:

  • Many people have done storifies or blogs or videos, and Glenn works the magic to get everything in one place. Go to and submit, including what KIND of thing you are submitting. Do double-check on copyright if you recorded someone's session.
  • Please take the final survey:
  • Lisa Henry will work on sending out certificates by end of July (some are done that were submitted earlier), monitor @TMathC. If you need last year's (or don't know where it is) they can be pulled up, let Lisa know. See also
  • The Twitter Math Camp Wiki often sees the most activity not prior to the conference, but in the week or two after. Editor permissions have gone out to anyone as a presenter, keep in mind you have to LOGIN before you can edit. If anyone with a flex session was missed, send Lisa a quick email.
  • Before you leave, post #1TMCThing as something to try. And find another on the hashtag that speaks to you, as a person or as a similar choice. Check in with each other, in particular on October 19th (exactly 3 months, aka Megan's birthday).

The "My Favourites" originally came out of not wanting to do more problem sets on the last morning. And Sean Sweeney came to Lisa saying he had one, but it had to be last. And Sean thought he was being super sneaky, but Lisa was next to him in the car, and it's dark, and her eyes wandered. So she had a sense, but not where he was going with it. It was a camp song, to give back to the community.

The "Party Rock Anthem" by LMFAO was then re-interpreted.

Finally, Lisa wrapped things up - "I recognize that I am responsible for the vision but there are many people who carry out the vision". She name dropped, noting she still needs to work on delegating, but is getting better. Also, shoutout to her parents and brother, who take the kids for a week so both she and Jason can be here.

Her recent fortune cookie was "Get away from home for a while to restore your energy". Stop and think about that - every year, without fail, TMC does that for her. And she hopes that for everyone else, some restoration has occurred in teaching energy. For her, this year has been one of those years, and she needed it. Moreover, four years ago, there's no way that she would have envisioned standing there doing it for the fifth time.

"We were looking for the people looking for us ... We were pulled together by passion. We couldn't NOT be ... and I'm still amazed at what this has created." Lisa wants this locally, in her own community. She suggests finding somebody. Shoutout to a person who got on Twitter because of a conversation they had. Connect with somebody, on a daily basis, start sharing about your craft and your work on improving yourself.

A book from Lisa's 9th grade English class was "Illusions", and it gives you quotes you need. When she opened it yesterday, the quote was: "You are never given a wish without also being given the power to make it true. You may have to work for it, however." We wish to be better teachers. "It's not my effort, not the community's effort, not the boards' effort ... it's all our efforts together." We can make that wish come true.

Lisa quoted again from Pat Summitt, she served as head coach of women's basketball, and recently passed away due to Alzheimer's. She expected excellence - and that's what greatness does, it inspires more greatness. Sometimes we think we're pretty lousy teachers. "But you're not. You are great, and you inspire me, and everybody in this room, and in the MTBoS community, and don't you ever forget it." Even if it's the worst thing, put it out there.

It's tough to leave, but a farewell is necessary to meet again, and meeting again is certain for those who are friends. July 28th 2017 is the next TMC, which is Atlanta - east coast, and south.


There were goodbyes. And as someone observed, I'm not really a hugger, but in some circumstances it's okay. I tried to make sure I said goodbye to a few people in particular, and Glenn took a selfie with me. The last thing in my 04 text file is a reminder to me that singing the 'My Favourite' meant a lot to Megan - perhaps because it was her tweet that sparked the song? I didn't think to ask.

Mark Sanford had generously been driving the Ottawa crowd (me, Al, Sheri and Mary) around since our initial arrival, and also drove us to the airport. We stopped for some food along the way, and in particular an ice cream place called "Izzy's" which I hadn't been aware of. We arrived, I got my map of the area (I collect maps)... and our flight was delayed. And a bunch of TMC people ended up stumbling across us, and so there were goodbyes all over again. I got to chat with Bob Janes about his music session though, and how you can break a periodic function down into sine waves, which you can't do with other functions (they have multiple decompositions).

We did get to Toronto, and after hurrying through customs, we found our 4th flight was ALSO DELAYED (that's 4 out of 4, Air Canada, impressive). In fact, it transpired that our plane had to be completely replaced with a new plane. After wading through Twitter for the first time since 11am, I bought a "Noble" sandwich to eat before we boarded.

Having my own headphones ended up being handy, as I started listening to the "Peanuts" movie on the entertainment system shortly after boarding. I didn't quite fit a 90 minute movie into a 50 minute flight, many pieces were seen on fast forward, but I got the gist. We landed over an hour late, at 10:45pm, and Al took a selfie. My wife had been kind enough to email me a bus route that would get me home (I don't take the bus much and it was now the late routes). Walked through the door a little after 12:15am on Wednesday. And dealt with a smoke detector.

All of that to say, excuse the lateness of this post! Shoutouts to people who have retweeted my recaps: Joel Bezaire, Audrey McLaren, John Golden and the MTBoS_Blogbot. Bonus shoutouts to Justin Aion & Morgan Ballantine for retweeting my comic, with Jami PackerMichelle Naidu for TMCTYs. Speaking as an author, visibility is everything. (Quick shoutout to David Butler also, for his comment showing me the recaps are making it outside the conference.) There will be one more post which is more personal reflection... likely tomorrow.


  1. Phew! OMG! Awesome recap! Good to meet you! Keep Singing!

    1. Thanks so much! I'm actually really pleased with how these recaps have gone over in the twitter community, what with Joel and Meg and others. Thanks also for the "New Teachers" session and the singing encouragement here - and the taking the time to comment. Not only on my blog, but I've seen you on a number of other blogs as well. That's appreciated. All the best!