Monday, 18 July 2016

TMC 2016 Entry 2: Getting Personal

I'm blogging about "Twitter Math Camp" daily while at the conference (for the moment at least). You can go check out Entry 0 (DesCon) and Entry 1 (So It Resumes) at those links. Looking forwards, I will end up sharing a bunch of personal stuff along with the facts today. Also, here are your three quotes. Who said each? Possibilities are: Michelle Naidu, Tracy Zager and Jose Vilson.

  • "I want you to drive this conjecture over to the high school, introduce yourself to them, and see if they'll play with this."
  • "The internet is a horrible black hole."
  • “Thank you for your vulnerability, take care all.”


#4: "Using the Engineering Design Process in Math Class" by Heather (@heather_kohn). After a quick plug for the Global Math Department (returning Tues Aug 2nd, tweet at her to discuss some of what you saw/experienced) Heather told us how at her school she was asked to "do STEM" (Science Technology Engineering Mathematics). What does that mean, how to do it authentically?

She considered the design process as a framework, discovering there were MANY options (see image), so figure out what works for your school. They picked eight steps: [1] Identify Problem, [2] Research (often left out in school!), [3] Develop Possible Solutions, [4] Select Best Solution, [5] Construct Prototype, [6] Test/Evaluate, [7] Communicate Solution, [8] Redesign (improve). This isn't engineering projects in math class, this is math tasks with an engineering framework.

The ubiquitous Barbie bungee can be an example of this. Other tasks are possible, like catapults, bouncing balls, food container design, etc. So where is the math? It's in whatever step you need it to be in, maybe not until step 6, the testing.

#5: "Maps and Math" by David Sabol (@Dave_Sabol). There's a task he does in geometry that can spill into other classes as well. As an introduction, Youngstown, halfway between the Cleveland Browns and Pittsburg Steelers - which NFL team do you root for? What are some things? He steers them towards the distance question; the perpendicular bisector goes through Youngstown (with Lisa Henry a point on the line).

Then David had a map showing bisectors between every NFL city in the vicinity. Can we erase some lines? He's done this task with Geogebra but also protractor and pencil. Ultimately he showed a full map of the US. But then what's the most liked team in the counties? In media markets? The most televised? The CommonCensus NFL Fan Map acknowledges regions where there is no discernible preference.

From there, into Voronol diagrams: Euclidean distance versus Manhattan (taxicab) distance. And which border of another country is closer to you, Mexico? Canada? Bermuda? Cuba? (If you should need that information for any reason...) David also had a line moving down turning dots into parabolas forming the borders. Why a favourite? Low threshold, high ceiling, with multiple branches.

#6: "Feedback meetings with students" by Anna (@borschtwithanna). She read a book last summer, "Creating Cultures of Thinking", more information at What is your least favourite task as a teacher? For a lot of us, it's grading. Shift from TIME being the most important resource (doing it faster) to ENERGY is the most important resource (doing it in a rewarding way).

Anna schedules 20 minute feedback meetings with students (can be done alone or in pairs or threes) every two weeks or so. To discuss work the student has turned in, giving detailed oral feedback, with one of you taking notes (if they do it, better to see if they understand). Later in the year, focus less on assignments and more on overall progress plus incorporation of previous feedback.

The benefits: Improved their understanding of her expectations, so better quality assignments. Improved relationships with students. Fewer slip through the cracks. Can give richer assignments. Grading is no longer the worst thing everrrrrrrrrr. To chat more, see the post on her blog from earlier this year.

At this point, Lisa Henry noted that we are in a chapel at a Christian University, take your things as you go, watch your noise level. And we returned to the morning sessions - mine is "Planning for Differentiation" with Michelle N.

I've moved that into a separate post; to move directly to the Day 2 session you should click here. There is a link to return.

At 11:30, I got earplugs from Norma Gordon (thanks!) then met up with John Golden to talk about collaborating on a personified math drawing. Edmund H joined us, and we went for Etheopian, where I ended up next to Justin Aion. Productive lunch (composite function personifications and some astronomy). I did start to stress when my bill was forgotten, then more delays, then I ended up sprinting down the road because I'm taking this live blogging VERY SERIOUSLY, please don't judge me too harshly.

#7: "Explore Math" by Sam (@samjshah). He gives some projects over the year with a couple weeks for students to complete them - and he approves almost everything. A website made after a year or two of this is with some things being looking at patterns in colouring books, podcasts, WODB, Numberphile, etc. Fascinating for kids that aren't fascinated by how things are taught, can learn a lot about kids this way too.

Keep it low stakes, keep it open, keep the mini-explorations mini (don't expect giant things). Don't compare them. Have two different due dates, return with comments first. Make your life easy (give 1 to 2 sentence responses). Many intersections and extensions.

#8: "Good Questions" by David (@davidwees). Questioning is a fundamental part of teaching, people often ask me how do I get better. Dylan William said there's only two good reasons to ask questions, to cause thinking and to provide information to the teacher; David would add #3, to prompt students to consider each others' ideas, developing a community of math learners.

What does the number 2,500,000 represent? How many questions a teacher will ask on average in their career. WOW. Think about how many neuro pathways are created. From 0 to 35 years, maybe "you are here" right now, lots of time to get better - but you've asked a lot of questions already. Patience, it will take you time to make the questions more useful, keep at it like the backwards bicycle.

#9: "Teaching is the same everywhere" by Connie (@CHaugneland). About 3 years ago, she started to sponsor a boy from Bugesera, Rwanda. Then she went to visit him and see aspects of the organization. Then three months later, went back to work with the teachers and students in the three Africa New Life schools. She couldn't go last year; she wants to move there.

This year, June 2016, she went again, this time with a week in the Kigali partner schools as well. She helped facilitate with a session on noticing/wondering at a conference in Rwanda, with thanks to this community. Of note, they only have a blackboard and chalk, so she really had to think through what strategy in her classroom would be most effective for that.

"We're exactly the same" because we all love teaching. We all love our students. We all love learning. We all love improving. We all love doing our very best. But they also have some challenges. New to speaking English. Having to teach in English. Having 50+ children in every class. Resources. And the government decided at the beginning of the school year that the whole country would change from teacher centred to student centred instruction. Whoa.

Does that sound familiar? Not enough supplies. Standards are changing. My class sizes are too large. Connie has gained tons from this community, now she can pour into others who have very little - and it's NOT one way sharing, she can take things to use in her classroom (like managing 60 kids). Next summer, she will likely spend all her time in Rwanda; to have a conversation, go find her, and see her blog with the Rwandan tab. (If you're interested? They need chemistry and male teachers, training trip is usually two weeks.)


I have a confession to make here. On Twitter, I would be less inclined to follow an elementary teacher over a high school teacher. Not because I felt that there wasn't anything to learn from them, more for my own sanity... because I don't only follow teachers but also writers. I felt my brain could only take in so much. But now that I'm over 800 followers anyway, and have lost the battle, perhaps it's time to change that based on today's Keynote speech.

Tracy Zagar is the writer of the upcoming book "Becoming the Math Teacher You Wish You'd Had". Lisa asked her to speak specifically as an elementary teacher to a mostly secondary group, which blew her mind. She hadn't come to previous camps in part over a worry about invading our space, in part to not take the seat of someone else who was secondary. (I'd previously been concerned about taking someone's place, which is partly why I'm so invested in these live blogs.)

"I have a different view of what I am able to offer you." Tracy started with a sketch from Ben Orlin's blog (Math with Bad Drawings) regarding content knowledge (increasing through grades?) and pedagogy (decreasing through grades?). She had us respond to some prompts, then spoke herself: It's not helpful to say you don't need content knowledge to teach little kids. K-2 deals with cardinality, representing symbolically and shape patterning. It's the introduction to mathematics and what it means to be "good at math" - not the basics. Rather, it's a field unto itself.

We tend to define how good we are at math by how FAR we go in the system. In China, most elementary teachers do not go past 8th grade math, yet 90% of them can write a story project based on fractions. Only 4$ of American teachers can do that. And on the flip side, it's not helpful to say that if you like the math more than pedagogy, teach secondary. Turning your back and holding a piece of chalk doesn't create high quality tasks, effective facilitation, or social and emotional safety.

Pitting pedagogy against knowledge (and elementary against secondary) is not helpful! Consider the visual of a suspension bridge. The towers, the "compression" is strong to build on top of them, these are both Content and Pedagogy. The wires draped on is Pedagogical Content Knowledge (PCK), the missing paradigm. Which is what matters as the emphasis shifts between the towers, since it differentiates someone who can DO math from someone who can TEACH math - or someone who can teach French. The PCK is how to create the conditions for students to learn the content from a pedagogical lesson/activity.

Tracy then gave four stories, briefly summarized here:

  1. Sept 14, 2014. When Kate "assigned her an algebra problem", and she became invested in the Twitter community. As they gave her space to answer, even as she feared making a fool of herself on the internet.
  2. Feb 2015. During "SlowMathChat", the idea of "Never skip the close" came up, and elementary teachers helped Dan Anderson with some ideas, since they have a whole filing cabinet (from gallery walk to connect/compare to looking at a common issue); in secondary it's more about the HOOK, not the close.
  3. Dec 2015. From PCMI, an assignment to shade in 1/4 of a drawing of five squares. Secondary teachers grabbed formulas, while Tracy folded and shaded to do it... and Heather Kohn tweeted it out, and David Butler sent back many versions including a proof, and it's "the Lunes of Alhazen", who Tracy looked up and he's on the money of Iraq, and Simon Gregg in France is later making his own out of quincunx and small pagodas. #QuarterTheCross
  4. Oct 2015. A student claims "everything with perimeter has an area", which leads to a twitter talk with Christopher D, and thought of a degenerate rectangle, and limits, and Matt Enlow saying "Much more of this and y'all are going to have me considering switching from HS to elementary".
Sounds like an elementary teacher learning content by hanging out with secondary teachers, doesn’t it? Sounds like a secondary teacher learning pedagogy through elementary teachers, doesn't it? Extraordinary things can happen when we do math and talk about teaching together from preK through to 16+. And who was in that conversation in Story 4? Six white dudes, who are supposed to be doing 'more advanced math'.

This is unthinkable - tell a fifth grade teacher, "I want you to drive this conjecture over to the high school, introduce yourself to them, and see if they'll play with this." They won't, because they're worried they'll be made to look stupid, that they'll be talked down to -- and some of that is insecurity but some is based on experience. And what are the fears talking to elementary teachers?

That vertical collaboration play and discussion happens nowhere else. For now. So there's two calls to action - to see who you're following on Twitter. We populate our staff lounges with who we want to be there. And to see what it would take to make vertical collaboration happen in real life. What are the obstacles, what are the necessary conditions? Please be in touch with what you tried.

From there, I went to "Debate That!" with Chris Luzniak. (The idea of "Critiquing Others" comes up in my Data Course in particular.) He started by showing this PBS Learning video that he was in. Debate works because teenagers love sharing their opinions. And there's a lot that can come out of a debate - see research, and though it's mostly seen in humanities, debate can meaningfully engage any large classes and is part of common core.

Know the definitions: An argument is "a statement made with sound reasoning" and has two parts, a CLAIM, which is your opinion (controversial opinionated statement) and the WARRANT, the reasoning or justification for your claim (as a warrant for your arrest is the reasoning you're being arrested). ARGUMENT = CLAIM + WARRANT

Regarding the language, it's a safety net for students, as it's not everyday words. Just what they're doing today (not a personal attack). It's easy enough to say a state test uses "justify" instead of "warrant", and this works well for proofs in geometry too. (If students don't have the "warrant" language after September, despite bugging them, give up as long as they have the two parts - giving a reason for their claims.)


  • Soapbox debating. "The most important math topic is?". Start off with favourite musician or something silly, for less stress, then transition to more math. Eventually this can be a warm up as students come in (perhaps twice a week or more).
  • Circle debating. After the first person, the next person SUMMARIZES before adding to the warrant, or refuting it. And people can call on the next, ideally Chris wants to talk as little as possible. Curve desks towards the middle, and sit down to not be a visual centre of attention.
  • Point/Counterpoint. Create fighting in the classroom, where the next person HAS to argue the opposing view, to force the first to reconsider their thought, no matter their actual opinion. Be ready for both sides.
  • Table Debates. Give debate cards in pairs with an argument for each. Eg. 3, 7 ... "This sequence is arithmetic" argues against "This sequence is geometric". There can be a concrete answer too, as opposed to an opinion, if there are misconceptions in the room.

Good debate-y words to use in making a question include "best/worst", "should", "biggest/smallest", "weirdest/coolest", "Always/sometimes/never", "Agree/somewhat agree/Disagree". With good questions (and maybe fake student work), you need structure. More good statements to use as the year continues: "I Concur". "On the Contrary". "To Supplement That". These sorts of things are printouts on the walls of Chris' class.

Things wrapped up with an attempt to modify regular questions for "debate". Note we don't want to push aside the math for fun, but make it less boring, more debatable. Instead of "graph this sinusoidal function", "the best way to graph a sine function is what?" or "what is the most common mistake made when graphing here?" Perhaps to test comfort level of fractions vs decimals, ask "which of these would you inflict on your worst enemy?"

It's not easy, but it gets easier. It is giving up some control, if you're a control freak. Don't feel you have to do it all the time, take your time with it.

My LAST session was "Racially Relevant Pedagogy: How Do We Get There?" with Wendy Menard and Jose Vilson (yesterday's keynote). Both from NYC. We started with a six corners activity, where you walk to the corner of the room with the answer you most closely identify with. The answers were: Ethnicity. Race. Class. Religion. Gender. Sexual Orientation. (or None/All) There was a short debrief after each of these questions:

1. Which do you most strongly identify with? I went to Gender, because I feel like being male, there's a number of things I don't have to deal with that others do, and it's on my mind more than race or any of the others.
2. Which did your parents most discuss with you? I went to Class, because my parents often emphasized how they wanted me to be better off, and saving, and not taking sugar packets from restaurants.
3. Which do you wish you knew more about in your own identity? I went to Religion, because most of the others are pretty clear cut, but aside from church on Christmas, it's never been a thing for me.
4. Which do your friends most often talk about? After spinning like a top a bit, I went to "none", because I don't know that I really have these conversations with friends, or if it comes up, it's not about any one thing.
5. Which do you talk about the least? Back to Religion for this one.
6. Which has the most conflict/issues for you inside yourself? After spinning like a top again, I ended up back in Gender. What I strongly identify with is what I have the most conflict with? Yeah, interesting that. I don't think I do stereotypical "male" things; I dislike beer, bbq and sports, preferring to watch magical girl anime. So if that's me, am I identifying with male in #1 due to the privilege? I don't really have an answer for you here.

Very briefly (because it's after 2am and I'm too tired to do this justice), some of the things that came up include how Q3 is VERY different if we don't specify it's about our own identity. That "Black" and "African American" are not synonyms (race versus ethnicity). What "intersectionality" means. How we are shaped by being repressed versus being oppressed versus being silenced. And that teaching may be a part of one's identity.

The second half of the session was a look at "Why Race?" - it impacts communication and learning in our classrooms and school communities. What are the manifestations of racism and power? Do we know what the key terms mean? We wrote how we defined racism, institutionalized racism, and equity, split into groups, read definitions out loud, then saw if our understanding changed. The idea of it being intentional or not was something I hadn't considered.

It was noted that both of these activities could be done with students. The resource list is on the wiki. And in conclusion, we were given 6 PostIts, where 3 would have a word (or phrase) in how we describe ourself as an educator and 3 would have the same but in how students would describe us. FWIW, I listed "Knowledgeable, Caring, Weird" along with "Approachable, Creative, Flexible". Jose finished with "Thank you for your vulnerability, take care all."


I spent 10-15 minutes chatting with John Golden afterwards with respect to our drawing collaboration, as related to my math comic. (Which I notice publishes in a few hours...) Then I went back to the dorms, dropped off my stuff, and almost immediately was back out again with a group headed for the Minnehaha Falls. We took the train down from Franklin Station, then from the falls a number of us took the walk all the way down to the Mississippi.

After some talk of books and cicadas on the beach, we returned, and a number of us had dinner at "Sea Salt Eatery". I had the 1 pound of catfish, served not with fries, but with melon - so that's interesting. There was a bunch of discussion over dinner, largely about the community, twitter etiquette, and where we were from.

On the trip back, we ended up on a bus because of construction shutting down a part of the train service after 8pm. I reached my room about 10pm, meaning I've been at this for over four hours again. So I'm done. Sorry if you wanted information about the "Trivia Night", but it's really not my thing (I even took time to answer the pre-TMC survey with it not being my thing). Though I'll footnote that I chatted a bit with Sean Sweeney about his sessions when he got in after midnight.

How are we doing, are these useful to people not at the conference, or are they simply too damn long?


  1. I think this one was useful for me not being at the conference. I can get a sense of what's happening and what you're learning, and what I could learn. Thanks.

    1. Thank you for letting me know that! Hopefully it's helping with learning even if you're not here.