*"Models are going wrong if they're not as simple as they possibly can be."**"I don't use a textbook. ... They are written for someone, but I am not that someone."**"I think we’re in for a real tweet today. ... You know what I meant."*

#### MORNING DIFFERENTIATION

After last night's dinner choice of ballgame food, I headed out by 7:30am to get to Perkins for something more substantial. Returned by 8:30am (discovering "Murphy Square" here is actually older than Minnesota itself), and went to the Foss Chapel for some general discussion. Then the Opening Session, led by Lisa Henry.

There was applause for Chris Smith locally, and the rest of the TMC team. Also, Andrea's birthday. TMC16 has 195 attendees, 98 are repeat, so half are new. "We need to build community. It's important to learn from each other." Not only here but at other conferences. T-Math-C is now a non-profit corporation formed in February, with a board of directors.

Quick summaries were given of morning sessions. The hashtag #1TMCThing can be used to flag one thing to take home and use. If seeing that speaks to you in some way, connect with that person, talk, check up again in 3 months. Don't forget to do surveys from before, and submit recap posts to Glenn's link. We split off for morning sessions.

I went to Michelle Naidu's

**"Just Enough" Approach to Intervention for Students with Gaps**. There were over 30 of us there. We started by introducing ourselves. Then there was a video on "Herding Cats" (From EDS.com), to discuss at tables where we were sitting. (Cats would become a theme.) Seemed to work as a metaphor. Students want to go anywhere, we have to get them to a certain spot at a certain TIME too.

The rest of the morning session I moved into it's own post; you can read it here, and there is a link to return to this spot in the post.

#### MY FAVOURITES #1-3

For lunch I hooked up with people going to "Afro" and had a lamb gyro. I ended up chatting a bit with some local math teachers (two of whom happened to wear similar shirts). I made it back for the 1pm "My Favourites".

__#1: "Shared Experiences" by Jonathan (@rawrdimus)__. What do you want your kids to walk away with? How to make "I love []" or "[] feels like family" to be [math class]? They have a math hallway and a public art program with chalk drawings on the sidewalk. Also an Avengers movie, long story. The big one, presented last year, is "Varsity Math".

A joke Jonathan made 15 years ago has launched into this juggernaut, to combat negative AP calculus culture. "I need 40 bucks, gimme. In exchange I promise you get a bunch of things." Swag, laser tag in cafeteria at end of year (40 at a time, so rotated with paintball) and see http://nhs.varsitymath.net. This year, they added Stats so the math choice wasn't based on getting a T-Shirt.

There's been promotional posters ("Varsity Math Needs You"), and a summer camp for incoming 11th graders. Now everyone here has been inducted into the club. Grab a sticker, you can put in a member number, take a picture wherever it ends up then send in "I'm on the team! #VarsityMath" so I can make a collage for my room, the kids will know they're not the only crazy ones.

__#2: "SMP3 & SnagIt" by Hedge (@approx_normal).__Recalled how the first "Fave" at TMC12 was the marshmallow gun and southern accent problems then went into (1) SnagIt by TechSmith which screen captures images, also screen casting now (pay for upgrade). Can capture student thinking in the class, use for Twittereen, will give away 3 versions worth $29.95. Why pay? (2) Fuse App which transfers mobile content to full TechSmith products, things you notice can be auto uploaded. Such as "Truly Unfortunate Representations of Data" (TURDs)

Finally (3) Why am I teaching this? For instance long division, when they'll get a calculator in middle school? Because they'll need to know for polynomial division in calculus. It's not that a teacher doesn't care, it's that they don't know. Share such things at http://whyamiteachingthis.weebly.com. See this summary at http://bit.ly/HedgesStuff

__#3: "Using Ms Pac-Man for Transformations" by Deborah (@debboden).__Relates to Robert Kaplinsky. Kids can learn about why they have to do transformations, and how you can do three things or one thing to get to the same place. Can have as a project or piece of a test.

With Lisa's remark “I think we’re in for a real tweet today. ... You know what I meant.” she introduced Jose Vilson, and that is it's own post that you can read here.

#### IN THE BOOKS

To start the Afternoon Sessions I went to Sue VanHattum's

**"Playing with Math and Getting Published"**. She had published the book of that name, and spoke a bit about the process. Seven years ago, she had joined a forum for home schoolers, to help with her teaching of community college math. She discovered a lot of amazing writing; most teacher bloggers at the start were high school, not elementary or college level.

Wanting to pull together the best articles, she asked people if they would like to be part of a book. Including one article she rewrote to have less (justified) anger in it. Finding a publisher, she had a year off, but it's such a strange niche. Progressive publishers weren't interested, nor were main ones. She ended up getting together with a starting publisher, Maria Droujkova (now of "Natural Math"). She deemed self published books to be perceived as terribly edited.

In terms of cost, wanted something not too cheap as to be undervalued, but not too expensive either, hence $19. She did alienate the artist due to the image on the cover - you need an artist who can see vision and and the mathematical aspects. For instance, a broken cookie insert that had to have it's pieces the same size was incorrectly drawn and had to be modified. Artists aren't necessarily paying attention to the math. Sue also asked artists if she could publish a piece of their math art as chapter separators.

Noted that a digital copy is possible for free (pay what you decide from 0 to infinity). It's allowed, under Creative Commons, with proper citation, to use any piece of the book. Sue then turned it back on me and Andre Verner, to see what we were involved with. I mentioned my three blogs and personified math. Andre has the site "Directed Discovery Mathematics", a compilation of things he hopes is useful for others - hence word documents for modifications.

John Golden's wife Karen was also there, wondering about the audience that Sue wrote it for. There was a crowd funding, which sold 350 books, and now with over 500 they're onto a second printing (and edits/corrections). Things were crazy on the personal side when it came out though, so she knows little on who, but someone did tell her "I love your book" here at the conference. As someone bringing in the element of homeschooling, few people here think about it.

Sue also feels more ownership, having worked through puzzles, and more like a professional than before she published.

From there I went to

**"What is Mathematical Modelling?"**with Edmund Harriss and Chris Shore. After getting our opinions, Edmund started by showing what he feels was a "model of what I think is mathematical modelling". You start with

*something to be modelled*, link it to a representation, do something, and then link it back to something significant. Ideally the direct path from

*something to be modelled*to the something significant is the same.

First, we need to represent, then second have actions we take on those representations. Let's move from the meta to a simple model of counting - how do you count sheep in English? Not 1, 2, 3, but rather it's Yan, Tyan, Tethera, Methera... (and that system seems slightly different for parts of the UK). It's a base 20 system, in that once you get there, you put a stone in your pocket and start over. If you have over 400 sheep (which never happened) you'd replace 20 stones with a superstone.

We can use the stones are a representation for adding sheep, addition in the model works the same as actually counting. Bear in mind that "models are going wrong if they're not as simple as they possibly can be." We don't care about the loss of information only if we only care about the 'total'. Edmund then looked at the coefficients of a quadratic versus a cubic in Desmos (and had wood as a physical representation). The more math you know, the more tools you can use up here, but if the mathematics is simply 'counting' then other models may be more clear.

Chris took over, pointing out that "math model" is a noun, whereas "math modelling" uses a verb. Modelling then is not a process you're giving, it's something the kids are supposed to be doing, it's an active process. Using a map is not modelling - the map itself IS the model, you're only modelling if you created that map yourself.

With the book by Pepper White, "The Idea Factory: Learning to think at MIT", Chris points out that if we're struggling with modelling, we have very good company. Looking at common core you see verbs like 'apply', 'solve', 'describe', 'interpret' and 'reflect'. Distinguish between modelling and the tools used to represent the model. Edmund added that we can teach kids the math techniques, but they may not know how to use them, even the smarter ones.

From there, it was "Speed Dating" (which last I knew at TMC14 was a random session not a group one, but it was perhaps upgraded last year). Run by Jason Henry, it's the session that doesn't start on time or end on time. How does he get stuck with this? He married his high school sweetheart. Jason notes spreadsheets are awesome, but you still have to put in the formulas, so tell your students to learn to do the math or to marry a math teacher.

We were put in different parts of the room according to a random categorization (where we were originally from, US or otherwise) and asked to talk to someone we didn't know for 2.5 minutes (which was "some number of seconds"). Then switch based on another feature (such as hair colour or shoe type). Here are the following people I encountered:

- Anna (@borschtwithanna) who was born in Ukraine
- Christy (@PettisChristy)
- Edmund (@Gelada) who I knew but others had paired
- Lane (@LaneWalker2)
- David (@Dave_Sabol)
- Chris (@Isomorphic2CRob) along with Mark
- no one; everyone had paired off in my area (I noticed this once or twice)

I left a little after 9pm, came back to the dorm, and have spent the last five hours blogging, no joke. So, I think I'll put this one in the books now; sounds like it might start to rain again. Hope you enjoyed reading!

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