# My Takeaways from #TMC16

I have all the feels, coming back from #TMC16, but they also have paralyzed me. There’s a disconnect between all the feels, my making sense of all the feels, and my ability to express all the feels in words. I felt paralyzed because I wanted to express things right. Since that was impossible, I did nothing. But to get past that, and because I need to collate the gems and thoughts from the conference to learn from them, this post is going to be a random collection of thoughts. It’s more for me — to consolidate my thinking and write down all the little things — so apologies if it feels like a confusing brain dump.

### What are you passionate about?

Sara VanDerWerf (her blog) gave a keynote that was reminiscent of a keynote last year. She said “What are you an evangelist for?” (For her, one of those things is Desmos, because of the equity and access it allows her kids.) Once you know that thing — the thing you are willing to go to bat for, the thing you want to spread — you should think consciously about how to best evangelize it. That might include having an elevator speech ready for you to give, and being conscious of the different audiences you may be talking with about it (students? parents? teachers? admin?). Being an evangelist isn’t just being passionate… it includes enacting that passion by finding ways to share “the best… with others who can benefit.”

Sara’s fabulous calculator museum (mausoleum!)… all your calculators are dead… all hail Desmos!

I know I am an evangelist for the #MTBoS. However in terms of math content or math teaching, I don’t quite know what I’m an evangelist for… yet. All this reminds me the end of this blogpost I wrote last year after TMC, where I was trying to figure out what my “brand” was (and came up emptyhanded). But I have faith that with enough time, I’ll figure it out.

Speaking of evangilism… Jonathan Claydon (his blog) shared a “my favorite” about Varsity Math, a community he’s built up at his school. I’ve had a teacher crush on this guy for years. There’s something about his energy and style and humor, and the fact that he is good at something I am not (yet) good at (being a “relational” teacher)… he’s a must follow. In any case, Jonathan is an evangelist for changing the way kids look at math at his school. Although ostensibly his goal is to increase the numbers of kids taking AP math classes and increase the AP scores of these students, he’s doing it by building a supportive math community — one that feels like a club. He is doing this by creating “shared experiences.” He knows he has succeeded if he can get kids to say “I love (varsity math). (Varsity math) feels like family. You couldn’t understand because you’re not in (varsity math).” The only way the last statement could make sense is if an entire culture is built around (varsity math). Of course what goes in the parentheses is open. Read about his project here. See a photo of @rawrdimus here:

This “my favorite” spoke to me. I’ve been consciously working at my school about raising the math department. Not in terms of teaching and learning (I don’t have much say in that), but in terms of getting kids engaging with math outside of the math classroom. I brought the New York Math League contest to school, I’ve worked (with another teacher) to concertedly increase the number of students taking the American Math Competition each year (from around a dozen to seventy+). I found a non-stressful virtual math team competition that students can compete in so that they can fit it in their busy schedules. I have co-advised math club for years. I started Intersections with a science teacher, a math-science journal for students to submit their works to (it’s now four years old!). Lots of things… I want spaces and times for students to engage in math outside of the classroom. But with all of this, I don’t see a culture of kids who geek out about math. There isn’t a community or culture around doing mathematics at my school. And Jonathan’s talk helped me realize that I have to think intentionally about building a community. It is more than “if you create it, they will come.” It isn’t the event or space that I design, but the “shared experience.” What does this mean? What does this look like? I don’t know yet. But perhaps having a student-created chant before each virtual math team competition, bonding field trips (math movies? museum of math? math scavenger hunt?), swag as proud identifiers, a wall of fame…

[Update: I was having trouble figuring out what precisely I want to accomplish in my school. And today is day 3 of a crazy math frenzy day where I’m having fun exploring and writing lesson plans and playing around and coding and getting stuck and getting unstuck and having frustration and elation — so much elation. And then I read this post by Annie Perkins, which talks about a sort-of-crisis I’m having (posts here and here). And in my current haze, I see the glimpses of what I want to achieve. Why do I want kids to engage with math outside of the classroom? Because it’s beautiful and fun to play with and just play mind-blowing cool. But they don’t get that in the classroom — at least not regularly enough. Jonathan created a community of kids who were vested in AP math. I think I want to figure out how to create a community of kids that love to (a) be exposed to interesting/strange things about math, and (b) play with math and explore it. Less “math team tricks” and “competition problem solving strategies” and more pure unadulterated fun. Things like this fold and cut problem that I did in geometry. Or generating and analyzing their own fractals. Taxicab geometry. And I think lecture might be okay for some of this — a lecture on infinity or Godel’s incompleteness theorem. Or following some internet instructions on how to build a planimeter out of a sodacan to calculate the area of a blob just by tracing around it. Or going as a group to a math lecture at the Museum of Math. Or learning about higher dimensions. Whatever! I want to get kids to geek out about how cool and fun math can be. I want a math is cool community, where there is a culture of nerd-sniping and geeking out and regular mind-blowing-ness. The truth is I probably don’t have time this year to come up with a plan to execute this to make it happen this year. I also think that the lack of free time that kids have in their schedules might make any plan of mine totally impossible. But I think it’s worth brainstorming… maybe not for this year… maybe for next year.]

### Desmos Features:

At the Desmos preconference, I learned about three things

(1) “Listening to graphs.” This feature was included for vision impaired students, but I think many of us teachers started dreaming up other uses for it. To get a sense of it, check out this piece (done by Rachel Kernodle and James Cleveland) playing “Mary Had A Little Lamb” (click on image):

To play (at least on a mac), press COMMAND F5 (which enables voiceover), go to the fifth line and press OPTION T (to tell the computer to “read” the graph with sound), and then press H (to play the graph). When it’s done, you can turn off voiceover by pressing COMMAND F5 again.

Some thoughts… Have the audio for some periodic and non periodic functions, and have kids do an audio function sort? Play audio of graphs (without telling kids that) and have kids do a notice/wonder (before sharing what they are listening to). Have kids identify if a graph has a horizontal asymptote for end behavior from an audio file? Have kids identify which graphs might have a vertical asymptote from an audiofile?  Play sine and cosine (or secant and cosecant) and have kids not be able to tell which is which (because they are just horizontal shifts of each other). Have kids devise their own piecewise functions and play them, while other kids have to graph them. Create a piecewise function and have a student who enjoys singing to sing it? I am not convinced that anything I’ve thought up could help a deeper understanding of any topic, but I also don’t think it could hurt. Some kids might really get into it and enjoy playing with math…

(2) Card Sort: You can create card sorts in desmos now! Check a bunch of them out (that were created at the Desmos pre-conference)! Or if you just want to go to one of them, click on the image of Mattie Baker’s card sort on visual sequences:

To gain this functionality on your desmos account, go to teacher.desmos.com and click on your name in the upper right hand corner, click on LABS, and then turn on Card Sort.

(3) Marbleslides: You can create your own marbleslides in desmos also! Turn it on in labs (see above). Then you have the capability of building your own! If you don’t know about marbleslides, check out this marbleslides activity made by the desmos folk on periodics.  At least to me, the use of marbleslides is to help students understand function transformations… so I can see it useful for helping kids gain fluency in transformations. (Anyone see another use for marbleslides, that I’m missing?)

### Showing Student Work

Hedge talked about how she uses SnagIt to display student work. She takes a photo of student work on her phone, and using an app called FUSE, transfers it to SnagIt (on the laptop) — as long as both are on the same wifi network. Here’s her blogpost showing it in action! It costs money (\$29.95) but I trust Hedge!

I attended PCMI years ago, and I recall Bowen and Darryl using this technique (kids working on problems, taking pictures of different approaches) to facilitate discussion to bring different ideas together. Nearing the end of a session, they would project pictures of student work, people would explain their thinking. Bowen and Darryl would sequence the pictures in a thoughtful way. They wouldn’t focus on those who “got the answer” but on various approaches (visual/algebraic) — whether they worked to get the answer or not. I liked that so much, and I suspect SnagIt could allow that to work for me in that way.

### Getting Triggy With It! Hands On Trigonometry

Fouss gave a wonderful hour long session on making trigonometry hands-on for students. Instead of telling us what she did, we got to do some of the activities, and that was powerful. There were activities I’ve read about that I thought “eh, okay, but it would be more efficient to do X, Y, and Z” and then I did them and I saw how the act of doing them could be helpful. Here are three that we got to do: understanding radians with smarties, creating a unit circle with patty paper, and creating a trig wheel to help kids practice converting between radians and degrees and visualize what the size of the angles look like.

All her materials are linked to from her presentation, and are easily found on this folder on her google drive. I have to scour them to find my favorites. I did love the radian activity. If you make the radius of the unit circle 7 smarties long, then you can have a good discussion on whether 3 radians is 180 degrees or not… (21 smarties won’t quite make it to 180 degrees… but 22 smarties will fit snugly… nicely giving the 22/7 approximation for $\pi$. Nice!)

Some of the ideas linked to from her presentations that I want to steal:
(a) Trig Stations
(b) Two Truths and a Lie (useful for more than just trig!)
(c) #TrigIs (useful for more than just trig!)
(d) If I choose to do ferris wheel problems, this ferris wheel comparison [but modified to be more challenging]
(e) Desmos’s Polygraph for Sinusoids and Marbleslides for Periodic Functions
(f) If I teach trig identities, use this matching game (and have kids check their answers once they are done by graphing on desmos!)
(g) Headbandz, trig edition! (for graphing trig functions)

### Variable Analysis Game

Joel Bezaire presented a great game that can be used in warmups to help students see relationships and patterns. His video on it is here, showing the game and how it is played:

### Nominations: Making Work Public

Kathryn Belmont (@iisanumber) gave a great way to have kids really put forth effort on open-ended assignments without using grades as a stick. She will ask kids to do this assignments, and then put their work on their desks. Each student gets posts its, and as they wander around the room, they put post-its on the works they see… They write two accolades for good things, and two ways to push back or improve the assignment. The way I envision this in my classroom, not everyone will see everyone else’s work, but everyone will see 5-6 other students’s work. After the walk about, the teacher says: “Do you have any nominations”? Jake might reply “I would like to nominate Kiara.” If Kiara feels okay about being nominated and “accepts the nomination,” the teacher takes Kiara’s work and puts it under the document camera. Then Jake might say, “Kiara did … and what I thought was so awesome about it was …”

(Her slides for her mini-talk are here. A video of her talk is here.)

The teacher is no longer the sole audience member for the work, and kids are defining what good work looks like. In Kathryn’s classroom, she saw a huge increase in kids putting in effort in these open-ended assignments. (I can see this being useful in my own class, especially when I do my explore math mini-explorations.)

### Intentional Talk

I went to a session by Jessica Breur (@BreurBreur) which was fantastic. Although it was only one hour, I wish it were a morning session. She wants to have teachers establish a culture where students:

• use the group to move the group forward
• talk, trust, and depend on classmates and the teacher
• persist — even in the face of a challenge
• view math as “figure-out-able” and accessible to all

She highly recommended Cohen’s Designing Groupwork (a book which I have but haven’t read).

To start, over the first week or two, students will be doing lots of groupwork activities. And at the end of them, they will (in their smaller groups) focus on what the group “looks like” “sounds like” and “feels like.” They don’t necessarily need to focus on all three at once — students could focus on “sounds like” during one activity and “feels like” on another. After the week is done, the class comes up with a set of norms in these three categories — where they talk about what successful/good/fun groups look/sound/feel like.

We did a lot of hands-on work trying out some of these groupwork activities — and she has included all of those activities in her slides. Here is one of my favorites:

This is the red solo cup challenge. A group of 3 or 4 is given 6 red solo cups, stacked inside each other, placed face up on the table (so like a regular drinking up face up). The students are given a rubber band with four strings tied to it (even if 3 students are doing this, keep the four strings). Student must put the solo cups in a pyramid formation. If they finish that, there are other configurations that Jessica includes in her presentations (or students can design their own challenge for others!). Afterwards, the group reflects.

Similar tasks can be done, like 100 NumbersSaving Sam, Four 4s [but making an emphasis that we want as many ways to generate the numbers 1-20, not just one for each], Master Designer, or Draw My Picture.

For more “math-y” things, you can do a Chalk Talk/Graffiti Board– where students answer questions before a unit to activate some old ideas. For example, “What do you know about the number zero?” [In fact, any sort of talking point/debate-y statement can be used here.] Kids write anything and everything they know on a poster in their group of four. Then hand the posters up and students walk around and read other students’ responses (if time, writing their own comments down). Finally, for closure, you can ask students aloud or using exit slips “What are two things you didn’t think about that you saw on the graffiti boards?” Another more math-y thing is a donut percent task. An example is here but I’m confident it could be modified for trigonometry (values of trig functions, identities, etc.) or rational functions (equations and graphs) or any number of things! The idea behinds this is that each person in the group is given four slips of paper, and as a group, four complete donuts have to be created.

Sounds simple? But here’s the rub… group members must follow the rules below to each get their own donut completed.

You should keep a poster of the 8 Standards of Mathematical Practice, and every so often during activities or groupwork, ask students which ones they are using.

Once norms are established at the start of the year, you consciously need to be doing activities that practice the norms. Be intentional about it. (If you find that kids aren’t listening to each other, find an activity that promotes listening.)

I loved this session. However what I need now are a set of activity structures that I can fit actual mathematical work into. So things which develop understanding, or practice solving something, etc. And it would be nice not only to have the activity structures, but the activities themselves all in one place (so, for example, activities for Precalculus!).

### Talk in the Math Classroom

My morning session was called “Talk Less, Smile More” and was led by Mattie Baker and Chris Luzniak. In the session, they provided various structures to promote math talk in the classroom. I am going to outline some of the ideas that I can see myself using in my classroom.

DEFENSE MECHANISMS & CLASSROOM CULTURE: Most importantly, to get talk in the math classroom involves getting over student defense mechanisms. Students fear being seen as stupid, and they fear being wrong. In order to do this, you have to lower the stakes so kids can temporarily bracket their defense mechanisms to create emotional safety. These could be by doing things like chalk talks (silently writing responses to questions, and responding to other student responses)  or doing notice/wonder activities where all responses are honored. Many of the ideas that Chris and Mattie shared in the session do this, by providing a structure for talking, and a bit of a safety net (often where no response is right, or students are required to give a particular answer and justify it).

When implementing it, you have to be consistent and do these structures fairly often. Start simple, and then get more complicated with the statements/questions. Give a lot of energy and excitement — especially if a student gives a wrong answer or a right answer (“Oh wow, what an interesting thought… let’s explore that…”). If students turn to the teacher and say “Mr. Shah, what about…” sit down and redirect it to the class. (Remember the teacher is not the center… this is about getting kids to be the center!) As teachers, we have to watch our own facial expressions (a.k.a. don’t make a face when you hear a totally wrong answer). You can avoid this (if it’s a problem for you) by looking down at a clipboard when someone is responding.

At the end of a class or a portion of a class with a lot of mathematical talk, do “shout outs” (shout out something they learned, or something someone else said that helped them). And ask kids (to fill out on a card) what they took away from class today (and what questions they still might have). Or “I used to think ____, but now I think _____.”

To give students some crutches when talking, have posters with these simple statement starters to help them (on all four walls):

TALKING POINTS: In this session I first got to experience Talking Points. I’ve read about them on Elizabeth Statmore’s blog (see links on the right… a bunch of talking points are hosted in one of her google drive folders). But the truth is: I wasn’t sure how much I could get out of them. Now that I’ve participated in one, I feel differently. This is how they work:

(1) students in a group of 4 get n statements. The first round involves one person reading the first statement, and then say “agree/disagree/unsure” and then explain why they chose that response. They must give the reason. The next person does the same, then the next, then the last. The important part about this is that no one can comment on another person’s reasons. They can just state their own reasons. They can match someone else’s reasons, but they have to be stated as their own.
(2) The second round involves the first person saying “agree/disagree/unsure” (after hearing everyone else’s thoughts) and then they can give reasons involving other people’s thoughts. Others do the same.
(3) The third round is quick and short. Each person says “agree/disagree/unsure” and gives no reasons. Then someone records the tally of the responses.

Here’s an example of what talking points can look like (when they aren’t about math content):

Talking points can also be math content related. Instead of “agree/disagree/unsure,” you can use “always/sometimes/never” or some variation that works for your questions. In our mini-precalculus group, we brainstormed some talking points around trigonometry:

After participating in talking points, we as a group came to the following realizations:

• Talking points were not as repetitive as we thought they would be.
• The more controversial a statement, the more discussion happens.
• You were really forced to listen to each other
• When the talking point includes “I” statements, you learn about other group members
• They are good for pre-assessments (and can be used before a unit starts, as a prelude)
• Give n statements, and then leave 3 blank statements. If a group finishes early, they can write their own talking point statements!
• Afterwards, you should have a “shout out” round. Kids should shout out something interesting/great they learned, and/or the teacher should shout out something good they heard/witnessed!

To debrief:

• Don’t go over all of the questions. That debrief will feel boring and repetative. Go over some key things you want to talk about immediately, and then revisit the others during the unit. (You want to make sure that kids don’t leave the unit with misconceptions.)
• Use the tally of A/D/U or A/S/N to see where the controversy lies! (You can collect their slips and talk about them later after seeing their responses…)

CLAIM AND WARRANT DEBATE: In a math class, you want students to justify themselves. To build that justification as central to the class, you can introduce the notions of an argument which is essentially a statement (a claim) made with sound reasoning (a warrant). (This language comes out of the speech and debate world.)

When responding to a question, a student must stand up (even the teacher should sit down) and say “My claim is _______, and my warrant is ________.” If the student messes up, that’s okay, just have them do it again. You have to build this structure as essential to answering questions. (To reduce the fear, you can give students some think time to write something down, or talk in a pair, before doing the claim/warrant step.) When doing this, I am not going to have kids volunteer… I am going to cold call using the Popsicle Sticks of Destiny (names of kids on popsicle sticks… I draw one randomly…).

When introducing claim/warrant, make sure you not only teach the structure, but also have kids who aren’t speaking face the speaker and put their eyes on them. Be explicit about the expectation. You can also have kids summarize another student’s point to make sure they’re paying attention. (If you catch a kid not following the audience instructions, you can walk over near them… if not, you can tap them on the shoulder… or kindly talk with them after class about how “it’s really polite to…”)

To build this up and create this as a routine and class structure, you should do claim and warrant debates every day or every other day at the start of the school year. Use the language “claim” and “warrant” on assessments too!

Types of questions you can ask to get kids started with this:

The best movie is ______.
The most important math topic is ______.
________ is the best method for solving the system y=2x and y=x+1.
[show a Which One Does Belong and say] ______ doesn’t belong.

Notice that each of these don’t have a “right” answer. It lowers the barrier of entry for kids.

One powerful type of question one can create are “mistake” questions. For example:

To extend claim/warrant, you can also create “circle debates” which truly forces listening. One person states a claim/warrant, and then another person summarizes that claim/warrant and then makes their own claim/warrant. This continues. It will sound like: “What I heard is that this statement is sometimes true because …. My claim is ____ and my warrant is ____.”  I think only very open ended questions would be good for this structure.

Another powerful way to extend claim/warrant is to engage is “point-counterpoint.” Let’s say the statement is: “Would you rather have crayons for teeth or spaghetti for hair?” The first person makes a claim/warrant, and the second person (no matter their true feelings) must disagree and make the opposing claim and give a warrant. Then the third person opposes the second person. Etc. It forces students to think of other points of view. In a question like “_____ is the best way to solve this system of equations” it forces students who might only approach a system in one way to consider other methods and justifications for those other methods.

CREATING DEBATE-Y QUESTIONS/STATEMENTS: Use the following words:

In the session, we took all types of questions (e.g. Graph $y=8\sin(2x-4)+1$) and came up with debate-y questions based on it (in this example, we said “what number would you change to change the graph the most?” or “what’s the best way to graph a sine function?”). I’m not yet good at this, but I found that even with a little practice and people to bounce ideas around, I’m getting better. We had fun in my group trying to come up with debate-y questions based on this random “do now” that Chris and Mattie found online:

I thought it would be impossible, but the group came up with tons of different ways to convert this to a debate-y statement: (a) without solving, which is easiest to solve? (b) which would you give to your worst enemy? (c) which are similar? (d) rank from easiest to hardest? (e) a 5th problem that would fit this set of equations would be ____ (f) a 5th problem that would not fit this set of equations would be ______ (g) which one doesn’t belong? (h) give -4(x+3)=-6 and ask what the most efficient way tot solve it? and then follow up with “how could you change the problem so that method is not the most efficient?”

After a month or two, the use of claim/warrant may die down. If kids get the idea and are justifying their statements, that’s okay! It’s not about the structure as much as the idea behind the structure!

QUICKWRITE: I love this idea because I make writing integral to my classroom. You give kids a prompt and you tell kids to write nonstop for 2 minutes without editing. They have to continually write. Examples:

It can help with vocabulary, but most importantly, I see this as a way to get kids to stop overthinking and looking for “the right” answer, and just write down anything and everything without self-editing of their thinking. It’s like a condensed noticing/wondering done individually. I can be used before a debate — to give kids time to think. Or perhaps depending on the question, kids can “shout out” one part of their quickwrite? But doing it at the start of the year — to help kids get comfortable writing in math class in an non-threatening, non-evaluative manner — is such a great idea!

RUMORS:  This idea was stolen from Rona Bondi at all-ed.org. On a notecard/paper, everyone write a response to a question or a couple questions (the one we used is “what is our idea setup of our classroom?” but I think it could be used at the end of class with questions like: “One thing I find easy to understand in this unit is… One question I still have about this stuff we’ve been working on…?” or “The most important mathematical idea from today is …?” or “The best way to approach graphing trig functions is…”).

After everyone is done writing, everyone finds a parter and reads their card, the other person reads their card, and then they discuss. There is a time limit (maybe 60 seconds). Then they swap papers. Everyone finds a second partner, and they read the card in their hand to the other person, and they discuss what is written on those cards (not their own cards) and then swap. This goes on three or four times. This forces listening, it allows ideas to slowly spread, and the papers can be kept anonymous.

ONE INTENTIONAL MISTAKE: [update: a la Kelly O’Shea] Each group of students gets a giant whiteboard and a problem (it could be the same problem as other groups or a different problem). They are asked to solve the problem making one “good” mistake (so nothing like spelling names wrong, transposing a number, or labeling the axes wrong). They then present their solution to another group — playing dumb about their mistake. The other group should ask good questions to help students get at the error. Questions like “don’t you need to add 3 to both sides” is too direct… You need to ask questions which lead the group to see and understand the mistake. So perhaps “what is the mathematical step you used to get from line 2 to line 3, and why is it justified?” might be better.

# Interested in Presenting at TMC16?

We are starting to gear up for TMC16, which will be at Augsburg College in Minneapolis, MN (map is here) from July 16-19, 2016. We are looking forward to a great event! Part of what makes TMC special is the wonderful presentations we have from math teachers who are facing the same challenges that we all are.

To get an idea of what the community is interested in hearing about and/or learning about we set up a Google Doc (http://bit.ly/TMC16-1). It’s a GDoc for people to list their interests and someone who might be good to present that topic. The form is still open for editing, so if you have an idea of what you’d like to see someone else present as you’re writing your own proposal, feel free to add it!

This conference is by teachers, for teachers. That means we need you to present. Yes, you! In the past everyone who submitted on time was accepted, however, this year we cannot guarantee that everyone who submits a proposal will be accepted. We do know that we need 10-12 morning sessions (these sessions are held 3 consecutive mornings for 2 hours each morning) and 12 sessions at each afternoon slot (12 half hour sessions that will be on Saturday, July 16 and 48 one hour sessions that will be either Saturday, July 16, Sunday, July 17, or Monday, July 18). That means we are looking for somewhere around 70 sessions for TMC16.

What can you share that you do in your classroom that others can learn from? Presentations can be anything from a strategy you use to how you organize your entire curriculum. Anything someone has ever asked you about is something worth sharing. And that thing that no one has asked about but you wish they would? That’s worth sharing too. Once you’ve decided on a topic, come up with a title and description and submit the form. The description you submit now is the one that will go into the program, so make sure it is clear and enticing. Please make sure that people can tell the difference between your session and one that may be similar. For example, is your session an Intro to Desmos session or one for power users? This helps us build a better schedule and helps you pick the sessions that will be most helpful to you!

If you have an idea for something short (between 5 and 15 minutes) to share, plan on doing a My Favorite. Those will be submitted at a later date.

The deadline for submitting your TMC Speaker Proposal is January 18, 2016 at 11:59 pm Eastern time. This is a firm deadline since we will reserve spots for all presenters before we begin to open registration on February 1st.

Thank you for your interest!

Team TMC – Lisa Henry, Lead Organizer, Mary Bourassa, Tina Cardone, James Cleveland, Cortni Muir, Jami Packer, Megan Schmidt, Sam Shah, Christopher Smith, and Glenn Waddell

# Jump in the online math teaching community!

A number of years ago, I had the idea of starting a little program to help those interested in starting a blog do so. And we’ve had some fun variations on a theme in the past few years.

Right now, we’re launching it again … but with an awesome twist!

There are going to be two things going on simultaneously.

Those who are comfortable blogging and tweeting, we’d love for you to sign up to be a mentor for someone just dipping their feet into the online math teacher world! You will be a person that newbies can ask questions to, connect ’em with people and blogs they might find interesting, and be a cheerleader as they get involved.

Those who are new are going to have someone help you out. You will be able to have a trusted person to ask questions to, help you find things that will be interesting to you, and encourage you. And through this, you’ll get to see if the online math teacher community has anything to offer that you want. You’ll get to dip your feet in, with no pressure, and a lot of support!

In December, we’ll pair up mentors and mentees. And during that time, we’ll all work on introducing those new to the online math teacher world to what we have to offer.

In January, we’ll have a 4 week “blogging challenge,” with prompts for both new and experienced bloggers.

If you’re interested in finding out more, or you’re ready to sign up to be a mentor or to get your feet wet checking out the online math teacher world (known as #MTBoS which is the unwieldy acronym for mathtwitterblogosphere), check out the exploremtbos website.

Huzzah!

PS. Please spread the word, if you can!

# The betterQs blog: A new #MTBoS adventure

For the past few years, I’ve been (sometimes daily, sometimes sporadically) posting on the one good thing blog. Last year I did it every single day. Often times it was a short post, especially in tough days where it was hard to find some little nugget. But what I loved was that it made me reflect consciously on joy and goodness, and pay attention to it. [1]

This year I want to spend some time thinking about how to question well. More specifically, thinking intentionally about what questioning looks like (and how it can be improved) in my classroom — both on my end and on my students’ end. I thought I would blog about it throughout the year, and figured it would be fun to blog with others. @rdkpickle had the same idea! So we figured it was a good idea, and set up a collaborative blog. All this is to say:

Check out the blog! Add it to your feedly or googlereaderreplacement. You’ll get posts by many people delivered right to your door.

But more importantly…You are warmly and heartily welcome to join us, and become an author. The blog just started and we’d love to get as many voices and experiences going on the ground floor.

Read a few posts. Browse a bit. It’s only a few days old, so there isn’t too much to gander at! And consider joining us. (If you want, there’s a tab at the top of the blog that tells you how to join, or just click here. We’ll add you as an official author!)

“But Sam,” you say, “I don’t have time to write every day…”

Silly goose, I respond! You can write however frequently works for you. Once a week? Once a month? Three times a year? The point is to take some time — however much of it — to think about questioning in your classroom.

“But Sam,” you say, “I don’t have a lot to write about…”

Silly turkey, I shoot back! I think it would be cool if you even wrote down a single question that you really loved asking because it provoked discussion. No need to deeply analyze it if you don’t want! Maybe a teacher reading the blog will read that question and think: “YAS! THIS IS EXACTLY THE QUESTION I NEEDED!” And if there were a lot of people just throwing down their good thought-provoking questions, we would soon have an amazing repository.

“But Sam,” you say, “I have a blog of my own! Why don’t I just post it there?”

Silly quail, I reply! You can post anything to do with questioning both on your own blog, and on this blog. No rule against that! In fact, I did that for my first post on the betterQs blog. And that way, someone reading the betterQs blog might get to know you and your own blog!

“But Sam,” you say, “I’m still scared… I don’t want to sign up and then not do it.”

Silly emu, I say. Why not take a baby step and just commit yourself to writing one or two things? Just keep a lookout in your school about how you question, or try to script a good question and see how it goes in your classroom, or rewrite a test question and explain how you rewrote it and why… Baby emu steps. And just see how it goes! You just might think: hey, questioning is something I want to pay just a bit more attention to!

Or, silly emu, don’t worry about signing up! As I wrote a couple years ago: “You should never feel guilty engaging with the community in ways that make sense to you. We’re all coming at teaching from such different places in our careers, such different backgrounds, and such different environments. We all need and want different things.” In other words, you do you.

[1] I also love the fact that because I’ve been using the blog semi-regularly, I can see an archive of so many good things of my own (in addition to seeing everyone else’s good things). On down days, it really helps me remember I’m not as bad as my brain tries to convince me I am.

# My Thoughts about the Evolution of the #MTBoS: 2015 edition

Twitter Math Camp just ended, and I’m feeling a sense of sadness because I miss my friends already, but that is counterbalanced by renewed invigoration. Although I’m not ready to return to the classroom yet, the reason is because now I have so many things I want to think about and implement, and I need time to sort all of that out.

## A Change Was A Brewin’

But while we were all together, something started occurring to me. I do a lot of thinking about this online community, the #MTBoS… who we are, why we came together, why we continue to come together, how are we inviting those who want to join in the fun, what we can do as a collective whole, and what we are doing as a collective whole. For me, this community started 8 years ago, and I’ve seen it grow from a nascent group of bloggers who shared their classroom activities and musings on education and their kids to a much more complex *thingie.* (Yup, I’m awesome at wording, right?!) Two years ago, after TMC13, I wrote:

the main takeaway of the conference was new. It was that we are a powerful force. We are not a loosely connected network of professionals, but we are a growing, tightly-connected network of professionals engaged in something unbelievably awesome. Through this community, we are all – in our own ways – becoming teacher leaders.

Around that time, I saw a lot of cool collaborative *thingies* just starting to bloom and blogged about how frakking awesome that was:

One thing that is now crystal clear to me is that we’re shifting into a new phase. (“We’re” meaning our little math teacher online community.)[…] Now in the past year or year and a half, there has been an explosion of activity. and this explosion seems to center around (a) collaboration and generating things which are (b) not really centered about us and our individual classrooms. We’re thinking bigger than ourselves.

I’m talking the letters to the first year teachers, I’m talking the Global Math Department, I’m talking thevisualpatterns website, I’m talking the month long new blogger initiation, I’m talking the freaking inspirational One Good Thing group blog, I’m talking Math Munch, I’m talking the collaborative blog Math Mistakes, I’m talking MathRecap to share good math PD/talks with each other. And of course, now we have the Productive Struggle blog, Daily Desmos, and the Infinite Tangents podcast. [1]

We’re still keeping our blogs, and archiving our teaching and sharing ideas, and talking on twitter. But now we’re also moving into creating these other things which are crowdsourced and for people other than just those in our little community…

It’s been a freakin’ pleasure to see all this stuff emerge out of the fertile soil that we already had. We’re starting to create something new and different… and… and… I can’t wait to see what happens.

At that time, it was just the beginning… So much has happened since.

## We’re at Someplace New

There are many more people who are jumping in. More initiatives and collaborative projects are happening. People are meeting up more and more in real life tweetups. There has been an NPR story on one of us. Multiple grad students are doing their dissertation and research about our community. The MTBoS has no official organization or centralized structure and doesn’t speak with a single voice (something I value greatly), but it has gotten the attention of the National Council for Teachers of Mathematics (NCTM). The president elect and the executive director of NCTM came to TMC15. They have given us booth space at their last national conference. There are a series of sessions at MTBoS (strands) that have happened (one, two).  It’s worth thinking about what this means.

When I was at TMC15, I noticed that there wasn’t as many conversations or mentions of “celebrities” or “rockstars” as in previous years. I think I heard those words at most twice. It’s not like people weren’t excited to meet their math teacher crushes, but something felt different. I think we’re shifting away from “celebrities” and “rockstars” and are moving towards brands. Okay, that’s not the perfect term, because there is something pejorative about that, and I mean anything but that, but people have their *thingies.*

Some quick examples:

@cheesemonkeysf is known for talking points and how the social-emotional life of a student has everything to do with their ability to learn

@PiSpeak is known for math debate in the classroom

@sophgermain is known for diversity and inclusion issues

@fawnpnguyen is known for visual patterns and her Sage Experienced Teacher Wisdom (aka her funny and emotionally charged stories from her classroom)

@mathequalslove is known for her work on interactive notebooks and her craftiness

@AlexOverwijk is known for activity based teaching

@mpershan is known for exploiting math mistakes and encouraging critical discourse

and the list can go on and on and on…

I think the idea of “celebrity” is being replaced with “brand” (or niche, or whatever). As the community grows, there are more and more voices. But there are certain ones that get a lot of traction. Of course the more involved they are (via blogging or tweeting), the more noticed they are. But that’s not enough. It’s their messages.

One came from Christopher Danielson’s amazing keynote at the conference. His message: “Find what you love. Do more of that.” Of course, that’s a little pat, and you need to see the whole presentation to truly understand. It isn’t “I love mathematics” or “I love kids.” He asked us to dig deeper, go a bit farther. What about mathematics speaks to us? What about working with kids makes us tick? His example: he loves ambiguity. The space between the certainties. And so a lot of his work as a teacher is exploiting those ambiguities with his students to get them to learn mathematics — but also hopefully appreciate (and dare I say, love) ambiguity too?

The other is from a reddit AMA conversation with Kenji Lopez-Alt. He writes the best food blog posts evar! And in this Ask Me Anything, he was asked for advice on starting a food blog:

I’m not posting this because I want to share his advice on starting and maintaining a blog. But I realized why I love his posts is because he does have a specific point of view, and that point of view speaks to me in spades. His passion about the science of foods and sharing his discoveries with others is so apparent. But I suppose what I mean is: he has found something he loves, and is doing more of that. He has a brand.

I suppose I’m saying that what I’m seeing is that there are a lot of others out there in the math community who have found that thing they love, that specific thing that makes them the teacher they are, the thing they are passionate about, and their blog and twitter conversations tend to revolve around that. They are doing what Kenji suggested — but I’m guessing without even consciously realizing it.

I don’t know, I’m just musing here. But I think ages ago there were “rockstars” and “celebrities” who were well-known — but some of their rockstarness was from being around for a long time and thus having a large network of people they could communicate with in a tightly knit community that was growing. Now I think that may be shifting. I think as we have more people, the MTBoS has a lot of mini-communities that exist within it — it’s a patchwork quilt. And that is a natural and good thing.

And I’m seeing specific people — old and new — speaking with clear voices and messages. This is what I’m passionate about. This is how I enact that passion. This is what I stand for. This is my brand. Hear me roar. [1]

And they are going outside of their schools and our smaller community to bring the thing they love to a larger audience. Creating websites, writing books, leading professional development, etc. They are expanding their brand. (And again, I don’t mean brand in a negative way!)

These are the people that speak to me. They have a voice. And I’m interested in hearing what that voice is saying. I would venture to say that they speak to others for that same reason.

What is so awesome sauce about this is that they are becoming teacher leaders. We don’t have models for what a teacher leader is in the United States. Once you become a teacher, unless you leave the classroom, you will always be a teacher. There are no ranks (except maybe the very expensive National Board certification), and there aren’t well-defined pathways to get more involved in the profession — again, without leaving the classroom. There aren’t a lot of models of those who are effecting change outside their own classroom. Think about it: excluding the MTBoS, can you think of five teacher leaders who are still in the classroom? One? [2]

But I see right now in this community the creation of new models for what a teacher leader can look like. Whether you have five years in the classroom or twenty five, there are pathways that people in the MTBoS are carving out in order to share what they love.  Help other teachers. Impact student lives. And more than anything, this is what I predict will be happening more and more as the community continues to grow and mature. [3]

## Back To Me

On a more personal reflective note, I realized I don’t think I have that brand. I think if 10 people were asked in the MTBoS, “what is Sam Shah about?” I doubt there would be a general consensus. Why? Because I don’t think I have figured that out for myself… yet. I know many things about myself as a teacher — I can be reflective as heck at times — but I still don’t think I speak with that voice or brand that so many others I admire do. And that’s not a bad thing at all. It’s just me still figuring stuff out.

[1] Again, I don’t think many would even say they’re aware of it…

[2] This is not a knock on those who have left the classroom to help our profession. I am just saying it’s hard to be a teacher leader and stay in the classroom. And I want to stay in the classroom.

[3] A lot of this part of my thinking came from @pegcagle and @_levi_’s TMC talk.

# Add yourself to the MTBoS Directory!

Jed Butler (@mathbutler, blog), in the past week or two, has worked to create a beautiful directory for math teachers who use twitter and who blog. We have had a few spreadsheets out there trying to do the same thing, but they tend to get outdated and lost. This directory is the real deal.

The point of this post is to get you to add yourself to the directory. If you’re already convinced, do it now. If not, read on to why you ought to…

It not only is beautiful, simple, and sleek, but it has the following features which blew me away:

(1) For each person, it creates a little index-card-like profile, which not only has our twitter picture on it but also has links with our interests. I confuse people easily (and really, why are 30% of math teachers named Chris?), and having a little picture icon, and all of their information easy for me to look at is going to be so so so helpful.

(2) It has a map which each person in the directory can easily add themselves to, and this map is searchable. I can, for example, zoom into NYC to see who the NYC educators are… or type my friend’s name into the search bar to remind myself which part of the country (world!) they are in.

(3) The directory itself is crazy searchable. Say you wanted to find teachers who have been teaching since 2000 who are in the Northeast US who teach Geometry and are interested in Groupwork. Done.

(4) If you want to quickly update your information, you can… no muss no fuss it is super easy!

Which is all to say: take 5 minutes and add yourself to the directory.

# Teacher Growth, the MTBoS, and TMC14

As usual, going to Twitter Math Camp has caused me to be all reflective and stuff. Barf. About myself and about this online community. And trust me, this self-introspection will be over soon and I’ll be back on my regularly scheduled program of procrastinating doing my prep work for school. But I should probably get it all out first, in one giant word-vomit. Ready? SPEW!

## I’m a Hobbit

To begin with, an oft retweeted and favorited thing at TMC was this (and heck, I probably retweeted and favorited it):

I strongly don’t put myself in that category. That isn’t part of who I am. I don’t teach to save the world. I don’t see myself as changing students’s lives, nor is my goal to have students come back to me and say “your class changed my life.” I don’t blog to change math teaching. I don’t have grand ambitions or even care to think on such a large scale. It’s a nice sentiment, but it’s just not me. I’m like a hobbit, happy and content with my little corner. Working at things with a small scale. Getting an ah hah moment, or altering the way a student sees and understands mathematics, or helping a fellow teacher out with this or that. This is what I enjoy doing.

## Inadequacy and Change

With that said, a lot of my thoughts around the mathtwitterblogosphere (MTBoS) and TMC in particular have come out of two things:

1. A post by Mo titled “I am a fraud” and as a follow up a post by Lisa Henry titled  “Hi My Name is Lisa” which resonated with me and with many others. Some key lines:

Mo: They were so honest, so completely naked, and I, wanting to join in “fit in” offered some of my fears but then as I awoke today I feel dirty. My heart is heavy, because I lied. Well I didn’t completely lie I just shared certain fears and strengths that manipulated people to see me the way I wanted them to see me. We were all skinny dipping but I had a flesh colored bathing suit on “with painted on abs”… And as I enter my 9th year of teaching, I could be entering my last year. There is a high possibility that I could be going into sales and this conference confirms my movement into that field, because I feel so inadequate….. so beyond inadequate.

Lisa: I am not the best math teacher. I am not an amazing math teacher. I have a LOT of work to do to improve. There. I said it. I wrote it in my blog and I am not taking it back. It is there in print. Ever since I have been involved with the Math Twitterblogosphere (MTBoS for short if you are not familiar), I have felt this inadequacy. I see what other teachers are doing in their classrooms. I have tried some things. Even blogged about what I have tried. But for the most part, I haven’t changed a whole lot in my teaching since I started Twitter almost 5 years ago.

2. A flex session held by Lisa Bejarano which was about how we leave TMC and change things — both in ourselves, and in our schools. I have personal notions about barriers involved changing things in my school, nor do I have the presumptuousness to say that I am The Person To Effect Change or that I Know The Right Ways. Because I too feel very much like Mo and Lisa in that I’m not “there” yet. I’m not a master teacher. However when it came to our discussion of how we change things in ourselves, Lisa B. threw up this great chart on the projector:

At first, I was skeptical. I have this bad habit of seeing charts like this and immediately dismissing them. They take something complex and box it in to something simple. But you know, the more I thought and looked at it, the more it made sense to me.

For example, I’m teaching geometry next year, and I have tons of resources, a vision for what I want the course to look like, I think I have the skills needed, I have the motivation/incentives to do well. But I don’t have a way to go through the massive amounts of ideas and resources to actually move forward. I don’t have an action plan. So I’m in the middle of false starts. And it feels that way.

But what I want to focus on is missing skills — and the resulting anxiety. I was thinking about the times in my classroom when I didn’t just take a little step forward but dove right in to make a big change because I had a bigger vision I wanted to accomplish. I can think of two:

1. Implementing standards based grading in calculus (four years ago)
2. Running a class entirely through group-work (two years ago)

Although I advise people to take baby steps, and change slowly, those times I didn’t take that advice were the times I grew the most as a teacher. Those were also the times I felt the most anxiety. Why? Because I hadn’t yet developed the skills I needed. I didn’t know how to organize standards based grading in a way that would work. I didn’t know how to make sure I would catch the conceptual as well as the procedural in this system, nor how I would get synthesis of skills. I didn’t know how to make sure students worked well together. I didn’t know how to create actvities and lessons so that students would have to rely on each other to progress. But you know what? Without jumping in, I never would have gotten the skills needed.

Let me tell you: those were high anxiety times. They required a lot of emotional energy and a ton of time. But they were also times of immense growth for me.

## Personal Inadequacy as Part-of-the-Deal

Now to the “me” part.

I don’t feel like I’m a master teacher or close to it. And I feel confident with that assessment of myself, because who knows me better than me?

As part of that, I also often feel inadequate, and sometimes like a fraud. If I look only at the world of my school, I think I wouldn’t feel this way. I’d feel fine. I’d actually have very little incentive to change, because it’s a lot of work for no extra rewards and I am doing well by the kids (see the chart above). But because there is this much bigger world, which I am exposed to (namely the math-twitter-blogosphere), things are different.

I am constantly exposed to many things online. A lot of them are resources and lessons, but sometimes there are ideas about good teaching that I wouldn’t have access too. Like the importance of mathematical discourse (talking, writing), or to question the nature of assessments and what grades mean, or the importance of having students see each other as mathematical authorities. I am not exposed to these ideas in my school constantly, so I would not think that these are things I believe in. But being bombarded by all the stuff out there online and at TMC, and seeing what resonates with me (or what inspires me to change), is helping me (probably subconsciously) evolve my personal, theoretical framework about teaching and learning (thanks Dan Meyer).

And that is where the anxiety comes in. Because now my bar about what is good teaching has been thrust upwards. And now I have to work on reaching it. It isn’t that I feel competitive with others, but that I feel competitive with myself [1]. I have a drive to be my personal best, and to do the best by my kids.

So because of this exposure to great ideas for the classroom, and bigger ideas about what makes an effective classroom, I get caught up in feeling like I’m not doing a good job, and the anxiety hits me. And sometimes this nadir will last for months. I don’t feel like I’m doing a good enough job in the classroom. I haven’t given any formative assessments. Kids aren’t engaging in real mathematical discussion. I haven’t improved at all from the previous year. Heck, maybe I’ve even de-evolved. And I get in this cycle of anxiety. It sucks.

But it’s a double edged sword, because it is this anxiety that drives me, that pushes me. I enjoy the intellectual challenge it gives me. And at least for me, it’s this anxiety and this feeling of inadequacy, coupled with my own personal desire to better myself, that provides a productive tension. I recognize in myself that I need those lows and those feelings of anxiety in order to get better. It’s part of my own personal growth process. And as much as I wish I could be confident and grow without the feelings of inadequancy, I’ve come to realize that’s what works for me. At least for me.

I end with a tweet from Jami Danielle who pretty much summed this up for me, and makes this whole post just a bunch of verbal spewage (didn’t I say that at the beginning)?:

[1] I suspect, though I do not know, that all this talk about “inadequacy” and how it resonates with so many people in the MTBoS and at TMC is tied up in some sort of cycle like this. Because of this, I don’t think it’s something to be “fixed” (e.g. how can we make it so when people come to TMC they don’t feel like crappy teachers?). At least I wouldn’t want someone to “fix” it for me.