Twitter Math Camp 2016: Get Uncomfortable

Debate – Chris Luzniak & Mattie Baker

“My claim is _____, my warrant is _____ .”


  1. Chalk Talk: Posters with questions on them, students respond by writing, no talking allowed.
  2. Talking points: read more here
  3. Debate! Argument = claim + warrant
    1. Soapbox debate: provide class with a debatable prompt, and a minute to think. Then student must stand and state their claim and warrant to the prompt. It’s more fun if you randomly call on students.
    2. Always, Sometimes, Never statements: students summarize previous idea, then state their argument.
  4. Point-Counterpoint: use would you rather questions. Students must alternate arguments, so they have to disagree with previous person.
  5. Table debate: assign student to teams to develop arguments, and then have the teams debate.

How to encourage debate:

  • add debatable terms to questions – best, worst, most efficient, should, biggest, smallest, most, weirdest, coolest, always, sometimes, never
  • Change boring math into a debate – Given an equation, ask,
    • What is the best way to graph this?
    • Which number would you change to change the graph the most?
    • This graph will never go below the x axis

Full Scale Debate:

Divide the class into 4 teams. Provide students with a carefully constructed scenario and 4 different stance’s to argue (example provided with musician recording contract).

  • have a rubric.
  • assign students roles (opening argument, , questioner, attacker, defender, closing argument)
  • takes about 3 class periods:
  1. understand the problem and develop a plan
  2. day research & begin calculations
  3. finalize arguments

Socratic Seminars:

Students read a variety of texts or resources on a topic, then consider questions in a large group discussion.

examples of questions to consider:

  1. What are some strengths and weaknesses of each presentation?
  2. When would each text be appropriate to use?
  3. What difficulties may students have?

This sounds like a really interesting thing to do in math class. I need to learn more and see it in action so that I can implement this effectively.

Critical thoughts to creating a successful debate culture:

  • the accumulation of many intentional, small teacher moves over time sets the culture of student talk
  • When you want students to talk to each other, the teacher must SIT DOWN. make yourself small, and not the center of attention. Encourage students to talk to each other. If it is a whole class debate, have the student talking STAND UP. Slowly back out of the center, have students call on their peers.
  • Start early
  • Keep it simple. Use basic soapbox debate for the first month or two.
  • explicitly talk about what active listening looks like – be very specific (not writing, looking at the speaker, knees pointing toward the person speaking…)
  • ideally, dedicate about 5 minutes per class 1-2 times per week
  • provide structure (argument = claim + warrant ) and verbal cues
  • Occasionally, have students do a quick write providing an image and a word bank. This will help students to practice communicating mathematically.

Keynote: Jose Luis Vilson

We need to talk about race with our students and give them a safe space to grapple with their thoughts. In math instruction, the goal is to teach students to grapple with tough problems for which the solution is not already know and work towards a logical and reasonable resolution. This same principal can be applied to social justice issues.

Some questions/statements for students:

  • I just want to hear what you have to say
  • Why do you feel this way?
  • Where is your compassion/empathy?

We need to become comfortable getting uncomfortable and evangelizing for our truths. Avoiding confrontation and being polite can be destructive in the end.

Getting Triggy With It – Kristin Fouss

This session made me think of this Kate Nowak blog post.

She shared a very complete and organized collection of quality, basic stuff. Progressions, lessons, strategies. I can’t wait to use and adapt it for my first year of teaching pre-calc in a while.

Experience Connecting Representations – David Weiss

This structure connects a visual model to more abstract expressions. This could be graphs & equations, trinomials and algebra tiles, quadratic expressions and their factored forms…


  1. post more equations than corresponding visuals (task is to match the visual to the equation/expression)
  2. provide individual think time – What do you notice?
  3. Time to discuss with a partner (teacher circulates, listens & asks a pair if they would be willing to present their thoughts to the class)
  4. display verbal cues:


We saw ___ so we connected ____.

_____ matches ______ because ______.


They noticed ____ so they _____.

Their connection works because ______.

5. Get presenter’s to the front. One can only speak and the other can only point. They explain their thinking for one pair. Keep this light, safe & fun. If a student does not explain clearly enough or missing key elements, just let it go, they will most likely come out in later explanations.

6. Ask a student in the class to re-explain the presenter’s thinking

7. Teacher record thinking while a new students explains.

Repeat from step 5 with a new pair of students.

Once all problems have been paired and described by the class, have the pairs try to create a visual mode for the remaining equation that was not paired to a model

Close by having students complete a written reflection.

Explore Math – Sam Shah

Sam talked about a low stakes high reward assignment that he gives his students. They have to complete 4 or 5 mini explorations on any math topics of interest to them (with incremental due dates) and complete a brief written description or some evidence of what they did.

A blog post about it

Site of suggestions

Johnathan Claydon – Varsity Math

He turned the advanced math classes into a ‘club’ called varsity math and created t-shirts, stickers, party’s and a summer camp to go with it. He also made recruiting posters and placed them at the middle schools in order to motivate students and create a buzz around taking more advanced math classes.

This is a great idea! I recently convinced 10 students at my school to take a more advanced math class and I think I will have to figure out how to adapt this concept to fit my tiny group in an effort to get this group to grow in future years.

Tracy Johnston Zagar’s Keynote – Link to slides

She opened my eyes to recognizing the different skill sets that elementary and secondary teachers have and the importance of valuing these skill sets and why we should try to break down our comfort barriers to get over ourselves and learn from each other.

I think I need to write a whole additional blog post on how individuals’ comfort seeking needs really limit our happiness, growth, empathy and success. (an ongoing theme this conference)

Variable analysis game – Joe Bezaire

The math game with the lame name

The basics of how it works:

  1. Students guess the rule then they add a line of values that matches the rule.
  2. Then these students become judges and let their peer know if they got it too.
  3. Write it as an expression. Make connections between the various student expressions.

This may be a good warm up activity, so I want to be sure to link to it here so that I can find it in the future.

Six Steps to Modeling – Brian Miller & Alex Wilson


Image from this Dan Meyer blog post


  1. Define the question
  2. Identify Variables & assumptions
  3. Develop Model
  4. Test Model
  5. Adjust / Improve Model
  6. Report out

Moody’s Math Modeling Guide – Free Download

In this session we progressed through these steps to develop a model for ranking roller coasters, but the big idea here is more about how to facilitate this process. It would apply well to geometry tasks including 3 act’s such as best square or Mathalicious’ Face Value (my post on this task).

More than Resources – Dylan Kane’s Keynote

Clever Ideas ≠ Coherent Curriculum

We need to be thoughtful and intentional, not just resource collectors.

This resonated with me as I am an avid idea collector, but I struggle with how to make a curriculum coherent. I want to work on criteria for coherence and re-evaluate the content of my current classes.


My (late) TMC13 post

Disclaimer: I am a very fact / list person, and I am not very organized, but I try to copy ideas from those who are and maybe trick folks into thinking I have my stuff together. This is the mess that is in my head after TMC13:

Websites to include in my life

    • remind101 – This is so cool, I don’t know why I did not know about this sooner. I’m all over this! Thanks @aanthonya
    • Use google voice so that you have a separate phone number to give to students & parents. Use message to text as an easy way to track parent correspondence.
    • 13 unsolved problems in mathematics w/ million $ prizes
    • Desmos – Its the best. Nerdgasms galore.
    • Bowman Dickson made a great Prezi describing SBG
    • Alabama has good lesson resources – whoulda thunk?
    • Insight has a nifty thing where it grades multiple choice test by holding the answer sheet up to the camera built into your laptop. Is free for 10 question tests, pay for more options. There is also an ipad app.
    • My students will benefit from my membership with Mathalicious.

Try in my classroom

    • Post or have available in a folder – a collection of constructable drawings for students to choose & attempt if there is down time.
    • Surface area “Tin Man Project
    • At the end of class divide a board or wall space into 4 quadrants, label them:

1) Work on         2) Don’t Forget     3) Question I still have     4) Aha! moment

Give students 4 post its and have them post 1 for each quadrant at the end of class.

    • Noticing & wondering – provides rich data about what students are ready to learn useful for instruction & providing feedback.
    • 4 to 1 – give each student in a group a different question, have them sum their solutions, then they can check their sum to verify that they are correct. If they get a different sum they have to talk and justify their work to try as a team to find & correct errors. I think Kate Nowak blogged about something similar a long time ago.
    • Ask: What is a ______? Have one group define then challenge other groups to draw their definition, but it is not a ______ (a counter example).
    • Use Oranges & marshmallows, or any 2 different objects to demonstrate combing like terms:
      • 5 marshmallows & 2 oranges = 5 marshmallows & 2 oranges cannot combine because they are not like terms.
      • 2 marshmallows & 3 marshmallows = 5 marshmallows see? they are like terms! you can add them!
    • After students finish a test, have them leave their pencil at their desk, check their work against an answer key, highlight their wrong answers, then get a “correction sheet” which they staple to the front of their test and they write problem #, why they are incorrect, and explain how to get the correct answer (or why they can’t). This really fits well with “How to Learn Math.” Mistakes are part of the process. The test becomes more formative, the teacher gets better information on where the student gets confused & bonus: less grading!
    • I’m trying Interactive Note Books with geometry.  Its going to be awesome. My dream is to bring a complete INB to TMC14 that is as useful & as pretty as the super organized and creative Sarah Rubin.
    • In Geometry, give an assignment where students have to write a program (using any platform they’d like – most would use TI-84’s) where they input 4 coordinates and it tell you the type of quadrilateral produced. Require that they include quality code notes & cite and sources.  Don’t be scared if you have no idea how to program. It will make you less helpful, which is kinda good. bonus: you’ll learn! Someone mentioned that would be good for this.

Philosophical shifts

    • In SBG, try to stick to around 5 skills / unit
    • Shut up & listen to kids
    • Notice & wonder: Max is really awesome, listen to Infinite Tangents & buy his book when it comes out
    • Be sure to ensure that students actively connect different solutions to a task (both correct & incorrect) This is step 5 of the 5 practices. Its often overlooked. I’m currently reading this and I love it!
    • If you are a teacher and you ask a question, wait for an answer! Don’t ask questions it there is no think time required!
    • Students ask 3 types of questions, only answer the questions that fall into the 3rd category:
        1. Don’t want to think anymore
        2. proximity questions – they ask because you are nearby
        3. they are genuinely curious about something

Tools / stuff I should buy & use in instruction

    • Bamboo writing pad – cheap easy tablet, but I have wireless slates in my class and I dont want to spend the money right now…
    • Circle Perfect compasses work well – I ordered these
    • Get small trash containers for each group for use with INBs from a dollar store: I think I may not do this because I have small classes and it is good for kids to get up & move during class.
    • Drill holes in my student white boards. Put those command hooks on the wall. duh. So simple. So wonderful. Kate in Conneticut knows things.