Two New Interviews with Yours Truly

I have two interviews out right now that I want to bring to your attention – a PDF and a podcast, so pick your medium! Both sets of interviewers were fantastic – well-researched and probing – and I did my best to rise to the occasion.

First, Ilona Vashchyshyn interviewed me for the May / June issue of Saskatchewan Mathematics Teachers’ Society magazine [pdf]. Ilona read my dissertation and her questions drew together themes of online math edtech, mathematical modeling, and Math Teacher Twitter. Here’s me:

The consistent theme in my participation [in online math teaching communities] is the fact that my thoughts always seem perfect to me until they escape the vacuum seal of my brain. Once they’re out in the world, in a blog post or a tweet, that’s when I realize how much work they need. I can’t get that feeling any other way.

Second, I have an hour-long interview out today with Becky Peters and Ben Kalb of the Vrain Waves podcast. They dug deep into my blog’s back catalog and asked questions about decade-old posts I had forgotten about. Halfway through, they asked about the role of memorization in learning mathematics. I confessed to them that I never want to be stuck driving on the road at the same time as anybody who derides the value of memorization in learning mathematics. I know a bunch of you will disagree with me there, so listen to the piece, and then tell me what you think either here or on Twitter.

Rough-Draft Thinking & Bucky the Badger

Student work on the Bucky Badger problem.

Many thanks to Ben Spencer and his fifth-grade students at Beach Elementary for letting me learn with them on Friday.

In most of my classroom visits lately, I am trying to identify moments where the class and I are drafting our thinking, where we aren’t looking to reach an answer but to grow more sophisticated and more precise in our thinking. Your classmates are an asset rather than an impediment to you in those moments because the questions they ask you and the observations they make about your work can elevate your thinking into its next draft. (Amanda Jansen’s descriptions of Rough-Draft Thinking are extremely helpful here.)

From my limited experience, the preconditions for those moments are a) a productive set of teacher beliefs, b) a productive set of teacher moves, and c) a productive mathematical task – in that order of importance. For example, I’d rather give a dreary task to a teacher who believes one can never master mathematical understanding, only develop it, than give a richer task to a teacher who believes that a successful mathematical experience is one in which the number on the student’s paper matches the number in the answer key.

A productive task certainly helps though. So today, we worked with Bucky the Badger, a task I’d never taught with students before.

Bucky doing pushups.

We learned that Bucky the Badger has to do push-ups every time his football team scores. His push-ups are always the same as the number of points on the board after the score. That’s unfortunate because push-ups are the worst and we should hope to do fewer of them rather than more.

Maybe you have a strong understanding of the relationship between points and push-ups right now but the class and I needed to draft our own understanding of that relationship several times.

The scoreboard for the game. Wisconsin scored 83 points. Indiana scored 20 points.

I asked students to predict how many push-ups Bucky had to perform in total. Some students decided he performed 83, the total score of Bucky’s team at the end of the game. Several other students were mortified at that suggestion. It conflicted intensely with their own understanding of the situation.

I wanted to ask a question here that was interpretive rather than evaluative in order to help us draft our understanding. So I asked, “What would need to be true about Bucky’s world if he performed 83 push-ups in total?” The conversation that followed helped different students draft and redraft their understanding of the context.

They knew from the video that the final score was 83-20. I told them, “If you have everything you need to know about the situation, get to work, otherwise call me over and let me know what you need.”

Not every pair of students wondered these next two questions, but enough students wondered them that I brought them to the entire class’s attention as Very Important Thoughts We Should All Think About:

  • Does the kind of scores matter?
  • Does the order of those scores matter?

I told the students that if the answer to either question was “yes,” that I could definitely get them that information. But I am very lazy, I said, and would very much rather not. So I asked them to help me understand why they needed it.

Do not misunderstand what we’re up to here. The point of the Bucky Badger activity is not calculating the number of push-ups Bucky performed, rather it’s devising experiments to test our hypotheses for both of those two questions above, drafting and re-drafting our understanding of the relationship between points and push-ups. Those two questions both seemed to emerge by chance during the activity, but they contain the activity’s entire point and were planned for in advance.

To test whether or not the kind of scores mattered, we found the total push-ups for a score of 21 points made up of seven 3-point scores versus three 7-point scores. The push-ups were different, so the kind of scores mattered! I acted disappointed here and made a big show of rummaging through my backpack for that information. (For the sake of this lesson, I am still very lazy.) I told them Bucky’s 83 points were composed of 11 touchdowns and 2 field goals.

Again, I said, “If you have everything you need to know about the situation to figure out how many push-ups Bucky did in the game, get on it, otherwise call me over and let me know what you need.” The matter was still not settled for many students.

To test whether or not the order of the scores mattered, one student wanted to find out the number of push-ups for 2 field goals followed by 11 touchdowns and then for 11 touchdowns followed by 2 field goals. Amazing! “That will definitely help us understand if order matters,” I said. “But what is the one fact you know about me?” (Lazy.) “So is there a quicker experiment we could try?” We tried a field goal followed by a touchdown and then a touchdown followed by a field goal. The push-ups were different, so now we knew the order of the scores mattered.

I passed out the listing of the kinds of scores in order and students worked on the least interesting part of the problem: turning given numbers into another number.

I looked at the clock and realized we were quickly running out of time. We discussed final answers. I asked students what they had learned about mathematics today. That’s when a student volunteered this comment, which has etched itself permanently in my brain:

A problem can change while we’re figuring it out. Our ideas changed and they changed the question we were asking.

We had worked on the same problem for ninety minutes. Rather, we worked on three different drafts of the same problem for ninety minutes. As students’ ideas changed about the relationship between push-ups and points, the problem changed, gaining new life and becoming interesting all over again.

Many math problems don’t change while we’re figuring them out. The goal of their authors, though maybe not stated explicitly, is to prevent the problem from changing. The problem establishes all of its constraints, all of its given information, comprehensively and in advance. It tries to account for all possible interpretations, doing its best not to allow any room for any misinterpretation.

But that room for interpretation is exactly the room students need to ask each other questions, make conjectures, and generate hypotheses – actions that will help them create the next draft of their understanding about mathematics.

We need more tasks that include that room, more teacher moves that help students step into it, and more teacher beliefs that prepare us to learn from whatever students do there.

2018 May 23. Amanda Jansen contributes to the category of “productive teacher beliefs”:

Doing mathematics is more than answer-getting.

Everyone’s mathematical thinking can constantly evolve and shift. Continually. There is no end to this.

Everyone’s current mathematical thinking has value and can be built upon.

An important role of teachers is to interpret students’ thinking before evaluating it. Holding off on evaluating and instead engaging in negotiating meaning with students supports their learning. And teacher’s learning.

Everyone learns in the classroom. Teachers are learning about students’ thinking and their thinking about mathematics evolves as they make sense of kids’ thinking.

The list goes on, but I’m reflecting on some of the beliefs that are underlying the ideas in this post.

2018 May 26. Sarah Kingston is a math coach who was in the room for the lesson. She adds teacher moves as well.

[NCTM18] Why Good Activities Go Bad

My talk from the annual convention of the National Council of Teachers of Mathematics last week was called “Why Good Activities Go Bad.” I hope a) you’ll have a look, b) you’ll forgive my voice, which as it happens I left at the Desmos Happy Hour the night before.

The talk is a deep dive on a single activity: Barbie Bungee.

But the goal of the talk isn’t that participants would walk away having experienced Barbie Bungee or that they’d use Barbie Bungee in their own classes later. Phil Daro has said that the point of solving math problems isn’t to get answers but to understand math. In the same way, the point of discussing math tasks with teachers isn’t to get more tasks but to understand teaching.

So during the first few minutes, I give a summary of the task relying exclusively on your tweets for photo and video documentation. Then I interview three skilled educators on their use of the task – Julie Reulbach, Fawn Nguyen, and John Golden. Two teachers saw students engaged and productive, while the third saw students bored and learning little.

What accounts for the difference?

My talk makes some claims about why good activities go bad.

BTW:

Here are the previous five addresses I have given at the NCTM Annual Convention.

2017: Math is Power, Not Punishment
2016: Beyond Relevance & Real World: Stronger Strategies for Student Engagement
2015: Fake-World Math: When Mathematical Modeling Goes Wrong and How to Get it Right
2014: Video Games & Making Math More Like Things Students Like
2013: Why Students Hate Word Problems

Watch the Four ShadowCon Talks from #NCTMAnnual and Sign up for the Follow-Up Conversation

Image of the ShadowCon Auditorium

On Thursday at #NCTMAnnual, four speakers urged teachers to reflect on their power not just to help students encounter mathematical knowledge but to change how students define themselves in relationship to math and to each other.

Video of each of their talks is online right now and each presenter invites you to join them in a follow-up conversation about their ideas over the next month. (More below.)

  • Lauren Lamb told us about her experience learning mathematics as a young woman of color, how she often felt invisible in her classrooms and unrepresented in her textbooks. She described the ways her teachers did and didn’t involve her in her own mathematics education.
  • Javier Garcia contrasted the ways we talk about students (as though they’re incomplete, fallible) and mathematics (as though it’s complete, infallible) and made a case that teachers should reverse those two descriptions.
  • Nanette Johnson impressed upon the audience the fact that each of them will leave behind a legacy for their students, an indelible imprinting of their efforts, either positive or negative.
  • Andrew Gael revealed the potency of our presumptions about student competence, and how students often live up and down to those presumptions. What we believe about student competence affects how we work with those students, which affects their opportunities to develop competence.

Great talks each one. Each one well worth your time.

But what happens to talks like these after they’re over? The ShadowCon Hypothesis is that the ideas from even great talks rarely survive contact with the reality of classroom instruction; that absent any kind of conversation or community organized around their implementation, those ideas are too easily put in a box labeled “Nice to Think About” or “Maybe Later.”

Each of our speakers agree with that hypothesis and each one wants to participate in a conversation with you over the next month. Sign up for a course you’d like to think and talk more about. We’ll place you on an email thread with a couple of random, interesting colleagues. Then you’ll receive a new discussion prompt once per week for the next four weeks, starting May 7. On a weekly basis, the speakers will summarize the most interesting ideas and answer the most perplexing questions from across all the groups.

It’s going to be a very interesting month.

[image via Cassie Sisemore]

Where You’ll Find Me at #NCTMAnnual

The icon on my airplane’s wifi signal indicates I’m somewhere over Wyoming right now, en route to Washington, D.C., for collaboration and conviviality with thousands of math teachers from all around the United States. I’m looking forward to reconnecting with old colleagues and meeting new ones so let me tell you where we’ll find each other. If we’ve met, let’s catch up. If we’re just meeting, let me know what you’re working on or wondering about.

Wednesday

Desmos Preconference Workshop

A picture of the Desmos preconference at TMC in 2017

My team will be running a morning workshop and an afternoon workshop on our newest, hottest technology and activities.

Also: Emdin’s opening session; NCTM Game Night.

Thursday

ShadowCon

ShadowCon will be at 6PM on Thursday in Ballroom B.

Zak Champagne, Mike Flynn, and I have recruited four interesting speakers – Lauren Lamb, Javier Garcia, Nanette Johnson, Andrew Gael – each offering their own variation on a similar theme. The presenters and the organizers collaborated on these ten-minute talks for the last several months. The process was a joy and the resulting talks are really exceptional. We’ll also introduce a new way to continue the call to action of those talks long after they have ended.

Desmos Happy Hour & Trivia

The Desmos Math Trivia Happy Hour is Thursday April 26 from 6:30-9:30PM at Clyde's of Gallery Place in the Piedmont Room 707 7th St NW, Washington DC.

Beep beep! Right after ShadowCon, I’m speed-walking straight to NCTM’s Top Rated Happy Hour Event. Then we’ll commence NCTM’s Highest Grade Trivia Competition. I can’t divulge any of the categories but if you were to brush up on your naughty words that rhyme with math vocabulary, I don’t think you’ll regret the effort.

Also: Sessions with Stiff, Rosen, Briars, Usiskin, Cirillo, Pelesko, and time at the Desmos booth, trying to convince people to buy our free calculators and free activities. (Pretend you don’t see me, friend. Pretend you’re on the phone with your mother. Pretend I didn’t invent those exhibitor-dodging moves. We are having this conversation, friend.)

Friday

Full Stack Lessons

I know my talk is at 8 AM. I know that. But I’ll be bringing coffee for at least me and one other person in the room. Maybe three more people if I can find one of those coffee carrier trays.

Here’s the description:

Two teachers can take the same idea for a lesson and experience vastly different results in class. This is often because one teacher taught from the full “stack” of questions and the other taught from just part of it. We’ll look at the contents of that stack and learn how to put the full stack of questions to work in your classes.

Also: Zager, Martin, United Airlines.