[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.


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

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


    • Hey Kevin, please find the Act One here. I’m afraid this isn’t a fully built out Three Act task, mainly because I suspect it’s best with actual dolls and actual rubber bands. I hope the video helps sets context though. (PS. Good running into you in DC!)

  1. Bethany Sansing-Helton

    May 3, 2018 - 7:46 pm -

    Wow! Thank you so much for sharing this talk. I’ve heard of Barbie Bungie but never done it in my classroom, exactly b/c I saw the worksheets and just could not figure out how it was going to be authentically engaging to students. Your breakdown and description of the ‘full stack’ is really excellent. I feel like creating effective cognitive, non-routine tasks is more attainable using that model. Super excited! Now, to find the time to watch all those other talks

  2. Jane Taylor

    May 4, 2018 - 4:08 pm -

    A couple of thoughts:
    1) This is why it is so difficult to write and to use curriculum that tries to teach using non-routine activities or even to share activities with others. The very act of writing down the instructions for the activity so that someone else can use it makes it routine. Each teacher has to take the instructions, internalize them, remove them from the paper, and make the activity her own.
    2) My best lessons have the least written down. After a decade of “perfecting” my notes handouts, I now find that my best lessons have very little written down for students. A few good visuals and some well chosen questions work wonders.

    • Scott Leverentz

      May 5, 2018 - 11:23 am -

      This is interesting. I think a few places, Mathalicious and Illustrative Mathematics to name a couple, have worked on providing ancillary materials that support a teacher to use a loose framework but to understand the intended outcomes and some likely student thoughts.

      I’ve at least found those ancillaries to be much more useful for me to read (at least the first time before I teach a lesson) than the ones that come with traditional textbooks.

    • It feels like there’s two kinds of “written” down in your comment, Jane: instructions for students and instructions for teachers. My experiences matches yours, that the more I pre-construct on paper for students, the more routinized the learning becomes. I have no reason to believe it’d be any different for teachers, that the more I’ve written down in my teacher materials, the more routinized the teaching becomes. But it raises the question of how best to help teachers enact non-routine teaching.

    • Bethany Sansing-Helton

      May 8, 2018 - 2:38 pm -

      Just to comment on ‘how best to enact non-routine teaching.’ I have first hand experience with getting excellent instructions for teachers for non-routine tasks. I teach the Carnegie Math Pathways (CMP) materials at a 2-year college, and the entire structure of the curriculum is contextualized lessons. The implementation of the lessons is meant to provide ‘productive struggle’ for students. I think their term ‘contextualized lessons’ and your term ‘non-routine tasks’ get at a very similar point… both are attempting to create a space where students engage fully in the learning. The folks at CMP call that full engagement ‘productive struggle.’ I have been teaching their curriculum for 4 years, and I love it.
      In the curriculum, there is very minimal instructions for students and almost every lesson starts with asking students to estimate and/or predict. A typical lesson for a student is about 4 pages. The Instructor Notes that go with it are more like 14 pages. In the instructor notes there are suggested ways to have students work on a problem (small group, class discussion), there are also suggested ways to question students to encourage them to think through the problems. There are also lots of possible solutions given that students might come up with and how to address misconceptions while still keeping the students in charge of their own learning. Another support provided to help me and other faculty teach non-routine content to students is professional development training. In the training we get to watch videos of experienced faculty engaging with students. We also get to collaborate and discuss how we would teach a lesson and support non-routine learning for our students. I have learned a lot about how to ‘be less helpful’ and support students through productive struggle from those instructor notes and the training. Finally, another support provided is a faculty mentor during the first year you teach it. I had a mentor my first year and now, full disclosure, I was so impressed and transformed by what I learned, that now, besides still teaching math, I am paid to mentor other new faculty.
      All of these supports make supporting non-routine thinking for students much more accessible and less scary for faculty that have little experience with it.
      Also, as a side note… Dan, you came to my college back in 2012 and did an absolutely amazing workshop around the 3-act tasks. I learned so so much from you in that workshop. One of the biggest things I learned was that I was delivering the first act all wrong. I was asking… “what questions come to mind” but really, what the student knew I was asking was “which student can tell me the question I am looking for.” Even with that knowledge, I still struggle with my delivery and with student engagement in the tasks. I think some of my struggle could be helped if I utilized the math community on twitter more. But, one way that I think it could also be alleviated (somewhat) is by creating instructor notes. Because it’s not just the *what* it’s the *how*

    • Thanks for the update, Bethany. Really fun to recall my time at Madison.

      I also find these terms can occasionally squish together in ways that leave teachers just leaning on their existing ideas — “contextualized,” “productive struggle,” “non-routine,” etc.

      That’s why I like Autor & Price’s description of “routine cognitive work”:

      “The core job tasks of [routine cognitive] occupations in many cases is to follow precise, well-understood procedures.”

      Precise well-understood procedures shouldn’t be avoided in math instruction, but we need to balance them in accordance with their value to a student’s math education and their preparation for future work.

  3. I’m not ashamed to say, because I know I speak for many teachers, that Dan’s comfort level with tech is way out of my reach at this time, Making videos is not gonna happen, not this year and not next. So I wanted to share a lower-tech lesson that worked wonderfully for me — it’s “How many days old are you?” by Jim McClain, http://www.solutionsquad.net/blog/2017/09/10/how-many-days-old-are-you-part-1/ — “co-construct” describes it perfectly. I brought this lesson to a class I subbed (i.e. not my regular students) and it went as well as with my own students. It’s low-entry… almost every kid gladly punched their age into the calculator and multiplied by 365… and then individual students pointed out “what about leap years?” “what if my birthday is next week?” and so on.

    • Thanks for sharing your lesson! I just want to clarify that digital technology is only one tool of many that helps me co-construct experiences with students. Simple conversation is another.

      “Let’s say you need to budget for Thanksgiving dinner. What factors will you consider?”

      Your lesson exemplifies the power of a short question (“How many days old are you?”) that is deliberately opaque, that requires conversation for clarification and solution.

  4. Thanks for your reply above. Actually, I’m not sure how much I value the data-collection process of this lab. I did it for 2 of the last 3 years (not this year). You lose a lot of excitement if they take data poorly and thus make a bad prediction. I’d rather have Desmos film the Ken-doll drops in slow-mo with a meter stick in the background, and let students work with those videos to record data and make their predictions. You’d end up with more time at the end of the lesson to debrief. I hate when I do one of these activities and the bell rings right after we do the big reveal, so there’s no chance to discuss students’ methods or the questions I heard them debating. E.g., is the y-intercept supposed to be the doll’s height? (It didn’t work for our class, but I think it’s supposed to be).

    You may think kids should conduct the lab measurements entirely on their own, but (if you do), I wonder if that disagreement maps onto your full-stack hypothesis or is basically orthogonal to it.

    It was great running into you, too!

    • You may think kids should conduct the lab measurements entirely on their own, but (if you do), I wonder if that disagreement maps onto your full-stack hypothesis or is basically orthogonal to it.

      Totally orthogonal. I’d like students to experience math as power in these situations. Like math helped them get a better answer than their intuition alone. Maybe that doesn’t happen because, as you suggest, the data is too messy and collection too error-prone.

    • If this were an intro to linear regressions, and if you let them plot points on Desmos and drag a line around to make their prediction, then students would disagree about how to drag their line to best fit the data. That disagreement would be a great way to motivate the lesson I then have to teach about using the insanely cumbersome Texas Instruments interface to enter data into STAT and then calculate LINREG.

  5. Dan, great talk. I missed it at Asilomar. I like how this presentation ties in a lot of your big ideas about estimating, 3 act, engagement, etc. and your quadrant about real work in the fake world totally reminds me of Open Middle problems, which I have only used as extension problems so far, never as the main lesson for a whole class. And the animation slide of the questions with the spaces below them really kills the back and forth that’s possibly when co-constructing a 3 act lesson. My favorites for these are Gfletchy’s Apple 3 act and Stadel’s File Cabinet.

    I’ve also noticed (pun unintended) that the Notice and wonder routine really seems to increase the cognitive work kids do. Thanks.

    • Thx for the feedback, Martin. Never a bad idea to skip one of my talks since they generally find their way online sooner or later.

  6. Kristina Linberg

    May 16, 2018 - 6:07 am -

    Wow. I’ve been following your blog for many years, and before I left the 7th grade math classroom to become a Digital Learning Specialist, your posts were a springboard for helping me re-evaluate my teaching and revise my methods. This presentation is by far the best snapshot of how we should be teaching math. Thank you for sharing this talk. “Non-routine learning” captures exactly how I felt math should be taught, which can be tough in a subject area so full of educators that prioritize “routine learning”. Thank you for nailing it!

    • Thanks for the feedback, Kristina! If you’re writing at all about your work in digital learning, please pass along a link.

  7. So much food for thought! Thank you. One thing I’m left thinking about is I wonder how I would present to my students the non-routine “fake-world” task you presented to estimate 32^35. When I first looked at it, my reaction was “I have no idea how anyone would estimate that!” and I think that my students’ reactions would be something along those lines. However, since I was watching the recording and not the live talk, I had the opportunity to stop the video and try out the math. Once I sat down and tried to do the math, not calculating, but playing tried playing around with the numbers to get a better sense of how many digits the number I was dealing with had, some really interesting math emerged, as well as an intellectual need to write out large numbers in shorthand (for which I turned to scientific notation). It’s fantastic! What age/grade level range do you think this task is appropriate for?

    • I’m the worst at thinking about alignment. My answer: “whatever age students who would find the question interesting and developmentally appropriate!”

  8. Bethany Sansing-Helton

    May 21, 2018 - 10:28 am -

    Dan – I’m so glad you recall your time in Madison fondly! Your workshop had a huge impact on me and I really appreciated being able to have you on my campus. I agree that it is important for people to be able to follow precise, well-understood procedures. I have found that precise procedures are pretty easy to create. The challenge comes in how to support students *wanting* to understand them. I think that everything I’ve been doing is around creating a need. That is where supports for teachers could really be improved. How exactly do I help my students understand the value of the order of operations? Teaching them an acronym to memorize does not help it be ‘well-understood,’ and neither does giving them tons of problems to practice. But, cognitive non-routine work can provide that ‘need’ that makes them WANT to understand it. Then, their minds are open and thoughtful when the procedure is introduced. So, I’m always looking for supports for as an instructor to skillfully engage students in non-routine cognitive work. That’s where I find the biggest challenge, and the biggest benefits for students.