Category: series

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How I Present

After last year’s NCTM annual conference, Avery Pickford suggested that someone who gives presentations should give a presentation on giving presentations.

Far too humble to nominate our own selves, Robert Kaplinsky and I nominated each other for the task and partnered up.

Robert offered advice on getting your NCTM proposal accepted by NCTM. (Proposals are due May 1!) I offered advice on how to present that session after it’s accepted.

I recommend the video of my half of our session because my presentations tend to move. However, you’re welcome to read my notes below.

In all of this, I am motivated by selfishness.

Of NCTM’s total membership, only a small fraction attend the national conference and only a small fraction of that fraction present there. The ideas that can push math education (and my own work) forward live inside the heads of people who really need to share them.

I will share some of my workflow and style choices with you but a lot of that is just how I present, not how you should present. I’ll offer only two words of advice that I think every single presenter should take seriously.

To preface that advice, I’d like you to make a list of what you like and dislike about presentations you attend. Keep that list somewhere in view.

When I asked that people on Twitter to make those same lists, I received several dozen responses, which I’ll summarize below:

(People really hate it when presenters read from slides, FWIW.)


My best advice to any new presenter is to “testify,” to prepare the kind of talk you’d want to see yourself. Your talk needs to include the features you like and it needs to not include the features you dislike. Anything less is a form of despair.

In every presentation I give, I’m trying to testify to these truths:

  • I love this work. I need you to feel that.
  • I think teaching is important work. Feel that too.
  • But not so important we can’t laugh about it.

If you don’t leave one of my sessions feeling all of that, I have failed to testify to my ideals as a presenter.

So look at your lists. Do the stuff you like. Don’t do the stuff you don’t like. Let your presentation testify to your ideals. Be the presenter you want to see in the world.


The facts of the matter are that I have been a terrified and terrible presenter. I was homeschooled for K-8 so I wasn’t accustomed to giving regular academic presentations in front of peers. The first presentation I gave in my first year of public school was so lousy that its ending crashed into a wall of what would have been total silence if not for Drew Niccoll’s sarcastic slow clap.

“Great job, buddy!” he said, a line I still hear when the sun goes down and the lights go out.

Cut to 2017 and I have presented in all fifty states and a handful of continents and provinces.

All of this is to say, presentation skills aren’t biological. They’re practiced.

Teachers know this. You know how much better your fourth period lesson is than your first period. I’m on my eleventh period of the other talk I’m giving at NCTM. It looks nothing like the first time I gave it. So practice as much as you can. Present your talk at your school or district, your local affiliate, your state affiliate, at regional conferences — the same talk — before you present at the national conference.

That’s it.

Testify and practice. I think presenters would be more effective and audiences would be more satisfied and the world would be better if everybody did just that.

But the rest of this is advice I only give to myself. It’s the method I’ve used to prepare and deliver all of my presentations from the last five years. I only offer it in case it’s helpful to you as you think about your own process.

First, I wait a very, very long time to open up slide software.

I suspect that many novice presenters begin by opening PowerPoint. Me, I didn’t open Keynote until the week before my talk, about 90% of the way into my preparation.

Why? Two reasons. One, I want slide software to serve the ideas of my talk. Starting with slide software means my ideas start to conform to the limitations of slide software. Two, a lot of slide software encourages lousy presenting. If you add an extraordinary word count to a slide in PowerPoint, for example, the slide software responds by saying, “Sure, buddy. Lemme shrink the font up for you. Keep typing.”

Instead, I start by asking myself the following questions.

  • What is your big idea?
  • If your big idea is aspirin, then what is the teacher’s headache?
  • If your big idea is the answer, then what is the question?

If you don’t have a big idea yet, ask yourself what you’re trying out in your classes that’s different and interesting to you. Zoom out a little bit and look again. Do you see trends and common features in what you’re trying? That’s where you’ll find your big idea.

The other questions try to focus you on the needs of your participants. How does your big idea respond directly to a felt question or need.

Once I can answer those questions, I set up a bucket in my head.

It’s important that I set that bucket up in my head as early as possible. The existence of the bucket tunes my eyes and mind to the world around me. I look at photos, student work, conversations, activities, handouts, YouTube videos, quotations, and academic papers differently. “Could this go in the bucket?” I ask myself.

This presentation was formed from the contents of a bucket that was a year old. I have buckets in my head that are older than that, preparation for NCTM 2019, for example.

I take the contents of the bucket and shape them into narration in Google Docs.

I don’t assume I’ll have any images. A lot of great speeches were given before the advent of slide software, right? Did “I’ve Been to the Mountaintop” need bullet points? Would PowerPoint have done anything but harm the Gettysburg Address?

The biggest mistake I see novice presenters with slide software is to assume that what they say is what audience participants should see.

My survey participants said they hate that kind of design. Cognitive scientists have found that you disadvantage your audience when you make them hear and read the same text simultaneously.

Advantage your audience, instead, by finding evocative, full screen visuals that illustrate, rather restate your narration.

Only now, with my talk almost completely developed, do I fire up Keynote.

I create loads of blank slides. In a note on each slide, I write what the image will be. In the slide description, I copy over my narration.

That was all I had three days before this talk. Loads and loads of blank slides. For people who start with slide software, that probably sounds terrifying. Me, I knew I had already finished the talk.

Creating the images for this talk took about a day and a half.

Here is that day and a half compressed down to 17 seconds.

From there I rehearse.

My goal for rehearsal is that you’ll sit in my talk and within minutes say to yourself something like, “I guess this guy isn’t going to screw up that bad.”

When your anxiety is high, your ability to learn from your experience is low. My rehearsal is an effort at settling your anxiety so you can learn.

Neutralize your fear.

You’re nervous. I get that. You work comfortably in front of 40 middle-school students but you feel paralyzed in front of a room of half that many adults. I get that too.

I only know one way to neutralize my fear, and that’s through love.

Love of myself, love of my work, love of the people I get to work with. As they write in scripture, “Perfect love casts out fear,” and “Love covers a multitude of PowerPoint sins.” (Paraphrasing there.)

In my next post, I’ll offer the presentation advice I received from 14 of my favorite math education presenters. Until then, add your own best advice in the comments.

2017 Apr 21. Updated to add the link to advice from the 14 presenters.

Partial Product

Imagine you’re at a store that lets you pull products apart and pay for as much or as little of them as you want. What will your total grocery bill be for these three items?

If a student has no idea where to start, you can prompt her to list a price that sounds fair to her for the three sodas or, failing even that, a price that seems unfair to her. (You’re basically asking her to give a wrong answer. It’s a lot easier to give wrong answers than right answers because there are a lot more of them.)

You’ll find students who divide all the way down to the unit rate (ie. each egg costs 19 cents) and then multiply back up. You may also find students who set up a proportion, which will disguise the unit rate in an interesting way.

You’ll find students who set up different but equivalent unit rates. (ie. 19 cents per egg and .05 eggs per cent.) You’ll find students who set up different but equivalent proportions.

One of your many challenges during this activity will be to select students to show work that highlights a) the different ways to find the unit rate, b) the different ways to set up the proportion, c) the equivalence within those methods, and d) the equivalence between those methods (ie. ask your students to help you find the unit rate within the proportions).

The Goods

Partial Product

Featured Comment

Larry Copes:

I’m with Christopher and, I think, Dan here: Toss it out with the understanding that students can use any method that makes sense to them. Then not only share those methods but compare them to see why they yield the same result. Love the word “catharsis” in this context.

Redesigned: John Scammell

So John Scammell uploaded this #anyqs, which captured an interesting moment. In his tweet, he wrote, “When I was a kid, I’d grind other kid’s pencils down to nothing.”

John Scammell – Original from Dan Meyer on Vimeo.

Some things I’d like to accomplish in the redesign:

  1. Get the camera lens parallel to the pencil, an angle that makes it easier to see the length changing.
  2. Convey to the student visually what John wrote in his tweet: that this pencil is about to get ground down to nothing.
  3. Postpone the pencil measurements until the second act. The moment where John measures the pencil is useful and necessary but the first act (the #anyqs) should focus exclusively on curiosity and context. The math introduces itself later in act two to help resolve that curiosity.

Act One

Pencil Sharpener – Act One from Dan Meyer on Vimeo.

Act Two

Pencil Sharpener – Act Two from Dan Meyer on Vimeo.

Act Three

Pencil Sharpener – Act Three from Dan Meyer on Vimeo.

The Goods

Download the full archive. [10.8 MB]

Dan Anderson’s Mathematical Story

Love it:

Large Candle – Stop Motion Teaser from Dan Anderson on Vimeo.

Frameworks are inherently limiting. The more guidelines you specify, the more material you exclude, some of which can be very good. Frameworks are great, though, because they make implementation easy. I know what happens in the first, second, and third acts of a mathematical story, so it’d be a simple matter to use Dan Anderson’s lesson in the classroom – no lesson plan or handout required.

[WCYDWT] Russian Stacking Dolls

2011 May 15: Major updates on account of useful critical feedback in the comments.

Let’s see how well the storytelling framework holds up.

The Goods

Download the full archive [5.5 MB].

Act One

Play the question video.

[anyqs] Stacking Dolls – Question from Dan Meyer on Vimeo.

Ask your students what question interests them about it. Take some time here. This is the moment where we develop a shared understanding of the context. If a student has some miscellaneous question to ask or information to share about the dolls, encourage it. That isn’t off-task behavior. This task requires that behavior.

Then ask them to write down a guess at how many Russian dolls they think there are. Ask them to write down a number they think is too high and too low.

Act Two

Offer your students these resources:

  1. The first two dolls side-by-side.
  2. The second two dolls side-by-side.

After you show them the first set of two dolls, ask them how big they predict the third will be. As one of the commenters mentioned, they need to discover the fact that these guys aren’t decreasing by a fixed amount every time, that a new model is necessary.

Once they have this new model in mind, they’ll keep applying it until they reach a doll height they think is impossibly small.

Act Three

That task isn’t going to win anybody a Fields medal. As students finish, ratchet up the demand of the task with this sequel. Say:

I need you to design me a doll that’s as tall as the Empire State Building and is made up of 100 dolls total. Tell me everything you know about that doll.

Ask them to generalize. Ask them to graph.

Host a summary discussion of the activity. At this point you’ve identified different solution strategies around the room. Have those students explain and justify their work to their peers. Everyone is accountable for understanding everyone else’s strategy.

Then show them the answer video:

[anyqs] Stacking Dolls – Answer from Dan Meyer on Vimeo.

Find out whose guess was closest.

[h/t @baevmilena who gave me the idea when I met her in Doha.]

Featured Email

Dawn Crane:

I recently took your nesting dolls activity and here’s what I did:

At the beginning of the unit on exponential functions, I followed your process fairly closely, except I used pictures of the dolls. I asked kids to predict the patterns, etc. Most kids went with exponential, though a few were strongly in favor of linear. At the end of the unit was where I believe the magic appeared and is what I will use in the future. By this point, kids had done work with linear and exponential functions and some kids had studied quadratics. I had 7 different sets of nesting dolls in the room. Kids were told they could pick any of the sets, but had to identify them. Their job was to determine an equation to model the growth/decay pattern of the dolls and use math “tools” to convince me that their equation did an adequate job at modeling the dolls. They had to do all of the measuring…some kids chose height, some volume, some girth.

I got a huge array of problem solving. Some kids used graphs to visually show more of a regression to see whether linear or exponential had a better fit. Some kids developed both linear and exponential equations and then used tables and graphs to see where each went off track. Some recognized a constant second difference in growth and used systems of equations to develop an amazing quadratic equation that appeared to fit their data perfectly.

This project really allowed students to take the problem as far as they wanted with an entry point for everyone. And the kids loved the nesting dolls so they were really engaged. I strongly recommend actually using the dolls rather than video-taping them as well. It adds a tactile dimension which is really valuable to many students.