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.

Math’s Storytelling Makeover

I highly recommend you read Anna Blinstein’s account of a math problem that went wrong in one class and right in another. The makeover she applied between classes is available to you no matter what classes or students you teach.


Blinstein notes that “the sheer wordiness and immediate jumping into very abstract ideas was a huge turn-off for many students.”


She describes the makeover as asking students “to try things, engage, take guesses, get a foot in the door, and progress towards increasing abstraction and formality at their own pace.”

Blinstein also notes that she “started with a story.” This is significant! Cognitive scientist Daniel Willingham describes “the privileged status of story.” Stories are often more interesting to people than expository texts and students often learn more from them.

Blinstein’s story:

It’s my birthday, but I’m really, really obsessed with all things square. My entire party has a square theme. Of course, I demand a square cake and that all pieces served to guests are perfect squares too.

Of course this isn’t real. No one, not even the spoiled princesses on My Super Sweet 16, has ever asked for such a party. But none of her students cares about that for the same reason that no one cares that the universe of Harry Potter isn’t real:

Blinstein’s students aren’t just reading a story. She’s made them a part of the story.

Crucial to Blinstein’s success here, in my view, is that she has deleted elements of the problem so that she could re-introduce them with her students’ participation. (Also that she has developed an enormous professional community online she could ask for help between classes.)

Her story deepens my conviction that the most productive and interesting problems aren’t assigned on paper, but co-developed by teachers and students in conversation with one another.

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Agreed, but it’s interesting to me how few “story problems” contain any of the elements of stories that people enjoy: heroism, conflicts, rising action, resolution, etc.

Say Hi at NCTM 2017!

I’m on a shortened schedule at NCTM this year but I’m making the most of it. Here’s where you’ll find me.


How to Present at NCTM

Robert Kaplinsky and I would like to help you propose a session and and present it at NCTM. Robert has served on the NCTM program committee and will help you understand how proposals are evaluated. I’ve presented professionally for nearly a decade and will offer my own playbook for designing and delivering presentations. Our motives are selfish. So many of you have stories to tell and insights to offer. Our profession needs them out of your head and into all of ours.

The Desmos Booth

Stop by the exhibit hall and say hi sometime between 3PM – 4PM. Tell me what you’re working on.

ShadowCon v3.0

For the last two years, ShadowCon has functioned as a sort of research and development arm of NCTM’s program committee. Zak Champagne, Mike Flynn, and I study an idea on a small scale (filming every presentation, for example, or giving every presenter a webpage for follow-up discussion) and NCTM uses our data to decide if they should expand the idea to more presenters. This year, we have four exceptional presenters – Cathy Yenca, Anurupa Ganguly, Kassia Omohundro Wedekind, Geoff Krall – offering provocative ideas and we’ll study a new template for conference follow-up.


Desmos Happy Hour

Even before I worked at Desmos, this was my favorite happy hour. Great energy. Great people from all across NCTM’s membership. Come for a free drink. Stay for the math trivia. Doors open at 7PM. Trivia starts at 8PM.


Math is Power, not Punishment

This is the last time I’ll give this talk, the accumulation of a lot of thinking and designing around Guershon Harel’s concept of “intellectual need.” I’ll start by pointing out that the software engineers at Desmos and the summer school Algebra II students I worked with in Berkeley had very different answers to the question, “What would your life be like without variables?” Then we’ll figure out how to bridge those answers.

There is a 95% chance that each of my sessions will be filmed. I mention that in case you can’t make the trip to San Antonio and also because, even if you can make the trip, there are lots of amazing sessions in each time slot.

In the comments, let us know what you’re excited to do and see at NCTM.

BTW. If you’re feeling even a little bit intimidated by the deluge of people and ideas at conferences like NCTM, I recommend you read Nic Petty’s 10 hints to make the most of teaching and academic conferences.

Bonus. In an example of the creative forces that can flow through tweeting and blogging communities of practice like this one, Meredith Thompson commented on my last post that:

… looking at climate change over a short period of time gives one picture, but enlarging the frame to geological scale shows great fluctuations in temperature. This argument becomes “fuel” for people who claim that global warming is not a problem – yet the current dramatic increase (sometimes called the hockey stick) convinces many people (myself included) that action is needed.

This seemed like a job for a Desmos activity. Here is one where students crop climate data in two different ways, using those selections to make two opposite claims about the data, experiencing firsthand how easy it is to distort data.

Teach the Controversy

Here is how your unit on linear equations might look:

  1. Writing linear equations.
  2. Solving linear equations.
  3. Applying linear equations.
  4. Graphing linear equations.
  5. Special linear equations.
  6. Systems of linear equations.
  7. Etc.

On the one hand, this looks totally normal. The study of the linear functions unit should be all about linear functions.

But a few recent posts have reminded me that the linear functions unit needs also to teach not linear functions, that good instruction in [x] means helping students differentiate [x] from not [x].

Ben Orlin offers a useful analogy here:

If I were trying to teach you about animals, I might start with cats and dogs. They’re simple, furry, familiar, and lots of people have them lying around the house. But I’d have to show you some other animals first. Otherwise, the first time you meet an alligator, you’re gonna be like, “That wet green dog is so ugly I want to hate it.”

Michael Pershan then offers some fantastic prompts for helping students disentangle rules, machines, formulas, and functions, all of which seem totally interchangeable if you blur your eyes even a little.

Not all rules that we commonly talk about are functions; not all functions are rules; not all formulas have rules; not all rules have machines. Pick two: not all of one is like the other. A major goal of my functions unit to help kids separate these ideas. So the very first thing I do is poke at it.

And then I was grateful to Suzanne von Oy for tweeting the question, “Is this a line?” a question that is both rare to see in a linear functions unit (where everything is a line!) and important. Looking at not lines helps students understand lines.

So I took von Oy’s question and made this Desmos activity where students see three graphs that look linear-ish. The point here is that not everything that glitters is gold and not everything that looks straight is linear. Students first make their predictions.

Then they see the graphs again with two points that display their coordinates. Now we have a reason to check slopes to see if they’re the same on different intervals.

Finally, we zoom out to check a larger interval on the graph.

I’m sure I will need this reminder tomorrow and the next day and the next: teach the controversy.

BTW. In addition to being good for learning, controversy is also good for curiosity.

Bonus. Last week’s conversation about calculators eventually cumulated in the question:

“Calculators can perform rote calculations therefore rote calculations have no place on tests.” Yay or nay?

I’ve summarized some of the best responses – both yay and nay – at this page. (I’m a strong “nay,” FWIW.)

1,000 Math Teachers Tell Me What They Think About Calculators in the Classroom

Yesterday, I asked teachers on Twitter about their classroom calculator policy and 978 people responded.

I wanted to know if they allow calculators a) during classwork, b) during tests, and also which kinds of calculators:

  • Hardware calculators (like those sold by Texas Instruments, Casio, HP, etc.).
  • Mobile phone calculators (like those you can download on your Android or iOS phone).

(Full disclosure: I work for a company that distributes a free four function, scientific, and graphing calculator for mobile phones and other devices.)

I asked the question because hardware calculators don’t make a lot of financial sense to me.

Here are some statistics for high-end HP and Texas Instruments graphing calculators along with a low-end Android mobile phone. (Email readers may need to click through to see the statistics.)

 cost ($)storage (MB)memory (MB)screen size
TI Nspire CX129.9910064320 x 240
HP Prime149.9925632320 x 240
Moto G Unlocked Smartphone179.993200020001920 x 1080

You pay less than 2x more for the mobile phone and you get hardware that is between 30x and 300x more powerful than the hardware calculators. And the mobile phone sends text messages, takes photos, and accesses webpages. In many cases, the student already has a mobile phone. So why spend the money on a second device that is much less powerful?

1,000 teachers gave me their answer.

The vast majority of respondents allow hardware calculator use in their classes. I suspect I’m oversampling for calculator-friendly teachers here, by virtue of drawing that sample from a digital medium like Twitter.

734 of those teachers allow a hardware graphing calculator but not a mobile phone on tests. 366 of those teachers offered reasons for that decision. They had my attention.

Here are their reasons, along with representative quotes, ranked from most common to least.

Test security. (173 votes.)

It’s too easy for students to share answers via text or picture.

Internet access capabilities and cellular capabilities that make it way too easy for the device to turn from an analysis/insight tool to the CheatEnable 3000 model.

School policy. (68 votes.)

School policy is that phones are in lockers.

It’s against school policy. They can use them at home and I don’t have a problem with it, but I’m not allowed to let them use mobile devices in class.

Distraction. (67 votes.)

Students waste time changing music while working problems, causing both mistakes due to lack of attention and inefficiency due to electronic distractions.

We believe the distraction factor is a negative impact on learning. (See Simon Sinek’s view of cell phones as an “addiction to distraction.”)

Test preparation. (54 votes.)

I am also preparing my students for an IB exam at the end of their senior year and there is a specific list of approved calculators. (Phones and computers are banned.)

Basically I am trying to get students comfortable with assessments using the hardware so they won’t freak out on our state test.

Access. (27 votes.)

Our bandwidth is sometimes not enough for my entire class (and others’ classes) to be online all at once.

I haven’t determined a good way so that all students have equal access.


These reasons all seem very rational to me. Still, it’s striking to me that “test security” dwarfs all others.

That’s where it becomes clear to me that the killer feature of hardware calculators is their lack of features. I wrote above that your mobile device “sends text messages, takes photos, and accesses webpages.” At home, those are features. At school, or at least on tests, they are liabilities. That’s a fact I need to think more about.

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Jennifer Potier:

I work in a BYOD school. What I have learned is that the best way to disengage students from electronic devices is to promote learning that involves student sharing of discussion, planning, thinking, and solving problems. When the students are put “centre stage,” the devices start becoming less interesting.

Chris Heddles:

The restriction on calculation aids and internet connections still stems from a serious cultural issue we have in mathematics teaching – the type of questions that we ask. While we continue to emphasise the importance of numerical calculations and algebraic manipulation in assessment, electronic aids to these skills will continue to be an issue.

Instead, we should shift the focus to understanding the situation presented, setting up the equations and then making sense of the calculation results. With this shift, the calculations themselves are relatively unimportant so it doesn’t really matter how the student process them. Digital aids can be freely used because they are off little use when addressing the key aspects of the assessment tasks.

In many ways our current mathematics assessment approach is equivalent to a senior secondary English essay that gave 80% of the grade for neat handwriting and correct spelling. If this were the case then they too, would have to ban all electronic aids to minimise the risk of “cheating” by typing and using spell checking software.

If we change what we value in assessment then we can open up better/cheaper electronic aids for students.

2017 Mar 24. Related to Chris’s comment above, I recently took some sample SAT math tests and was struck by how infrequently I needed a calculator. Not because I’m any kind of mental math genius. Simply because the questions largely concerned analysis and formulation over calculation and solution.

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