Category: design

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Mathematical Surprise

I gave a talk at the Wisconsin state math conference earlier this month and this woman was the best part.

I don’t know her name. I’ll call her Jan. Jan is about to testify to the power of surprise.

I asked the crowd to give me three numbers between 1 and 6, numbers you might get from a roll of the dice. They said 2, 3, and 5. Then I asked all of them to evaluate those numbers in this expression.

Most of the crowd started working on that task, but Jan didn’t. She laughed and said, “I teach second grade,” excusing herself.

I encouraged her to show off whatever she remembered from the last time she worked with expressions like this. She scribbled on the notebook in her lap and we managed to evaluate x = 2 in the time we had, but not 3 or 5.

I asked the crowd to call out the result for 2, 3, and 5. They called out 2, 6, and 20, one after the other.

Then I asked the crowd to evaluate those same three numbers in this expression.

Jan tossed her notepad on the desk, a reaction of “no way, no thank you” to the length of that expression. I decided not to press her at that exact moment, because I had a secret everyone in the crowd would come to understand at different times, Jan last of all and perhaps best of all.

I asked for their result for 2.

“0.”

“Okay, what about 3?”

“0.”

“Okay, that’s weird. What about 5?”

“0.”

I played up my surprise, acting like I didn’t know all of those terms would simplify to 0.

That’s when I noticed Jan. Out of the corner of my eye, Jan straighted up in her chair and then picked up her notebook to sort out what just happened.

I wish I had a sharper vocabulary to describe this transformation, as well as more strategies for provoking it. By showing Jan a situation where order arose from apparent disorder, she felt something in the neighborhood of … cognitive conflict? Intellectual need? “Surprise” feels closest.

I don’t know all the words and I don’t know all the strategies, but I know there are few gifts a teacher can give a student more satisfying than helping her transform from “no way, no thank you” to “okay, let’s sort this out.”

Discuss:

  • I don’t think this experience has much to do with Jan’s growth mindset about herself, or mine about her, but I’m willing to be proven wrong. How was this experience distinct (or similar) to a mindset experience?
  • Think about the design of this activity, all of its different permutations, and how each one might have affected Jan. What if, for instance, I had given given the class those three numbers instead of soliciting them from the class? What if I had only solicited one number? What if all three numbers didn’t evaluate to the same number? How would these permutations have affected Jan’s interest in picking up her notebook?

Every Handout from NCTM 2017

tl;dr –

  • There were 740 total sessions at NCTM’s 2017 annual conference. I wrote a script to find and extract the 279 sessions that included handouts, slides, or other attachments. You can also download the entire mess of attachments with a single click. (1.28 GB. Not small.)
  • The process of writing and running that script maps almost perfectly onto the process of mathematical modeling. If the same defective wiring runs through your brain as mine, you’ll understand how that was a total rush.
  • I hope NCTM will make these resources easier to find in the future, especially for non-members.

This is just like mathematical modeling!

I’d been using the same script for this task for the last two years, but NCTM switched website vendors this year and I had to create a new one. On the one hand, accessing handouts from the conference probably shouldn’t be so challenging. On the other, this process is such a fun puzzle for me, and maps almost perfectly onto the process of mathematical modeling.

Here is what I mean. The third step in the modeling cycle is to “perform operations.” I’m not here to tell you that people (old or young) should never perform operations, just that computers are generally much faster at it. When I thought about the task of poking my head into all 740 NCTM session websites and asking, “Hello. Any handouts in here?” I admitted defeat immediately to some software.

So the human’s job is the first two steps: identifying essential variables and describing the relationships between them. Computers are much, much worse at this than humans. That meant looking at cryptic computer chicken-scratch like this and asking, “What do I need to tell the computer so it knows where to look for the session handouts?

If you notice that each session has its own four-digit “id” and that each handout has been tagged with “viewDocument,” you can tell the fast machine where to look.

But the modeling cycle doesn’t end there. Just like you shouldn’t paste the results from your calculator to your answer sheet without thinking about it, you shouldn’t paste the results of the fast machine’s search to your blog without thinking about it. You have to “validate the results,” which in my case meant poking around in different sessions, making sure I hadn’t missed anything, and then revising steps one and two when I realized I had.

I hope NCTM will make these easier to find.

These handouts are basically advertisements for the conference without substituting for attendance. (No prospective attendee will say, “I was this close to attending but then I found out some of the handouts would be online.”) If they’re easier to find, not only will existing attendees be happier but non-attendees will have a nice preview of the intellectual activity they can expect at the conferences, making them more inclined to attend the next year. Nothing but upside!

Previously

Presentation Advice from 14 of My Favorite Presenters

As I prepared for a presentation on presentations, I asked fourteen of my favorite math education presenters, “What is your best advice for preparing and delivering a presentation?” Here is their advice, edited for brevity and sequenced for story.

Michael Serra, author of Discovering Geometry:

Watch others and take note of what you want to see and do not want to see in your presentation.

Matt Larson, President of NCTM:

Whose style do you like and want to emulate? You can’t be someone else but what elements from other presenters can you make your own and integrate into your own style.

Patrick Callahan, Callahan Consulting:

I prepare the talk that I would like to see. I like to be surprised and challenged. I don’t like things tied up in a neat bow. I like talks that I have to keep thinking about.

Jo Boaler, author of Mathematical Mindsets:

Relax! Find some space to think. We now know that there are different modes of thinking and that speed and pressure block creative and innovative thoughts. I always like to plan talks when I feel like I have some good time to think expansively and creatively. I don’t do it in in-between moments, I do it when I have a good block of time and I feel as though I can think deeply and well.

Preparing a talk is like writing a book or a paper – think through the key ideas. How do they flow to and from each other? Don’t overwhelm your audience with too many ideas. Keep them all connected.

Cathy Yenca, Apple Distinguished Educator and awesome edtech blogger:

Ideas come at weird times – intentionally jot down every idea as it comes to you. I tend to have Post-its on my nightstand, in my kitchen, on my teacher desk, on my laptop (yes, on the flat spots to the left and right of my trackpad). I transfer these to a Google Doc, giving myself permission to brainstorm freely. Not every Post-it will make it to the final talk. That’s okay.

Matt Larson:

A good presentation is like a good classroom lesson – it is based on extensive planning and preparation. I have been working on the “versions” of my annual talk since last August. I have literally spent hundreds of hours doing research, putting together hundreds of “potential” slides, double checking citations, messing with the order, eliminating slides, etc.

Tracy Zager, author of Becoming the Math Teacher You Wish You’d Had:

Story first, slides later. The most important thing is to plan the storyline of the talk first. Weekend Language is great on this, as is the one-minute video you made a few years ago. Both helped me break the habit of how we were all taught to start preparing your presentation by picking a theme for slide one in PowerPoint. Instead, I start with my big idea. Every talk needs to have a central big idea, and I spend a lot of time clarifying that idea before I get anywhere close to Keynote.

Elham Kazemi, author of Intentional Talk:

Don’t just build a talk by cutting and pasting slides together. Build the experience and then the slides.

Fawn Nguyen, middle school math teacher and awesome blogger:

A good image is better than text. For example, I have a picture of Robert Kaplinsky hiding his face under his [shameful] UCLA sweatshirt. That picture is more powerful than a slide that reads “The Bruins are getting pummeled on their own turf by the Oregon Ducks.”

Matt Larson:

I try to find a place to “test drive” the presentation, perhaps at a smaller conference. In some cases, I’ve simply given the presentation to 3-5 people in a small room.

Jose Vilson, author of This Is Not A Test: A New Narrative on Race, Class, and Education:

Preparation is really similar to the classroom. Eat breakfast. Go through normal routines. Do a few vocal exercises to get your vocals right. Make sure you’re just full enough and that you haven’t had too much to drink.

Tracy Zager:

Create contingency plans. What if the wifi doesn’t work? Be prepared for that. It’s frustratingly common. If you’re playing videos and they’re embedded in your slides, also open the files themselves and minimize them. Sometimes they don’t play nicely and you need to find the originals quickly. (I learned that one the hard way.) What if you’re running long? What will you cut? What if you’re running short? Where can you go deeper? What if the mic sucks and you’re tethered to the lectern area by a wire? That’s my least favorite scenario. If the room is small enough in that situation, I toss the mic in a heartbeat, use my teacher voice, and get out in the crowd.

Elham Kazemi:

Arrive early and greet people that took the time to come to your talk. learn as much as you can about whose in the room in the 10-15 minutes before the talk begins. Use that knowledge during the talk.

Barb Dougherty & Karen Karp, authors, editors, and co-presenters:

We attempt to make a personal connection with participants by going through the room and meeting people prior to the presentation.

Cathy Humphreys, author of Making Number Talks Matter:

Most of us get nervous before a large talk, and once early on when I was in that state a mentor said to me something like, “This talk is not about you. You aren’t the point. It’s the ideas you are sharing that matter.”

Patrick Callahan:

Delivery is about reading the audience and being flexible. You can tell when the room is with you and when it isn’t. Based on that, it’s important to be flexible: skip slides, slow down, speed up, give time for folks to turn and talk, ask questions.

Michael Serra:

Be enthusiastic. Your audience needs to feel that love you have for what you are presenting. Know your stuff but don’t be a know it all.

Jo Boaler:

I never like to talk for more than 15 minutes without asking people to watch a video, do a maths task, or discuss with each other.

Michael Serra:

Your first presentation will probably not be to hundreds of listeners but to a small group of participants. So make sure they are participating and not just listening.

Jose Vilson:

If you’re doing PowerPoint, you’re doing something more image-based, but the images should remind you of what you’re saying to your audience.

Marilyn Burns, founder Math Solutions:

I use PowerPoint slides as guides for my session, to trigger my thoughts and keep me on course. I use the notes section to remind myself about what I was planning to say. I try to avoid presenting lots of information to be read, and I work hard to avoid ever reading what’s on a slide. If there’s something for people to read, I stop talking and give them time.

Barb Dougherty & Karen Karp:

Tell stories, including those that show your own foibles along the way. For example, with our 13 Rules That Expire, we share that we know these rules because at one time we taught them!

Jo Boaler:

Try and tell a connected story, talk about the personal connections to you.

Steve Leinwand, author of Accessible Mathematics:

A good talk or presentation is like a good lesson. You start with classroom action and later summarize the purpose of those tasks or activities. In other words, I think that a good presentation models good instruction

Tracy Zager:

If possible, do just what you do in a classroom, where you listen in on conversations and then ask those people to share out in the larger crowd when you come back together. Those organic moments are to be treasured.

Fawn Nguyen:

Go along with an unintended diversion.

Matt Larson:

Think about how you can be “inspiring” or have a “call to action” at the end. I’ve attended this presentation, now what?

Fawn Nguyen:

Is there a take-away message or a call-to-action from your talk?

Great, right? Test all of this and keep what’s good for you. It’s time to propose your session. Everyone: your NCTM proposals are due May 1. Californians: your proposals (North, South) are due the same date. Share what your ideas and questions.

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.)

Testify

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.

Practice

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.

#CMCMath Opening Keynote Address – Practice Problems

This is the keynote address I gave at CMC North this weekend with my co-presenters Shira Helft, Juana de Anda, and Fawn Nguyen.

The premise:

For a long time I worried I had chosen the wrong career. Other careers seemed like they had so much in their favor – better pay, less homework, more flexibility on the timing of bathroom breaks, etc. If you followed this blog ten years ago, you witnessed that worry.

Then a conversation with some of my close friends convinced me why I – and we – never have to envy any other career:

We have the best questions.

At least for me, no other job has more interesting questions than the job of helping students learn and love to learn mathematics.

A career in teaching means freedom from boredom.

To illustrate that, I interviewed three teachers at different stages in their careers – a teacher in her first decade, her second decade, and her third decade of teaching. I asked them, “What questions are you wondering right now?” Then we each took ten minutes to share our four questions.

But our talks weren’t disconnected. An important thread connected each of them, and I elaborated on that connection at the end of the talk.

Chapters

Please pitch in. Tell us all in the comments:

What question motivates you this year? What question wakes you up in the morning and energizes you throughout your day?

Featured Comments

Kathy:

The question that drives me is “How can I present this in a fashion that will be so interesting that they will not only want to learn it, but they will remember it next week, next month, and next year?”

Andrew Stadel:

Whether with my family (most important), the teachers I support, or students I work with:
How am I being present?