Category: presentation

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Dismantling the Privilege of the Mathematical 1%

[This is an elaboration on a talk I gave at #MAAthfest in Chicago.]

It’s wonderful to be here. I spend most of my days with people who don’t fully get me. Wife, friends, dog – none of them gets me like you get me.

None of them understands the feeling of mathematical epiphany that motivates my professional life, the sudden transition from not knowing to knowing.

One of my earliest mathematical epiphanies was the realization that if you let the number of sides on a regular polygon increase without bound, you get a circle.

And that all the relationships you find in a regular polygon have analogous relationships in a circle. For me, that realization was literally a religious experience. I finished that limit on the back of a church bulletin while a churchlady glared at me.

So on the one hand it’s great to be in this room – I am among my people – but on the other hand it’s really uncomfortable to be here because you all make me really aware of my privilege, and aware of how many people are not in this room.

The economic 1% gets a lot of grief lately and whether we know it or not, whether we like it or not, we are all also in the 1% – the mathematical 1%.

In 2014, 2.8 million degrees were awarded in US universities – bachelors, masters, and doctorates – and 1.1% of them were in mathematics. If you change the denominator to reflect not advanced degree holders but anyone with a high school diploma our elitism becomes even more apparent.

I was on Instagram last night checking out the #MAAthfest hashtag along with The Rich Kids of Instagram. While there are fewer yachts, bottles, and shrink wrapped stacks of bills on the left, and maybe more plaid and elbow patches, there is still the same exuberant sense of having arrived. We have made it.

And just as the economic 1% creates systems that preserve its status – policies like the mortgage interest deduction for homeowners, discriminatory lending policies, and lower taxes on capital gains than income – through our action or inaction we create systems that preserve our status as the knowers and doers of mathematics.

When someone says, “I’m not a math person,” what do you say back? Barring certain disabilities or exceptionalities, everyone starts life a math person. Infants can recognize changing quantity. Brazilian street vendors develop sophisticated arithmetic algorithms before they set foot in school.

It is our action and inaction that teach people they are not mathematical. So please consider taking two actions to extend your privilege to the other 99% of humanity.

First, change the definition of mathematics that people experience.

[Here we explored together Circle-Square, a task that involves questioning, estimation, intentionally declaring wrong answers, recalling what you know about circles and squares, computing an answer, and verifying it. You can watch it.]

Now I don’t want to suggest to you that this is the experience that will change a person’s definition of mathematics and extend our privilege to the 99%. I just want to suggest to you that you just had a very different mathematical experience than the people who encountered that problem in its original form:

Mark an arbitrary point P on a line segment AB. Let AP form the perimeter of a square and BP form the circumference of a circle. Find P such that the area of the square and circle are maximized.

That experience offers people only a certain kind of mathematical work. You recall what you know about perimeter, circumference, and area, compute it, and verify it in the back of the book.

Those verbs are our mortgage interest rate deduction, our discriminatory lending policy, and our tax advantages. Through our action and inaction, society has come to understand that math is a merry-go-round revolving endlessly through those three verbs – remember a procedure, compute it, verify it.

You might think, “Well that’s what math is,” but the definition of math isn’t a physical constant in the universe. It’s defined by people, just as people define the ways that wealth and power accrue in the world. That definition is then underlined, reflected, and enforced in public policy, curriculum, and syllabi.

So, second, let’s change the definition of mathematics in public policy, curriculum, and syllabi.

To begin with, let’s eliminate policies that require intermediate algebra for college study.

The facts as I understand them are that:

  • College completion is increasingly essential to even partial economic participation.
  • College study is generally predicated on a student’s ability to pass a mathematics entrance exam. In the California State University system, that exam is heavily weighted towards intermediate algebra, problems like these, the majority of which depend on the recollection of an obscure and abstract procedure:

  • Students fail these exams in staggering numbers (68% nationally) placing into “developmental math” courses, courses which cost time and money and don’t offer credit towards graduation.
  • Those courses are disproportionally composed of African American and Latinx students.
  • Only 32% of students in developmental math ever take a math course required for graduation.

It’s hard to imagine a machine more perfectly configured for the preservation of mathematical privilege.

Those statistics would bother me less if either a) I believed in the value of intermediate algebra, b) better alternatives weren’t available. Neither is true. That intermediate algebra has little value to the majority of college educated professionals hardly requires a defense. As Uri Treisman said, “The most common use of algebra in the adult world is helping their kids with algebra.”

I am sympathetic to the argument, however, that we shouldn’t choose college requirements solely because they’re useful professionally. College should offer students a broad survey of every discipline – a general education, as it’s called. That survey should generate intellectual interest where perhaps there was none; it should awaken students to intellectual possibilities they hadn’t considered; it should increase the likelihood they’ll speak favorably about the discipline after college.

Those goals are served poorly by intermediate algebra. And better alternatives to intermediate algebra exist to serve the CSU’s desire to “assess mathematical skills needed in CSU General Education (GE) programs in quantitative reasoning.”

Specifically, statistics.

When 907 CUNY students were assigned either to remedial algebra, remedial algebra and supplementary workshops, or college-level statistics and workshops, that latter group a) passed their course in greater numbers (earning credit!) and also b) accumulated more credits in later courses.

So we should be excited to see the California State University drop its intermediate algebra requirement for graduation. We should be excited to see a proposal from NCTM that reserves intermediate algebra concepts for elective courses in high school. But we should regard both proposals as tenuous, and understand that as people of privilege, our support should be vocal and persistent.

We can choose action or inaction here. Through your action, the definition of math may change so that it’s accessible to and enjoyed by many more people, so that many more people understand themselves to be “math people.” I want to be clear that our own privilege will diminish as a result, that we will become less special, but that humanity as a whole will flourish. Through your inaction, or through your tentative, private support for initiatives like these, the existing definition will endure, along with the existing distributions of privilege. Choose action.

2017 Nov 14. Please read a follow-up comment from Alexandra W. Logue, one of the authors of the CUNY study:

Three years after the intervention, although 17% of the traditional remedial group had graduated, 25% of the statistics group had done so (almost 50% more students). To graduate, students had to pass, not only their general education quantitative requirement (which could be satisfied by college algebra or statistics), but also their social and natural science course general education requirements. So, for many students, passing remedial algebra was not necessary in order to pass these other courses. Further, there were no differences in our results in accordance with students’ race/ethnicity. Given that Black and Hispanic students are more likely to be assessed as needing remediation, our results mean that our procedure can help close graduation rate gaps between underrepresented and other students.

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.

#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?