I Have Big Reservations About Chalkbeat’s Teaching Competition

At SXSW, Chalkbeat is hosting The Great American Teach Off:

Top Chef. Project Runway. The Voice. Live competition shows have introduced audiences to the worlds of cooking, fashion, and singing — and opened a window into the intricate craftsmanship that these industries demand. Now it’s time for one of America’s most under-recognized professions to get the same treatment. Hi, teachers!!

Two teams of math teachers will teach a lesson to a live audience and receive judgment from a panel of “teacher celebrities.”

I linked to that description on Twitter and people were unsparing in their criticism:

I agree with the spirit of those criticisms, and David Coffey’s in particular:

Good teaching requires complicated decision-making based on a teacher’s long-range knowledge of a student and of mathematics. We should reach for any opportunity to make those decisions transparent to the public, who will always benefit from more education about good education. But a live event with an audience you don’t know and can’t interact with individually will necessarily flatten “teaching” down to its most presentational aspects, down to teachers dressing up in costumes, down to Robin Williams standing on desks in Dead Poets Society.

Not good teaching.

I asked teachers what kind of TV show would do justice to the complexity of teaching, if The Voice and Top Chef were the wrong models. Jamie Garner and James Cleveland both suggested The Real World, which seems dead on to me.

The Real World a) isn’t a competition, b) allows for characters to develop over time, and crucially, c) isn’t a live event. It is edited. You don’t watch the cast members do anything mundane. In the case of teaching, we’d love for the public to understand that good teachers assess what students know and adjust their instruction in response. But no one wants to watch a class work quietly on a five-minute exit ticket in real time. So the show would edit quickly past students completing the assessment and straight to the teacher trying to make sense of a student’s thinking, involving the audience in that process.

The challenge I’d like to see the folks at Chalkbeat take up is how to make those invisible aspects of teaching – the work that takes place after the bell – visible to the public. The work of presenting is already teaching’s most visible aspect.

BTW. Jamie Garner expands on The Real World: Math Class.

2018 Jan 1. Chalkbeat’s Editor-in-Chief, Elizabeth Green, clarifies her rationale for launching the competition and responds to some concerns raised here and on Twitter. She describes lesson study as the touchstone for her Teach Off and how she’s had to alter that format to fit SXSW.

It’s a really interesting article, full of references to the education scholars who have inspired her work for a decade. But I still tend to think she and the members of her design team have underestimated the magnitude of those compromises and how they’ll distort the approximation of good instruction her audience will encounter.

2018 Jan 8. In a revised contest page the organizers have eliminated the competition and clarified other aspects.

Featured Comment

Organizer Elizabeth Green weighs in:

I’m weighing in late here, but in response to one of the above threads, we never intended to have the whole audience serve as the students. As we’ve clarified in our revised page, which has more specific language, we’ll have 7-10 adult audience volunteers serve as students. Imperfect as a representation, for sure, but we still think everyone will get something important out of the 20-minute instructional activity + the followup discussion — that “something important” being better understanding about the nature of teaching and math teaching in particular. And for the record, Dan, at the 1,000-person “Iron Chef”-style teach off in Japan that Akihiko described, the students were the teacher’s actual students, and they all sat onstage.

This Episode of “Arthur” Gets Basically Everything Right About Math

Depictions of mathematics in TV and film generally lack nuance. When Hollywood doesn’t hate math, it reveres it, genuflecting before the eccentric, generally white male weirdos taking up space in its highest echelon – your Will Huntings, your John Nashes, etc. – with little in between.

But Arthur nails the nuance in “Sue Ellen Adds It Up,” and reports three important truths about math in ten minutes.

We are all math people. (And art people!)

Sue Ellen says No one in my family is a math person.

Sue Ellen is convinced she isn’t a math person while her friend Prunella is convinced there’s no such thing as “math people.” You may have this poster on your wall already, but it’s nice to see it on children’s television. Meanwhile, Prunella is convinced that, while she and her friend are both “math people,” only Sue Ellen is an “art person.” Kudos to the show for challenging that idea also.

Informal mathematical skills complement and support formal mathematical skills.

Prunella says You were using math and just didn't realize it. It's called estimating!

Sue Ellen says that she and her family get along fine without math everywhere “except in math class.” They rely on estimating, eyeballing, and guessing-and-checking when they’re cooking, driving, shopping, and hanging pictures. Prunella tells Sue Ellen, accurately, that when Sue Ellen estimates, eyeballs, and guess-and-checks, she is doing math. Sue Ellen is unconvinced, possibly because the only math we see her do in math class involves formal calculation. (Math teachers: emphasize informal mathematical thinking!)

We need to create a need for formal mathematical skills.

Prunella says Now let's measure the space on the wall.

Sue Ellen resents her math class. She has to learn formal mathematics (like calculation) while she and her family get along great with informal mathematics (like estimation). Then she encounters a scenario that reveals the limits of her informal skills and creates the need for the formal ones.

She’s made a painting for one area of a wall and then she’s assigned a smaller area than she anticipated. She encounters the need for computation, measurement, and calculation, as she attempts to crop her painting for the given area while preserving its most important elements.

Nice! Our work as teachers and curriculum designers is to bottle those scenarios and offer them to students in ways that support their development of formal mathematical ideas and skills.

[h/t Jacob Mehr]

[Presentation] Math Is Power, Not Punishment

I’m happy to release video of the talk I gave throughout the 2016-2017 school year, including at the NCTM Annual Convention in San Antonio, TX.

This is my best attempt to tie together and illustrate terms like “intellectual need” and expressions like “if math is aspirin, how do we create the headache.” If you’re looking for an elaboration on those ideas, or for illustrations you haven’t seen on this blog, check out the video.

The Directory of Mathematical Headaches

This approach to instruction seriously taxes me. That’s because answering the question, “Why did mathematicians invent this skill or idea?” requires a depth of content knowledge that, on my best days, I only have in algebra and geometry. So I’ve been very grateful these last few years to work with so many groups of teachers whose content knowledge supplements and exceeds my own, particularly at primary and tertiary levels. Together we created the Directory of Mathematical Headaches, a collaborative document that adapts the ideas in this talk from primary grades up through calculus.

It isn’t close to complete, so feel free to add your own contributions in the comments here, by email, or in the contact form.

Watch an Expert Math Teacher Put Three Kinds of Knowledge to Work in the Same Class

Lisa Bejarano’s post Two Kinds of Simplicity offers a useful idea about teaching complex fractions, but much more interesting to me are the three kinds of knowledge she puts to work in her class.

Knowledge About Teaching

Lisa has read widely from sources online and offline and has a great memory. So when she asks herself, “How am I going to teach [x]?” she can quickly summon up all kinds of helpful posts, essays, books – even the mental recording of previous classes she’s taught on [x].

Knowledge About Students

I stopped to think about how this would work with my class.

Lisa has taught long enough and knows her students well enough that she can test each of those resources out in her head, all during the lunch break before class. You can see her swiping right and left on each of them – “Yeah, maybe this idea. Definitely not that one.” – as she sees her students in her imagination. I’m sure Lisa is open to the possibility that her flesh-and-blood students will differ in surprising and awesome ways from her mental model of those students. I wouldn’t bet against her intuition, though.

Knowledge About Math

She ultimates decides to start her precalculus students with the elementary school analog of their lesson, turning an abstract fraction division problem into a more concrete one.

Then, as her students acquaint themselves again (or in some cases for the first time) with helpful models for that division, she builds back up to the abstract version of her task.

Lisa is only able to move up and down the ladder of abstraction like this because she knows a lot of math – specifically where it builds from and towards. If she doesn’t know that math, her options for helping her students basically shrink down to “let’s solve a few together.”


I don’t know if it’s possible to practice what Lisa is doing here. It’s knowledge, the tightly connected kind you get when you spend thousands of hours in math classes, reflect on those observations, write about them, talk with other people about them, and then use them to inform what you do in another math class.

It’s possible, even easy, to spend the same number of hours without acquiring that tightly connected knowledge.

It’s something special to see it all put to use.

BTW. My guess is a lot of those knowledge connections were tightened because Lisa is a dynamite blogger. On that theme, let me recommend The Positive Effects of Blogging on Teachers, an article which does a great job describing ten reasons why teachers should think about blogging.

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.