COVID-19 Exposes Mathematics Education Inadequacies: A modicum of (secret) relief for Educators.
Mathematics teachers are fabulous. The past number of weeks have proven to be particularly challenging for all teachers to turn their standard curriculum into online experiences almost overnight (and for some districts, literally overnight). First natural step, just to get something underway: convert the upcoming worksheet into PDF format and email it to students. And then ….
… the reality of matters hit home.
I’ve been privy to a number of recent departmental conversations with high school teachers and principals about how to possibly conduct remote teaching and learning the next two months (and perhaps longer) and I’ve been invited to give my informal thoughts on possible next steps in zoom conversations, in email, and in example by leading guest class sessions, creating new videos for a flipped classroom, and so on. Because times are stressful, some comments made in conversation are raw and not uplifting, but it is clear they are not meant that way: emotions are simply complex right now. But three types of comments I’ve heard repeatedly — I stress, not to be taken at face-value — are deep and revealing.
- My kids are cheating. They are clearly using online resources to answer all the questions to suddenly become “geniuses” in my course.
- I can only get about 30% of my students to actually do anything on the worksheets I send them.
- My kids say they can get what I send them done in 15 minutes, not in the usual 55 minutes we spend on it class.
Here’s how I interpret these comments, in turn.
a. Our kids are citizens of the 21st century and they know it. Of course, any citizen of this time is going to use all the resources available to her to complete any given task. It is the mathematics curriculum that is out of whack, not our wonderful kids.
b. Our curriculum is not inherently interesting as we present it. Think about it, who in their right mind wants to do a sheet of work?
c. Left to their own devices — when motivated to do the work presented— kids are absurdly capable and fabulous. What is all the clutter within the four classroom walls that turns 15 minutes of engaged work into 55 protracted minutes of “work”? (Do we want to return to this when school rooms reopen?)
And here’s the thing: I believe every mathematics educator knows and thinks all this, that our curriculum as we conduct it is absurdly anachronistic (really, you are expected to solve a division problem in real life by pulling out pencil-and-paper to do long division? What interesting tasks could we devise knowing full well students can google anything at any moment?), the curriculum as we chiefly present it is as dull as beans (really, I need to do every odd problem at the end of the chapter, just variations of the same problem over-and-over again, when I get it after just doing three of them?), and students are far more capable than we allow them to be.
We are in extreme times, with all usual norms of learning and success out the window. And the usual norm has been to deem the standard high-school curriculum math content as sacred. We say we value grit and innovation and flexibility of thought in problem-solving, but we all know — students and teachers alike — that we actually don’t give those ideals any weight or value in the end, we actually can’t! “Success” in mathematics is still ultimately defined by test scores, standardized test scores. Educators are beholden to the demands of that testing. Students are too. We all know it and we say it in closed conversations, but we don’t say it publicly too much.
But we must do so now. COVID-19 has put us in a teaching crisis, and the crisis is really the unspoken crisis we have been in the last number of decades, now finally laid bare.
What is our job right now, right this week?
It is not to attend to standardized testing. Those testing folk have no idea what they are doing right now or are to do for the immediate future. We have no idea how that is going to shake out. Our job is to keep learning going. And to do that our first step is to simply ENGAGE. If we don’t engage our students in this remote context we’ve lost them for sure. We can’t worry about “sacred” content done in its previous standard sacred ways. If students are simply not engaged in some form of mathematics conversation, we have immediately failed.
Our task at hand right now is to engage students in mathematics conversation: no more, no less.
Conclusion: Us educators .. we’ve finally been set free! We can do mathematics! We can define and practice success in mathematics as what it truly is.
A successful citizen of a mathematical mindset is someone
- able and willing to be an active participant in mathematics conversations by offering ideas that might — or might not — prove to be helpful in solving a problem, but nonetheless spur on conversation, thought, and progress;
- able to ask questions or offer new twists or connections that are interesting, provocative, relevant, and exciting.
A successful citizen of mathematical competency
- has the confidence to take a first step — any step — towards solving a problem, and
- is willing to probe what she knows and how she thinks she knows it.
(And I am sure we can add more descriptors to this portrait.)
For the sake of fostering engagement and online conversation, I’ve been advising teachers to run weekly Sudoku or KenKen puzzle conversations with their students. “Just post a puzzle and invite students to chat about why they think a certain number should go in a particular cell. If classmates agree with the reasoning, then write in that number.” Such logic of thinking and effective communication of thinking is pure mathematical work.
So, step 1: Have our students genuinely engaged in mathematical conversation.
We educators can bring curriculum content to a Sudoku mindset, once we are conversing about math. The imperative now is to converse.
In a standardized test a student is meant to answer specific detailed questions under pressure and with speed and be correct essentially on the first try each time. But imagine if a student wrote during the freedom of conversation something like
Well, I tried doing this [details provided] but it proved not to be helpful because the odd number of the right side got in the way. Maybe doubling everything will fix the problem? I am not really sure. It’s got me confused. Give me a little while. I want to sleep on this. I’ll get back to you.
or
Well, I know the answer I am meant to write is 43 degrees. But isn’t this question assuming that is “obvious” that any straight line that cuts through a triangle passes through exactly two sides of the triangle? I know that seems obvious when you draw pictures on a piece of paper. But is it obvious? What if we drew a really big triangle on Earth? After all, the Earth is actually a sphere. Is this idea still obviously true? For that matter, what does it mean for a line to be “straight” when it is drawn on Earth? I think I am realizing I don’t know anything!
I would hire either of these students right away!
We’ve trained our students not to think and question and doubt nor to write this way. A standardized test with only a bubble to fill or a box to enter a numerical answer will never let a thinker full of questions and deep thoughts reveal themselves. But with COVID-19 and learning from home, a truth has been made loud and clear: speed answers to “what” questions are absolutely best and most-sensibly answered with Google, Desmos, WolframAlpha, and the like. Or just ask Siri. The dictated high-school mathematics education culture has disallowed students being intelligent citizens of the 21st century.
“It is all about the Thinking”
We teachers all say this and know this and want it, in the end, to be this. (“Those darn State/Provincial and National assessments!”) We know that the content isn’t sacred. We don’t teach the quadratic formula, or trigonometric identities, or rationalizing the denominator simply because one always has and so one always must. We teach — at least, we want to teach — this content for the thinking it illustrates, for providing students practice to rely on their own fabulous wits (using 21st century tools, if desired), for the opportunity to have students process content, to question content, and to ask “How do I know what I think I know?”, and for the chance it offers students to practice taking steps, first steps, any steps, to solve a problem in math or in life. I truly believe
High school mathematics content is a wonderful vehicle for teaching powerful, human thinking.
To illustrate this, as part of my “flipped classroom” advice of late, I put together some videos on discussing “straight up curriculum mathematics for the 21st century.”
Here’s a video on graphing factored polynomials, which, in many curricula, is a piece of “sacred content.”
Why does one need to do this in life? One doesn’t!
What’s the most sensible way to get the answer? Type the equation into Desmos.
So why are we doing it? Because it is an invitation for YOU to see how powerful YOU can be just following your nose and playing with ideas. It’s a safe (and actually cool and quirky) place for you to practice the life skill of taking steps forward when faced with a challenge, despite how emotionally weird or scary or overwhelming the challenge may feel.
All of high-school mathematics content can be — and should be — seen in this light. (Some more examples are here.)
I am not the only one saying this. The inimitable Grant Sanderson of 3 Blue 1 Brown, for instance, has recently started live sessions to discuss standard high school topics with a focus on trans-formative and expansive thinking. But secretly, mathematics educators have been feeling this and saying this amongst themselves for decades.
One small silver-lining of COVID-19 is that it might now give us public permission to set mathematics teaching free and let high school mathematics serve the tremendous good for society it is, and has been, poised to do — finally!
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ENDNOTE: When the curriculum is presented as a joyous story of empowered thinking, students are capable of grand things when left to their own devices. The young lad of the photograph decided to figure out how to divide polynomials after seeing place-value in a brand new light.
