Learning math is more dangerous than skiing
If we don't provide the instruction students actually need, they will get hurt.
Imagine that someone who loves you buys you a ski lesson.
So you bundle up and head to the nearest ski slope - I realize this may be far-fetched, bear with me here - and show up to ski school. When you arrive, you see this sign:
“Wait a second,” you say. This doesn’t seem right. Your age isn’t relevant here: it’s your level of skiing experience! A 20-year-old can be advanced and a 50-year-old can be a beginner. The instruction you receive should address your needs, not your age.
“Don’t worry,” the instructor says. “This is the way we’ve always done things, and 22% of our students become competent skiers. Plus, we use the best ski equipment on the market, and we tell our ski instructors to differentiate.”
You don’t have much choice here - this ski lesson was a gift, after all, and you do want to learn. So you strap on your skis and head up the mountain.
But at the top of the ski slope, you might start to wonder. Is this really a good idea?
If you’re new to skiing, but happen to be too old for the Beginner classes, you’re probably going to get hurt. And if you’re an experienced skier whose age places you in the Beginner classes, you probably won’t improve.
Fortunately, ski schools don’t work like this. In fact, basing the instruction a skier receives on their age alone would be a pretty terrible idea.
So why do we run our regular schools that way?
We set millions of young people up to fail - every single day.
I’ve never taught skiing. But I was a high-school math teacher, and this situation is deeply familiar to me. In fact, it may be the best way to describe what I faced every day.
In each of my classes, I had:
Advanced students, who needed to be challenged.
Students with learning gaps, who needed additional support.
Those students happened to be the same age, but they needed vastly different things. I often saw students with college-level skills and students with elementary-level skills sitting next to one another.
And there was no way that a single lesson - taking these kids down the same slope at the same pace, so to speak - could appropriately challenge and support them all.
So all too often:
My advanced students were bored.
My struggling students fell further and further behind.
And this wasn’t just in my class! We know from decades of NAEP data that, as early as 4th grade, most young people in the United States are below proficient in math.
What’s a fifth-grade teacher to do? Some of the students are ready to ski faster, and some are probably going to get hurt.
And in fact, many do fall off along the way. So by 8th grade, this is worse.
And by the time they graduate, only 22% of American students are considered ready for college.1
We as a society may have become inured to these numbers. (We’ve certainly seen them for long enough). But they should shock us! These are our kids and our future we’re talking about here! And despite all of our hard work, these results are abysmal.
We love our kids and we send them to school and far too many of them fail.
This really hurts.
What’s above are statistics. But behind every number above is a young person - an infinite spark of potential - who, like everyone else, desperately wants to succeed.
And I wonder: what does sitting in class feeling bored or falling short, day after day, over weeks and months and years, do to a young person’s soul?
Having taught high-school math, I can tell you:
Many of my students felt deeply inadequate. They’d tried to learn math for many years, and failed every year. (Their test scores revealed as much.) As a result they hated math, and lost belief in themselves.
Other students were overconfident and underprepared. They had rarely been challenged, and as a result lacked the skills and mindsets to persevere when they were. These students could have learned so much more.
What ALL of my students felt was ignored. They came to school with needs, and those needs were rarely met. Every day they squandered a little more of their potential. It was because they were usually skiing on the wrong slopes.
You might think I’m overstating the problem here. This is just the way schools work, isn’t it? Students get bored or lost, but they all end up okay in the end, right? No broken bones here.
I disagree.
In fact, learning is more dangerous than skiing.
Skiing is physically dangerous, yes. But, compared to skiing:
Students spend more time in school. You can go skiing once, hate it, and never go again. But you can’t really just ignore school. If school is miserable for you, you’re going to spend a lot of your youth feeling miserable.
School has longer-lasting impacts. If you break a leg skiing, you can go to a hospital and your leg will heal. There’s not such an obvious way to recover from years of feeling inadequate in math.
School matters more. It doesn’t really matter if you can’t ski. If you can’t read or do math, however, it’s inevitably going to limit what you can do for the rest of your life.
I grant that this isn’t a perfect analogy. (Trust me - I’ve spent years looking for a better one!2) But I hope it illustrates my real points here, which are that:
Learner need, not learner age, should determine the instruction a learner receives.
Age-based instruction is dangerous.
If you agree with me here, then I hope you’ll also agree that we need a change.
How do we fix this?
One thing I like about the skiing-learning analogy is that it helps illustrate, at least in my mind, the fundamental challenge of teaching: on a daily basis, many of our students are being asked to learn the wrong things. Somewhere in America a nine-year old who understands trigonometry is being taught to draw triangles, while a 16-year-old who doesn’t understand triangles is being taught trigonometry.
This means that a lot of promising and important efforts in education fail to achieve their full potential. For instance:
High-quality curriculum is unevenly implemented. It’s difficult to teach grade-level content when some students are far ahead, others are behind, and others aren’t there at all. So teachers using high-quality curricula often end up reducing rigor, teaching to the middle, or skipping content entirely.
Edtech tools are underutilized. A platform like Khan Academy has the potential to facilitate truly need-based learning experiences. But when teachers expect all of their students to cover the same content every day, these powerful platforms become little more than digital worksheets.
Differentiation becomes aspirational. Research-backed frameworks like Universal Design for Learning sound promising in theory. But it’s very difficult to provide multiple access points when students and teachers are scrambling just to keep up with the content they are supposed to cover every day.
It’s impossible, in other words, to benefit from the latest advances in ski equipment when students are on the wrong slopes.
And these things all matter! As a parent, I want my kids to learn from high-quality curriculum, use technology to enhance their learning, and receive evidence-based interventions when appropriate.
But first I want to make sure they’re on the right mountain.
What (ski) teachers can do.
So imagine that you’re a ski instructor with a class of skiers, who have different levels of skill. Seriously - what would you do?
Whether you’ve ever skied or not, I think you’d probably try to:
Figure out what each learner already knows how to do.
Identify what each learner should learn next.
Give each learner some way to practice.
You might show a beginner how to brake by putting the tips of their skis together. You might show advanced skiers how to go more quickly, by keeping their skis parallel when they turn. Then you’d help both sets of learners practice.
What matters for this example isn’t really what you teach, but how. You’re probably going show different skiers different things, then let each of them practice it until they feel comfortable. And you’ll do this for one simple reason: because that’s what each skier needs!
This post is already long, so I won’t get into the details of how this actually looks in a classroom setting. I wrote a book about this (Meet Every Learner’s Needs), and the Modern Classrooms Project (MCP) has a free online course that can teach you everything you need to know about self-paced, mastery-based instruction. In practice, however, it looks something like this:
The takeaway here is that it is actually possible to meet every learner’s needs at the same time. Thousands of Modern Classroom educators, all around the world, do this every day! And there are simple steps that any teacher can take - like recording a video or creating a mastery check - today to teach lessons like these tomorrow.
But there’s a larger problem too.
I co-founded MCP and wrote Meet Every Learner’s Needs because I believe that any teacher, anywhere, can create a classroom where every student is appropriately challenged - and appropriately supported - every day. Teaching is really hard, but there are techniques and tools that make it manageable.
The larger question, however, is whether teaching needs to be so hard in the first place. Should we really put students who just happen to have the same age onto the same ski slopes, and hope that they’ll figure it out? Or might there be better way of organizing school, which would let students learn based not on their birthdays but based on what they already know and what they feel ready to do next?
I think there is a better way. And I don’t think we need to look far to find it. In fact, I think the right paradigm of instruction is actually the typical ski school!
At a school like this:
Learners learn with their similar-age peers. This is good for social and emotional development.
Learners receive appropriate challenge and support. In skill-based groups, it’s much easier for instructors to provide what learners actually need.
Learners can easily move between groups. If a learner progresses fast, they can move to the next group quickly. If they need more time to learn, they can have it.
I’m not advocating for a traditional system of “tracking” here. It’s not fair to put young people in skill-based classes for one school year at a time, nor does it really solve the fundamental challenge: students’ needs evolve, so even in an “advanced” or “remedial” class some students will inevitably become bored or fall further behind.
I am instead proposing flexibility and responsiveness, whether in a single Modern Classroom (good) or an entire school system (better). I am suggesting that:
When a skier needs more time on the beginner slope - or a learner needs more time on their current lesson - they get it.
As soon as a skier is ready for a steeper slope - or a learner is ready for the next lesson - they move there.
That’s it!
This is possible.
This may seem impractical. It might mean, for instance, that:
Students move from class to class during the school year.
Students of (somewhat) different ages work and learn together.
Students take assessments only when they’re ready to demonstrate understanding.
But while these ideas may feel different, none seems impossible. In Modern Classrooms around the world, in fact, these kinds of shifts have already happened! So now we just need to redesign instruction at scale.
Otherwise, our young people are going to crash. And they deserve better.
This is the percentage of students who met all four college-readiness benchmarks on the ACT test. See “Grad Class Database 2022 - ACT Research.” 2024. ACT. www.act.org/content/act/en/research/services-and-resources/data-and-visualization/grad-class-database-2022.html.
In my mind, the biggest limitation of skiing as an analogy is that it’s inaccessible: skiing is largely an activity for very privileged people. But I suppose in that way it really is like learning, at least in our vastly unequal society: rich people get more of it.
MCP lets me meet each learner's needs at the same time!