In the clear afternoon sun of October 7, 1903, on a bank of the Potomac River just outside of Washington, D.C., a “large and distinguished company” of government officials, reporters, and scientists - including inventor of the telephone Alexander Graham Bell - assembled to witness what they believed would be a major turning point in history. With his impressively named “Great Aerodrome,” Samuel Pierpont Langley, world-renowned scientist and the Secretary of the Smithsonian Institution, was about to make the age-old dream of manned flight a reality. Langley’s Aerodrome, sitting atop a houseboat from which it would be catapulted - could not have been a more impressive sight. Generously funded by both the U.S. War Department and the Smithsonian, and scaled up from a series of successful models Langley had created and funded himself, the Great Aerodrome, with its dramatic 50-foot wingspan and powerful 52-horsepower engine, was poised to change the world.

If only it had been able to fly.

Upon being launched with fanfare from the catapult, the Great Aerodrome “simply tumbled over the front of its launching track and plunged, like a broken windmill, into the water,” according to an eyewitness. Blame was immediately laid on a malfunction of the catapult system and not on the craft itself, but a second attempt two months later - witnessed by an even larger crowd of dignitaries as well as members of the public - failed even more spectacularly, with the rear wings of the Aerodrome buckling and collapsing upon “liftoff” and the “aircraft” falling backwards into the water, “a tangled wreck.”

Nine days after the second failed flight of the Aerodrome, on a barren windswept beach near Kitty Hawk, North Carolina and with only five spectators braving the frigid December air to witness it, the “Wright Flyer,” a modest wood-and-canvas aircraft designed by trial and error over the previous two years and funded only by profits from a small bicycle shop in Dayton, Ohio, conquered the air. Piloted by designer Orville Wright - and later in the day, by its other designer, brother Wilbur - the humble Wright Flyer would go down in history as the world's first airplane.

How were the Wright brothers, amateur tinkerers with no scientific credentials whatsoever and no financial support other than what they had managed to generate on their own, able to succeed where Samuel Pierpont Langley - the pre-eminent scientist with the resources and backing of the Smithsonian Institution and the U.S. military - failed?

By giving control of the aircraft over to the pilot.

Of all the reasons for the Wright brothers’ success that day - and for Langley’s previous failure - one stands above the rest, even if it has seldom been remarked upon: the Wright Flyer gave the pilot full control of the aircraft in all three dimensions. The Wrights’ “3-axis control system,” which enabled the pilot to adjust the three dimensional movements of pitch, roll, and yaw, was the world’s first such system. Langley’s Aerodrome, by contrast, gave the pilot only limited control of pitch and yaw - and no control of roll whatsoever. (How did Langley miss this could-not-be-more-critical detail? The fact that he never piloted the aircraft himself provides a clue. As author Nassim Taleb has pointed out, “skin in the game” frequently explains the difference between success and failure in the real world. If the Wright Flyer failed, one of the Wright brothers could have died; if Langley’s Aerodrome failed, pilot Charles Manly’s life - not Langley’s - was on the line. It’s a good bet that if Langley’s life had been on the line, he would have found a way to give himself full control of the aircraft - and not merely scaled up his models as he evidently did, with Manly functioning more as passenger than pilot.)

Now I know what you’re thinking. Cool story, bro, but what does any of this have to do with getting math education off the ground?

Plenty. The Wright brothers didn’t just learn how to build a flying machine - they learned how to fly. And they did it by giving full control of the aircraft over to the pilot (themselves).

It’s time to give full control of the learning process to the students themselves.

Why?

Because only they know when they need to slow down and study an example in detail. Or when they need to go back to review previous learning. Or when they can skip something they’ve already mastered. Or when they need more practice with a skill or concept they thought they had mastered. Or when they’re ready for feedback. Or when they need more of a challenge. Or when they need assistance from the teacher.

In other words, only they know what they need to fly.

When we try to make these kinds of decisions for students, we’re repeating Langley’s mistake: we’re assuming we know the situation in the cockpit without actually being in the cockpit.

And we’re making crashes much more likely.

Sound like an overstatement? When students give up because they can't keep up, that's crashing. When students stop caring because there's no challenge, that's crashing. When students are feeling helpless, or suffocated with busywork, or failing to see the point of math class day after day after day after day? Crashing, crashing, crashing.

And many of those who crash in math class never recover. 

But is giving them all control over their own learning possible?

Well, I used to think it wasn’t - all of my searching along these lines had come up empty - but then the sheer number of self-starters I saw in my classroom over the years got me thinking that maybe interactive technology was a possibility. So I taught myself to code and spent a decade creating hundreds of interactive math activities for my students to use at their own pace, turning my classroom into a mini computer lab.

Again, no dice. Calling something interactive and having students interact with it the way you want them to, I’ve found, are two entirely different things - a problem AI developers are still not even close to solving. (Call it the “Oregon Trail Effect,” for those who remember the software simulation that was supposed to teach students about what it took to survive on the Oregon Trail, but actually taught them how to get their virtual settlers to die from funny-sounding diseases like diphtheria.)

So then I gave up.

And then Covid hit.

And then remote instruction got me thinking again about self-instruction - you know, because trying to teach all of my students myself without actually being in the same room with them wasn’t even close to working.

And then I had an idea (along with the time to carry it out):

What if I created a sequence of pencil-and-paper math activities with a pre-worked example for every single practice problem along with access to a fully-worked solution? John Sweller’s concept of worked examples had worked beautifully for me in the past - what if I went further and let students have all the worked examples they needed (or didn’t)?

Wouldn’t such a “see it, do it, check it” structure allow students to learn by themselves? Wouldn’t it allow them to all work at their own pace? Wouldn’t it reduce anxiety for those who needed extra time? Wouldn’t it increase the challenge for those who were eager to explore on their own and move ahead? Wouldn’t it give them all the ability to learn by doing and master every single aspect of a concept, sticking points and all? Wouldn’t it lead to higher-level thinking, especially if I scrambled the examples and problems so that mere copying wasn’t an option? Wouldn’t it give them all the ability to try things, and discover things, and learn from their own successes and mistakes?

Wouldn’t it give them full control over their own learning?

This time the answer was yes, yes, yes, yes, yes, yes - and yes.

There was a time not so long ago when people thought flying machines would always be imaginary - even Wilbur Wright himself, in a rare moment of despair, claimed that “man won’t fly for a thousand years.”

Two years later he was in the air.

Students have the ability to teach themselves. Of course they do. They just need the means to do it.

Thanks to John Sweller and worked examples, they now have the means.

Let them fly.