School Yourself's technology is very good. I have tested many intelligent tutoring systems in the past — it's one of the holy grails of education — and even tried to design one myself when I wrote my chemistry textbook,

*Chemistry from the Ground Up*. This is the first system that I've used that feels like it may actually be ready for the classroom. But no matter how intelligent it is or how much data it has, a tutoring system is only as good as the curriculum it has at its disposal.

I am going to dissect the curriculum used to teach students about rainbows and Snell's law that School Yourself has up on its website. First, let me say that if a teacher that I was evaluating or coaching had designed this curriculum, I'd be very pleased and full of positive feedback. Compared to what is in common use today, it is very, very good. But the goal of Vertical Learning Labs is to elevate what we consider good curriculum, and the curriculum designed by School Yourself is not nearly good enough. It needs to be much better if they have any hope of reaching their ambition to be "the future of math and science education."

The lesson begins by telling students that light travels through different media at different speeds and that light traveling from point A to point B will travel on the fastest path possible. The cool thing about this is that it enables students to find the path light travels between two points by trial and error. Doing this a few times will then help them develop their own intuition about light paths. The problem with this approach is that it doesn't help a student understand

*why*light travels on the fastest path possible. What is the local mechanism that causes this to happen? Photons clearly do not have brains to figure out which path is fastest or guidance systems to then follow that path. You are essentially giving the student an abstract rule to follow, one that is not grounded in the physical world at all.

This is not a deal-breaker. I think it is okay to develop a lesson or unit around an abstract rule, and then have students explore the implications of that rule. I've taught a four-week unit on square roots grounded in the definition of a square root. That is pretty abstract! But the kids thoroughly enjoyed it as interesting brain exercises that also happened to help them learn math stuff. However, I do feel that a curriculum developer should be aware when a unit isn't grounded and avoid it when possible.

A more serious problem occurs when Snell's law is finally introduced. The equation for Snell's law is simply given to the student to memorize and practice using. The curriculum developer has chosen not to have the student derive the equation for Snell's law using the rule that light follows the fastest path, and I actually think that was the right decision. Having the student derive the equation for Snell's law would have been cumbersome and time-consuming, and the student would not have gained a deeper understanding from doing it. The problem is that the curriculum developer gives the student a tool (find the fastest path possible), and then promptly abandons that tool once Snell's law is introduced. If the student forgets the equation for Snell's law, will he or she be able to re-derive it from the fastest path rule? No. If the student is struggling to apply Snell's law, will the intelligent tutoring system or the student's teacher suggest that the student go back to the foundation of the unit and apply the fastest path rule? No.

The fastest path rule ends up being a device, or hook, to introduce the student to Snell's law. It is not a tool that the student will be using over and over again in the future. This is the kind of bait-and-switch that curriculum developers use on kids all the time, and kids resent it. It also teaches kids that the fun, hands-on activity that opens a unit is just a gimmick and that the "real" learning starts once the textbooks come out.

But the biggest problem occurs at the end of the lesson. By the end of the lesson, I actually have a fairly deep understanding of rainbows. I know what causes rainbows, why rainbows are in the form of an arc, where to look in the sky to find rainbows, why it is brighter inside of the rainbow than on the outside of the rainbow, and why there are secondary rainbows. I even have the tools and understanding to reason about rainbows and answer questions that I wasn't directly taught. In fact, I'm feeling pretty good about myself. But in the end, there is still a one-to-one correspondence between teaching and learning. You taught me something and I learned it. I learned it really well. And then you'll teach me something else, and I'll learn that, too. For some kids, this is more than enough. But for others, the pay off from understanding rainbows isn't enough. Maybe you can keep them interested if the thing they learn about is personally relevant, but that wears off over time also.

What kids want is to get off of that treadmill, the one-to-one correspondence between teaching and learning. We keep promising them a future where they will be able to learn for themselves, but for most kids, that day never seems to arrive. Some curriculum developers believe that the solution is to let kids pursue their own interests from an early age. I believe that the solution is to make learning exponential. I teach you one thing, you learn two. I teach you a second thing that builds off that first thing, and you've learned four. I teach you a third thing that builds off of the first two things, and now you've learned eight. When kids see that happening, they can see and believe in that future where they are powerful, capable, and learning for themselves. That future is now.

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