Circular Logic

A few weeks ago, I summarized my thoughts on improving schools in a post titled Pulling It All Together. As I was working on the post, I kept getting stuck because I felt like I couldn't ground each point I was making as I was making it. The point would make sense by the end of the post, but some of the points couldn't quite stand on their own. I finally had to accept that I was constructing an argument that had internal dependencies and couldn't be laid out in a linear structure. The best that I could do was to be clear and concise, giving the reader a chance to stitch everything together in the end.

Here is one point. Not too exciting, is it?

Here are some more of the points. That argument looks like it is about to collapse!

Here are all of the points, assembled and supporting one another.

On Tuesday, my friend Lee was telling me about the machine learning course that he is teaching. His students were using gradient descent to find local minima for a cost function. There are so many variables when it comes to learning that we tend to oversimplify things just to understand them. This can lead us to getting stuck on a local minima or maxima that is really just a blip on the landscape. Instead of throwing away variables, we need to embrace and understand the complexity and interdependencies involved.

In my last post, I wrote that giving students' ownership of the curriculum was necessary but insufficient for designing a good curriculum. There are plenty of things that students want to learn in life that they are unable to learn on their own. I believe that enabling students to make sense of the curriculum is also necessary.

But you really can't isolate ownership from sense-making. I believe that if you enable students to make sense of the curriculum, then over time, students will take ownership of the curriculum. If the school's curriculum does not give them what they need, then these students will simply learn what they need elsewhere. They will have the sense-making skills needed to learn on their own, and they will be driven to make sense of things. Once you make sense of some things, you can't stand not making sense of other things.

Similarly, if you give students ownership of the curriculum, over time, they will want that curriculum to make more and more sense to them. The question is, what happens if the school doesn't or isn't able to respond? In my experience, the students' sense of ownership diminishes if they don't get what they want. They may be happy with choice and relevancy for now, but they will want things to make sense eventually, and something doesn't make sense just because you want it to.

This really isn't a choice between ownership and sense-making. We also shouldn't optimize for both ownership and sense-making. Optimizing each variable in isolation is a mistake. Doing that over and over again is exactly why we are stuck in the mud and unable to gain traction. We should be trying to figure out the direction of the steepest gradient from our current location. I believe it lies primarily along the sense-making dimension, but that's an argument for another day. Namaste.