Blog 0: A Guide to Neural Networks --- by Neurons, for Neurons

Hi everyone! Whether you’re accompanying me on this journey or from a future when this project’s already complete (please tell me if it went well), I hope I can lay a solid foundation for the basic philosophy and methodology of my project.

Project Description

So what is my project? From the title and abstract, I’m sure you can guess that it involves neural networks. More specifically, I plan to create a set of lesson plans aimed at educators that will progressively give high school students an intuitive sense of what neural networks are and the problems they were created to solve.

The highlight of each lesson will be an interactive model created through Desmos.

Why Desmos?

Because of familiarity, of course! Over the years, Desmos has become the go-to online calculator for teachers and students. And recently, it’s been introduced as the built-in calculator on the SAT and AP tests. That’s all to say that Desmos is a program that people have experience using. So, rather than mimicking the other learning courses that require prerequisite programming knowledge, I hope that using Desmos as the basis will allow for a tool whose functionalities are plainly visible.

Of course, I readily admit that programming experience will inevitably become necessary for students who want to go deeper into neural nets; it nevertheless shouldn’t be a hurdle in the way of understanding their mathematical basis and core ideas.

Preliminary Work

To demonstrate what I plan to create and quell skepticism that a graphing calculator can be used to create interactive models, here are a few barebones graphs I’ve created as a proof of concept.

Mean Squared Error Linear Regression visualization:
https://www.desmos.com/calculator/axdtzkspyy

Hidden layers as coordinates:
https://www.desmos.com/3d/9qygtumzjr

And just for fun, here’s a brick breaker game:
https://www.desmos.com/calculator/xuvt5fsfco

Don’t worry if you don’t understand what’s happening; that’s what my project is for. In fact, my initial senior project proposal got rejected for just that.

That earlier proposal focused narrowly on visualizing hidden layers by treating their outputs as coordinates and plotting them in 3D. While interesting, it became clear that the model alone couldn’t sustain an entire senior project and assumed too much prior understanding for the intended high school audience.

This new version is aimed at addressing those issues. By designing a sequence of lessons, I can gradually build students up to the level needed to make sense of visualizations like that one while also giving time for other creative approaches along the way.

Tangent aside, if any of this sounds interesting to you, I hope you’ll tag along. If you’re not one of those time travellers and are actually viewing these posts while I’m posting them, please do let me know if something is unclear. I’ll do my best to clear it up. This project is as much teaching as it is learning how to teach. It’s hard to know what’s effective when one already understands the material, so any feedback will play a big role in shaping these lessons as they evolve.