Hypercubes could teach any of the levels.
AdamAI could actually teach two to the power of n there. AdamAI could teach factorials and n choose r there, and dividing two to the power of n over two to the power of k.
All of those could be taught there, and that could actually be an algebra lesson. It could also be a geometry lesson.
- Arithmetic Counting & doubling
- Algebra 2n
- Higher-dimensional geometry Faces & dimensions
Below and above
A lot of it congregates around their level, but they’re learning lots of things below and above.
If the student’s interested in calculus and they’re still learning Algebra 1, then we can focus on e to the power of x. We say there’s a special number here. We don’t have to introduce limits yet.
That doesn’t mean they don’t get exposed to calculus in a qualitative way. We need to emphasize the different levels of learning. There’s qualitative; there’s the more rigorous.
“What are you interested in?”
“Oh, I’m interested in the Julia set.”
“Okay, well, you’re interested in the Julia set, but you’re an Algebra 1 student. So let’s talk about y = x² + a constant. What does that mean?”
Or let’s say you’re a precalculus student. “Okay, well, let’s talk about imaginary numbers, and let’s see if I can determine your fluency around that.”
y = x² + c
(a + bi)²
They’ll learn more than Algebra 1
That’s not to say that we can’t emphasize Algebra 1, but I don’t think a student will only learn Algebra 1. They’ll learn more, more than Algebra 1.
The proficiency will actually be developed. We’ll see two to the power of x, three to the power of x, e to the power of x in other places.