I am an Antirealist (see this for explanation Is Math a Feature of the Universe or a Feature of Human Creation? ) when it comes to math in that I believe math is 100% made up.I don’t mean it is fake. I mean it is not discovered like science. Math is created to explain our universe. If the universe was different all the math would be as well. I see math as more of an Art. We are trying to paint a picture when words and pictures won’t work. Try to draw a 10 dimensional space. String theory says we exist in one but only the language of math with its numbers, symbols, and graphs can “paint” it with any accuracy.
So what is the conclusion of this? Find things students can’t explain or draw without the aid of Math. Show any student a set of points and have them choose a way of making it make sense to themselves and to the world around then. Maybe it’s a graph, maybe it’s a 3D model. Math lets us rework the world around us so we can perceive it, explain it, and feel ourselves fit into it.