Thats a somewhat crazy question. I came across this video, and i would say its quite a nice watch.

This video makes a compelling case for the why and the how of teaching maths in a visual way. After all, maths is not about words or languages, is it? If so, why should mathematics education be so language heavy? It should be about the concepts of mathematics. And i have found that the visual impact of mathematics is quite powerful. I tried this trick with my then 10-year-old … I introduced him to the concepts of integers, and multiplication with negative numbers without bringing in negative numbers to begin with.

We started with directions. Left and right. So, theres 3 to the left and 2 to the right. Or, 4 to the right and 5 to the right. Now, adding the 4 to the right and the 5 to the right is easy, but how does one add 3 to the left and 2 to the right? This is where the concept of the negative sign came into the picture. And once this was done, then it was a simple extension of this to see how multiplication with negative numbers simply changed the direction and nothing else.

What this did is help him build a mental picture of these concepts. In my experience as a trainer, i have found that these mental pictures are far more enduring than theoretical concepts. To take an example, i used to teach the concept of min-max planning, or the sawtooth curve, using the analogy of mom planning to go out and buy rice. Now, a few days after the class, the students, even if they had forgotten the min-max planning theory, or the sawtooth curve, still remembered the rice story, and this helped them to relate to the concept. The rice story here helped build a mental picture which is more enduring than theoretical concepts. So this isnt just about children learning mathematics, but also about adults learning.

Now, knowing him, he would have built a picture of Ben10 doing something which saves the world from the wildest aliens imaginable while multiplying two negative numbers, but hey, thats a picture i can live with!

Oh by the way, where there are integers, can vectors be far behind?

The video makes some rather important points. That mathematics has nothing to do with language makes sense, and language only comes into the picture in order to communicate concepts from teacher to pupil, is apparent, and with technology changing the way that can be done, this sounds like a really cool idea. On the other hand, there is also that if students can articulate the logic of solving sums, that would help them to understand better too. Or could we use this to teach both language and mathematics? If we build examples which the child can relate to, why not!

I am writing a post on lines somewhat similar to what you are saying.