I grew up with a strong interest in Math based on what has been taught to me. Which is just the concrete details to clear the exams and nothing more. Only much later in life did I realize there are many abstract concepts that are beautiful and have much wider implications to our understanding and reasoning. So, my desire is to teach my son not just the concrete concepts of math but many abstract concepts. For someone soon turning to be 6yrs, it’s a lot to take. But to be clear, I don’t force on him or don’t spend teaching even a single extra minute the moment I see his interest waning. For a kid who needs to go to KG for just 4 hrs, and have 4 different private classes (none of them related to studies) during the week he has enough fun. Some parents send their kids to Math classes like Kumon. However, I don’t send my son to such programs. For one, I actually know a lot more math still at my finger tips than many of my age 🙂 and second, I enjoy teaching and finally having that personal attention helps me to access his progress. It helps me understand not just how he is learning but why he is not able to learn. That makes me figure out the gaps in his knowledge and understanding and come up with topics to bridge those gaps.
One of the things I have been trying to get into that little head is the notion of functions. I think some folks are getting their kids on to programming at a very early age but this is not about programming functions. Tools like Scratch are making people get their kids to start learning programming early. I have mixed feeling about it. I mean, not about how early they should start but whether that’s the right way to start. I actually lik the Lego “Fix the Factory” game. It is lot more structured and helps think through strategy and convert the strategy into instructions that indirectly teaches programming.
I am talking about mathematical functions. Like f(x). I tried teaching it a few months back but realized that he was not ready yet. I tried again a few days back and didn’t find much progress. I usually try to go with simple and make it more complex. So, we tried f(x) = x+5, f(x) = x^2, f(x) = 2^x , f(x) = x^x and so on. I would give him f(x) and ask him to write the expression for say f(5). He just wasn’t getting the idea of what’s happening. Just when I think he made progress, say with x^2, he would have trouble with 2^x. It shows clearly that he is trying to memorize or just understand specific examples but not getting the underlying concept.
I changed my strategy. Rather than making him learn f(x), I thought I will play with him a language game. As he is always ready to play than learn, I told him that I have a new game for him called “Secret Message”.
Say there is a sentence “The quick brown fox jumps over the lazy dog” and I need to replace all the ‘0’ with ‘8’. Then it becomes “The quick br8wn f8x jumps 8ver the lazy d8g”. He immediately got it. So, I gave him a few sentences and create the corresponding secret messages with different replacement strategies. Like changing ‘e’ to ‘3’, ‘s’ to ‘2’ and so on.
Then I asked him the following which I tried earlier as well but didn’t succeed:
f(x) = 5+x+2^x+x^2+x^x
f(5) = ?
And he did it without a single mistake. I was happy and proud. I don’t think he still has a very good understanding but I can see some improvement. Because, before asking him like what is f(x^2) didn’t work at all. But now that’s working out better. g(f(x)) is where we are currently stuck :). Then imagine going to f^n(x) and relating addition to multiplication via functions! I know we will get there.
Even with all of this, I am sure he is probably not understanding what a function means mathematically in a formal manner. But introducing such concepts can help him to improve his overall understanding is my hope. And doing it in the best possible way is my desire.
When a good student understands, it’s to his credit. When a good student doesn’t understand then it’s his teacher’s fault :).