I try to push the boundaries when it comes to teaching Math to my son. First, I am very proud of his achievements so far. Next, it depends on his mood :). There are times where he does great and then there are times he comes across as not so bright. The later part is to do with his concentration skills :).
Anyway, after having him master the 4 basic math operators and the powers, it’s time for the bigger things like gcd, lcm and so on. I usually introduce something a little more advanced for him than he is used to and see how he is doing. Things usually go over his head but from then till he gets the concepts is where I try to brainstorm teaching him the missing gaps to get him where I want him to be. In the process, I try to draw various analogies to explain concepts. Sometimes, explaining those other concepts themselves take time but there are benefits in doing it. That is because, the same concept might be tractable in one example than the other.
Because of my recently found interest in all things “quantum”, he knows a little bit about atoms and molecules as he watches all those videos with me on Youtube. So, then it stuck me that I could actually teach him a bit of those advanced math concepts using atoms and molecules.
He knows water is “H2O”. I also told him about Carbon DiOxide (CO2) and Carbon Monoxide (CO). Then I asked him what’s common between H2O and CO2. Essentially I was trying to get him learn that both the symbols and their counts contribute to “commonness”. We did the same exercise with CO and also Hydrogen Peroxide (H2O2).
So I was explaining him how the atoms like Hydrogen and Oxygen is similar to Prime Numbers (which he kind of knows) and Molecules like Water and Carbon DiOxide while are like Composite Numbers. I think this explanation really helped him. What’s more, I am essentially setting the stage to make him understand GCD, Greatest Common Divisor.
In our learning process, he wondered a couple of things.
1) Why in Chemistry it’s written as subscript while in Math it’s written as a superscript.
2) Why do you have to use numbers at all. Why not HHO? This is reasonable given in both cases 3 letters are used. Then I explained how there are chemical compounds where the atoms repeat quite a bit. Methane for example is CH4. So, obviously it’s easy to write CH4 instead of CHHHH. And that there are complex chemical compounds that are even bigger.
One thing I have been trying to do is to make him engaged with me like asking questions and coming up with his own ideas. He wasn’t doing that for a while but seems like there is a change. He seems to be more engaged and trying to come up with question and answers.
Growing up I never liked mugging up formulaes and so I am not much of a fan of memorizing a lot of things. So, rather than being hung up on waiting till he memorizes all the multiplication tables or other things, I am trying to just keep going at all the beauty that is there in Math and the Universe :).