At a charity walk, 150 participants were adults. 1/3 of the children were boys. If 1/4 of the participants were girls, how many people were at the charity walk?
Can I do it? Of course, but I've to use algebra. I managed to get it in the first try, maybe in less than 3 mins? But you and I know that primary school maths do not involve a lot of algebra, if at all. And the way to solve such problems is to use the 'model' method and I know how I suck at this method of doing math. I tried for a good 30 minutes before giving up, attempting another question, hit an inspiration and went back to do it for another 15 minutes before I finally got the answers using this weird blocks of rectangle that is so typical of the model method.
Am I bad in math because I couldn't solve the problem using the prescribed method? Obviously not, because I can solve it so much faster using another method of doing it. Similarly, for someone who is so good at using the model method, does it mean that he is good in maths? I've seen many students who had very good scores in primary school maths (obviously they must know a great deal about the model method) but failing miserably when the model is no longer used in secondary school. Does it mean that they are no longer good in maths?
On reflecting, a few thoughts came to mind:
1. Don't be judgemental. Perhaps a person's potential is not shown because the the right method to bring out his best is not there yet. Also don't be judgemental on your own abilities. Just because you can't do it now doesn't mean that you are bad in it. Perhaps you haven't found the way that best suits you.
2. Don't be too proud of your success. Perhaps you just happened to hit on something that just comes naturally to you. When the full extent of the problem is shown to you in the future, you might not be able to transfer whatever worked for you in the past to the future. At best, it's just domain-specific success; once you're out of that specific domain, you're not longer that good.
3. Be open minded and try out new ways to do things. Don't be stuck in ways that worked for you in the past.
We tend to diss things that we're not good at, and praise the system that had been working so good for us. In this case, I can always complain why can't primary school use algebra to solve math problem - it'll be so much simpler (for me). Or I can start teaching primary school kids algebra, because that's the way to solve such problems (for me).
Or if I'm superb at the model method and is very good at primary school math, when I enter secondary school and I suck at algebra, I'll start using modelling model and diss the teacher for teaching me algebra. Why learn something so complicated (for me) when I can draw models and get the answer anyway?
Ultimately, I think that whoever is good in maths isn't necessary someone who is good in maths right now at this moment or worse, in the past. He is someone who exhibits the ability to be good in maths in the future. In the future, there's so many problems and challenges that are thrown at you from all sorts of angles that you have no way to succeed without being non-judgemental (so that you don't give up when you encounter new things), humble (so that great teachers can appear and can teach you) and being open-minded (so that you can use new ways to solve old problems).
That, is why you learn maths. That, is what you tell students when they ask you why they need to learn how to integrate and solve trigonometry problems when in real life they don't even use it. That, is the reason for learning anything at all, really. Because when the subject matter has long been forgotten, the way you approach life's multitudes of problems and the way you tackle them will always be the same as the way you handle your humble maths problems.
(For those who tried the question and wants to know the answer, it's 240. At least that's what I got.)