Gifted Issues Discussion homepage Forums General Discussion DS' approach to a test question

Hmm. Interesting all the ways to approach it. I must be visual in my math approach. I immediately pictured 25 trays in line as if set on a long table. Starting from the left each tray had a cup and starting from the right each tray had a plate. Then I just looked at how many trays had both=11. My mental picture even included small blue teacups and pink plates like my DD teaset. Weird. Its a wonder I passed calculus.

That's the same method I used too.

I had a visual approach, too. In my mind I constructed a 5x5 grid of trays, then filled in the grid with 21 plates. That immediately told me there were only 4 "cup only" trays, and the other 11 cups had to be on "cup and plate" trays.

Wayyyy easier than calculating percentages.

I solved this as follows:

1. If 15 trays have cups, 10 trays must have ONLY plates.

2. There are 21 plates. 21-10=11 left over to go with cups.

ETA:

I think there's a lesson here in learning to recognize when you're doing something in a way that's unnecessarily complex. Does your son prefer to create a complex solution (because maybe it's enjoyable?) or does he just go the complex route naturally? Somewhere in-between?

IMO, learning to recognize that there may be an easier way to see or do something that appears to require many steps and conversions is a fundamentally important skill.

I agree with Zen Scanner that some very mathy people intuitively see many math problems in a way that's fundamentally different from most other people. But that doesn't mean that mathematics (or whatever subject) is an either-or proposition or that one way is universally better than the other. There are times when being able to visualize something in a complex way will confer a huge advantage. But the thing is that there are also times when this same approach will cause a huge disadvantage because it makes something basic way too messy. (And of course the reverse is also true for always seeing things in simple terms).

Maybe you could try to teach your son how to see both sides of the coin.

It should be said that OP's DS solution was basically totally standard except for a very minor unnecessary diversion into percentages.

Indeed. Throw out the conversions into and then out of percentages, and the kid basically performed the following:

21 + 15 - 25 = 11

He seems to gravitate toward the complex rather naturally, although I would also say he tends to prefer it in some cases. His GT math teacher spent a lot of time last year working on getting him to see how other people solved various things, so he would have more tools in his box. She will not be there next year, so I'm hoping the next teacher will continue that.

I drew that picture in my head as well, a line of trays (and drew them as a 5x5 square), but it took me a while to realize that every tray had to have something on it -- if that weren't the case, there were quite a few possibilities.

There's plenty of sense to it and it will work on other similar problems. Please note that he is doing two extra steps by converting to and from percent. On the other hand, that is simply the way he thinks and he can obviously do it quickly enough for it not to be an issue so I would leave it other than show him the quicker way (21+15-25=11) as well.

I wonder how often his path to the answer is actually a highly efficient method, and it is only under probe that the convoluted process is invented. The Heisenberg uncertainty principle as applied to the mathematically gifted?