AOPS=overcomplicating easy problems?

[Dmmetler]

DD is working through the geometry section on mathletics after doing the similar section in AOPS, and what I'm noticing is that she's doing things like breaking down shapes into smaller shapes and finding additional faces, then putting them back together to find area but missing that "Gee, this is a right triangle that's sitting on it's hypotenuse. Therefore, the other two legs are base and height"

She's actually having a harder time on the easy, straight-forward, all the information is there problems than on the more complex ones. She's getting the correct answer, but she's going to a lot more work to do it.

 

 

Any suggestions? Or is this just a matter of not having enough practice on the skills yet for her to be able to automatically "See" what the best process is?

 

 

 

[wapiti]

The problem-solving process you describe sounds good to me!  I would go over the "easier" (more elegant) way to do it after she solves it, the bigger picture, so to speak.  Looking for that perspective is something to be learned, IMO - that is the point of AoPS.

 

I don't think this is related to what your thread title would indicate, AoPS overcomplicating easy problems - I assumed you were talking about the solutions.  If it were really easy, she'd see it sooner, no?

[regentrude]

It takes a lot of experience to see the easiest way. It is great that she is able to break down the figure and mess around with it - maybe even more valuable than seeing the right solution immediately.

Even with my rather strong math background, I occasionally approach a geometry problem by making it "more complicated", because I don't see the simpler, more elegant solution.

 

I suggest you let her figure it out the way she does, and then go over the more elegant solutions afterwards. It could simply be that she is expecting the problem to be more complicated than it actually is, especially if she has worked more complicated problems before. I observe this with my students that they sometimes tend to overthink the easy problems and make them more complex because they did not believe it could be that easy.

[kiana]

This is very common and my math majors do it in proof-based courses. I always prepare solutions for them so they can see the "easy" proof after they have struggled through it. (Their own correct but very long proofs get full credit, of course).

[Dmmetler]

That makes sense. On the title, I titled it that way because I think that AOPS has taught her to look for parts of a problem and break it down to solve it and she's missing that sometimes, she has the whole information. It's the difference between a regular middle school "Here is the algorithm, use it 10 times" and "here are some problems to play with to find the algorithm. Now we're going to give you more problems, where the algorithm may or may not be useful"-and she's expecting the latter.

[regentrude]

That makes sense. On the title, I titled it that way because I think that AOPS has taught her to look for parts of a problem and break it down to solve it and she's missing that sometimes, she has the whole information. It's the difference between a regular middle school "Here is the algorithm, use it 10 times" and "here are some problems to play with to find the algorithm. Now we're going to give you more problems, where the algorithm may or may not be useful"-and she's expecting the latter.

 

And I think that is fundamentally a GOOD thing!

She expects to think instead of turning the crank.

 

[quark]

Thanks for bringing this up dmmetler. Glad to know DS is not the only one. DS and I have a family joke about overthinking things. He's quite aware of it now (at 11, but wasn't at 9!) and has learned that if something seems way too complicated at first try, there really can be a simpler way (and he finally believes me when I tell him that too). Then together, we nod our heads and shout (while grinning)..."we are overthinking it again!".

 

It was a little worrying for me when he was younger, and frustrating for him. There have been hot tears and but also adamant refusal to give up. I am extremely glad he gradually realized it for himself. It does lead to very long math sessions with only a few problems solved at a time (also due to the slow writing/ graphing by hand) but I definitely see improvement and more confidence with practice.

[EndOfOrdinary]

My son does this in his chemistry stuff. I have to go check on him when things are taking way too long and then he has done three or four problems elaborately when it was plug and chug. I think there is the need to explain that some curriculum/expectations are different that others. It seems he is thinking that AoPS is sort of the base standard, not realizing that in many areas it is more direct instruction.

[Crimson Wife]

We haven't used AOPS, but I do sometimes see my kids do this on Singapore problems. I don't really care so long as they get the correct answer, but I will show them the easier way after they've finished.