What really matters in problem solving?

[Ebolamonk3y]

I want an honest opinion of this... so...

What matters more?

The answer or the process leading up to it?
For those who know Feynman or Ramanujan... you know their magician abilities...

Yet some people, especially teachers or AP exams, love for you to show everything, the work, and the answer is worth everybit as much as the process leading up to it...


So I wonder... Is the work a delusion? Some just keep solving problems without an answer... And the worse is when there is no "answer in the back of the book" that leaves one to doubt their "work" and "steps" and, the demon of all, "arithemtic mistakes." Yet, in the end, we get an answer or we get nothing... time passes, an answer, time passes, an answer or bunch of paper gone...

So...some can get lost in the little stuff and never come out of the mess... then what? is that really problem solving or just another pass time activity that yields nothing?

Ponder about that...


LOL, for me, if I just start cranking out Integrals in my head or with some weird method, I be a little scared...

Maybe not...


Chang

 

[matt grime]

Teachers of courses of the level I presume you are talking about (what is AP, apart from associated press?) have a different set of interests than Feynman et all and the level of maths there. Up to a certain point arithmetic is what counts as you're doing things which one day, as an engineer say, will be needed with accurate answers.

At the end of those courses where there is book work, and perhaps even calculator's are needed, the answer is important, you're learning to crank a handle, set up the model, solve it, and realize if the answer you've got is plausible. Important life skills.

If you're at the point where doing integrals is still important then you aren't doing pure maths of Ramunajan (which isnt' to say they aren't important but that solving them is dull). I haven't had to actually do an integral in the last 6 years and I'm a working mathematician (well, right now I'm a buggering around not working PhD student). And let's face it in applied if you're doing an integral chances are you've cranked up a computer to do it for you cos it's a little tricky.

You need to demonstrate that you've grasped the basics, and if you're good at the level of abstraction that occurs later chances are that you can do the bookwork in your sleep anyway.


A very common problem (scarily if you ask me, cos I wonder what some teachers actually do) is for people to say 'I understand the product rule, honest, but I can't differentiate xcos(x)sin(x)' so you see they don't actually understand something very important (not the product rule, I mean), so the examples can be useful for seeing where people aren't thinking clearly.

 

[HallsofIvy]

It depends upon the question and the reason you are asking it!

If I have a question that I need an answer to NOW and will never need to answer again (what needs to be done to fix my car?) then the answer is important- I'll hire someone who knows how to do it and not worry about how they do it. If the only reason you are asking the question is to learn how to answer similar questions (i.e. homework questions), then it is the process that is important, not the answer itself. I suspect most questions fall somewhere between.

(Of course, if you are asking this in order to be able to say to your teacher "See, I was using the right process, you shouldn't mark it wrong just because I made a silly mistake"- one thing you are trying to learn is: Don't make silly mistakes! Your teacher is helping you learn that.)

(One reason for silly little mistakes is not paying close enough attention- which is due to not caring enough about what you are doing.)

 

[honestrosewater]

Matt,
AP- Advanced Placement. They're "college level" courses you can take in high school. Now you know :)
Rachel

 

[cookiemonster]

AP is introductory college level. It's comparable (or at least it's supposed to be) to taking the beginning level class of the subject. Like AP Physics = Physics 101.

cookiemonster

 

[honestrosewater]

****, I can't get anything right around here ;)

 

[cookiemonster]

You certainly weren't wrong! I just didn't think you were specific enough...

cookiemonster

 

[honestrosewater]

Exactly ;)

 

[Ebolamonk3y]

AP=work with Tensors...