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[quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous]The way I explained it to my kid was that 
(1) the teacher didn't actually need to know the answer to the problem.  They need to know whether the kid understands the math.  If you do it in your head and make a mistake, the teacher doesn't know whether you understand or whether you just made a careless mistake. They can't see where you went wrong.
(2) At some point, you won't be able to do the math in your head.  The numbers will be too big or there will be too many steps.  Best to get in the habit of showing your work.
(3) You can get partial credit if you show your work.  [/quote]

This is the most important response. The problem is that with homework, teachers want showing work to include steps and no shortcuts on like 100 problems in hand writing and that's just for one class on one assignment. It's tedious. Especially for somebody who's not making those mistakes.

I remember when we first learned system of equations and would get 20 problems a night and I wouldn't do them and I'd get in trouble. I knew the material and Aced the tests. That's all that mattered. [/quote]

You didn’t ace the tests if you didn’t show your work.[/quote]
Why don't you re-read the part where PP said they aced the test?[/quote]
I believe that they did.  There are very few tests where teachers have the capacity to hand grade and check that work/approach was shown. Certainly not any tests administered online or by scantron or equivalent means. This is, btw, not totally unreasonable when problems are posed in a way that guessing is not possible and cheating is ruled out. In this case, finding the correct answer is sufficient proof of mastery.

In general, though, the details are what matters.  There is probably a tendency by some teachers to ask for work to be shown that's actually not necessary when a subject matter experts evaluates it.  An example would be to show your work when multiplying 7 and 9.  In general, it's highly context dependent as math builds on previously covered topics and techniques. A solution to a problem in a prealgebra textbook must prove facts that later are perhaps mentioned as steps, and even later simply omitted and left to the reader. Or take the simplification of expressions.  This can be spelled out in 10, 5, 2, or 1 steps, and how many are reasonably needed depends on context.
[/quote]

We're differentiating between homework and tests. On the syllabus/syllabi I've seen homework vary from 2% to 10% of the total grade. Tests on the other hand were going to take 10 - 25%, sometimes more for classes I didn't take but heard about from classmates and teachers I didn't take. So I just didn't care about putting that much effort into a problem that is going to take the same amount of time on a homework assignment but only be worth a small fraction of the test question grades while being exponentially more in quantity, it was almost no question that I would do things in my way. Especailly when I was in seventh grade and my first punishment was only -10, so for the year, I was able to simply turn in the answers (show no work) and only lose .10 points off my final grade max. It was a no brainer. Other classes treated homework differently, but no teachers wanted to punish the smarter students too harshly, so I would get stern lectures about the need for work and I'd let them know about how I have no time because I'm playing basketball and lacrosse and debating and running track and keeping a 3.5. Time isn't free.

Then on the tests I would always show my work. For the system of equations stuff for example, I'd use substitution or addition method or something like that to show them I know what I'm doing. But on a test there are whAat 5-10 problems in 60 minutes, thats a lot easier to do and manage. So I would always ace my tests. I hated this type of math though. Proofs are a lot more fun and should be taught in more High Schools. [/quote]

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