First:

in a real world situation, it is wonderful to be able to solve a problem in various ways. The fact that you can rationalize the problem and draw upon alternate methods of solving is excellent. It shows that you truly understand the question and can think through the matter.

(Here comes the ‘but’)

However:

the goal of your algebra class is to teach algebra.

It is not really about solving those specific examples.

Many examples in the book and on the board can be solved mentally without algebra. That is because you are just being introduced to the material. You are not ready for the very complicated problems. Unfortunately, the ‘very complicated problems’ can ONLY be solved using the logic and techniques taught in algebra.

Summary:

¤ If you solve these early problems using non-algebraic techniques, you won’t get practice in using the algebraic methods.

¤ If you don’t practice the algebraic methods on easy problems, you won’t be able to do the harder problems.

¤ The harder problems CAN NOT be solved with non-algebraic techniques.

¤ For the harder problems, algebra IS the most EFFICIENT way.

Hope that makes a little sense. I always try to explain to my students that these examples are to prepare them. The examples are not the goal of the course. The goal is thinking in a logical manner to develop an accurate mathematical expression. Solving the expression is actually the easiest part!

Your teacher makes you show your work because unfortunately, s/he can’t get inside your head to check that thought process. It isn’t so much the arithmetic and answers that the teacher is looking for, as do you “get” the process. Showing your work, as boring though it may be, is the only way to evaluate your work. If you’d rather have zero’s, that’s your only other alternative…

It’s not about being efficient. It’s about training your brain to be able to reason through really abstract things (like trig and calculus) down the line. The practice problems are what forms those pathways, those habits in your brain – of course there’s a more efficient way to solve them, but the answer isn’t really what’s being worked toward here. The process is.

I think what the problem might be is that your teacher didn’t explain the reasoning behind Algebra – why it is so different from other math classes you’ve taken in the past. The arithmetic that you’ve learned up till now has probably been very concrete – you have the info, you need an answer, you solve for the answer. Boom, you’re done. Algebra is a whole different ball game: say a question is worth 10 points. You get the answer wrong because of a silly arithmetic error somewhere, but your process was still completely correct (and you bothered to show your work). In most cases, you’d still get 8 out of 10 points for it, because you met the main objective of the thing.

I know it seems wierd, but there really is a purpose for it. And while you might not like it…it is required to graduate. It’s one of those things that you may see the purpose for today, in 20 years, or never – but it does have a purpose.

My advice would be to trust your teacher on this one and learn what they have to teach you. If you decide to never use it again, well, that’s your choice; but if you learn the thought processes now, the concepts rather than just the answers, you’ll find that a lot of other things come easier to you later in life.

Think of it like you go to a gym. The weights trainer teaches you about how to lift the weights but you figure out a way to lift more weight by doing something different. What happens? You don’t get the effects the gym was suppose to give you. It was never about actually lifting weights, it was about becoming stronger. Its the same with the math, no body cares if you can get the right answer, they care that you become mentally strong and brilliant, and the best way is through the process not with just the answers.

Now I am a teacher, and the reason why you have to show work is because of statistics and such. You personally probably don’t need to show work on algebra. You will need to show work on higher level math, but if you know how to work through problems you’re fine.

However, for every you, there are probably 4 more kids that think they can do the problems and they can’t.

Also, kids cheat and showing your work is less about you sometimes, and more for the teacher to know that you did the work.

And since you sounded similar to me until the clueless rant about efficiency (if you really can’t figure out why, you have no business questioning anything really), here are some things that I enjoyed doing as a form of revenge in math classes.

1. When you go up to do work on the board, go Calvin and Hobbes style. Start adding 7 to each side, divide by 18, take a squareroot, all for no reason. It will confuse everyone, especially if you have the reputation in the class as the smart kid that is better at math than the teacher.

2. Read about math at home (it’s very interesting when you get to higher level math, don’t think that what you learn in high school is math, that’s just numbers). Then ask your teacher questions about higher level math and see if they know they’re stuff.

Also, if you truly hate showing work, this is what I do in my class and I like it. I reward for showing work a lot on tests and such.

My grading goes like this

Right answer no work – full points

Right answer with work – full points

Wrong answer no work – 0 (out of a lot sometimes)

Wrong answer with work – ranges depending on the quality, but getting 5/10 instead of 0 for the same answer is usually worth it.

Ask your teacher about it, the only dilemna is cheating, so you’d have to convince them of that.

As for showing your work, math class is not only about finding the correct answer, but learning different techniques on how to find them. A teacher is not only grading you on your answers, but also your thought processes. A student can find the answer to 5x+3=13 without algebra; he can just guess and check using arithmetic. However, this is an algebra class, not an arithmetic class and using no algebra shows you have learned nothing. I have had experiences where teacher give me full credit for a problem with a wrong answer because I did all the work correctly and my only error was a small arithmetic mistake.

first of all, you seem to be very bright. things make sense to you in ways that they don’t to others. you probably get good grades in math, don’t you?

second of all, thank you! i hate it when teachers or textbooks show you one way to do something then in the next lesson they’re like “oh, by the way, here’s the easier way to do it”.

anyway, algebra is to teach us different ways of thinking about problems; being able to look at a situation from many different perspectives. because sometimes the easiest way to solve a problem won’t be possible because of a lack of information or whatnot.

they also have to teach us the methods in the textbook and such because those are the methods that standardized tests expect us to know. sometimes questions on those tests will ask you the answer to a problem and then ask you to show how to get that answer using a certain method. if you are unfamiliar with the method, you lose points.

i’m sorry that i’m giving a reason for why teachers and textbooks do this to us, it frustrates me as well. but it’s always good to be able to look at things from the opposing side’s point of view. hope this helps.

But it IS SO

There is a METHOLOGY

Don’t ask why

There just is

I hate it

I solve problems at the CROW FLIES

But that is NOT Algebra

We have to live with it