You're sitting in class listening to an algebra lecture when you start to think "Why do my teachers always expect us to do problems THEIR way? Why can't I do it the way that makes sense to me?" Well, I would like to answer that question.

Your teachers are not simply being picky or inflexible. They often have very good reasons for requiring you to use certain procedures to solve problems. One of the biggest reasons is that some problems have only one mathematically correct way to solve the problem. If you find a different way to "solve" the problem, it may or may not be mathematically valid.

When I taught in the classroom and students would ask if they could solve a problem their own way, it would often reveal that they did not completely understand the material. Be sure that you completely understand why your teacher asks you to complete each step before you try any "shortcuts."

Another reason teachers may require a certain procedure to solve problems is that they may be trying to prepare you for the next lesson. Even if you know a different correct way of solving the problem, you may have to understand a new way of solving the problem in order to be successful in the new material.

On a related note, students often do not understand the purpose behind showing their work, thinking, "Why can't I just do it in my head?" Let me give you an example: when looking at the problem x + 1 = 4, most students will be capable of doing the mental math to find that x = 3. However, when faced with more difficult numbers like fractions or decimals (x + 4.25098723 = 10.23894728) or with more difficult problems (x + 3(x - 3) - 2x = 10 - 8x + 2(x + 6)), most students would not be capable of doing the math mentally, or of keeping track of their work without writing it down. In other words, if you don't learn how to do the easy problems properly, you won't have a chance of solving the more difficult problems later.

So next time you are wondering why your teachers demand you do a problem THEIR way, give THEIR way a chance!