"But I got the answer right."

"You didn't show your work."

"But I got the answer right."

"You didn't show your work."

"What's the big deal?"

"Ok. The answer you wrote is 14x. Can you prove that you did not guess it?"

No response. Now do you know why it is important to show your work?

The concept of showing your work when you deduce the answer of a math problem shows all the steps that were required to arrive at the correct answer. For example, the answer to the following problem (4 + 2) x 3 is 18. How is this answered arrived at? We can see how it is arrived at by actually showing the work:

1.) (4 + 2) x 3

2.) 6 x 3

3.) Answer is 18.

Of course, this simple math problem is very easy to answer incorrectly because many people violate the PEMDAS principle. (PEMDAS stands for the order then you need to follow when solving a problem: parentheses, exponent, multiply, divide, add, then subtract. Then, this order is followed step by step to arrive at the correct answer.

Primarily, the main person you do a favor for when you show your work is yourself. That is, showing your work greatly allows for a reduction in the potential errors that you may make. After all, if you have all the steps written out in front of you then the chances for an errant omission of a major part of the problem solving process is reduced. Sure, accidents happen and people make mistakes, but you want to reduce the potential for making mistakes.

Let's go back to the example of (4 + 2) x 3. If you were to tell someone to answer that in his or her heard they may come up with the answer of ten. But, look at the steps they followed:

1.) (4 + 2) x 3

2.) 4 + 6

3.) Answer is 10

The final answer is correct but showing the works displays a critical flaw in the student's skill. He divided before he multiplied. In this particular situation, the answer may be the same as the proper way to solve the problem but what if the math problem was the fact that the parentheses step was completely ignored. Because of this the student multiplied with adding the numbers in parentheses first, This is because he added first and then divided. The correct answer, however, is:

1.) (4 + 2) x 3

2.) 6 x 3

3.) Answer is 18

Clearly, showing one's work provides an insight into where problem areas may lie. This is a critical component to the instructor's ability to isolate and correct the student's mistakes and get him or her back on the right track. For a student who lacks mastery in a subject trying to solve a problem in your head is not the way to go. Instead, put it all on paper and person you save may be you.

When it comes to showing work it is critical to show the work in a complete and clear fashion. That is, it can not just be understood by you but it must be understood by anyone else who reads it - particularly the person grading your test. Jotting down loose or fragmented bits of your work in a sloppy manner will not instill the confidence in the instructor that you have truly grasped the concept of solving the problem. It also does nothing to disprove a notion that you arrived at the answer through guess work. So, let's repeat: show all work completely and in a neat and clear fashion.