"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.