Show Your Work!

Summary: Every instructor tells you to show your work, but surprisingly many students just write bare answers. This page explains what, why, and how.

What Your Instructor Means

Showing your work means, when any calculation is involved, writing down enough to let someone familiar with the course reproduce what you did. If a classmate or your instructor can tell how you reached your answer, without having to guess, you have showed your work.

Source: What’s so Funny about Science by Sidney Harris (1977)
(Permission requested 2013-03-24 of sciencecartoonsplus.com; awaiting reply)

Why It’s Important

There are several good reasons:

• Showing your work in an organized way helps you organize your thoughts, which in turn makes you less likely to make a mistake.
• On homework, usually you have answers available. If your answer doesn’t match the book’s answer, showing your work helps you figure out what you did wrong. It can also help a tutor figure out what you did wrong, if you go for help.
• On tests, if you get a wrong answer your instructor can use your work to figure out what you didn’t understand, and point it out so that you avoid that mistake in the future.
• On tests, if you get a wrong answer but your work shows you understood the core of the problem, most instructors will allow partial credit. A bare answer that is wrong has to count as a zero.

You may still think of this as an extra requirement. After all, when you’re out in the real world, all that matters is getting the right answer.

That’s true, but there’s a difference between being in the real world and preparing for the real world. (Last I checked, when you get a wrong answer in class nobody gets injured or goes bankrupt.) Your job at school is to learn thought and work habits that ensure you will get the right answer when there’s nobody around to check you. And part of that is exposing your process so that problems can be corrected.

This is so important that I give only half credit for a correct answer that earns a WTCF, which stands for “where’d this come from?”

How to Show Your Work

When solving an equation, write down the equation and then show each step on a separate line below. If you divide both sides by 20, show that. If you add 2x²−3x to both sides, show that.

When evaluating a formula, write down the formula in letters, then on a separate line below show the formula with the letters replaced by numbers. Then show the evaluation. If you can finish in one step on your calculator, your next line will be the answer. If you need more steps, write down each one on a separate line.

Many statistics procedures on the TI-83 involve setting some numbers on screen, selecting a menu item, and then reading off the answer. Remember the principle: show enough that someone familiar with the course (which includes the calculator) can reproduce what you did. Here are some guidelines:

• Don’t do double work. There is no need to work out something like standard deviation by formula when your instructor lets you use the calculator.
• Focus on commands, not keystrokes. If you’re doing 1-VarStats L1,L2, write that. For pity’s sake, don’t write [STAT] [►] [1] [2nd] [L1] [,] [2nd] [L2] [ENTER]. Someone familiar with the course knows how to get the 1-VarStats command and how to get L1. All those keystrokes take longer to write and are harder to understand.
• Show all command arguments. If you’re using randInt to get five random integers from 1 to 100, write down randInt(1,100,5). That’s the only way your instructor will know that you know how to use that function. If you think the command is randInt(5,100), now is the time to correct that misunderstanding.
• Abbreviate repetitive information. When you put a column of numbers into list 1, you don’t have to write down the column and say “L1”. Instead, just write “x’s in L1” (use the actual column description if it’s not “x’s”).
• Show inputs first, then outputs. Many students show their answer, then as an afterthought they write down the command. It is best to write down the command before you enter it in the calculator. When writing down the outputs, you can omit any that are the same as the inputs or that you don’t use to solve the problem.