Showing Work For Math

There is often a deep mismatch between how showing work is taught in schools versus how the most advanced students experience math. Therefore, I wanted to share this stellar Art of Problem Solving blog post that helps parents understand and communicate with their child why, where, and how showing work matters.

https://artofproblemsolving.com/blog/articles/why-wont-my-child-show-any-work#:~:text=Early%20in%20their%20first%20AoPS,need%20to%20be%20broken%20down.

Here is a quick summary (with a few of my own tips added) :

1) Why to show work:

• When you are submitting answers to someone else, whether on a test or at a conference, you are partly producing answers and partly communicating the steps you took. In this context, it is not about whether or not you know the answer; you are communicating a process to another human who can't read your mind.

• Mental math is excellent for many steps, but sufficiently complex problems benefit from using just enough scratchwork along the way. Mental math exists to speed you up, not slow you down; use paper if that's not happening! If you're using brain space to remember the previous step of your computation, just write it down so that you can use your full brain to focus on the next step. You don't need to waste time solving 2+3 with steps because your teacher said so -- but when you're actually solving interesting questions (and if you want help finding a class hard enough to have interesting questions, please reach out), scratch work should be legitimately necessary because the overall question is complex.

2) What work to show:

• If you are submitting work that will be graded for partial credit, write out enough steps to fully convince your grader that you know how to solve the problem. It's not a matter of needing the steps yourself -- it's a matter of communicating what steps you took so that your grader knows.

• When you solve a problem that involves more than 3-4 steps, write down critical information along the way. This can be a line of algebra, the result of a multiplication step, how you're dividing up a shape in a geometry question, or any other partial progress that gave you a result that you need to remember as you proceed.

• If you are really stuck or confused on a problem, draw a diagram!! This is especially useful when geometry is involved, but it is also very commonly useful for counting and number theory, as well as some word problems for algebra.

3) Where to show work:

• If you are under the age of 15 and taking a math competition, I recommend writing your work for each question on a separate piece of paper. I don't care if all you write down is a single line of algebra or draw a single triangle -- keep your work organized during the test, then recycle later if you feel bad about the trees. Additionally, write the question number in the upper left corner of your page so that you can quickly identify which page is which without extra thinking.

• If you are age 15 or older, then you may either use the above strategy, or separate your paper into an organized grid. The question numbering system should either go down the rows, or down the columns -- either works, so long as you're consistent.

• Regardless of your age, as you solve the problem within the space you've allottted yourself, work from the top of the space to the bottom of the space. If you need more room, use another piece of paper or another box on your page.

• Even if your test provides spaces on the side, use additional pieces of paper if permitted.

Getting your child to show work should not be a battle; there are legitimately good reasons why they should show work beyond compliance, and kids are much more receptive to it when they understand the reasoning. By helping your child comprehend the benefits of showing work, students gain needed life skills with enthusiasm.