Learning to write math is part of learning math
If other people (or future you) can't read how you solved a problem, did you solve it?
You are sitting at a table with your kid after school doing math.
They've just finished a problem, and they get an answer.
When you ask them to explain it step by step, they point to their paper and explain what they did.
Did they write down the steps in explaining how they arrived at their solution?
Can you read it?
Will their teacher be able to follow it and grade it properly?
Can your kid even read it?
What happened in their head may not be what was written on paper
Whether they got the correct answer or the wrong answer, you'll often find that it takes a lot of work to read what they wrote, what steps they followed, and, if they got the wrong answer, where the mistake was introduced.
They may have crammed everything into one long line.
They may have done multiple steps on one line and only one step on the following line.
They may have introduced a sign error without noticing.
They may have made copying from one line to the following line error, either forgetting a term or adding a few extra!
And most surprising of all is that they may have even copied the initial problem incorrectly, so although their work is 100% technically correct, they solved the wrong problem.
Learning math involves learning a sequence of logical steps
Learning math involves using mathematical tools in logical steps to arrive at an answer.
So when someone (you, your kid, your kid's teacher, future kid, etc.) goes to read the math your kid produced, they need to repeat the same sequence of logical steps to arrive at the same answer in their head.
For better or worse (topic for another time), most math seen in elementary, middle, and high schools is learning and applying a technique.
So when your kid does homework, the idea is to check whether they understand the technique through solving a series of very similar, but different enough, exercises that allow for rote application to be tested, as well as whether the kid understands a few (all) of the edge cases.
So the teacher looks to see if the kid
a) Knows when to apply the technique
b) Knows when not to apply the technique
c) Knows the logical steps of applying the technique
e) Knows how to double-check the technique
f) Knows when the technique breaks down (in elementary school, you can't subtract eight from 3... That is, 3-8 is not something they know).
Are all the steps there?
Grading math exercises is a reading exercise for the person trying to understand how the kid solved the problem.
This means that for the kids to show they understand the math, they need to write all of the steps they took to solve the problem so that they are easy to follow, read, and understand.
Mainly because in some (lots of) schools and homes, the person reading the math the kid produced is someone other than a person who enjoys math or fully understands the math they are teaching.
So, the kid needs to produce math that is blindingly obvious to the reader.
It turns out this is similar to a research mathematician producing a paper - if other colleagues can't read what math you wrote, they won't understand what discoveries you are making.
What to look out for the next time you help your math kid
Here are a few things to look out for:
Did they copy the problem correctly
Did they do one operation at a time per line
Can they clearly explain what operation they did and why
Is the answer written so that someone else would know that is the answer?
This will help them develop their writing and math skills early, which will benefit them in higher grades, into college, and afterward. You'll often hear people, and I say this as well, that one of the great things about doing math is that it forces writing and thinking to become very logical and straightforward, which is helpful in academic and non-academic settings.
Even if you don't have a math background, you'll learn some logical thinking alongside your kid and help them be able to speak how they solve problems.
The perseverance in mastering this aspect of math will be helpful to their public speaking as well.
Best of luck, and enjoy the math!
Until next time,
Sebastian