“You mean I have to write stuff in this class?!”
Something I hear all the time in my math classes!
Take it from a college professor — YES, you need to write in my math classes!
Communication. Yep, the most clichéd of statements. True for a reason.
- If you become a professional mathematician, you’ll have to write for publication for other mathematicians and you’ll have to write grant applications.
- If you become a chemist, you’ll have to write reports or white papers that explain either the technical or the business side of your work.
- If you become a novelist, you’ll have to plot your novels, and frankly knowing how to write a proof teaches you to think about how to wrap up loose ends. The romance novelist Courtney Milan was a math major and then a law professor, and she’s definitely putting to use those logical writing skills.
- If you go into business, there’s a good chance you’ll need to write to explain decisions to others.
There are plenty of jobs where you won’t have to write, but college does concentrate on preparing you for jobs in which writing is an asset. Chefs and personal trainers and portraitists and cellists and plumbers don’t need to write, but many do anyway and see career boosts or alternative revenue streams come their way because of it.
(I thought we were talking about math?)
Why is explaining your math reasoning or proving your result at all related to this? Because in math writing, you are focused on proving — PROVING — that you are right. There can be no argument if you’ve done it well. Your work is clear to the reader and has an air-tight argument. This is very different than writing in economics or history class (there will always be a Marxist or libertarian to argue with you), or writing a literary short story (you want people to find alternate meanings!).
Skills for writing your math solutions
A good skill for someone writing their math problems up is critically reading their own work. After you write things down, look for all the problems you can find: unclear bits, leaps of logic, typos, etc. With a poem you wrote about a break-up, you just want to express your feelings and you don’t want to be harsh on yourself. With a math solution, it’s outside you. It’s not about your feelings, it’s a sequence of equations or logical statements with connecting English sentences. This is liberating. Since the math solution isn’t about you, you can rewrite it and argue with it and throw it in the trash and try again all you like! When someone points out a flaw in your argument, you can say, “Yeah, you’re right! … I’ll try to figure out how to fix that!” instead of feeling that they said anything about your self.
Realize that writing up your solution isn’t about showing your thought process, it’s about proving you are right. On some level, no one cares how you got to what you think. (On another level, I definitely do care how you got to it!) Again, liberating. If you got super-confused along the way and then figured it out, you don’t need to show that. You just write up your finished reasoning and make it look good.
Say as little as you can while saying everything you need to say. You need to tell me what k is. If you just start using k and it wasn’t in the problem, I have no idea what you’re talking about. You need to use units if there are units. You need to name theorems or ideas you’re using. You don’t need to explain everything you know that’s related to the topic.
Show the reader what your final answer is and why it answers the question. Gymnasts end routines with their arms up and backs arched to show they stuck the landing; musicians and actors end a performance with a bow. You too have to show you’re done!
I’ll end with a two final exams I have given. One of them is a test for people who are working on getting into a master’s program, so don’t worry if you don’t understand the questions — but notice how many questions ask you explain something. The other was a precalculus final from a few years ago. Again… lots of ‘splaining to do.