Dear math students,
As you work through your mathematics practice, I’m going to challenge you to embrace making errors in an entirely new way.
Many students believe that every problem in math homework should be perfectly constructed with no errors. It might look something like this:
But when it’s time to study after the initial problem run-through, what does this perfectly constructed problem say? Does it coach you on remembering how you struggled? Does it remind you where you made an error? No.
When you make an error as you’re working a problem, please don’t erase it from the face of the earth. Certainly you should learn from the struggle and complete a correct solution, but record your deviations from the straightforward solution path in another color. Leave yourself notes (also in a different color) to remind you what you should have paid more attention to the first time around. Maybe that would look something like this:
Sometimes you’re going to recognize but you don’t have the right answer but you’re not going to be sure what’s gone wrong. You should always try first to figure it out yourself first. This process of error analysis in a variety of different situations is key to developing problem solving skills in mathematics. Without exploration of the problem space (which happens with error analysis), your brain is just recording rote procedures without the ability to transfer those procedures to new kinds of problems. It will, essentially, stunt your mathematical growth.
Now, I don’t want you to get to the point of tears or breaking your keyboard out of anger. If you get near that stage please just ask a question (email, discussions, chat-a-friend, etc), leave a sticky note on the page as a reminder to go back, and move on to the next problem or section of problems. Just switching to a slightly different problem can not only get you unstuck, but sometimes give you insights into the “stuck” problem.
When you figure out how to do the problem you were stuck on, make sure to go find that flagged problem (remember the sticky note?) and annotate your corrections.
Now you might be thinking “why do all these error corrections and problem annotating in another color?” When it comes time to study for your major assessments, you will be able to see the places where you stumbled the first time you tried the problem. These “notes to self” are the places where you’re most likely to make the same mistake again. They benchmark places to remember to be careful and show you problem types to repeat practice before an exam.
Celebrate your errors.
Embrace the messiness.
Learn from your mistakes.
Study from your struggle points.
And be great at mathematics!