I've been asking students the following question for years: "Why do you show so little work, and where are you completing the problem?" Most students I have worked with write less down than I do, and I have quite a bit of math under my belt. I still have not found the answer to this question. Some students say it’s because they don’t see the point, but they have been cheated if teachers have given them credit for answers without work. As math gets complicated there is more and more work that needs to be done, and if a student has bad habits of doing mental math, then this will be a hindrance to success.
These are things that all students of higher mathematics should do:
1. Write the original problem down. When solving problems you want to make sure that you are staring at the actual problem. You don't want to look at your paper and then back to the book or sheet of paper that the problem is on.
2. Show your work just like your teacher does when they are introducing the material. It is not a sign of weakness to show work, it’s how the problem is supposed to be worked out. It’s just a good habit. Sure sometimes it’s something that you can do in your head, but what does it hurt to just write it out.
3. Plug your solution into the original problem whenever you can. If you do this, then you don’t even need to wait to see if you got it right, you can tell immediately. It’s like immediate feedback.
4. Does your answer make sense? Take a look at the answer and see if it would make sense in the context of the problem.
5. Make sure you can read your own handwriting. Don’t write too small and make sure your numbers are legible. If you can’t read your own writing, it will be harder to get to the correct answer.
6. If a shape is being discussed, draw a diagram when necessary. This visual representation can be good for any kind of learner, not just the visual learner.
7. If you are stuck on a problem, start writing down things that you know, and see if you can solve for something. Sometimes you have to solve a couple of things to get to the answer the question is asking for.
These are some tips that can help each student be more successful in mathematics.