I agree because when you are thinking mathematically, you think of reasons why things could happen. When you are doing math your just doing the writing and not the thinking. Thinking mathematically, you think about WHY things happen the way they do. Mathematical thinking helps you understand things better. Thinking mathematically also helps you solve an answer to it's most accurate or the exact answer. Doing math is just plain writing and solving problems. Maybe a bit of critical thinking, to solve a problem logically, other than that though.... Nothing interesting.
Characteristics of a good mathematician...
- Thinking logically (Critical Thinking)
- Thinking of ways to make things easier, simpler
- Writing neatly
- Thinking why things happen
- Checking over your answers
- Trying your best
- Trying to deepen your understanding of something if you don't understand it