[Feature photo above by Texas A&M University (CC BY 2.0) via Flickr.]
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What does it mean to think like a mathematician? From the very beginning of my education, I can do these things to some degree. And I am always learning to do them better.
(1) I can make sense of problems, and I never give up.
- I always think about what a math problem means. I consider how the numbers are related, and I imagine what the answer might look like.
- I remember similar problems I’ve done before. Or I make up similar problems with smaller numbers or simpler shapes, to see how they work.
- I often use a drawing or sketch to help me think about a problem. Sometimes I even build a physical model of the situation.
- I like to compare my approach to the problem with other people and hear how they did it differently.
(2) I can work with numbers and symbols.
- I know how numbers relate to each other.
- I’m flexible with mental math. I understand arithmetic properties and can use them to make calculations easier.
- I’m not intimidated by algebra symbols.
- I don’t rely on memorized rules unless I know why they make sense.
(3) I value logical reasoning.
- I can recognize assumptions and definitions of math terms.
- I argue logically, giving reasons for my statements and justifying my conclusion.
- I listen to and understand other people’s explanations.
- I ask questions to clarify things I don’t understand.