The Math Student’s Manifesto

[Feature photo above by Texas A&M University (CC BY 2.0) via Flickr.]

Note to Readers: Please help me improve this list! Add your suggestions or additions in the comment section below…

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.

(4) I can model real-life situations with math.

• I recognize joining, separating, comparing, and sorting situations and can describe them with mathematical expressions or equations using addition or subtractions.
• I recognize proportional, grouping, or sharing situations and can describe them with mathematical expressions or equations using multiplication or division, or with fractions.
• In algebra or geometry, I know how to recognize typical function or shape relationships.
• I can make assumptions or approximations to simplify a complex situation.
• I always ask myself, “Does this make sense?” and try to make my mathematical models better.

(5) I know how to use math tools.

• I can make a chart, graph, data table, or diagram.
• I can use a ruler, protractor, or compass.
• I know how to use a calculator when I need it. I never copy down all the digits on my calculator, but round numbers to the appropriate degree of precision.
• I like to experiment with online graphing tools.
• I know how to look up information online and how to recognize a trustworthy website.

(6) I communicate my ideas clearly.

• I know how important it is to define my words and symbols.
• I don’t misuse the equal sign.
• I’m careful about units of measurement.
• I label my graphs and diagrams.

(7) I look for patterns and use them.

• I know that patterns can make math easier to work with.
• I use common number patterns to simplify arithmetic calculations.
• I use common algebra patterns to simplify equations.
• I use common shape patterns to simplify geometric and trigonometric puzzles.

(8) I make generalizations and justify them.

• If I see a new pattern, I don’t automatically trust it. I always ask, “Does it make sense?”
• I ask myself, “Will the pattern always work? Or does it only work in special cases?”
• I look for ways to explain the pattern in general terms.
• When I find a true general pattern, I use it to help me solve new problems.

[Based on the Standards for Mathematical Practice, translated into conversational English.]