What does a mathematician do?

We live in a world filled with mathematics. You measure and count from the moment you wake up. A measuring and counting device, called a clock, probably wakes you. There is a lot of mathematics behind the design of clocks.

Barkley and Ted realize that mathematics is not just numbers and number facts. Mathematicians look for and describe patterns. Applied mathematicians may use what they've learned to draw conclusions about the world, or they may look for these patterns simply because it's fun.

Mathematicians begin with a set of basic assumptions that seem reasonable. From these ideas they develop systems of thinking that are useful in solving problems and working in the real world. Euclid's geometry is one example of a system of thinking that is used by builders and physicists the world over.

Mathematicians use a common vocabulary, conventions, and similar experiences to share what they learn with other mathematicians. In many ways, we are all mathematicians as we recognize patterns and apply abstract concepts.

The National Council of Teachers of Mathematics (NCTM) has identified several topics or strands of mathematics important for all learners. These include:

• Number and Operations - the ability to understand numbers and the meanings of operations and how they relate to one another
• Algebra - the ability to understand patterns and relationships
• Geometry - the ability to analyze characteristics and properties of geometric shapes and locations
• Measurement - the ability to apply techniques, tools, and formulas to understand an object's attributes that can be measured
• Data Analysis and Probability - the ability to select and use appropriate statistical methods to analyze data
• Problem Solving - the ability to solve problems and build new mathematical knowledge through problem solving
• Reasoning and Proof - the ability to recognize and use various types of reasoning and methods of proof
• Communication - the ability to communicate mathematical thinking to others
• Connections - the ability to recognize and understand how mathematical ideas interconnect and build on one another
• Representation - the ability to create and use representations to model and interpret mathematical ideas

NCTM would agree with Barkley's computer that there's much more than numbers and number facts to mathematics and what mathematicians do.