The Big Idea

Matthew Bardoe

Ask a math teacher (as I have) what a "big idea" in math is, and you are likely to hear, "The quadratic formula." Unfortunately, the quadratic formula is just a disposable fact, essential to some but inconsequential to others. The value of math education must be found in its lasting benefits. As the response about the quadratic formula shows, teachers often don't have a strong idea of the value of mathematics.

It starts with expanding children's abilities in two central areas:

• Abstract Thought: Abstract thought is so essential to mathematics that we often overlook it. We treat things like "three" as a noun, as in "Subtract the three." But in reality, three is an adjective. It is a word that describes a quantity or value. In mathematics, we see the universality of threeness. There can be "three" of almost anything, and that concept has value beyond a specific situation.
• Logic: The mechanics of reasoning are behind every math problem. Logic is a fundamental tool in any discipline, but mathematical abstraction truly distills these rules of thinking.

Abstract and logical thinking are immensely valuable skills, but to what purpose? The value of math is made substantial by its vast number of connections to real-world, practical applications, such as measurement, statistical inference, engineering, or computer programming.

• Connections: The majority of concepts taught in math classes today have such a huge array of purposes. In fact, the universality of math is often a burden for math teachers. It is impossible for one teacher to reasonably describe all the ways in which each piece of math connects to students' future lives.

Is the value of a vaccination the pain of the needle? No, it's the vaccination's capacity to effect lasting resistance to a disease. Math is similar; the value of the quadratic formula is not as an incantation, but that in all subjects we can use abstraction and logic to solve a whole range of problems rather than solving them one at a time. Didn't know that? Maybe that's why so many people question the value of math.

Matthew Bardoe is a middle school/upper school mathematics teacher at the Latin School of Chicago. He received his doctorate in mathematics from the University of Illinois at Chicago. Visit his blog about mathematics education at http://mattamatical.blogspot.com.