Unlocking magic of math requires confidence, tenacity

There has been increasing discussion about preparedness in STEM subjects. The focus on science, technology, engineering and mathematics often drifts away from the central issues that subliminally affect all of us, specifically in mathematics.

Is proficiency at four-function operations — add, subtract, multiply, divide — mathematical proficiency in general? Is it only geniuses who can learn math, or is it accessible to the rest of us?

From the Principles and Standards for School Mathematics: "A good student not only understands how and when to use facts, procedures and concepts, but he or she also wants to figure things out and perseveres in the face of challenge."

The heart of mathematics is arithmetic. Math originated with writing, counting and record keeping. Arithmetic is nothing if not a formalization of counting, with the added sophistication of a system of shortcut rules known as the four functions.

Understanding addition, subtraction, multiplication and division as rules helps to remove some of the mystery and fear, but with too much focus on the rote, the magic behind the curtain is either glossed over or omitted.

For example, counting in groups and adding is a great timesaver over counting a whole lot of things all at once. Think money. Banks transfer cash wrapped in counted bundles, or in bundles of bundles, which involves multiplication.

Distribution of bundles is easier and more efficient than recounting everything. Let us say there are 1,000 bundles to distribute evenly to five receivers. OK, 200 each, no problem.

Now to divide the bills, imagine tearing apart the bundles, separating all the bills, then dealing them out like cards to each receiver one at a time, and then recounting them.

Likewise, fractions are easier to understand using pies.

Try adding one-half, one-third and one-sixth using arithmetic. Then try it again using a pie. Cut it in half, then cut one half into three pieces and try it again. If that does not make it clear, then cut the other half into three pieces.

Expanding this intuition into decimal numbers, geometry, trigonometry and graphical representations is a logical step that is not broached properly to allow students to think through problem solving in related areas such as physics, chemistry and engineering.

Although higher math may be too complex for many people, basic math is only out of reach because classroom activities do not pursue it above rote memorization. So frightening to students are word problems that curricula often drop these entirely. Yet in solving word problems lies the core of mathematical reasoning that relates numbers and operations to other subjects and real-world problem solving.

In October, authors Miles Kimball and Noah Smith summed it up succinctly in the Atlantic magazine: "For high-school math, inborn talent is much less important than hard work, preparation, and self-confidence. … The idea that math ability is mostly genetic is one dark facet of a larger fallacy that intelligence is mostly genetic."

Until we stop thinking that being bad at math is funny or cool, or that we are born without math ability, fearing it will continue to be socially acceptable, and the United States will continue to lag behind the rest of the world.

Richard Brill is a professor of science at Honolulu Community College. His column runs on the first and third Fridays of the month. Email questions and comments to brill@hawaii.edu.