In John Noble’s Algebra 10 class, the hills are polynomials. The gold is a wealth of information that his students can pull out of a complex equation.
With a bit of mathematical skill and a problem-solving mind, of course.
Dr. Noble’s students have learned how to take an equation that would mean pretty much nothing to most of us — say, x4 – x3 – 10x + 4x +24 — and milk it for valuable data. They can tell what “factors” multiply together to bring this equation into being and, even more helpfully, what it looks like on a graph. The graph shows all the combinations of numbers that “work” in the equation, from negative infinity to infinity.
The girls now know how to unpack equations for all kinds of useful facts. Where does the line it makes on a graph touch the X and Y axes? How many peaks and valleys does its line have? What exactly is the line doing as it crosses the X axis?
Most of us don’t need this kind of knowledge to live our daily lives. But these girls will, because many of them are headed for calculus — and potentially beyond.
“The graphical analysis skills they are learning are very important to the study of calculus, but they are also important to most areas of higher mathematics,” Dr. Noble said. “Understanding what graphs of functions look like helps in understanding how they might be good models of real-world data.”
