How We Should Be Teaching Math

Barbara Oakley, Ph.D., P.E.

Barbara Oakley, engineering professor at Oakland University in Rochester, Mich. writes, "One of my engineering students recently approached me with a mixture of anger and befuddlement, thrusting toward me a quiz sheet covered with red pen marks: "I just don't see how I could have done so poorly. I understood it when you taught it in class."

I smiled encouragingly, but inside I sighed. The semester was just beginning. I hadn't had time to disabuse the student's naïveté. He still thought that because he "understood" the material, he was all set. 

I'm now a professor of engineering, but in my mid-20s I was an artsy language lover who had flunked her way through elementary-, middle- and high-school math and science. What I discovered when I started over at age 26—first tackling remedial middle-school math and then working my way toward a Ph.D. in systems engineering—is that a conceptual understanding only gets you so far. 

Conceptual understanding has become the mother lode of today's approach to education in science, technology, engineering and mathematics—known as the STEM disciplines. However, an "understanding-centric approach" by educators can create problems.
Today's Common Core approach to teaching STEM is at least superficially appealing. The goal of placing equal emphasis on conceptual understanding, procedural skills and fluency, and application is laudable. But as with any new approach to teaching, the Common Core builds on the culture that's already there. And the culture that has long reigned in STEM education is that conceptual understanding trumps everything. So bewildered math teachers who are now struggling to teach the Common Core are leaning on the old thinking, which has it that if a student doesn't understand—in the "ah-ha," light-bulb sense of understanding—there's no way she or he can truly become expert in the material.

True experts have a profound conceptual understanding of their field. But the expertise built the profound conceptual understanding, not the other way around. There's a big difference between the "ah-ha" light bulb, as understanding begins to glimmer, and real mastery. 

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As research by Alessandro Guida, Fernand Gobet, K. Anders Ericsson and others has also shown, the development of true expertise involves extensive practice so that the fundamental neural architectures that underpin true expertise have time to grow and deepen. This involves plenty of repetition in a flexible variety of circumstances. In the hands of poor teachers, this repetition becomes rote—droning reiteration of easy material. With gifted teachers, however, this subtly shifting and expanding repetition mixed with new material becomes a form of deliberate practice and mastery learning.
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Source: Wall Street Journal