Barbara Oakley, a self-confessed math phobe, nonetheless became a professor of electrical engineering at Oakland University in Michigan, as well as an author. In 2014, she offered some secrets: at Nautilus. Be warned: Her secrets are not “Forget homework!” or “Math is a tool of oppression!” No, this is quite a different message. It’s about neuroplasticity, the ways our brains adapt to our circumstances, to give us the tools we need. But to adapt, the brain needs practice:

Japan has become seen as a much-admired and emulated exemplar of these active, “understanding-centered” teaching methods. But what’s often missing from the discussion is the rest of the story: Japan is also home of the Kumon method of teaching mathematics, which emphasizes memorization, repetition, and rote learning hand-in-hand with developing the child’s mastery over the material. This intense afterschool program, and others like it, is embraced by millions of parents in Japan and around the world who supplement their child’s participatory education with plenty of practice, repetition, and yes, intelligently designed rote learning, to allow them to gain hard-won fluency with the material.

Barbara Oakley, “How I Rewired My Brain to Become Fluent in Math” at Nautilus (September 11, 2014)

What about the importance of understanding the mathematical principles behind the problem-solving?

The problem with focusing relentlessly on understanding is that math and science students can often grasp essentials of an important idea, but this understanding can quickly slip away without consolidation through practice and repetition. Worse, students often believe they understand something when, in fact, they don’t. By championing the importance of understanding, teachers can inadvertently set their students up for failure as those students blunder in illusions of competence. As one (failing) engineering student recently told me: “I just don’t see how I could have done so poorly. I understood it when you taught it in class.” My student may have thought he’d understood it at the time, and perhaps he did, but he’d never practiced using the concept to truly internalize it. He had not developed any kind of procedural fluency or ability to apply what he thought he understood.

Barbara Oakley, “How I Rewired My Brain to Become Fluent in Math” at Nautilus (September 11, 2014)

Thus she emphasizes the importance of constant practice in order to attain fluency — or ease — in an intellectual endeavour, not just understanding:

As I discovered, having a basic, deep-seated fluency in math and science—not just an “understanding,” is critical. It opens doors for many of life’s most intriguing jobs. Looking back, I realize that I didn’t have to just blindly follow my initial inclinations and passions. The “fluency” part of me that loved literature and language was also the same part of me that ultimately fell in love with math and science—and transformed and enriched my life.

Barbara Oakley, “How I Rewired My Brain to Become Fluent in Math” at Nautilus (September 11, 2014)

Perhaps it is much the same in math as in arts subjects. A student who wishes to succeed as a writer, for example, should acquire a deep and accurate knowledge of grammar and style. A grammarian must be sure both of the correct answer and the grammatical reasoning that makes it the correct answer. The stylist must be well aware of the varying impacts of different words. But that understanding is founded partly on the memorization of the underlying reasoning and examples. Thus the knowledge is both instinctive and intellectual at the same time.

So far as math is concerned, all this is a far cry from the war on math currently sponsored by a surprising number of educators.

In 2021, Oakley also shared her thoughts at Expensivity, where, interviewed by Fred Bech, she goes into more detail:

Barbara Oakley: I remember once, after having spent several hours trying to understand a concept on one page, I finally turned the page to discover an image where it all suddenly made sense. If only I’d turned the page earlier, glancing through the chapter ahead of time to get a feel for what the chapter was about! I remember thinking: “Why doesn’t someone write a book about how to learn effectively—something based on what we know from science about how the brain learns?” I was very aware that the way I was studying wasted a lot of my time, and often left me feeling very frustrated. I was blindly feeling my way forward in learning how to learn effectively.

Fred Bech, “Math You Need to Succeed in Life and Business” at Expensivity (December 30, 2021)

Do teachers matter?

A study by the Cambridge, Massachusetts–based National Bureau of Economic Research found that a student can learn as much as three times more from a very good teacher as opposed to a poor teacher. In fact, good teachers can provide as much as a $400,000 lifetime bonus to a student’s income. If the bottom five percent to eight percent of teachers were replaced with average teachers, the added benefit to the economy would be over $100 trillion dollars. The country would simultaneously vault to near the top of international science and math rankings.

Fred Bech, “Math You Need to Succeed in Life and Business” at Expensivity (December 30, 2021)

It feels odd, seeing it put into numbers like that but, yes, teachers matter too.

You may also wish to read: Study: Loss of half the brain doesn’t mean loss of word, face contact. Researchers astounded: Contrary to theory, in a recent study, the single remaining brain hemisphere supported both word and face reading functions. One significance of these findings is that they show that the mind–brain complex in the human being is not at all like a computer — as is often assumed.