I just read an article by What Does Fluency Without Understanding Look Like? In the article, he argues that nobody knows what anybody means by “conceptual understanding.”. The article is an answer to an article in The New York Times written by By Barbara Oakley, an engineering professor and the author of a book on learning. The reason why I found this intriguing is that Barbara Oakley is visiting our school this Thursday to talk about study techniques a topic introduced to us by Olav Schewe this fall. I’m enclosing some paragraphs from the article in the Times here. The discussion that followed is also an interesting read, but probably mostly for those who like to debate the different approaches to learning. One of the comments to her article was this:
Anyone who teaches children that they need to silently comply through painful experiences before they will be allowed to let their brilliance shine has no intention of ever allowing that brilliance to shine, and will not be able to see it when it does.
You can see all the comments here.
I’m sharing some of Barara’s article in the Post here. Perhaps you can use this to start a discussion with your staff. I think it is an interesting view on why girls would tend to think math is difficult compared to language and arts and how they would go from that to assuming that they are not good at math. And she argues that learning is not always fun, and I can relate to that as well. I sure look forward to meeting Barbara this week.
A large body of research has revealed that boys and girls have, on average, similar abilities in math. But girls have a consistent advantage in reading and writing and are often relatively better at these than they are at math, even though their math skills are as good as the boys’. The consequence? A typical little boy can think he’s better at math than language arts. But a typical little girl can think she’s better at language arts than math. As a result, when she sits down to do math, she might be more likely to say, “I’m not that good at this!” She actually is just as good (on average) as a boy at the math — it’s just that she’s even better at language arts.
Unfortunately, thinking you’re not very good at something can be a quick path to disliking and avoiding it, even if you do have natural ability. You can begin to avoid practicing it, because to your mind, that practice is more painful than learning what comes more easily. Not practicing, in turn, transforms what started out as a mere aversion into a genuine lack of competence. Unfortunately, the way math is generally taught in the United States — which often downplays practice in favor of emphasizing conceptual understanding — can make this vicious circle even worse for girls.
All learning isn’t — and shouldn’t be — “fun.” Mastering the fundamentals is why we have children practice scales and chords when they’re learning to play a musical instrument, instead of just playing air guitar. It’s why we have them practice moves in dance and soccer, memorize vocabulary while learning a new language and internalize the multiplication tables. In fact, the more we try to make all learning fun, the more we do a disservice to children’s abilities to grapple with and learn difficult topics. As Robert Bjork, a leading psychologist, has shown, deep learning involves “desirable difficulties.” Some learning just plain requires effortful practice, especially in the initial stages. Practice and, yes, even some memorization are what allow the neural patterns of learning to take form.
Take it from someone who started out hating math and went on to become a professor of engineering: Do your daughter a favor — give her a little extra math practice each day, even if she finds it painful. In the long run, she’ll thank you for it. (And, by the way: the same applies to your son.) Barbara Oakley is an engineering professor at Oakland University in Rochester, Mich., and the author of “Learning How to Learn.”