I’m always encouraged by writers who advocate for “non-traditional” people going into mathematics and science careers (I just recently did a hard-sell to a Haitian-American accountant on the A train between Columbus Circle and 125th Street. She promised she would call me…), but not all help is really “helpful.” This opinion piece, published in our hometown rag, The New York Times, is a good case in point.
I’m totally down with the author’s opening paragraphs, which points out an interesting paradox: if you are good at one thing, and even better at another, you tend to choose that thing which you are even better at to focus your attentions: if a girl is good at math, but marginally better at language arts, being the rational person she is, the girl will go with what she believes is her strengths. This concept of “relative expertise” (my words) both important and novel, and should be explained to all teachers, so they can give students more choices about where they want to put their attentions. Of course, the author cites a “wide body of research,” but does not cite even a single study or meta-study. C’mon, doesn’t evidence count in writing as much as science?
The second place this piece goes wrong is this statement:
“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.”
You know, I’ve been hearing about this (non) issue for over 30 years, and again and again I’ve asked the person to name a single mathematics curriculum that does not advocate for skill acquisition. Each time I’ve been told, “well, I’ve heard about them….” which is the same technique used to promote the myths of the Loch Ness monster and something called “compassionate conservatism.” The fact is this: all teachers know that practice is essential to mastering a skill, whether it is spelling or recalling multiplication facts.
The only question is what is the best way to promote this? This is where Oakley goes further off the tracks: her simplistic education view is that acquiring these skills can only be seen as drudgery worthy of a Charles Dickens novel. Um, message from reality: practice can be fun and lead to long term skill acquisition, if done correctly. Conversely, practice done as a series of mindless and “boring, but this boredom is totally good for you” steps can be both detrimental to the soul and actually diminish performance and understanding.
(One person’s idea of “fun.”)
I’ll cite actual examples from “real” curricula that is out there, because that’s what is called “evidence.” TERC’s “Investigation into Numbers, Data and Space,” as well as the University of Chicago’s “Everyday Mathematics” are both held up as curricula that are “light” on fact acquisition by those who are misinformed. The fact is, both advocate for skill acquisition, but instead of doing it in the traditional way, through endless worksheets, they embed practice through a variety of puzzles and games that can be played over and over again, and can easily be modified to remove “obvious” and “learned” facts. Seriously, do students really need to practice multiplying by 0, 1 and 10?
Along with this, an entire industry of apps has sprung up that promise to help students practice mathematics facts, although I have many criticisms about those as well (and it has nothing to do with whether they are “fun.”) Dr. Oakley clearly has a position to push, but the problem is this: it throws the baby out with the bathwater.
Alternatively, mindless practice, besides being boring (and thus confirming that mathematics is a dull subject where all you have to do is repeat what the teacher showed you), can also be destructive. Imagine a student who has been told to practice multiplying whole numbers by powers of 10 (that is, multiplying by 10, 100, 1,000, etc.) The student quickly picks up that this can be easily accomplished by adding a certain number of zeros to the multiplicand (the first number in a multiplication problem, because these problems always look like “55 x 1,000” and never “1,000 x 55”) and then moving on to the next problem.
All good, right? The student practices a skill, does a few dozen and the skill is tested and then considered “mastered.” Um, not quite: the “add the number of zeroes” property only works with whole numbers! Later in their studies of mathematics, the student encounters “5.9 x 100” and what do they write down? Well, because they practiced and “mastered” this “skill” a few years back, the answer to any reasonably intelligent student is 5.900. And so the teacher has to “unteach” a skill that was thought to have been mastered.
Finally, please allow me to put a nail in the coffin of any opinion piece that uses PISA data to prop up their case. PLEASE STOP USING PISA DATA TO PROP UP ANY ASSERTIONS YOU HAVE ABOUT MATH EDUCATION IN THE UNITED STATES. PLEASE!
We can go through this hundreds of times, but using PISA data to support an argument is not only intellectually weak, it is downright fraudulent, on the level of “fake news,” but even more so, because it is nothing short of “fake data.” I don’t know where to start, but I think this article sums up the issues pretty well. If Forbes can see why PISA data is useless, then you should as well.
So what is the “solution” to encouraging more girls (and I mean girls of color as well) to go into mathematics and science related fields? The answer is not more practice. One of the answers is to give them more “role models,” including Dr. Barbara Oakley, as well as giving them more opportunities to see that you can be good in both math and humanities and not choose one or the other. This is the life story of Maryam Mirzakhani, an Iranian woman who loved novels as a student and applied her appreciation of storytelling to her work in mathematics. Maybe a better use of our girls time would be to watch Mirzakhani at work, instead of completing another round of boring worksheets.
Dr. Oakley could definitely do a lot to advocate for the cause of girls and mathematics, but her prescription lacks any fundamental logic and her conclusions are not only simplistic, but can ultimately be misinterpreted and lead to another generation of girls who are under-represented in the field of mathematics.
Addendum: I contacted Dr. Oakley about my concerns, detailing my misgivings about using PISA data as well as conflating “practice” with “fun.” Her response is as follows:
Thank you for your insights.