Women are increasingly prominent in medicine, law and business, yet not in science, math and engineering. A new report released by the American Association of University Women points to environmental and social factors.
The report cites a promising statistic: the rapid increase in the number of girls achieving very high scores on mathematics tests (once thought to measure innate ability) suggests that cultural factors are at work. Thirty years ago there were 13 boys for every girl who scored above 700 on the SAT math exam at age 13; today that ratio has shrunk to about 3:1.
In a nutshell, from the report, these are the cultural factors at work:
1. Stereotypes that boys are better than girls in math.
2. Beliefs about innate intelligence that are influenced by stereotypes.
3. Girls assess their math abilities lower than do boys with similar math achievements.
4. Boys outperform girls in spatial skills.
5. There's a need for more courses that provide a broader overview of the STEM fields in introductory courses to attract more females.
6. Departmental culture in STEM fields can be improved to promote the integration of female faculty.
7. People have an implicit bias to associate science and math fields with "male" and humanities and arts fields with "female".
8. There's a workplace bias because people often hold negative opinions of women in "masculine" positions, like scientists or engineers, making it more difficult for women to succeed.
These nuggest are just scratching the surface of the 134-page report, which goes into depth about each of these barriers.
I personally find implicit bias to be very fascinating. Mahzarin Banaji, who's one of the leaders in that work, has an online implicit bias test that people can take to identify and understand biases they may not realize they had so that they can work to compensate for them. It may surprise you!
Steven Strogatz strikes again! Don't miss the latest installments of this wonderful series of articles on math for the general, adult public. He is working his way up the curriculum, the latest article dealing with geometry and square roots.
One of the highlights for me was his suggestion that we use little square crackers to mess around with the Pythagorean theorem, satisfy ourselves that it works, and understand why. Cheez-Its came immediately to mind.
What I love about this series is that it aims to take some of the bad mystery out of topics in math and replace it with good mystery -- decreasing that ratio in our systems, perhaps a bit like bad cholesterol and good cholesterol.
While keeping things interesting for the math conversant, he speaks directly to the math-apathetic, the math-fearful, and the math avoiders, and is probably changing more than a few minds.
It's all too familiar: A student prepares for a math quiz by looking at the example problems and solutions and thinks to himself, "Yep, that makes sense," and proceeds to not do any of the practice problems. He thinks he knows the math, but he doesn't, and his grade confirms that.
What happened and how can it be prevented?
In a Washington Post blog post last week, Daniel Willingham tackled that question through his lens as a cognitive scientist and researcher.
Feeling that you understand material as it is presented to you is not the same as being able to recount it yourself. And that false "feeling" comes from familiarity with the information (which, in the above example, was accomplished by looking at example math problems) or knowledge about related material. Willingham goes into depth about research studies that illustrate how our mind can trick us:
"...subjects saw a set of trivia questions, some of which used words that the subjects had just been exposed to in the previous task. Subjects were asked to make a rapid judgment as to whether or not they knew the answer to the question - and then they were to provide the answer. If the trivia question contained key words from the previous task...those words should have seemed familiar, and may have led to a feeling of knowing. Indeed, researcher L.M. Reder found that subjects were likely to say that they knew the answer to a question containing familiar words, irrespective of whether they could actually answer the question."
To combat cognitive roadblocks, Willingham suggests making it clear to students that the standard of "knowing" is the "ability to explain to others," not "understanding when explained by others." In other words, knowing is not simply familiarity. From personal experience, I couldn't agree more. One of my favorite professors would give us time to solve review chemistry problems at the start of class before showing the answers, walking down the aisles to see when the majority of the class was done. Those couple of minutes were key to my learning. So many times, my feeling of knowing was challenged once I put my pen to paper, which kept me on my toes day to day.
Maybe it would be helpful to have a lesson on the tricks of the mind for both teachers and students.
M.K.T. stands for Mathematical Knowledge for Teaching - and could be the key to more effective math teaching. M.K.T. is not a new concept, but was featured at length in this weekend's beefy New York Times piece, "Building a Better Teacher", by Elizabeth Green.
M.K.T. is the brainchild of Deborah Loewenberg Ball, one of the nation's foremost experts in teaching education. The article describes M.K.T. neatly:
"Mathematicians need to understand a problem only for themselves; math teachers need both to know the math and to know how 30 different minds might understand (or misunderstand) it... This (is) neither pure content knowledge nor what educators call pedagogical knowledge... It (is) a different animal altogether."
This means that an algebra teacher, for example, needs instantaneous access (think ACME delivery) to a deep understanding of the many, many ways their students might go wrong - enough to get there with them, AND bring them back.
Ball has done research showing a correlation between a teacher M.K.T. and student performance that outshines any other. But as you'll see if you read the full article, figuring out how to convey M.K.T. to student teachers has proven elusive.
There's tons of food for thought in this comprehensive article, and I've touched on only one aspect. Be warned: it may have you jumping up and down in excitement, or rage, or both.
Photo credit: http://www-personal.umich.edu/~dball/
This was the question posed by James Gee of Arizona State at the annual meeting of the American Association for the Advancement of Science. ("First_Person Solvers: Learning Mathematics in a Video Game")
Stay with me; this not the usual old wine. Gee is basically inviting us to steal ideas that work, and points out that we can do this with or without technology.
Think about your basic video game environment. I mean really think about it, if you can bear it. (This part is hard for me.) What works? Break it down to its elements, and then picture how those might translate to the classroom. Gee highlights the following:
- Feedback is immediate, continuous and plentiful.
- Information is provided when it is needed, near to the point when it will be used (rather than all at once, as is often the case in the classroom).
- Game designers encourage "modding," and this invites meaningful engagement. ("Modding" is when players use the actual game software to modify or add to the game.)
- The environment is a big "problem-solving space" which Gee calls "pleasantly frustrating. The tasks are challenging but doable. That's a very motivating state for human beings," says Gee.
If you know your video games and what makes them tick, let us hear from you. What you might add to this list? A sense of accomplishment and progress? A game's multiple entry points? The ability to personalize an experience? Is it modding when your students write a story problem? (Do you like just using the word "modding"? I do.)
Most importantly of all, what do these things look like in the math classroom? What are you already doing that has a parallel in the world of video games? What features, small or big, could you see yourself adopting? It's an interesting thought experiment -- please do let us know if you make it a real experiment.