My favorite book in that realm is Sheila Tobias' Overcoming Math Anxiety. Her story was being one of those people who had been scared out of math and science. Later, she decided that she liked physics and would slog through the math she had to, that was preventing her from doing the science she liked. Along the way, she discovered many myths that she had bought in to, things that produced anxiety in her when math was mentioned. Hence the title.
In talking with people, anxiety stands out as a major barrier. One of the myths I'll mention here is that some people just have some magical 'math gene' that makes it easy for them, and nobody else can do any math. But it's only math that needs this magical gene. Nobody says "I can't play basketball, I don't have the magic gene for it." Basketball, we all know, you can play regardless. If you practice more, you'll get better. If you want to play professionally, then, yes, you need good genes. And that's probably also true for mathematics. But you don't need to be a professional level basketball player to enjoy playing the game. And you don't need to be a professional level mathematician to do science.
If you had to be professional level at math to do science, I couldn't be doing science. I'm pretty good with math. But, to continue the basketball analogy, I'm more the level of a very good high school player or decent college player. I did earn a bachelor's degree in applied mathematics. But only that much. And that puts me with more math than most scientists -- folks who are doing quite good science.
More specific to pre-teen and early teen age girls is Danica McKellar's Math Doesn't Suck. I mentioned this book before in holding place, and surprised quasarpulse (my daughter) by mentioning it favorably. See her comments there in full.
My pro- comments stand. But quasarpulse's objections also do. Summarizing a little:
Pro:
- The mathematics is explained correctly, and conversationally.
- Beyond the mathematics, there is a strong positive 'you can do it' message.
- For the target audience of middle school to junior high (call it 10-15 years old) girls who are reading or watching stereotypical (and stereotyping) magazines or shows aimed at the same age group, it includes enough references to that culture (personality 'quizzes', for instance) that the book is not alien.
- Too much following the stereotype. To quote quasarpulse ... they seek to feminize math not just by making it look pretty, but by making its content and application appropriately feminine.
My take is that for the level of McKellar's books, most math examples from any book are functionally equivalent to that shopping. In quasarpulse's terms, I think it is merely a matter of painting the power tools pink. In these books, the girls are shopping for cute shoes. In older math books, the examples were shopping for baseball gloves. You understand as much mathematics either way. And if, after going through your math class (or math book), you can't figure what a 12% discount on a $23 pair of shoes is, but only if it were a $23 baseball glove (or vice versa), you haven't really learned the math. But that isn't the fault of the examples.
There's a different matter quasarpulse raised, and on that we're in complete agreement. I just don't think it's an issue to be addressed best by math books. That is the experience gap. People who never do any things like throw balls, run around, play with rockets, build bridges from toothpicks, and so on, find it difficult to learn physics. Usually it's girls who don't have that experience. Best way to address it, I think, is for kids to do and try as many different things as possible whether at school or at home. My ideal math book would also pull its examples widely.
All that said, of the two of us, only quasarpulse has been a girl age 10-15. And she is heading towards her math/science/engineering degree, because of, and in spite of, her experiences along the way. So I weight her opinion highly.
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People who never do any things like throw balls, run around, play with rockets, build bridges from toothpicks, and so on, find it difficult to learn physics.
I guess Lego was my primer for physics then. Maths was very tough though, more due to a missed year of schooling than lack of aptitude (I tell myself that anyhow).
While I also got a little tired of the cheerleader-cum-mathematician examples in either Math by McKellar book, any book that makes math more accessible and understandable -- even workable -- in the minds of its readers is great with me. That said, we all have parts of our jobs/ homework/ etc. that we don't like. But we get better at whatever we practice. For me, math is and always has been a combination of accounting, measurement and geometry. The fun part for me is convincing my students, and children, that no matter what their interests are, they're going to use math :-)
It's interesting that you gave "playing basketball" as an example.
The idea of "playing" is really the key to whether a person will like something or not.
When you like something, you are more likely to do it often ( "practice it") and get better at it, which makes it more likely that you will do it again. the better you get, the more enjoyable it becomes (just as with sports).
But unfortunately, for whatever reason, math is not usually taught as a game to be "played."
That's a shame, because there are lots and lots of great math "puzzles" and even games like chess, backgammon, etc that teach people math and logic skills (even though they may not realize they are doing math!)
yea-mon:
There are a host of reasons other than lack of aptitude that one might not have smooth sailing through math classes in school. Yours is one of the examples. Miss a lot of school in one year, or miss the year entirely, and math will show the problem more than probably any other area. It is, generally, incremental. Still, you make it through and do some catching up.
For you it was Legos. People make their connection to the physical world in different ways. For me, throwing balls (usually in a direction I didn't intend, but that's another story) and building the toothpick bridges was the thing. For my daughter, building and launching rockets was more significant. The reason I like trying a lot of different things is that it's hard to predict what will work for any one person. But I'm confident that if we let our kids play with a bunch of different things, one of them will 'work'.
Anon:
Keep up the good work with your students! They are indeed going to use math. Maybe it'll be fun, and maybe not. But they can do the math.
Maybe it's like me in music as opposed to my sisters. But that's fine, too. (I'm the oldest, by the way.) The thing was, I have no particular talent at music. My sisters, however, are from extremely to unbelievably talented. So the two of them with very little practice sounded quite good and could play the music that they had in band (and so forth). I didn't have that kind of talent. But with a lot of practice, I could sit near the top of my section (and not a small section at that). Ok, I had to work hard to get there. But I did get there. Same as your math students could. (You know this, but you can quote me :-) My sisters being talented and practicing (working) a lot were in a different league entirely. So I got to listen to some good music, at least when I was not playing.
Horatio:
I agree entirely. There is a lot of 'play' possible in math. I invented that for myself at an early age. That, and I discovered that math could help me answer questions that I was interested in (how well does my team have to play to win its division? ...). I then wound up on the route to my applied mathematics bachelor's degree.
I'm not sure where the tragedy occurs. I was talking last week (at the physical therapy center) to a woman who had problems with math. Now she's a grandmother. We're not looking at someone who just had a bad 3rd grade experience and this messed up their schooling. And, as I gently posed the questions, she allowed as how she could do 'practical math' -- but that wasn't, in her mind, real math.
Er, math is math. If you can do mathematical reasoning, it's mathematical reasoning. End, as far as I'm concerned, of the story. But a lot of people have this notion that, basically, if it's math and they can do it, it doesn't count. Grr!
Math is great! So many interesting questions, the issue I have is finding the rights sources and figures to use it for some of my questions. For instance, I'd like to try to show how our carbon dioxide emissions have contributed to the changing pH of the surface waters of the ocean. There's a few things to think about, but maybe someone else has done an accounting like this already. How has the airborne fraction changed with time? Has there been any other factors which would decrease H+ concentration? How much carbon dioxide is taken up by sinks other than oceans? How does all this come together and square with estimated change in pH?
Any help would be greatly appreciated :D
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