Let me just say, first of all, that I had a great bike ride today, and although I may have worked so hard I’ll still be tired on Saturday when I race next, I don’t really care. I wouldn’t want to not have done this ride today. Really, great training rides are SO much more fun than races. Sometimes I feel like my racing gets in the way of my riding.
Anyway, I rode with Hobgoblin and two other friends with whom we’ve got a semi-regular Thursday ride going. We rode for three hours, although we were out closer to four when you count the stop at the coffee shop, the stop to fix a flat, and the stops to regroup. It was a fast ride, something over 18 mph (fast for me), covering 56 miles. We rode down to the Long Island Sound and back, and the weather was beautiful — in the 70s and dry. We couldn’t have asked for a better summer day.
But now on to books. I’m really enjoying Keith Devlin’s The Math Gene and am about half way through it. I like math a lot and wish I knew more about it. I haven’t studied it since high school, since I got far enough there to test out of my college requirements. It didn’t occur to me then to study it just for fun, although it occurs to me now; someday I’ll take math classes at my school, since I can do it for free.
But even if you don’t enjoy math or think you aren’t good at it, you can still read and get something out of Devlin’s book. He’s very good at writing for non-math people, and, in fact, large portions of his book are devoted to the question of why some people just can’t seem to do math — or think they can’t. You won’t be surprised to learn that he doesn’t buy the idea that some people simply can’t do math; he argues that those people haven’t been taught to understand what math is all about — they don’t get it because they don’t understand the meaning behind it. They were taught rules but have no idea what the rules mean or why they matter. This makes me appreciate my high school calculus teacher who took great pains to teach us just what calculus is useful for and how it began.
My favorite part so far is where he gets into some actual math instead of talking about it more generally; he has a section of a chapter where he explains group theory and gives the equations that explain some of the relevant concepts. He introduces this section by saying that it’s okay to skip it if the math becomes too hard, although skipping it will mean you won’t understand all of his later points fully. Of course this laid down a fun challenge, and although I struggled a bit, I made sure I understood what was going on with those equations. But I also like the way he takes care to reassure the reader that not getting it is okay. He’s a very kind and understanding author that way.
The book is also fun because it explains things like why lots of people count on their fingers, why parts of the multiplication tables can be so hard to remember (why many people, including me, have to think a bit about problems like 8×7, 8×6, and 9×6), and why Chinese and Japanese students tend to do better at math in school than Americans. This is not entirely explained by the relative quality of education, but it also has do with language: numbers are easier to learn in Chinese and Japanese because the words for numbers are easier. One study shows that most Chinese and Japanese children can count to 40 by age 4, while it takes American children one year longer to reach this point. We know this difference is due to language because, interestingly, there are no differences among these children when it comes to learning numbers 1-12, numbers that are easy to learn in English as well as Asian languages. It’s the numbers 13 and beyond that trip American children up because of the complicated way they are formed.
Devlin is excellent at explaining things — at using clear examples and telling interesting stories. If you aren’t a “math person,” but are at all tempted by this, be reassured that he makes the subject accessible and interesting. I’m looking forward to the book’s second half!
Of Books and Bicycles 
I was dismal at math in school. As a matter of fact one year I had to take summer school to ensure I could stay with my friends in regular math class in the Fall. I think he’s right about having good teachers that take the time to explain the concepts. I think it’s possible to have a teacher that is a great mathematician or scientist and really know his or her stuff, but not able to convey it to the class in a meaningful way and then forever thereafter you’re lost!! My niece does really well in math and I hope she keeps it up and try to encourage her lots. I’d love to study math and science now–maybe I should check out the Devlin book, too!
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This book does sound like a lot of fun. I loved math in school but then just kind of gave it up when I discovered foreign languages. It’s only now that I realize you lose math when you stop using it. I may have to find this book and check it out as well. Thanks!
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Emily made it sound like fun, now you are making it sound like fun! I am a confirmed finger counter, always have been. I also live with a human calculator. He tries to explain to me “easy” ways to do large-number math and percentages in my head but I just can’t. Fingers rule!
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What a great-sounding bike ride (but a little long for me). Your take on the book may help you understand what I do in my job, which is to help teachers learn to get away from teaching through the memorization of rote procedures in math and to help their students understand it and to make it relevant to their lives. It’s fun stuff, and math doesn’t have to be hard. I maintain that teaching it procedurally is the problem, why so many get turned off to it. Not many people would learn or enjoy reading if we never moved past the formation of letters and putting them together to form words and sentences without paying attention to why we do it or what they were saying. Lucky you to have had that calculus teacher!
I thought the first half of the book was better than the second. His arguments didn’t always stand up so well in the second half. I’ll be interested to hear what you think.
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I love people who make maths fun. I was one of the lucky ones who never had any trouble with it at school – I could always see the patterns. It did, however make it difficult for me to teach to children because I could never understand where their problems were, not having experienced them myself.
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What a lovely sounding bike ride! Although we are having a big bike race here in pittsburgh next weekend and I watched some footage from previous races and I must say I really admire you for being able to race – it looks terribly scary to me…the bikers are all so close together!
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Danielle — if you were to look at the Devlin book I think you would enjoy it and be pleasantly surprised at some of the arguments he makes. And definitely people can be good at their subject but have no idea how to teach it — unfortunately so.
Verbivore — yeah, you do lose math ability if you don’t use it, although I hope that it will come back to me quickly if I were to review. I’d have to start out at a low level, but I think I might be able to work my way up fast. It’s interesting that you gave up math for foreign languages — I did something similar, and then I gave up foreign languages for English.
Stefanie — whatever works, right? I can’t do fast and complicated math in my head very well either, although knowing some tricks is kind of fun. But you’ll be pleased to know that Devlin doesn’t think all that highly of being able to do arithmetic fast in your head!
Emily — oh, it’s too bad the second half doesn’t live up to the first because I really enjoyed the first half! I can see, though, that when he gets into the language part of the argument it might not work as well. It’s very interesting to hear a little more of what you do in your job — what a great goal you have!
Ann — there IS something valuable in knowing what children struggle with and what it’s like to not get it, isn’t there? I’ve discovered, though, that I can get a sense of what it’s like not to understand my subject, over the course of many years of teaching (and I’m sure you found ways of communicating with your students too) — it’s an interesting process.
Courtney — oh, it is scary! I get very nervous when I’m in the middle of a tight pack. Many of my races aren’t so large or so close, thank goodness. I watch the pro races and marvel at what they can do.
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If you like great math embedded in great math stories, I warmly recommend the books by Simon Singh (Fermat’s Last Theorem is a gripping epic; the Code Book is a broader tapestry).
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