• Mathew Crawford Mathew Crawford is an Education Engineer, textbook author, and CEO of MIST Academy, a school for gifted students in Birmingham, Alabama.
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    Seen today on my Google+ feed:

    “Even failed experiments and theories teach valuable lessons.”

    Not entirely disconnected, here is an email I recently received from Jason Knapp of Ohio:

    For what’s it worth – I have a great amount of respect and admiration for what you’re doing, and what you have achieved with your Academy. My son loves your Number Theory book – it’s his favorite out of the AoPs set.

    [anecdote for your classroom]

    I have a mathematics background, and I direct research for a small biotech company. I’m honestly dismayed by the ever increasing difficulty of finding people with good problem solving skills – from finding interns to hiring PhD level scientists. I have actually recommended some of the AoPs books to some of our interns (kids working on their masters – smart, but poorly trained). Not because they need to know power-of-a-point or sum-of-cubes, but because the process of solving those types of problems is remarkably the same as that used to solve *real* problems: getting organized, searching for patterns, thinking of a simpler problem, changing your point-of-view, etc …

    Two very bright guys I met while I lived in Southern California will soon host a television show on the History Channel called Invention USA in which they interview modern inventors and discuss their amazing inventions.  These invention experts are Garrett Lisi, sometimes known as “the surfer dude physicist” and Reichart Von Wolfsheild, perhaps best known as producer of the famous Goldfish Aquarium screen saver used at least partially to highlight the advent of modern computer/TV screen technology.

    I suspect with good reason that the show will be very good.  While I only met Reichart once very briefly, he has a big personality and strikes me as an entertaining guy.  Garrett has become well known for his Theory of Everything — long sought after in physics — is a very comfortable public speaker.  Unfortunately I’ve been unsuccessful in finding a debut date for the show, so stay tuned.

    I’m no expert at this, but I get better at it the more I work with children.  Here’s a post by Tyler Cowen (actually, mostly Gareth Cook) about bribing children.

    I like the post, but I dislike the perspective of “bribery”.  What we’re talking about might be deemed “artificial positive reinforcement” with the goal of helping kids set goals and achieve rewards that dovetails with our immediate needs as adults to get children beyond the point of being dependent on us in particular capacities.  Here’s one quote I like:

    Stay positive. In our house, we call them “challenges.’’ It is not about “fixing’’ a negative. Don’t nag. Let it be their choice. Pile on the praise.

    Exactly.  The greater goal is not short term (unless you just don’t care about the future of the child/student).  The greater goal is the long term development of the child into someone capable of independently handling his/her own affairs.  This reminds me of one of my favorite quotes:

    “Love is a better teacher than duty.” — Albert Einstein

    The webcomic xkcd has become a geek favorite, and for good reason.  Aside from funny moments, there are moments of truth that separate xkcd from so many trite sources of humor:

    But you don’t become great by trying to be great.  You become great by wanting to do something, and then doing it so hard that you become great in the process.

    This is a good article on the potential pitfalls of normalizing the unusual students.

    Why can’t we simply celebrate how differently we all see the world?  Is it that hard to see how beneficial diversity is?  Or at least how valuable the mental outliers are?

    Truth seeking is the motivation behind the scientific method, hence behind all of science.  So it stands to reason that any system through which we put future scientists should encourage honest behavior.  Unfortunately our current system of compulsory education does the opposite (hat tip Eli Ross).  Unfortunately this discussion isn’t likely to find footing in today’s political environment where those in charge of the system routinely castigate anyone with criticisms inherent to the system — because creative destruction is not a political option [or so the people in charge believe].  And so we’ll see even the reformers fail (hat tip James Johnson) time and again.

    The solutions are surprisingly simple, but I suspect that it will take the further development of disruptive technologies to lead people to those solutions, because we’ll need to excuse people for their “involuntary” behavior.

    When class looks like this, you have the trust of your students that it’s going to be a good class:

    Hat tips: Bill Dorminy and Patricia Li

    The other day I discovered Garrett Lisi‘s TED Talk.  My second favorite thing about the talk is seeing how Lisi’s imagination works.  The theory is very imaginative.  My favorite thing about the talk is that it gives insight into a particular motivation for his explorations into the fundamental physics of the universe: he assumes that the universe must be beautiful.  I think this is much of the reason I would bet on his theory over string theory.  Aside from that point, I think motivated modeling is one of the most precious lessons in math and science. Enjoy.

    This evening I arrived at my office to write student evaluations. I’ll likely be here until around midnight because I want to get them out as soon as possible and focus on more interesting work – like designing more interesting lessons!

    But I’m quickly derailed in my goal. Gustavo Lacerda sent me this article and asked for my thoughts.

    Unfortunately I have a number of thoughts on this article and feel compelled to be an insufferable blowhard blog them.

    My first thought is that the post/article needs to be longer because I don’t feel like the subject is adequately explored (or even defined well). Maybe. Or maybe it’s fine as it is – short enough that more people will read it and think about it. But the points discussed are important. After all, they point toward the design of our educational system, the mental health of our children, and possibly billions or tens of billions of dollars misspent in the educational system. Not that Gray takes the time to highlight all of these points, and maybe he doesn’t need to.

    But I need to. Like a compulsion. Because I love trying to solve these kinds of education problems. I love optimization problems. So let’s dive in.

    The article begins with a critique of an educational system that has packed more and more into the days of elementary school children. I strongly agree that children should not spend all their time at school work. We are a long way from developing a curriculum for life better than childhood play and socialization.

    But I’m not going to pretend that the educational system developed purely as a mechanism for directed play and socialization. That such a system might be better than our doesn’t mean that we’ve explored the best possible world!

    And that may be my biggest gripe with this article – an article that I do praise for (re)raising important issues. Yes, we put mathophobes in charge of…teaching math to the children. Yes, exactly. Right out of the gates, the damage is done. Then those children grow up and run the educational system reinforcing a vicious cycle. Then the article, along with the research it reports on, make one enormous leap – reform the system by dropping arithmetic altogether! As if no other solutions are possible!

    I admit that other solutions are difficult, if not simply unviable, but I’ll come back to that.

    It is simply incorrect to say that Benezet’s experiment removed arithmetic from the curriculum. As I see it, Benezet’s experiment changed the following variables:

    • Arithmetic was taught contextually, based on topics in which the students already showed interest.
    • The teachers acted as social intermediaries instead of…machines of dull hate.
    • Though the article did not say as much, both students and teachers likely did less work.

    The third point is not so minor as it may seem. After all, the article begins with the supposition that students are overworked. It then transitions into a picture of teachers of elementary school students as disinterested in math if not terrified of it. In other words, there is a mental health component.

    Under this reinterpretation of Benezet’s experiment, I am happy to discover that I follow Benezet’s philosophy to the extent that I teach EVERYTHING contextually. Okay, maybe not every little thing, but I teach contextually as much as possible. I tell stories. I encourage students to tell stories. When students get stuck with problems, I make up a story in which the approach to the storyline problem illuminates the problem they’re working on. I teach base numbers by asking students to image how we’d pack widgets to send them to Springfield, where the Simpsons and all those eight-fingered people dwell. I teach the locus of points equidistant from two intersecting lines (angle bisector) by having the students imagine that the universe is reflected over a line, then asking what happens if I drop them to the ground from a point on the reflection line. I have fun and make jokes and encourage them to do the same.

    But I do teach advanced to very advanced math students, and they do need to learn the notation and formality along the way. I just make sure that conceptual understanding and joy of the subject matter take center stage.

    I’d also point out that while some of the parents of my students pressure me to give more homework, I resist. I give some homework – enough that I know that the students are exploring some hard problems and getting comfortable with the mechanics. But I give very little to my middle school students during most of the year.

    The students who really want to achieve some measure of perfection with their skills can and do work more problems. No external pressure required.

    So, here’s where I stand with (and part from) Benezet. Yes, math education is done so poorly at the elementary school level that it’s more beneficial – at least to very many students – to get rid of the dull exposition of arithmetic by mathophobes. That’s different from not including arithmetic in curriculum – it’s just “taught” at a contextual level. So long as the vast majority of elementary school teachers are mathematically illiterate, this solution is fine with me.

    And my fiscally conservative side loves the fact that we might even save money by reducing the number of hours in the school day!

    But let’s not get carried away! One size never fits all. What about the kids who are wired to find math to be the most amazing art in all this great big universe? You can probably tell from the construction of that last sentence that I’m talking about me. Math – weeeeeeeeeeeeeee! Math was my play time at school. I like music and I liked it then, but singing in choir got old much quicker than learning how to count quickly through numbers that were 3 more than multiples of 7. Recess was great. I was a pro at running over tires half-buried in the sand and leaping off swings from twelve feet in the air. But I also liked computing the sales tax at the grocery store before the cashier would ring it up. I craved more time to explore and think about mathematics. And I truly loved those occasions in elementary school when a teacher taught me some math I hadn’t learned from my father or discovered myself. Both of them!

    To some students, math is play. And that’s both important to mathophiles who’d like to also be represented in the conversation, but important to a world so complex that we need highly trained mathematical minds to engineer all the Asimovian magic around us.

    Gifted class saves some kids from missing out on interesting math. Math team starting at the middle school level catches a lot of kids and inspires them. But even before that, we can give kids a taste of math as an art, and see who gets hooked.

    This is the solution to the Mathematician’s Lament!

    And even if only a portion of the students want class time in that art called “mathematics”, we absolutely do need to provide for it.

    After all, haven’t we discovered that you can’t be Tiger Woods if you start playing golf in middle school, Lebron James if you start dribbling at the age of 11, or Venus Williams if you haven’t handled a tennis racket by kindergarten? Should we expect the art and sport of mathematics to be any different? Should we hold back Terrance Tao from explorations until he’s in the sixth grade?

    It’s hard for me to defend such a position.

    Addendum (because I’m so sleep deprived that I just forgot to say it):

    So, no, I can’t support the idea of making Benezet’s solution universal.  I just think we need to make elementary math into something like art class.  And, just like art, let the kids who are great at it have the resources to take them as far as they’d like.  I think this can be done without needing more than a few elementary school teachers to have a good sense of math and math education.

    And now it’s nearly midnight and I have successfully found a way to enjoy my time at work. I’ll get my evaluations done tomorrow and I’ve had a more fun and inspiring night for having thought this through. Thanks for reading.

    Ordinarily it’s not easy to explain the relative sizes of sesame seeds, blood cells, viruses, and atoms, but this is a great view based scaling the size of the pictures exponentially.

    HT: Jessica Richman

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