## Tuesday, May 26, 2009

### Left-brain epiphany: incidental, hands-on learning yields disembodied facts

This struck me during some recent visits to local museums.

Playing with pendulums, I witnessed how periodicity relates to length. Moving on to levers, I witnessed my muscles working harder when levers got shorter. Moving on to rotating platforms, I saw my son spin faster as he drew his legs in. Wandering on into the aerodynamics room, I quickly forgot these details and witnessed how paper airplanes with different shapes followed different trajectories. But there were too many variables for me to draw firm conclusions. In the meantime, I forgot the specifics of pendulums and levers. By the end of the visit, all I could remember were vague impressions and a few fragmented details I've since forgotten.

It's not that I wasn't interested; it's that I no longer have active recall of a structured knowledge base--e.g., in basic mechanics and aerodynamics--in which to store these facts and find meaning in them.

Imagine a child who never gets this foundation. Imagine a child whose classroom science instruction eschews the structured facts provided by decent science textbooks and dynamic science teachers, and instead resembles that provided, in an incidental, hands-on kind of way, by a science museum.

Incidental learning is great, but it only works atop a foundation of structured knowledge. Today too few classrooms provide this, and the sad result are fragmented, and therefore meaningless and ultimately forgotten facts...

...of the sort that people who tout incidental, hands-on learning love to say they hate.

Beth said...

Can we work toward a compromise? What I find with a lot of the constructivist approach is that it's a good place to start, but you shouldn't end there. You can use the hands-on, constructive approach to get the kids interested and show them that there is a real-life basis to the abstraction. Then you move on to the abstract.

Recently my 5th grade daughter asked me why multiplying 12 by 1/2 is the same as dividing 12 by 2. This was after months of "covering" fractions at school! The only thing that turned the light bulb on for her was when I took out some math cubes and we acted it out. (If you're interested, here's what I did: I took two cubes stuck together and told her it was a new unit I just invented, called a "scuzzle". Then I asked, what is one cube? She answered correctly, "half a scuzzle". Then I gave her 12 individual cubes, in other words 12 half scuzzles, and asked her how many scuzzles she could make. It was amazing to see the light go on in her eyes.)

So, at least for my daughter, the hands-on approach really is a useful starting place. But I'm more than aware that there is no "one size fits all" in education. It could be that it's better for your kids to start with the abstract.

If school could be about helping kids learn with whatever method works for them, and less about marching all the kids lockstep through the same paces, we would all be better off.

lefty said...

Beth, Your hands-on lesson sounds great! But I'd call it guided discovery. What I have a problem with is incidental discovery, where there's little interactive guidance from a teacher. That's what I find problematic, except when there's a solid foundation--or, as you say, when it's used as a lead-in. A good compromise?

Anonymous said...

Its not so much the approach I dislike as the reform textbooks and their avoidance of appropriate content, like traditional algorithms and definitions. Like that of a line as a discrete set of points and not a continuum. As an exercise, try describing a parabola using iteration. Its only being done here in the US with idiot textbooks.

The blatant dishonesty that is endemic in kids is a symptom of a much wider guilt-ridden school-dominated society.

It is possible to develop curriculum that is popular with both teachers and students. There are many examples in this world. Why even Polya would have to agree that Singapore Math is a far superior textbook to anything published in the US.

And secondly, a book's success should not be measured by the quality of the instructor. That is simply wrong-headed. It is like saying any car can be used for racing if its being driven by a race car driver. Only instead of trying to improve the book, you keep retraining the driver? Its ludicrous speed.

I'm in five classrooms everyday with 35 students that have not mastered their times tables and the state is telling our school, if you don't get these kids up to our standards we'll be forced to do something drastic or we'll close down your school.

Furthermore, lets say we met our AYP then our school does intakes of other students from around the district and our AYP goes down. That's another challenge. NCLB is meant to fail our public education system. They mean for it to crash.

And math reform says how about a compromise? How?

Math education researchers haven't shown the slightest inclination in providing honest or accurate information about what is truly happenning in our schools.

Math reform supports their own selfish profit-driven agenda that discrimates against marginalized people. They have done more harm to our inner city public schools than they will ever publicly admit.

The truth is in the details. The real evidence should be what's getting produced after 12 years of public schooling. Hardly a college-ready education in math or science.

Politiicians want to start a witch-hunt, lets start at the colleges of miseducation and their largest supporters - the Achieve, Inc and the NSF.

bky said...

Anon -- I don't know why I still read your comments on this blog. Are you a shill for the publishers of Singapore math textbooks? Did they know your propensity for off-topic gibberish when they signed you on?

Lefty, I don't mean to be incivil, but jeesh.

Anonymous said...

Well Mr. Incivil, there's no need to shill Singapore - its a fact - Singapore is the best curriculum available in the English-speaking world - so live with it. Do your homework. Everyday Math is a big, fat, Cretan hoax.