Theory is practical
“Education would be much more effective if its purpose was to ensure that by the time they leave school every boy and girl should know how much they do not know, and be imbued with a lifelong desire to know it.”
- Sir William Haley
I’ve always been interested in math education for the main reason that mine worked out so badly. As a dyslexic child, I had a difficult time reading numbers (still do) and the first six grades seemed to consist almost exclusively of memorizing tables. Until that was done, no logic! no problem solving for you! But since it was almost impossible for me to memorize tables, I grew up believing I was “bad at math”.
Fast-forward a number of decades.
DOF co-author Lucas, who has some serious math chops, told me he’d rather kids spend a lot of class time understanding one problem very deeply than ploughing through a whole page of the same kind of problems. And yeah, that sounds right. He translated that to science with ‘more time on theory than lab work’ and, hmm… I wasn’t sure about that. Lab work is important, I thought. Wouldn’t you get theory from lab work? Well not necessarily…
Along comes this report on ScienceDaily, Concrete examples don’t help students learn math, study finds. Professors at Ohio State put it to the test and found out, maybe we should be going from theoretical to specific:
A new study challenges the common practice in many classrooms of teaching mathematical concepts by using “real-world,” concrete examples. Researchers led by Jennifer Kaminski, researcher scientist at Ohio State University’s Center for Cognitive Science, found that college students who learned a mathematical concept with concrete examples couldn’t apply that knowledge to new situations. But when students first learned the concept with abstract symbols, they were much more likely to transfer that knowledge, according to the study published in the April 25 issue of the journal Science.
“These findings cast doubt on a long-standing belief in education,” said Vladimir Sloutsky, co-author of the study and professor of psychology and human development and the director of the Center for Cognitive Science at Ohio State. “The belief in using concrete examples is very deeply ingrained, and hasn’t been questioned or tested.”
The words; “hasn’t been questioned or tested” make for low-hanging study fruit. Common sense often knows a lot of things that ain’t so:
For example, there is the classic problem of two trains that leave different cities heading toward each other at different speeds. Students are asked to figure out when the two trains will meet.
“The danger with teaching using this example is that many students only learn how to solve the problem with the trains,” Kaminski said. “If students are later given a problem using the same mathematical principles, but about rising water levels instead of trains, that knowledge just doesn’t seem to transfer,” she said.
“It is very difficult to extract mathematical principles from story problems,” Sloutsky added. “Story problems could be an incredible instrument for testing what was learned. But they are bad instruments for teaching.”
“That knowledge just doesn’t seem to transfer.” This lines up with my experience in technical support. The most challenging client is the one with a yellow legal pad next to their keyboard. They ask how to do something; I already know they are NOT interested in the theory behind it. They want an exact formula – “Click here, then click there, type these words in, press enter…” They’ll write down every step word for word. But they can’t transfer that ‘knowledge’ to new situations.
In tech support, you’ll get the lion’s share of phone calls from clients who are overly focused on the immediate problem. To them it seems extraneous to learn why something happens. But as soon as any little thing changes, they’re reaching for the phone again. When I’m with them, I want to say; “Put your pen and your legal pad down and let’s just talk a little about web pages and servers and stuff.”
Teaching is a kind of tech support. Maybe the way we educate now is too heavy with “click here, type these words in…” Arthur C. Clarke said the ideal classroom was a log, with a teacher at one end and a student at the other. They could talk, explore ideas, figure things out and be able to adapt when things change. But the school district has a number of board members who want to make sure there’s no evolution or sex education on the log. And the parents come in to yell at the instructor for asking mean questions that made the student stay up half the night thinking about them. Then the Department Of Education shows up and starts insisting on standardized tests and whether the students know enough random trivial facts. Now the kid goes home with a sheaf of homework to be sure he can spew out those facts come NCLB test time. Education just ain’t the same on the log anymore.