Many of my students attend a private K-8 school that offers a very traditional math curriculum. Students in grades 5, 6, and 7 spend many months studying shopkeepers' math. The main focus is percentages - discounts, sales tax, tip, simple and compound interest, commissions, annuities, etc. Each of these variations is taught as a series of formulas to be memorized. The vocabulary is beyond the comprehension of most 12 year olds. Even the numbers themselves are quite tedius. Students spend hours calculating 17.25% of $12,650.85 by hand.
A group of 7th grade boys came in with homework from their new math unit - an introduction to linear relationships. They each had a worksheet with about 15 tiny grids upon which lines were drawn. The students were asked to calculate the slope of each line. That was it. No context and no explanation. That was their starting point.
"We don't really know what we're supposed to do," said one student.
"Yeah, it's just a bunch of lines," said another.
"We're lost," said the third member of the group.
The other two solemnly nodded in agreement.
Maybe it was the fact that I had just watched Stand and Deliver over the weekend and wanted to be like Jaime Escalante but I grabbed the worksheet, pretended to scrutinize it, and delivered the following line with exaggerated astonishment and admiration.
"Whoa!!! You guys are doing this? Wow! I can't believe it."
"What do you mean? What is this stuff?," they asked, almost in unison.
I walked to the door, checked to see if anyone was around, then closed it.
"Alright, I'll show you," I said.
One of the advantages of working in a defunct science center is access to a closet full of physics toys. I grabbed a few matchbox cars, ramps, and books and set up an impromptu math lab. What ensued over the next 45 minutes was a spirited look at independent and dependent variables, data plotting, best fit lines, and, of course, the meaning of slope.
At the end of the class, one of the fathers came in to pick up the students. I was putting away supplies but I heard him ask his son if he got his homework done. The boy said no. The father, clearly upset, asked his son for an explanation. The boy said....
"Dad, I can do my homework later. I didn't do it here because I was busy learning."