80% is a lot, and other intuition
Today, my favorite store at the mall was having a 50% off sale, and so I bought a nice $122 jacket for $61 plus tax. After that, I wandered over to the shoe store and used my 10% off coupon to get $9 off of my $90 shoes. (Yes, I know, those are some expensive shoes. But I am tired of uncomfortable ones.) All in all, this trip cost me about $150, as you or I can easily calculate in our heads.
My former students could not.
A few years ago, I was tutoring adult learners for the GED, a high-school equivalency examination for people who never graduated from high school. My students were all native Spanish speakers, studying for the Spanish-language version of the exam. Ranging in age from 20 to 50, many of them had never even finished grade school in their home countries of El Salvador or Mexico or Peru– let alone high school. And some of them had no intuition for math, simply because they had never learned it. For me, it was amazing to realize how many of the day-to-day skills I take for granted were actually learned back in first, second, or third grade.
Here are some examples. Ask my students how much my $122 jacket should cost if it is 50% off. What do they answer? One or two of the students in the class may realize that 50% is the same as half, and divide by 2 to get $61. But if you ask them how much the jacket would be at a 70% discount, and they have no idea. None. They guess wildly: $100? $50? And so, first I taught them the meaning of percentages, and then how to calculate percent discounts on paper. I could only hope that some day the calculation would become easy enough for them to do it in their heads.
Another thing my students found nonintuitive was estimation. The only adding, subtracting, multiplying, and dividing they ever did was on paper (or, more often, calculators)– and everything was calculated to the last decimal point. Teaching them how to do practical, approximate calculations was a lesson in itself. Say you go to Target and buy one shirt ($15.99), a blender ($29.99), and toothpaste ($3.78). How much did you spend? Again, they had no idea. The idea that $15.99 is pretty much like $16, and $29.99 like $30, and $3.78 like $4 is something you have to learn. And apparently, you can get to middle age without ever doing so. But I imagine it had to be difficult; imagine being surprised by every cash register you encountered.
After a year of volunteering, very few of my students had passed the GED– only two or three who had come in at a more advanced level, having finished most of high school in their own countries. Every four or five weeks, a group of new students would show up in the class, and the whole curriculum seemed to start again with decimals, never making it to trigonometry. (The social services agency only had money for one teacher, and I was the only volunteer tutor.) But the students kept coming to class, two nights a week, two hours per night. So they must have been getting something out of the instruction– I think, in many cases, the pride of finally getting an education. I hope that they also started to see a little bit of math in everyday life.
