Only one more week before the kids come in. Four classes of Algebra II (three of them are for freshmen who passed Algebra I in middle school) and one class of AP Stats. So far the rosters are manageable, between 25 and 30 kids per class. What do I want to do with them? What do I want them to get out of their respective courses by June?
I want them to delight in thinking. I want them to delight in thinking mathematically. I want them to stretch their brains. I want them to grow mathematically. With all due respect to all the great middle school math teachers out there, I think that to some degree we infantilize these kids. A poster with glitter, with an illustration of the Pythagorean Theorem and the formula next to it is NOT the same as understanding how to apply the Pythagorean Theorem.
Math is about solving problems – that is all. Too often what we do in math is boring and repetitious. The textbooks rarely have challenging problems. We are giving the kids recipes, but we are not teaching them to cook. We are teaching the kids to make a French onion soup, we have them do it 30 times until they get bored with it, but we never ask them “What do you do if you run out of onions?”
The situation is less dire in AP Stats – I continue to have a tremendous respect for those who put the course together, who wrote the main textbooks and who are coordinating and grading the AP Stats exam. But in Algebra, arguably the foundation stone of mathematics, we (as a country) are falling behind.
Take a look at some of the textbooks American schools used in the 60s. Take a look at Smith and Fagan’s “Mathematics Review Exercises”, at Weeks and Adkins’ “A Course in Geometry”. Those had truly challenging problems. What happened? Have we become dumber? Take a look at Singapore’s “New Syllabus Mathematics.” Those are good problems! Take a look at today’s Exeter problems. How come we don’t have more teachers using them?
Of course there are explanations. As a nation, our classes are more heterogeneous, and in general we expect everybody to graduate from high school with Algebra II and Geometry level mathematics (at least), whereas 40 years ago we did not expect everybody to do so. We have provided opportunity for more, but we have at the same time lowered the quality and rigor of our courses. And of course there are the standards – and we are evaluated on how our kids perform on those standards. We are truly in Lake Woebegone – where “all children are above average.”
Indeed there are many causes that one can list to explain the decline in math education – from parents, to administrators, to politicians, to video games and so on. But I think we – the teachers – bear a heavy burden also.
We have failed to hold the line.
We are coddling the kids, we try to make it interesting, painless,visual, relevant and in the process we have sacrificed rigor. We need to ask more of them…and more of us.