I think it’s a good idea to see how other countries teach and assess math (and other subjects), so we can compare and contrast and decide what of our own we want to keep (if any) and what of our own we want to throw out or modify (again, if any).
Having gone to school in France as a kid, and actually having taken and passed their baccalaureat exam in the stream that they used to call ‘mathematiques elementaires’ many decades ago, I have some sort of a mental model of a little bit of how they run their schools in France. I found they did some things very well, but some things really annoyed me to no end. Yes, the common conceit here is that the French do everything wrong, and lose all of their wars, but none of that’s true. For many centuries, they were probably the most warlike country in Europe, which is why lots of military terms come from the French. And without huge French military and financial support, the Americans would probably have lost the Revolutionary War. In fact, of all of the major powers in the world, I think that France is one of the few that the USA has never formally gone to war against.
Again, not that they do everything right!
I am NOT going to say that we should imitate whatever they do in France, or in Finland, Canada, Singapore, or anywhere else. But I do think that when you look at the way they do things elsewhere, you get the idea that we don’t have to do things the way that we’ve always done it — and that the approach of our current crop of Educational Deformers won’t help us at all.
So please allow me to present to you a translation that I did of this year’s French final secondary school exit exam for math, entitled “Baccalaureat Specialite Mathematiques.” It’s simultaneously their national university entrance exam, and if you doubt my translation, you can find the original source here.
Here’s the kicker: this is NOT a version of the math bac designed for students who really concentrate in math. Instead, this is for students who concentrate on literature, and only do math as sort of a required sideline subject. Because in France, they really start concentrating hard on one area about the middle of high school. And, the students are generally about a year older than our high-school seniors when they take the Baccalaureat exam. Also notice that this is not a multiple-choice, machine-scored test. Every single section of very single final exam is scored by a teacher who has zero connection with the student or the school in question. So, naturally, it takes a few days for the results to come back. (Notice: they process all those tests faster than we correct NCLB exams, using machine scoring! It’s probably because the test graders in France are all actual teachers, who have been doing this sort of thing for years. Rather than what we do here, which is farm it out to anyone who has a pulse and whose job choices are telemarketing, waiting tables, or correcting ‘brief corrected responses’ for some billionaire publisher.
If you just write a numerical answer for a problem without showing and explaining all of the steps, I am reasonably sure that you will earn a score of zero for that question. It’s all about the explanation. If you get the final answer wrong because of some silly arithmetic error, but you show how to go through all of the steps of the problem and explain them all, you will earn nearly full credit.
Another thing: a passing grade on these tests is 50% (10 out of 20).
If you get a 60% (12 out of 20), it’s quite good.