Euclid would feel right at home in a math class in Paris. The geometry problems on the blackboard would look familiar to the third-century B.C. Greek mathematician, as would the method of work: methodical, clear, and anchored in the language of proof.
"This is an easy one. Who wants to go to the board?" asks teacher Daniele Glaziou at the Lycee Henri IV, a top high school in France.
Hands fly into the air - even though the experience of puzzling out a geometry problem in front of a French math class often includes a level of sharp criticism inconceivable in most American classrooms. Here, it's not enough to get it right. It's just as important to get it fast.
"Yes, that's right, but she got through it quicker than you did," comments the teacher on a student's performance.
What's telling about French math instruction is the assumption that runs through society that mathematics is important. Mathematicians figure prominently along with generals and writers among those deemed the great heroes of France. The habit of systematic "analysis" as a basis for solving problems is developed young - and persists long into life.
"The US doesn't care much about the results of mathematics education, because thousands of very capable Russians and Koreans come in every year. But France has a very selective elite culture. There's a very generalized opinion that math not only allows you to understand everything, but that the only way to understand anything is to understand its mathematical structure," says Jean-Michel Kantor, a professor of mathematics at the University of Paris 7.
Yet even here, there's a new focus on how to make make math instruction less abstract and more accessible to all students. "It's long been accepted that if a student doesn't grasp a math course, it's probably because his father and grandfather weren't good at math, either," says Jean-Pierre Kahane, chairman of a government commission to reorganize the teaching of mathematics. Failure in math is just seen as an inevitable part of the system. What we're trying to do now is introduce more interdisciplinary, problem-solving into the curriculum. It's a good idea, but difficult to put into practice."
Many of the students at Henry IV plan to continue in two grueling years of preparation seminars for entrance exams into elite professional schools, such as the cole Polytechnique. That's what students call "the royal way," and it opens doors for professional careers in government and industry. But to get through that door, math skills must be rock solid.
"Those that make it through the top mathematics programs leave with the certainty that they will always be able to make a good living," says Catherine Dupr, national chairperson of the Mathematics Teachers Association.
Math instruction begins early, and there are clear national objectives. Some 90 percent of three-year-olds in France attend free, universal preschool. Even preschool is treated as a professional activity for students, who are treated as if they are there to learn. Preschool lessons often include math games and problem-solving with double-digit numbers.
Moreover, teaching - especially math teaching - is a high-status profession in France. Even preschool teachers are highly qualified, and they're paid as much as elementary school teachers. The notion of perfecting and sharing lessons is built into the professional culture. "The children really work in a French pre-school. It's not babysitting. Even mathematics has its role to play," says Philippe Wolf, director of studies at the Ecole Polytechnique.
Early on, French students are encouraged to become proficient at "calcul mental," or solving problems quickly without pen or pencil - and most certainly without a calculator. While use of calculators in math classes is permitted, it is still strictly limited. (In France, it's not unusual to see a clerk in a shop or farmer in a market tote up a bill mentally before confirming the sum on a calculator.)
Students at the St. Bernard Elementary School in the north of Paris come from some of the poorest families in the city. Teachers say it's even more important for these students to get the solid grounding in math.
Madame Szerman urges her 11-year-olds to come up with a method for determining how many quadrilaterals there are in a geometric figure on the board. They've been thinking about this problem overnight, and have worked in small groups. But it's getting messy on the board, as students realize they can't quite tell if they're counting the same four-sided figure twice - or not at all. "You need a method, or you'll get lost in disorder," their teacher says.
Her elementary school class takes a break from geometry to review the "calcul mental" they've been taught since pre-school. "What's 23 x 12?.... What's 33,475 - 999?.... What's 47,873 - 999?" she asks. "You don't need pencil and paper. Just use your head. You can master it. What if I were to give you, 5,472 X 104?" She asks students to explain their answer. "Let me show you how to do that still faster," she says.
"Sometimes, when a child tells me they don't understand why they have to learn all this hard math, I tell them: 'Math is a way for lazy people to learn how to do things quickly and well.'
"It's a way to have a well-organized mind, and it will help you solve all kinds of problems later on in your life," she adds.
There is not tracking, in French math instruction, and, until this year, no remedial classes to help kids catch up with material they have not understood. Teachers say there is still considerable prejudice toward students with physical and learning disabilities.
Such a system produces many highly competent students who perform exceptionally well, especially on international exams, such as the Third International Mathematics and Science Study (TIMSS).
But many educators worry that that system could leave some children behind. "Once a child loses his way in math, it's very difficult to get back," says Gerard Champeyrache, who is assigned by the national Education Ministry to assist and monitor teachers.
Often, it's parents who take up the slack. Madame Szerman says that her son was good in mathematics; he could always get the right answer, but it took time. She hired a senior math instructor to tutor him out of class. "He gained a half an hour in solving the more difficult problems," she says.
Of course, it's a lot easier for well-educated, well-connected parents to find this level of support for their children. That's a concern for teachers like Professor Kantor, who says he is encouraged by the growth of math clubs and festivals of mathematical games, especially for children who do not come from elite Parisian backgrounds.
"There's are lots of things happening outside of class," he says.
"Math is coming to be viewed as a sport here, not unlike swimming or cycling, especially outside of Paris. And these competitions are helping to reveal the talents of young people who aren't viewed by their schools as being talented in math," says Professor Kahane.
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