I recently read a fascinating three book series by Catherine Fosnot and Maarten Dolk entitled Young Mathematicians at Work that shares their inspiring approach to teaching mathematics to elementary children. Broken into three sections to deal separately with primary and intermediate topics, Young Mathematicians at Work succeeds at convincingly illustrating what is wrong with how mathematics is taught in most American schools, and shines a light on what the Math in the City program based out of New York City is doing to reform the teaching of mathematics.
From the beginning children are essentially taught math as a set of rules and procedures that were established hundreds of years ago and that they are simply being asked to absorb because they will eventually need it somewhere and someplace. This has led to mass numbers of children hating the subject, failing the subject, and as adults knowing little if nothing about the subject. In having taught math to adults for six years in educational programs it is disappointing, to say the least, to see fifty year old men and women not knowing how to add fractions with unlike denominators. Not only because they have forgotten the tedious procedures that they were given in elementary school as the only means of solving said problems, but because they don't have any clue that there might be other ways to solve a given problem without that procedure.
Fosnot and Dolk argue that math needs to be taught as a living, breathing discipline that is ever changing. Contemporary children don't know that they can actually contribute to the evolution of mathematics, create groudnbreaking new ideas, new methods, and new procedures. Essentially, they are taught algorithmic approaches that were invented over a thousand years ago to make calculating easier in the marketplace.
Fosnot and Dolk highlight a progressive program that includes children discovering big ideas, hitting landmarks in math at their own pace, working with their peers in "math congresses" to learn from one another, seeing the elegance in calculations, and constructing their own meaning. All through the means of teachers settting up strong contextual investigations, sound mini-lessons that guide children to discover number relationships, and math congresses where the class gathers to share ideas and talk about their own unique solutions.
Imagine how much more a child understands about math when he can calculate 43 x 50 by thinking that (43 x 100) / 2 will yield the same solution as if he were to use the boring algorithm which is less efficient. Or that 38 x 15 can be quickly figured by (15 x 10) x 4 minus (2 x 15). As educators we need to lead children to understand the beauty and elegance of mathematics. Who said we have to or should memorize basic addition or multiplication facts by taking time tests or using flash cards? Rote memorization does not equate to understanding, afterall. They may know that 9 x 6 = 54 because they used their finger trick or finally memorized it after fifty shuffles of the flashcards, but do they know that (10 x 6) - 9 or 6 x 9 or (9 x 3) + (9 x 3) also equals 54? If not, why not?
Mathematics is truly an art that teachers need to fully understand and appreciate before they can essentially teach it as such. It is not enough says Fosnot and Dolk to teach alternative calculating strategies, however, but that opportunities must be structured so that children can consctruct these ideas on their own. Fosnot and Dolk never use the words "skill" or "concept." Instead they refer to the "big ideas" of mathematics and offer a structure that will lead to the children constructing these big ideas, though most importantly not at the same time.
The strong contextual investigations that are essential to this program have been spoken little of in this article, but play an important role as children investigate teacher-prepared situations that are meaningful and open-ended enough for the children to solve in many different ways. Their investigative procedures and processes are shared in the math congresses.
There is too much to say about Young Mathematicians at Work for one article, but for those in need of a more sensible way to help children in their class learn, understand, and to appreciate math this is a program that cannot be overlooked. Especially in light of the NCTM's demand that math me taught in a more constructivist light.
