CONSIDER A TEACHER in a traditional classroom who tells students what a ratio is, expecting them to remember the definition. Now imagine a teacher in an integrated mathematics classroom who has her students figure out how many plastic links placed on one side of a scale are equivalent to one metal washer on the other side. Then, after discovering that the same number of links must be added again to balance an additional washer, the children come to make sense of the concept of ratio for themselves.

Or consider a traditional mathematics class where students are told to solve yet another contrived word problem ("A train leaves Washington, D.C, heading west at 65 mph ... .") Now imagine an integrated mathematics classroom where students are asked to compare the weight of two pieces of bubble gum - one chewed and one not, one with sugar and one without - making predictions, recording results, explaining the differences, all the while adding, subtracting, multiplying, dividing, using decimals, percentages, learning to estimate and extrapolate. In which classrooms are they more likely to see math as relevant, appealing and something at which they can be successful?

Integrated mathematics was developed about 10 years ago because more than 80 percent of U.S. students were graduating with poor mathematical understanding or hating mathematics. In traditional mathematics programs, students are required to put fragmented and forgettable facts and formulas into short-term memory so they can pass the next test. But integrated mathematics programs actively engage students in applying mathematical ideas to real-life problems. Integrated mathematics seeks to help students make connections between mathematics and other disciplines and their own lives. Integrated mathematics engages students in making sense of and applying their mathematical understanding.