If 255 children are going to camp by bus and each bus can hold 60 passengers, how many buses are needed?
The correct answer is five buses, but many students who work the problem will get it wrong. While most will do the division calculations correctly, they'll come up with a remainder and fail to realize that their answer isn't finished yet. Instead of a remainder, one additional bus is needed.
This type of problem has become something of a classic among math educators, who cite it as an example of the difficulties students have in relating the math they do to the real world.
"What has happened is that too often we've been so dependent on exact answers, on pencil and paper, that students have not come away with a feel for what an answer is and why it's right," said Iris Carl, president of the National Council of Teachers of Mathematics.
So now, math teachers across the country are being challenged to develop in their pupils a certain common sense about numbers and how math is used in the real world. This ability to do mental calculations, to estimate and to have an instinctive feeling about whether or not an answer is correct is being called "number sense."
"When students have number sense, they know why math learning is important," Mrs. Carl said. "You move away from youngsters saying, 'Who needs this?' to students who see the need for the math they're learning and know how to apply it."
To help elementary school teachers understand what "number sense" is all about, a series of training videotapes is being developed in Maryland for distribution to school systems across the country.
Francis "Skip" Fennell, professor of education at Western Maryland College, is heading the project, which is funded in part by a grant from the U.S. Department of Education. Robert Sapora, also a Western Maryland professor, is project technical director. They have been working closely with public school math supervisors and teachers in Baltimore, Carroll and Howard counties as well as Washington to develop sample lesson plans which emphasize number sense.
The lesson plans will be presented on videotape in real classroom settings by the 20 elementary level teachers who were involved in developing them and who received expert training in the field.
Number sense stresses number meaning and the relationships between numbers: What numbers are between 17 and 25? Is 17 closer to 10 or 20? It also deals with the concept of magnitude: How old do you think your teacher is? How many paper clips can you hold in your hand? Students learn to estimate and also learn what happens to a number when they add, subtract, multiply or divide.
While students have always studied these things, number sense places a greater emphasis on skills that are needed for use in real-life situations.
"People use estimation more than actual computation," Dr. Fennell said. "When you go shopping, you carry about the amount you need, not the exact amount. In fact, when you go shopping you tend to overestimate.
"Number sense isn't fancy. It's not new math. It's just understanding numbers and what they mean. It's real intuitive. Kids who have number sense understand numbers and how and when to use them. Sometimes I think we went so fast in learning how to do problems that we never understood what we were doing and what it meant. We want kids to think about the math they're learning."
L. Carey Bolster, the coordinator of mathematics for the Baltimore County public schools and an adviser to Dr. Fennell, praised the number sense project for its "connections to the real world."
"International studies have shown that there's a great need for reform in math," Mr. Bolster said. "Our students have got to do better. We must move them toward excellence in math. And these videotapes will tell teachers how to implement this in their classrooms."