Like thousands of schoolchildren around the country, Jill Ashworth’s 5th graders in Franklin County, Tenn., equated mathematics instruction with tedium. “Even the best students will tell you it’s boring,’' the Franklin Middle School teacher says. “They look at the word problems in books, and it just doesn’t have meaning to them.’'
Now, however, Ashworth and teachers in eight other states are involved in an experiment with researchers at Vanderbilt University that is designed to dispel such notions. The unlikely tool at the center of their strategy is a multimedia series known as “The Adventures of Jasper Woodbury.’'
Developed by a 25-member research team at the university’s Learning Technology Center, the series is based on emerging principles of cognitive science. So far, it consists of four video productions featuring the fictional Jasper Woodbury and his teenage friends. Each tape tries to engage students in solving complex problems by bridging the gap between school learning and learning in the “real world.’' The 15- to 17minute programs employ a story format to present students with a complicated, true-to-life mathematical problem.
One difficulty with the more traditional word problems found in textbooks is that students tend to divorce them in their minds from reality. Students asked to determine the number of buses needed to take a specific number of people on a field trip, according to one classic illustration of the phenomenon, typically came up with answers like two and onethird. They failed to take into account the impossibility of having one-third of a bus.
“As adults,’' notes Nancy Johnson, a private school teacher in Nashville who is taking part in the project, “we won’t be asked to turn to page 25 and solve the problem on that page.’'
The Jasper video programs, by contrast, force students to think about mathematical problems in a more realistic way. The problems, stated by a character in the story at the close of the program, are usually the equivalent of a word problem of 15 or more steps.
The production Ashworth’s 5th graders are watching today, for example, asks students to develop a defensible business plan for a recycling project to raise money for a high school field trip to Washington. To project how many residents would take part in the recycling project, the students have to determine the population of the town and understand survey techniques. They also have to find out how many cans an average household uses on a weekly basis and determine the weight of the cans in order to project their revenues. And they have to deduct expenses, such as the cost of renting a pickup truck to transport the cans, from their proceeds.
The information needed to solve the problems is contained somewhere in the video story. For example, in the recycling story, titled A Capital Idea, students see the population figure on a road sign. A truck driver tells a character in the video how many pounds of aluminum cans a pickup truck holds. The percentage of county residents favoring recycling is revealed in a radio news broadcast.
“They’re made like good detective stories,’' says John Bransford, the Centennial Professor of Psychology who helps direct the Vanderbilt center. “You get to the end, and you realize you’ve already had all the clues. Students have to go back and search.’'
The project, referred to simply as “Jasper’’ by the researchers, is part of a new wave of technologybased initiatives aimed at developing practical, classroom applications for findings from cognitive science. Though their forms vary, a common thread in all of them is the effort to break away from traditional “drill and practice’’ uses of the medium and to inspire a more active and, in the words of one leading proponent, a more “rounded,’' kind of learning on the part of students.
In scope, however, the Jasper project, begun more than four years ago, is among the largest. Funded with three-year grants totaling $1.3 million from the James S. McDonnell Foundation and the National Science Foundation, it involves 11 sites in nine states.
A key goal of the researchers who created Jasper is to eliminate what is known in the field as “inert knowledge’'-- knowledge that students possess but, for some reason, do not apply beyond the context in which they learned it.
One way to tackle the inertknowledge problem, Bransford says, is to have students pose their own problems as well as solve them. In A Capital Idea, for example, the students must figure out what subproblems need to be solved before they can answer the central question: How much money can they raise by recycling? A subproblem to that question would be: How many residents would participate in a recycling project?
The kind of classroom situation that lends itself to this kind of problem solving is what the Vanderbilt researchers call a “generative learning environment.’'
“Generative learning is really the ability to work in groups,’' Bransford says. “What makes groups work well is the nature of the problem being solved; a problem that can be solved in 30 seconds won’t do it.’' With Jasper, whole classes or smaller groups of children spend three to five days solving the problems posed.
Ultimately, the research team hopes, students will use Jasper as a springboard for more authentic activities. An Arkansas class participating in the project, for example, developed a business plan and raised money to finance a field trip to Vicksburg, Miss.
The researchers chose video productions as the means for creating their generative learning environments, in part, because the medium permits information to be transmitted on a number of levels, thus providing a shorthand way to transmit more data. “If you think about what the videos would look like in written form,’' says Nancy Vye, assistant director of the Vanderbilt technology center, “it would be something you could not give to kids.’' Moreover, the teachers and researchers note, video technology is “the kids’ medium.’'
“It’s better than looking at a book all day,’' says a 5th grade boy in Ashworth’s class. “It’s like Teenage Mutant Ninja Turtles.’'
One strength of the approach, according to the teachers, is that it allows all children to participate--even those who do not normally do well in mathematics. Likewise, students who have not had much preparation at home for learning can contribute as much as those with richer home lives--a benefit in classrooms such as Ashworth’s, where, the teacher says, “children who have been to Europe sit alongside others who live in a crack house.’'
“It minimizes the diversity,’' she asserts.
The biggest challenge for the research team now is finding an accurate way to measure how lessons with Jasper contribute to students’ learning. “We wouldn’t be happy with just standardized test scores,’' Vye says. Tests administered so far evaluate students’ attitudes toward mathe- matics, their ability to solve similarly complex problems, and their understanding of basic mathe- matical concepts, such as fractions, decimals, or time.
But some teachers say they are doubtful that such tests can gauge the value of the program. “I don’t think anything can accurately measure what the children get from this,’' Ashworth says.
“What this does is teach them to be independent and flexible thinkers,’' Johnson, the private school teacher, says. “These are skills that are almost impossible to teach in a textbook.’'
Debra Viadero
