Modeling the scientific method

University researchers have helped achieve a startling effect by using models to teach mathematics and science to elementary school students: Fifth graders are performing at 12th grade levels.

Those Verona fifth graders use models of all sorts to learn the process, not just the results, of science. They’re modeling well, for they visualize and interpret data like high school seniors, as measured by questions taken from national assessment tests.

Second graders slide toy cars, constructed of Lego building blocks, down inclines to demonstrate the effects of weight and friction.

Verona teachers in grades K-5 have worked on modeling for four years with researchers Richard Lehrer and Leona Schauble, members of the educational psychology faculty with appointments in the Wisconsin Center for Education Research.

Among other things, the students have created a compost column to observe rotting; a map to display fruit fly density based on available food; and graphs and other visual displays to represent variability and rate of change as plants and insects grow.

“The students are visualizing their thinking through models,” says Lehrer. “Historically, mathematics started with geometry, which is very visual, but in the past two centuries, mathematics has increasingly emphasized abstract algebra and related forms of symbolization.”

The Verona project uses more visual, observation-based mathematics. “We are not abstractly dropping math into children’s heads,” says Lehrer. “That approach is why a lot of people don’t understand math. Instead, we help students learn math by building on their experience.”

Second graders, for example, slide toy cars that they construct out of Lego building blocks down inclines of different steepness. “The students explain variations in the speed of the cars by considering things like friction and the weights of the cars, and by mathematically representing the steepness of the inclines,” says Schauble.

That modeling exercise and others, says Lehrer, “encourage students to think about regularities and patterns that describe and organize what they observe around them. It’s what scientists do.”

Models give students room to think on their own two feet. For instance, when the compost column was used for observation of rotting, students were interested in mold but had a basic misconception: The mold couldn’t be alive.

Rather than simply telling the students they were wrong and moving on, the teacher designed a way of enabling students to observe more mold, this time on bread. When they examined it under a microscope, they concluded that the mold was indeed alive. This modeling allowed students to expand their web of inquiry, just as a scientist does.

“Textbooks hide models,” says Lehrer. “They just list the facts of science, which are the outcomes of models.”

That’s why it’s important that modeling transcends mere fact listing, says Schauble: “Making knowledge, which students are doing with models, is far different from just consuming it.”