Modeling Experience: A Key to Understanding

Dvonte Miller and Yazmin Urrutia control the behavior of their agents and observe the results on a projected graph. They respond to modeling technologies with the same enthusiasm as they do to playing video games and are motivated to learn math and science.

Photo courtesy of the Center for Connected Learning and Computer-Based Modeling.

Uri Wilensky, associate professor of learning sciences and computer science, came to a discouraging yet pivotal realization while a graduate student in mathematics at Harvard. He had just been named the best calculus teaching fellow at the university, but the honor felt a bit hollow to him.

"I looked at my students and saw that they weren't really understanding the subject," Wilensky recalls. "My main virtue was motivating them, but despite that I was not helping them to understand."

He then met a professor at MIT, Seymour Papert, who was excited about how computers could make mathematics more accessible and concrete. Wilensky observed a program this professor had developed to teach geometry to elementary school students. "I saw young students do incredible geometry on computer screens and thought, 'Maybe this is a whole different way of learning about math.'"

The more Wilensky thought about computers as educational tools, the more he saw their potential to help students comprehend important scientific as well as mathematical concepts. "There's a lot of science where either the subject is so small you can't see it, like microbes, or too big, like galaxies, or too slow, like life spans in populations being studied," he notes. "The computer is able to change scale and time and space and conduct experiments over a few minutes that would otherwise take years."

As a result of his growing awareness of computers' potential, Wilensky changed the course of his career, leaving mathematics to blaze new trails in the development of mathematics and science learning tools. Today he directs Northwestern's Center for Connected Learning and Computer-Based Modeling (CCL), which promotes the creative use of technology to deepen learning. Funded by Northwestern, the National Science Foundation, and commercial sponsors, CCL comprises staff and students working with researchers, software engineers, curriculum developers and model builders from Northwestern and several other universities.

"A big driving force for me is that so much of math and science instruction is disconnected and unmotivating and removed from connections to students' life experience," Wilensky explains. "Many educators try to teach students in artificial ways without making connections to their mental models and lived experience."

Most of what CCL does grows out of the study of complex dynamic systems, which offer a new framework for looking at the world. All around us, in nature and in society, we find regularities and patterns — in the formations of flying birds, snowflake crystals and the activities of the stock market. Scientists call these patterns "emergent phenomena," which result from the interactions of large numbers of individual entities, typically called "agents."

"Almost all patterns in nature are emergent," Wilensky says. "For example, there is no leader bird that other birds follow. Patterns emerge out of the behavior of individuals and the adjustment of that behavior in interaction with other individuals, sometimes in surprising ways."

For the last 16 years Wilensky has created computer-modeling environments that enable students to take part in simulations of emergent phenomena. The modeling environments give students a chance to experience situations ranging from the behavior of ants in colonies to the effect of racial prejudice on segregation in cities. Wilensky notes that computer models can be used by a wide range of learners — from young children to university researchers — and across a wide variety of domains, including natural sciences such as physics, chemistry and biology, and social sciences such as psychology, sociology and economics.

NetLogo is one of the core modeling languages Wilensky has developed. It enables learners to give simple rules to agents in a simulation and observe the collective result of the agents' behavior. In one model high school students study a simple predator-prey ecosystem on a computer screen. Students create and give rules to "wolves" and "sheep" to govern their interactions. Rules might include assigning an energy level to each wolf and sheep that increases when they eat and decreases when they move, with death resulting from an energy level falling below zero. Students watch the ensuing action on the screen, as wolves pursue sheep, which may or may not escape being devoured. A graph beside the image translates the fluctuating numbers of each population into what look like ragged sine waves.

While the equation on the graph presents a classic mathematical result from the experiment, Wilensky argues, students' interaction with the factors involved in arriving at the result give it new meaning. "The students control the behavior at the micro-level of the agents, and then observe the results at the macro-level of the populations," he says. "In doing so they reach a powerful understanding of predator-prey dynamics."

Many patterns in human society can also be modeled emergently. Economists traditionally model economic scenarios using equations that average over the population characteristics. But if we use an emergent modeling approach, we model individuals by giving them different endowments and purchasing and spending habits, and then observe how such values as the price of a commodity emerge from the actions of individual buyers and sellers. This kind of approach has the advantage of being much more accessible to students and non-experts as well as allowing the model to be continuously questioned and improved.

With HubNet, a newer modeling program for doing "participatory simulations," each student controls his or her own virtual agent or "turtle" with either handheld calculators or laptop computers. Information from each child's device is processed through a wireless network and magnified on a screen through an overhead projector. In one popular activity called "Disease," students participate in a hands-on lesson in epidemiology. One student's agent is randomly infected and infects other agents it touches. As in NetLogo, a graph charts the rate of infection. The students can see how their actions influence the outcome of the predictable "S" curve on the graph.

"It's like a video game in a sense," observes Dor Abrahamson, a learning sciences researcher engaged in modeling research at CCL and in classrooms. "Kids have an immediate sense of identification with their 'turtles.' They say things like 'I am next to you' or 'I'm coming to get you' or 'Oh no, you made me sick.'

"In a normal lesson the intricacies of complex phenomena remain opaque," Abrahamson continues. "At best you'd end up with a mathematical equation, but you'd have no prospect of understanding why this input yields a certain outcome. We're making the process into a glass box you can see through."

Wilensky and Abrahamson say that models can create dynamic simulations of virtually any complex system and are as accessible to neophytes as postdocs. "That's one of the cool things about modeling—there are so many possibilities," Wilensky says. "Even children exploring could find things that scientists haven't found."

Although a body of classroom cast study evidence suggests that students, teachers and administrators find modeling technologies effective and motivating, Wilensky and colleagues want to quantify these effects on learning. A couple of years ago they embarked on a project called "Modeling Across the Curriculum" (MAC), which includes a longitudinal study intended to measure the impact of model-based technologies in high school science classes.

Wilensky hopes that MAC will prove that modeling helps students learn science and math concepts. "We have seen dramatic gains in learning and motivation, but they can be hard to formally assess. Current assessments are asking static questions, not about the dynamics of change. We are researching authentic assessments of that learning and how it develops."

He also says that using the technology poses a few challenges for schools, the most formidable being the demands it can put on teachers. "Some teachers are comfortable with using the technology and others less so. It depends on how much they think their role is to be the expert. The more teachers think of themselves as partners in knowledge gaining, the easier it is for them. Of course, we work to give teachers professional development on the use of our materials."

In addition, most schools have limited funding for computers in the classroom. Wilensky, however, asserts that the cost of much of the technology isn't prohibitive. For instance, running the HubNet programs requires equipment already found in most classrooms — inexpensive calculators, one computer, one projector and an inexpensive network for the calculators. "When I started doing this work, I needed a supercomputer to run the models. People thought I was crazy," Wilensky says. "They said, 'How are the schools ever going to afford it?' But you can see the tide is changing. The models now run on PCs and handhelds, and there clearly will be a time when computers are natural parts of students' interactions with schools."

Wilensky is quick to add that not all technology made for the classroom is worthwhile. "I am not a blind fan of technology for technology's sake. Lots of uses of technology in education aren't creative or fun and don't take advantage of the computer's power to visualize behavior and change, such as computer-based tutors that drill students through standard stuff."

But he predicts that as time goes by, modeling will become more and more important in almost every sector of learning. "We are at the dawn of modeling as an education tool. More and more educators are recognizing its value. Now it's a matter of when and how, not if."

Lisa Stein (GJ94) is a freelance writer.
By Lisa Stein