UCSC Review Fall 1992
Partners in the Classroom by Jennifer McNulty
Lectures are obsolete in Jeanette Duran's sixth-grade math class in Watsonville. Instead, Duran's students work together to tackle assignments and projects. When students get stuck, Duran offers encouragement and direction, but they're often able to help themselves and move on. Researchers at UC Santa Cruz say Duran's classroom is a snapshot of what math education in American schools could--and should--be. Unfortunately, it's an anomaly in a country where a recent report by the U.S. Department of Education concluded that half the graduating high school seniors lack the ability to do much more than simple problem solving. "Most people would be embarrassed to say they can't read, but it's not uncommon to hear people say 'I can't do math'," says UCSC mathematics professor Ed Landesman. The outlook in science education isn't much better: Performance among 9- and 13-year-olds was static between 1970 and 1990, and achievement among 17- year-olds actually dipped.
As the nation faces dual crises in math and science education, UCSC researchers are working with classroom teachers to improve teaching techniques, design more captivating lessons, and meet the needs of students in today's increasingly diverse classrooms. UCSC has a long tradition of working in partnership with local schools, and faculty believe strongly that professors and teachers can learn from each other.
This collaborative approach reflects contemporary education theory, which asserts that learning is a creative process of social interactions between teachers and students, and among students working together. It's a hands-on, cooperative effort that differs from the traditional "drill-and-practice" model of teachers lecturing to students who learn by rote.
Three local UCSC research projects capitalize on this teamwork approach to better math and science education: One project, in which Jeanette Duran is involved, is designed to get students hooked on math by making lessons more relevant to their lives; another seeks to unlock the secrets of math reasoning by studying the learning process itself; the third is an ambitious, three-year science education project that will train 300 science teachers and give them the special skills they need to reach children whose first language is not English.
A thematic approach to math education
In Jeanette Duran's classroom at E. A. Hall Middle School, students were introduced to geometry by building cardboard models of space stations during a lesson on the solar system. Students huddled in pairs to figure out the surface area and volume of their models, and then raced to do three-dimensional drawings of their creations. The activity is typical of what's called a "thematic" approach to math education. By developing math lessons around themes students can relate to, researchers are integrating math into the curriculum in a way that has meaning to youngsters. "We're playing and learning at the same time," says 12-year-old Gladys Jimenez.
Math professor Ed Landesman and Ron Henderson, a professor of psychology and education at UCSC, are involved in ongoing research with Duran and three of her colleagues at the middle school. With the classroom as their laboratory, the team has already tested several themes to see which appeal to teenagers-so far, sports was a hit, as was outer space, but everyone's favorite to date was a segment on careers that focused on bridge building.
Students were exposed to the fundamentals of running a business when they formed "companies" and designed and built model bridges. The youngsters learned about geometry, architecture, accounting, engineering, and even physics during the project, which ended with stress testing of their toothpick models. "The kids got all excited about bridges, and we threw in a lot of math. They're learning just as much, but they're having fun, too," says Landesman.
Research shows that students typically learn math better if it is directly related to their everyday experiences. And working on themes allows students to bring together their different math skills and apply them in an integrated manner that mimics life outside the classroom. "In traditional classes, students are moved from one topic to another in a very fragmented way and they never get an opportunity to use what they're learning,"says Henderson. "That's not the case with thematic education." It's a method that educators say is long overdue, and that students and teachers applaud.
"Teaching them how to do the practical things, applying math to practical things, that's what counts," says Duran, head of the math department at the school. "In the beginning, it takes a lot of work to get it set up, but then the kids can take off with it because they've got the basics."
Adam Jones, who teaches seventh-grade math at the school, says students respond with gusto to almost any innovation. During the outer-space segment, Jones's students made paper space shuttles and used balloons, string, and a stopwatch to learn how velocity relates to distance and time. "It's better than having to work out of the book," declared 13-year-old Tony Lopez. "You get to see how this stuff works."
After class, Jones was pleased. "My goal is to keep kids from disliking math," he says. "I use games, lures, gimmickswhatever I have toand I sneak the math in."
Landesman and Henderson, who hope ultimately to package the best of the theme-oriented lessons for distribution to other schools, are reviewing the success of the various themes with the middle school teachers. Meanwhile, the teachers are back in the classroom, perfecting the lessons. "We're not telling the schools what to do," says Landesman. "We're working together to make better environments for learning."
Unlocking the Secrets of Math Reasoning
One clue to the problem of math education in this country can be found in patterns of student achievement: The math proficiency of American children is average through the eighth grade but drops toward the bottom of the range for industrialized nations at about the level of tenth-grade algebra. "Our kids can do simple mathematics-they can add and subtract and do basic operations to solve problems," says UCSC education professor Laurie Edwards. "But they can't do two-step problems, measurement, geometry, and more complex problems."
To help bridge that gap, Edwards has set her sights on demystifying the math reasoning process, which most people would recognize as the formal task of developing and testing hypotheses in geometry. But Edwards uses a broader definition, saying kids who get beyond the trial-and-error stage of problem solving and can logically explain their findings are beginning to "think like mathematicians."
For example, when Edwards asks students whether they get an odd or even number when they add two odd numbers, most will say even and explain it by saying that's what happened every time they tried it. But if they can explain why that is true, then they're heading for the next stage of math reasoning. The ability to demonstrate one's reasoning process is a skill that spills over to areas outside of mathematics, and Edwards would like to see children encouraged to develop such skills throughout their K¯12 education.
To glean insight into how the reasoning process works, Edwards videotaped ten tenth-graders from Santa Cruz High School as they tackled the even number-odd number query, observing as they attempted to explain their reasoning to her. In another phase of the project, she videotaped the students working in pairs at a computer workstation as they puzzled over problems in geometry, watching as they tested their ideas and collaborated to solve the problems.
Edwards, who is analyzing the videotapes, says the number problem reveals that the most successful students relied on visual images to explain their thinking. Experienced mathematicians use visual images, too, but they also use the formal, symbolic systems of algebra and geometry to explain and test their ideas. Edwards is intrigued by the early indication that even students who had studied algebra for a year in school turned to visual images such as number lines to explain their conclusions. "We know quite a bit about how experienced mathematicians use these formal systems, but what we don't know is how teachers can encourage kids to go beyond everyday reasoning and become more disciplined thinkers--which is useful even if they don't all want to become mathematicians," says Edwards.
Improving the Way Science Is Taught
As our lives become increasingly driven by technology, vast sectors of Americans will be left behind if the high dropout rates and low representation of minorities in the sciences are not reversed. At Watsonville High School, one of the largest in Santa Cruz County, one-fifth of the freshman class drops out by the end of ninth grade; 90 percent of the drop-outs are Latino.
In order to stem the flow, UCSC researchers are joining forces with the Santa Cruz County Office of Education to oversee "Science Connections," a three-year collaboration designed to improve the quality of K¯12 science education. Ten outstanding science teachers from area schools and ten graduate-level student teachers at UCSC will receive in-depth science training from UCSC faculty and will learn the latest teaching methods from education professors, says Eugene Garcia, dean of the Division of Social Sciences and a professor of education and psychology. Together this force of 20 science educators will share their newfound expertise with 200 veteran teachers and 100 student teachers in UCSC's Teacher Education Program.
Planners hope Science Connections will revitalize science education the way literacy campaigns stirred educators to focus attention on reading and writing. Too often, Garcia says, ill-equipped science teachers are only "one page ahead of the kids." Moreover, the project offers teachers a rare opportunity for professional growth, says codirector Nancy Giberson, assistant superintendent for educational services in the Santa Cruz County Office of Education. "Teachers are so busy taking care of business on a daily basis that they don't have time to go out and develop professionally," she says.
A key goal of Science Connections is to reach out to students with limited English proficiency--about 22 percent of students in Santa Cruz County. To do this, administrators will call on faculty affiliated with the National Center for Research on Cultural Diversity and Second Language Learning, which is based at UCSC.
But Science Connections doesn't stop there. Project planners hope to broaden the base of expertise by involving the local science community and utilizing the region's vast natural resources, such as the Monterey Bay Aquarium, Elkhorn Slough, and UCSC's Long Marine Lab. Even the roller coasters at the Santa Cruz Beach Boardwalk could play a role during an introductory physics lesson. "Science is like writing. You don't learn it in the abstract--you learn it by doing it," says Garcia.
Each of these projects relies on the creativity and enthusiasm of committed teachers--educators who are finding ways to do their jobs better despite increasing challenges in the classroom.
Although the projects are being carried out independently, they use similar strategies to make lessons more meaningful to students: hands-on learning, cooperative education, and relevant subject matter.
They also share an intellectual base that is rooted in the work of Soviet scholar L. S. Vygotsky, who died in 1934 but whose ideas evolved and came to the attention of Western intellectuals in the 1970s. Out of the movement known as social constructivism has emerged a new understanding of how knowledge is acquired. Contrary to earlier thinking, which saw knowledge as a fixed thing imparted from teacher to student through memorization or the even more passive process typified by the image of a teacher "pouring" knowledge from a full pitcher into an empty head, the new paradigm sees knowledge as the result of social interaction. In the case of education, that interaction focuses on the exchange between teacher and student and the process of discovery among students that underscores learning.
There has been an explosion of interest in this approach to education in the last decade, says Roland Tharp, chair of the Board of Studies in Education at UCSC. "This approach emphasizes continual creation, a lot of experimentation, and demands great vigor," says Tharp.
Researchers at UCSC are modeling their collaboration with local schools on this theory. In a traditional approach, Landesman and Henderson would have developed their ideas about thematic education on their own, trained teachers to use the ideas, tested the children afterward, and written a report on the results-perhaps not even sharing the evaluation with the teachers. "When we say we believe in cooperative knowledge in the classroom, we believe in cooperative knowledge for ourselves, too," notes Tharp.
"The driving principle is that we may know some things, and practitioners may know some things, but together we can know more," says Garcia. "It's real teamwork that requires the endorsement of administrators, teachers, the teachers' unions, everyone."
Tharp calls this approach "the wave of the future"--both in the classroom and in collaborations between schools and university researchers, but he concedes that there are some major obstacles to overcome before the tide ushers in a new era of educational progress in this country. For the approach to work on a large scale, teachers will need time off to expand their own knowledge and renew their energy. "This kind of work will kill you. It's exhausting," Tharp says bluntly. But costly radical changes would pay off in the long run with less teacher burnout and, most importantly, better educated children.
In the midst of the clamor over low test scores and the failure of American schools, Tharp urges Americans not to lose sight of the loftiness of our goals. Unlike many industrialized nations, we strive to educate each and every child through the twelfth grade and to accommodate the tremendous diversity in today's classrooms. That, he says, is an enormous task.