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MISSOULA, Montana— For David Bixby, steering a roomful of fifth-graders through the treacherous shoals of learning is like climbing the icy north face of Mt. Rainier. "There's a potential for disaster all the time, and there's also the potential for glorious success," says Bixby, a first-year teacher at Hellgate Elementary School in Missoula, Montana. "I get the same kind of high from teaching that I get from mountaineering.
Things can go so well, and they can go so wrong, and I need to continually improve my skills." Hellgate Elementary offers plenty of opportunities for Bixby and his colleagues to build their skills. A hotbed of technology set implausibly in the wilds of western Montana, Hellgate has five computers and a color printer in every classroom. It has digital cameras, LCD (liquid crystal display) projectors, a flatbed scanner, and access to a sophisticated lab at the middle school next door, where students can experiment with real-world skills such as computer animation, robotics, broadcasting, rocketry, and Web page design. Field studies-an ongoing archaeological dig, for example, and a habitat study carried out jointly with the University of Montana, the U.S. Forest Service, and Montana Fish, Wildlife, and Parks-provide more opportunities for linking technology to learning goals. This high-tech haven was just the place for Bixby, who had used state-of-the-art hardware and software to crunch data and map coastal waters as a hydrographer (an underwater mapmaker) for the National Oceanic and Atmospheric Administration. He weaves his techno-tools into all corners of the curriculum. For example, his students will become amateur surveyors and hydrographers when they use rods to measure the depth of local McCormick Pond, and then enter the data on spreadsheets to graph cross-sections of the pond (software: Microsoft Excel). Bixby hopes to find a piece of "shareware" on the Internet that can use the students' data to create a contour map-the first one ever made of McCormick Pond. Posted around the room are Web sites for general research, such as the self-described "mother of all search engines" (http://www.mamma.com), or for specific information, such as the journals of Christopher Columbus (http://www.fordham.edu/halsall/source/columbus1.html). Bixby's kids build skills in tracking down data through Internet scavenger hunts. His students' research reports take the form of "virtual field trips" where classmates can share, for example, an exploration of Mt. Rainier, a walk on Mars, or a wild-mushroom hunt. Students are learning to bring their multimedia presentations alive with music (software: Microsoft PowerPoint). One recent morning, for instance, Nicole, a student with Blackfeet ancestry, was noodling with the sound mixer on her computer, trying to coax just the right tones from her Indian Moments CD for her presentation on Montana's Native American tribes. Even free time in Bixby's room is laced with technology. Instead of offering extra recess as an incentive for good behavior, Bixby pulls in hordes of kids every Thursday for a planetarium presentation on a Power Macintosh (software: MacAstro). Night sky images projected on a screen can zoom in for a close- up view of planets, stars, and whole galaxies. By year's end, students will have added celestial navigation to their accomplishments. A recent lesson on mathematical pattern analysis had Bixby's kids transfixed. The problem-about a Web-savvy queen and a math whiz named Bob in a land where the coin of the realm was a golden bean-went like this: Once, a long time ago, the queen of a far-away land needed to hire a gardener to take care of her garden of a thousand roses. Soon after she put a notice on her Web site saying she needed a gardener, she received an e-mail message from a mathematician. His letter stated that work in the math field was hard to come by and he wanted to take a try at gardening. The queen replied, "Since it sounds like you have very little gardening experience, I would have to start by paying you 100 gold beans for the first year. After that, for the next 15 years, I will increase your pay by 100 gold beans each year. For surely you will become a better gardener and worth more beans each year." The mathematician, who called himself Bob, replied with a fax: "I cannot take such a generous offer. I propose that you pay me just one gold bean the first year, and then as I become a better gardener, double my pay each year until I retire in 15 years." The queen created a spreadsheet to determine whether she should take Bob's offer or stick to her own plan.¶
The students' task was to respond to the following instructions and questions:
Describe your plan for solving the problem.
Pairs of students confer at their desks as Bixby strolls between desks, offering guidance and answering questions. Student pairs begin heading for the waiting computers, spilling into the spare classroom next door to attack the problem. Using a spreadsheet (software: Microsoft Excel), Jeff and Jesse collaborate on entering the queen's beans in one column, Bob's beans in the next. They then instruct the computer to fill in the numbers for the next 15 years. Across the room, Derek has an insight. "Hey, she was trying to cheat him," he protests, as he discovers, along with Jeff and Jesse, that the queen's offer nets Bob only 12,000 beans. Bob's plan, on the other hand, would earn him 32,767 beans. The color printer begins to hum, and soon out rolls Jeff and Jesse's bar chart-a graphic depiction of the ever-widening discrepancy in projected earnings between Bob's and the queen's plans, generated instantly by the computer. "I liked that," Jeff enthuses afterwards. "That was a cool problem." Remarks Bixby: "I could never get them to be on-task for so long in paper and pencil. They really get focused when they work on the computer." Teaching kids how to use spreadsheets "makes a valuable pre-algebra lesson," Bixby observes. "Spreadsheet functions, formulas, graphs, and charts are algebraic." Spreadsheets also give students "a clear visual layout of numbers and number relationships independent of the child's drawing and organizational skills," he notes. Another advantage of keyboards over graph ite: Kids can think more deeply and broadly without getting bogged down in computations. While computational skills are important for kids to master, an error in arithmetic can mask the student's mastery of a larger concept, Bixby notes. "The computer can perform higher-order operations on data much more quickly than students could do with paper and pencil," Bixby explains. "It extends their thinking." Getting kids to reason, analyze, and evaluate-the "higher-order" kinds of thinking that countless reformers and critics say schools should cultivate-is Bixby's true quest. Setting students loose on the Internet, and then having them assess the quality of information they encounter, is an authentic exercise in critical thinking, he says. "There's no limit to who can place information on the World Wide Web," he says. "Consequently, there's no guarantee as to the quality of information on the Internet. Students need to become critical information users." Bixby suggests that teachers have their class develop a system for rating the quality and reliability of Internet sites. A checklist might answer such questions as: What is the goal of the site-education, advertising, entertainment? Who maintains the site, government agency, nonprofit organization, business? Is the site trying to persuade the user to adopt certain ideas, or is it just providing factual information? Does the site give sources for its information? Summing up the plusses of computers for students, Bixby says: "Technology in our classroom offers immediate feedback to students during problem-solving activities. "And," he adds, "it gives us a direct link to the real world."
On presentation software:
On the story problem:
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Date of Last Update: 9/28/01 
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What will she find out? Make a prediction.
TEACHER'S
FOOTNOTES
