"How'd you get that?" one boy says, an edge of frustration in his voice.

"Push the funky button at the top," another student calls out from the next aisle. Across the room, a third student crows triumphantly: "I got it! I got all three!"

"You suck," mutters the boy behind him as he continues to punch buttons on his hand-held calculator, the Texas Instruments TI-83.

At the front of the room, teacher Wendy Driscoll guides the Helena High School freshmen through a problem that blends concepts from physics, biology, algebra, and pattern analysis. As she enters numbers and functions on her pocketbook-sized TI-83, her work appears bigger than life on an overhead screen.

Students began exploring the problem a day earlier in the science lab, where they burned cereal to estimate the amount of energy (kilocalories) locked inside the grain. Now they're tackling the math, some hunched intently over their calculators, others slouched casually in their chairs, all fully engaged at 7:45 on this chilly Montana morning. They're computing the amount of time it takes a person weighing 60 kilograms to burn 100, 200, 300, 400, and 500 kilocalories when doing each of three different activities-one requiring a high amount of energy (playing basketball), one requiring a moderate amount of energy (lifting weights), and one requiring a low amount of energy (watching TV). Then, using their TI-83s, the students are entering the results to create a "scatterplot" graph showing the relative slope of each activity. The calculator/ computers can generate a graph instantly with a few taps of the finger. The old way-plotting points on a piece of graph paper-is by comparison slow and laborious.

"For this particular lesson," says Driscoll, "we couldn't have covered that much territory if we were doing it by hand-plotting all those points and doing three different sets of equations. There's no way. The TI-83 allows us to investigate a lot more equations-and a lot more sophisticated equations-than we can with pencil and paper. My seniors are doing some really sophisticated polynomials that they probably wouldn't be doing without this technology."

The problem that engrosses the freshmen is from a module called "Yesterday's Food Is Walking and Talking Today"-part of a technology-intense mathematics curriculum developed and field-tested by teachers in Montana. A five-year project launched in 1990 and funded by the National Science Foundation, SIMMS (the Systemic Initiative for Montana Mathematics and Science) had several major goals:
Incorporate technology into all facets and at all levels of the math curriculum
Integrate high school mathematics with other disciplines, including science, social studies, and language arts
Design a curriculum that reaches all students, both college-preparatory and non-college bound
Draw more females and American Indians into math and science

The SIMMS Integrated Mathematics curriculum (published by Simon and Schuster) from which the Helena students are working presents math problems in real-world contexts. Instead of just "solving for X," Driscoll says, kids get a chance to predict, explore, interpret, evaluate. They get a chance to think like geologists, sociologists, engineers, architects. Working in pairs or in teams, they use real data to solve problems encountered in the home, the workplace, the community, and the environment.

"What you don't hear in a SIMMS classroom is, 'Where are we gonna use this stuff?'" reports Driscoll, who worked as a computer program analyst for oil and gas with the Montana Department of Natural Resources and Conservation before returning to the classroom several years ago. Now chair of the Helena High math department, Driscoll spent four summers in Bozeman writing modules for the SIMMS curriculum. The Level I (freshman) module in which Driscoll's students are working presents these kinds of problems:
During a unit on volume, Driscoll's students will use data from the infamous Exxon Valdez oil spill of 1989 to calculate, among other things, the volume and surface area of the spill. Students are encouraged to search the Internet to find data on other disastrous spills.
After creating a kaleidoscope with hinged mirrors, students explore mathematical properties of a variety of polygons (triangles, quadrilaterals, pentagons, etcetera). Students then use their understanding to explore such real-world problems as laying pipe for an oil pipeline, building a trail, and predicting the path of radio waves and laser beams.
A unit titled "So You Want to Buy a Car" looks at a number of variables in car design, including the relationship between highway fuel economy and weight. In one problem, students create scatterplots of data from various car models, then use the graphs to estimate how far each car can travel in a given number of seconds.

Electronics play a role in virtually all the SIMMS modules. "The technology serves as an investigating tool," says Driscoll. Throughout the six levels of the curriculum, students use the graphing calculator, which has built-in software and can be networked so students can share data. Higher-level students also use another Texas Instruments device, the Calculator-Based Laboratory (CBL), which uses a probe or sensor to collect scientific data (temperature, motion, heart rate, pH, light, sound, and so on) in the classroom. One unit for juniors involves calculating the rate of change in the motion of a soccer ball rolling down a ramp. The CBL picks up the ball's motion. The data flows into the graphing calculator, to which the CBL is linked, to produce an instant graph.

Personal computers are used, too, for spreadsheets, geometry construction, statistics, symbol manipulation, and word processing. But the hand-held graphing calculators have one obvious advantage over PCs: Each student can have his or her own piece of equipment.

"On computers, it's four students to one piece of equipment," says Dave Campbell, a Helena math teacher who works closely with Driscoll in delivering the SIMMS curriculum. And, he notes, the hand-held calculators can be linked to the school's computer network to produce printouts of graphs and other data.

The best thing about SIMMS, Campbell and Driscoll report, is that through open-ended exploration of math concepts, students can attack problems with greater depth-and with more daring. "The teacher plays much less of a role in SIMMS than in a traditional math class, especially at the higher levels," says Driscoll. "There are a lot of independent learners in SIMMS. And they're really good risk-takers. But weaning them away from being spoon-fed is not easy."

TEACHER'S FOOTNOTES

On integrated math:
"It seems to work well with some kids who have never been successful before. At the same time, there are some very bright students in the class who prefer it because it's more meaningful to see (math concepts) in context. But it has its detractors. There are some people who feel that it isn't really math because it isn't what they had when they were growing up. They want more drill and kill."

On costs:
"The graphing calculators cost $88. Most kids buy their own. For students who can't afford them, the principal has a fund that will pay for half. Once in a while at an open house, a parent will say something about the cost-that it's an outrageous expense. We point out that a pair of basketball shoes costs $110 and only lasts for a season. Students will use the same calculator all through high school and on into college."

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