On the cusp of a revolution: new software tools help students see and make connections in math classes and more. (PC Software).
One variety didn't really understand the concepts Keyton graphed on the board but could see a pattern emerge and then could imitate the drawings pretty well with a protractor and compass. The second sort had innate spatial intuition by which they grasped the meaning behind the proofs Keyton was teaching. But the third, blessed with neither skill and confounded by the abstract, rarely was successful in geometry class.
Then along came calculators and computers that run programs like TI's Cabri Geometry II[TM] computer software. Keyton has witnessed a transformation.
Instead of taking hours to painstakingly construct triangles on dizzying graph paper, Keyton's students can graph them in seconds with the help of Cabri Geometry II, a dynamic, interactive geometry software package.
Students can graph triangles, for example, changing one vertex then watching as the program redraws each triangle. Keyton confirms that this software has helped geometry "click" for many of his students.
"Those kids have been drawn in tremendously," says Keyton, who teaches math at the Illinois Mathematics and Science Academy in Aurora, Ill.
Jill Gough can relate. As a math teacher at the Kiski School in Saltsburg, Penn., Gough and her students often use PC software called TI InterActive! for class work. This versatile program includes an enriched word processor that will create documents mixing text, mathematics and graphics.
Gough first uses the program to download information from the Internet for a lesson, then her students use it to graph and plot the data before writing about what they observe. TI InterActive! is an invaluable tool for students who don't easily grasp abstract concepts, Gough says.
"There are lots of kids that need to see it and make it happen themselves," Gough explains. "TI InterActive! allows kids to do that."
Assisting With That Middle Step
Since the mid-1980s, the use of graphing calculators and educational software in high school math classes has exploded. Research from the early 1990s showed that graphing calculators brought many benefits to math class, from increasing student confidence to helping them better understand math concepts to improving students' problem-solving abilities.
Building upon this background, software like TI InterActive!, and other offerings from Texas Instruments have led math educators to what Keyton sees as the cusp of a revolution in mathematics education.
Math requires three stages: converting real-world problems into equations, finding the answer through the process of solving the equation, and turning the solution into a real-world answer. Educational technology is easing movement from the first step to the third--the two most difficult steps--by speeding up the second. That's going to help math teachers reach more students, especially those who get bogged down by the second step, solving equations, says Keyton.
"I think there's still a big emphasis in understanding what math is and how it works," Keyton says. "But we're now at the stage of having kids learn how to use math in daily life, rather than abstract concepts with no connection to reality." And that's a real change, he says, for math instruction.
Texas Instruments has helped educators reach this stage through their long-term commitment to finding out what teachers and students need, Keyton says. Rather than taking existing products developed for the business world and tweaking them for the classroom, Texas Instruments has always involved professionally trained math educators in their product development.
"That's what our business is built on--developing educational tools with educators," says Tom Ferrio, vice president of the Educational and Productivity Solutions Business for Texas Instruments.
The resulting products are as powerful as are they are tailored. The following provides some details on several TI software programs and tools:
Integrated computer software for math and science classes, TI InterActive! encourages high school and college teachers and students to investigate ideas. Teachers can use the software to download data for interactive lessons that integrate exploration, visualization, data analysis and writing. Students then can use the same software to master difficult concepts, improve their problemsolving skills and download lessons.
TI InterActive! includes an enriched word processor; TI graphing calculator functionality and connectivity; a symbolic computer algebra system; an integrated Web browser; and a data editor with spreadsheet capability. This versatile tool is designed in all respects to "enable learning."
Indeed, Texas Instruments developed TI InterActive! to marry the highly useful technology of graphing calculators with the ubiquitous presence of personal computers. The software makes many of TI's most popular graphing-calculator capabilities more accessible to teachers who want to use computers in the classroom, too.
Gough stresses mathematical modeling to her students so she and her students use TI InterActive! almost daily, she says. The program has a unique "smart" extraction feature, which allows her to copy and paste data from Web sites or other sources directly into a table template where it appears pre-formatted. Thus, her students can get right to the business of interpretation and analysis.
"You get to the math part in an easy fashion," Gough says. "It's just a really powerful tool."
Cabri Geometry II
With Cabri Geometry II, students can see patterns and draw their own conclusions. The comprehensive software includes Euclidian, transformational and analytic geometry, and students and teachers report it's easy to learn and use.
Designed for use on personal computers and with TI-92 Plus and TI-89 handhelds, Cabri Geometry II features Cartesian and polar coordinates. With it, students can draw lines on their computers or handhelds as they would with pencils, protractors and compasses, but they can do it much more quickly and easily. With the program's property-checking system, for example, students can perform tests based on Euclid's five postulates. Cabri Geometry II is the first interactive geometry package with analytical geometry built in.
The software's interactive nature helps students construct a solid foundation for understanding the basis of math, Keyton says.
"Rather than be told," This is a proof, now discovery is part of the equation," Keyton says about his students' use of the software. "A lot of times there's no reason to buy into the proof. Once they discover theorems, they're curious about whether or not they're true. Eventually [using Cabri Geometry II] They see what appears to be true. That's the essential reason for proof."
In other words, some students have to see it to believe it, and TI's dynamic geometry software lets them see it.
Derive 5--Higher Math
Derive 5 college software does for the higher math of algebra, trigonometry, calculus and linear algebra what the scientific calculator did for arithmetic. Gone are the hours performing long and tedious computations. Like TI's other software, Derive 5 allows students to get to the business of math more quickly.
This program is used mainly by professional and research mathematicians and in higher-order math classes in college. Teachers hail its use as a tool to explore different routes to solving problems, while researchers like its reliability in quickly solving complicated problems.
Derive 5, needing fewer than 4MB of disk space, solves both symbolic and numeric problems and can plot the results in two or three dimensions. It comes with a library of utility files that define functions for solving first- and second-order ordinary differential equations; users also can create their own utility files.
TI-Graph Link and TI Connect Link Software
TI-Graph Link is software that connects calculators to the rest of the world, and keeps them up to date. The TI-Graph Link is a cable that enables users to upgrade TI's Flash-based graphing calculators by downloading new software and data from the Internet.
It's one piece of technology that makes TI's products a bargain for educators, most of whom can't afford to buy new equipment every time new software comes out, says math teacher Keyton.
Although TI-Graph Link still is going strong,TI recently released its successor, link software called TI Connect. This newest product is designed to enhance the connectivity between TI's graphing technology and the Internet.
TI Connect includes every feature and capability of Ti-Graph Link, as well as some new ones: Smart Connections makes connecting cable, calculator and computer easier; TI Connect automatically detects and notifies users of updates to the TI handheld's operating system or Flash applications; and the software can be set up to download upgrades manually or automatically.
"Texas Instruments has done things great," Keyton says. "They've gone to great expense to produce affordable calculators that have lots of power."
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|Date:||Nov 1, 2001|
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