Concern about mathematics and science education stems at least partly from the perception that today’s students need to be more “technologically literate” than the students of any previous generation. And the challenge posed by computers can, in turn, be met by using computers in the school.
On that much, most educators agree. But just how educational technology can be used--and, in fact, whether it ever will--is a constant source of dispute.
Technology is likely to be used increasingly in all subjects, but experts believe that it holds special promise for math and science. The computer’s potential for “mass delivery” of instruction might help address the shortage of teachers, some educators say. Furthermore, computer use could make math problems less abstract, reduce tedious operations, and teach logic. And computer simulations could demonstrate complex physical phenomena that are impossible to show in standard science laboratories.
Some experts say “mass delivery” of instruction is where the computer’s greatest potential lies. Computers can illustrate the abstract concepts of mathematics and science better than traditional methods, they say, and will be able to help alleviate the shortage of teachers in those areas.
Others hold that to use the computer as a “solid-state Socrates,” or a means of delivering instruction, would be a waste. They say the computer is best used as a tool for doing tedious computation, working with complex mathematics problems, and aiding with some laboratory work.
Educators appear to agree that the computer is useful to introduce students to the basics of information technology, such as programming--which, according to a recent survey, is now one of the most common uses of the machines.
That study, conducted by the Center for Social Organization of Schools at the Johns Hopkins University, found that the computer so far has simply been “grafted” onto the traditional mathematics curriculum. The nationwide survey of 2,209 schools found that most teachers put greater emphasis on programming and less on computer-assisted instruction as they gain experience with the technology.
Such a practice has both positive and negative effects, says Arthur G. Powell, executive director of an independent national study of high schools. On one hand, such courses can attract students who normally would not take part in any program with a mathematical component. Computer science could teach many of the reasoning skills that are considered central to other math subjects, he says.
But such courses also serve as a way for schools to “get around” state mandates for stiffer graduation requirements. “It’s one way the school can respond without making the teaching of math more strenuous ... and you don’t have to deal with problems of sequence,” Mr. Powell says.
THE COMPUTER AS TUTOR
Educators say the professional arguments about computers will intensify in the next several years as the number of computers in the schools and the range of educational software increase.
Few experts expect computer-assisted instruction to make the teacher obsolete, but many believe that the computer can at least free the teacher from many tedious tasks and do a better job teaching students basic skills--especially in areas such as mathematics and science.
According to a report by Technical Education Research Centers (terc), commissioned by the National Science Foundation, there are now 1,000 science and 650 mathematics software packages on the market, and 100 new mathematics and science packages appear every month. Those programs represent almost half of all of the educational software available. More than 90 percent of all the math software programs are for drill and practice.
There is almost no software for elementary-school science classes and for many high-school topics, terc found. Many software topics overlap, the survey found, and teachers reported that they are not aware of what software is available.
Robert Kansky, professor of mathematics education at the University of Wyoming, says many schools in his state “can’t afford to hire math and science teachers.” The only way students will be able to take advanced courses in these ares, he says, is through computer hookups.
Mr. Kansky, who in 1981 and 1982 served as a consultant for a computer-assisted-instruction experiment in South Africa, says a three-tiered computer systems--with mainframe computers on the top, minicomputers in the middle, and microcomputers on the bottom--eventually will make delivery of sophisticated programs cost-effective. In such an arrangement, desktop computers would be able to use more sophisticated programs now available only on the larger machines.
In addition to increasing access to math and science education, Mr. Kansky and others say, computer-based education can also actually improve student performance.
A recent analysis of data from 52 independent studies found that students who receive computer-based instruction in all subjects perform better academically than those who do not. The study, conducted by three researchers at the University of Michigan, found that students using computers earn better scores on tests in less time than other students.
Despite such findings, many experts contend that using the computer as a means of instruction will not be worthwhile for many years. Other methods of expanding schools’ teaching capacity, such as cross-peer tutoring, are more effective, these people say. For now, they conclude, the computer should be used only as a tool--to perform time-consuming computations, gather laboratory data, and analyze data--and for the practical skill-training that programming offers.
For tutorial software to keep the interest of the student, says Robert B. Davis, associate director of the research laboratory on computer-based education at the University of Illinois at Urbana-Champaign, it needs to be much more sophisticated--and for the software to be more sophisticated, the hardware needs to be more sophisticated. Mr. Davis said that almost all of the hardware available to schools is not powerful enough to handle worthwhile software. Because “the great pressure in education is to get something cheaply,” many schools buy the least sophisticated machines.
“Sitting in front of a computer for seven hours” will not keep students engaged, adds one science educator. “They need to talk to people, work on real-world activities.”
THE COMPUTER AS SIMULATOR
The value of simulation programs for the sciences is almost as much a matter of controversy as the tutorial programs. Simulations show simplified models of physical phenomena, such as biological functions.
At the recent National Educational Computing Conference in Baltimore, a panel of computer scientists and educators extolled the virtues of simulation programs that allow students to learn about science “intuitively.” But the participants also agreed with Tom Snyder, the president of a software firm, who said, “Right now, there is just a handful of good programs. It will take time and money to develop good programs.”
The participants never questioned whether simulation programs were worth developing. They agreed that some programs already available showed that simulations give students a better “intuitive” and “hands-on” understanding of mathematics and science than they had been able to offer.
Alfred Bork, professor of physics at the University of California at Irvine, says that his colleagues sometimes do not have a complete understanding of some physical concepts because they have not worked with variables in a dynamic setting such as a computer simulation.
“As soon as they saw a plot that didn’t appear in the books they had problems,” Mr. Bork says, referring to problems dealing with electrical phenomena.
Robert F. Tinker, director of the technology center at terc, says he has seen students develop a “working vocabulary” in complicated subjects such as nuclear power and the ecology with computer simulations. “There’s a lot of good science in it,” he says, referring to a simulation entitled “Three Mile Island,” in which students are required to operate a nuclear-power plant both safely and profitably.
But some science educators say they doubt that either computer-based tutorials or computer simulations will improve enough to make them worthwhile. One educator explains that simulations he has seen are not only inadequate, but harmful in some cases. The computer models, he says, oversimplify scientific phenomena to the point of teaching invalid concepts.
He cites two simulations--one which demonstrates the ideal gas law, and a second which demonstrates the law of universal gravitation--that “teach something that’s wrong.” Gases hold dozens of properties that cannot be expressed accurately in a simple model, the educator says.
The “intelligent videodisk” machine, a device that connects a videocassette player with a microcomputer, holds more promise, some educators believe. Using a computer program, the teacher can move to any single frame of a video tape in seconds.
The most useful tapes, these educators say, would demonstrate laboratory experiments with many variations. The teacher would be able to show students in seconds how hundreds of changes would affect an experiment’s outcome.
Educators also agree that the computer could be an important laboratory instrument--as long as it is used merely to manipulate data and not to replace most experiments.
An official with a leading manufacturer of laboratory equipment says that computer-based laboratory programs are so expensive that only about 300 have been sold nationwide. But, he adds, less expensive equipment that measures and analyzes data digitally is selling well.
The company has sold “thousands"of MPUTE “photogate” instruments, which measure the acceleration of objects at several points on an “air track,” and similar instruments that measure the movement of objects too small for the human eye, the official says.
Because mathematics and science require that students build on their knowledge, educators say, the computer can be valuable as a “manager’’ of educational programs. By entering data on student performance, teachers can track students’ progress in specific curricular goals--and give special attention to their weaker skills.
The computer can receive such information in several ways. Some testing programs evaluate the data and indicate which areas should receive special attention. Other programs require special “inputting” of information.
“These [computer programs] can analyze patterns of errors. Worksheets can’t do that,” says Mr. Powell.
THE COMPUTER AS SUBSTITUTE
The computer eventually could lead to fundamental changes in the mathematics and science curricula, the experts note. The computer not only requires greater familiarity with some complex mathematical concepts, they say, but it can also reduce the need for much of the arithmetic that is usually taught throughout elementary school.
Mr. Powell says students will need to have more advanced mathematics and science backgrounds than their parents. “In Japan, virtually every kid has some kind of calculus,” he says.
Jonathan Choate, chairman of the mathematics department at the Groton School, has developed a two-year mathematics curriculum for the computer that teaches high-school students systems dynamics--a subject that he says normally is not taught until college.
Mr. Tinker of terc and others say educators should at least partly “prune” several areas from the math and science curricula because of the computer.
Among the topics that Mr. Tinker says he would give less emphasis are: rote algorithms; fractions; axiomatic geometry; several operations typical in algebra classes, such as root extraction, simultaneous equations, and trigonometric functions; many calculus proofs; and much of the specialized science vocabulary, which he says means little to most students.
“Much of what we now teach in elementary school can now be done with a $5 calculator,” says Mr. Kansky. “You could release students for at least half of their time ... and move on to more problem solving.”
