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| Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning. |
Electronic technologies—calculators and computers—are essential
tools for teaching, learning, and doing mathematics. They furnish visual
images of mathematical ideas, they facilitate organizing and analyzing
data, and they compute efficiently and accurately. They can support investigation
by students in every area of mathematics, including geometry, statistics,
algebra, measurement, and number. When technological tools are available,
students can focus on decision making, reflection, reasoning, and problem
solving. »
Students can learn more mathematics more deeply with the appropriate use of technology
(Dunham and Dick 1994; Sheets 1993; Boers-van Oosterum 1990; Rojano 1996;
Groves 1994). Technology should not be used as a replacement for basic
understandings and intuitions; rather, it can and should be used to foster
those understandings and intuitions. In mathematics-instruction programs,
technology should be used widely and responsibly, with the goal of enriching
students' learning of mathematics.
The existence, versatility, and power of technology make it possible and necessary
to reexamine what mathematics students should learn as well as how they
can best learn it. In the mathematics classrooms envisioned in Principles
and Standards, every student has access to technology to facilitate
his or her mathematics learning under the guidance of a skillful teacher.
Technology can help students learn mathematics. For example, with calculators and computers students can examine more examples or representational forms than are feasible by hand, so they can make and explore conjectures easily. The graphic power of technological tools affords access to visual models that are powerful but that many students are unable or unwilling to generate independently. The computational capacity of technological tools extends the range of problems accessible to students and also enables them to execute routine procedures quickly and accurately, thus allowing more time for conceptualizing and modeling.
Students' engagement with, and ownership of, abstract mathematical ideas can be fostered through technology. Technology enriches the range and quality of investigations by providing a means of viewing mathematical ideas from multiple perspectives. Students' learning is assisted by feedback, which technology can supply: drag a node in a Dynamic Geometry® environment, and the shape on the screen changes; change the defining rules for a spreadsheet, and watch as dependent values are modified. Technology also provides a focus as students discuss with one another and with their teacher the objects on the screen and the effects of the various dynamic transformations that technology allows.
Technology offers teachers options for adapting instruction to special student
needs. Students who are easily distracted may focus more intently on computer
tasks, and those who have organizational difficulties may benefit from
the constraints imposed by a computer environment. Students who have trouble
with basic procedures can develop and demonstrate other mathematical understandings,
which in turn can eventually help them learn the procedures. The possibilities
for engaging students with physical challenges in mathematics are dramatically
increased with special technologies.
The effective use of technology in the mathematics classroom depends on the teacher. Technology is not a panacea. As with any teaching tool, it can be used well or poorly. Teachers should use technology to » enhance their students' learning opportunities by selecting or creating mathematical tasks that take advantage of what technology can do efficiently and well—graphing, visualizing, and computing. For example, teachers can use simulations to give students experience with problem situations that are difficult to create without technology, or they can use data and resources from the Internet and the World Wide Web to design student tasks. Spreadsheets, dynamic geometry software, and computer microworlds are also useful tools for posing worthwhile problems.
Technology does not replace the mathematics teacher. When students are using
technological tools, they often spend time working in ways that appear
somewhat independent of the teacher, but this impression is misleading.
The teacher plays several important roles in a technology-rich classroom,
making decisions that affect students' learning in important ways. Initially,
the teacher must decide if, when, and how technology will be used. As
students use calculators or computers in the classroom, the teacher has
an opportunity to observe the students and to focus on their thinking.
As students work with technology, they may show ways of thinking about
mathematics that are otherwise often difficult to observe. Thus, technology
aids in assessment, allowing teachers to examine the processes used by
students in their mathematical investigations as well as the results,
thus enriching the information available for teachers to use in making
instructional decisions.
Technology not only influences how mathematics is taught and learned
but also affects what is taught and when a topic appears in the curriculum.
With technology at hand, young children can explore and solve problems
involving large numbers, or they can investigate characteristics of shapes
using dynamic geometry software. Elementary school students can organize
and analyze large sets of data. Middle-grades students can study linear
relationships and the ideas of slope and uniform change with computer
representations and by performing physical experiments with calculator-based-laboratory
systems. High school students can use simulations to study sample distributions,
and they can work with computer algebra systems that efficiently perform
most of the symbolic manipulation that was the focus of traditional high
school mathematics programs. The study of algebra need not be limited
to simple situations in which symbolic manipulation is relatively straightforward.
Using technological tools, students can reason about more-general issues,
such as parameter changes, and they can model and solve complex problems
that were heretofore inaccessible to them. Technology also blurs some
of the artificial separations among topics in algebra, geometry, and data
analysis by allowing students to use ideas from one area of mathematics
to better understand another area of mathematics.
Technology can help teachers connect the development of skills and procedures to the more general development of mathematical understanding. As some skills that were once considered essential are rendered less necessary by technological tools, students can be asked to work at higher levels of generalization or abstraction. Work with virtual manipulatives (computer simulations of physical manipulatives) or with Logo can allow young children to extend physical experience and » to develop an initial understanding of sophisticated ideas like the use of algorithms. Dynamic geometry software can allow experimentation with families of geometric objects, with an explicit focus on geometric transformations. Similarly, graphing utilities facilitate the exploration of characteristics of classes of functions. Because of technology, many topics in discrete mathematics take on new importance in the contemporary mathematics classroom; the boundaries of the mathematical landscape are being transformed.
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