From geographic and census data, to current information about almost any mathematical or scientific subject, to rich sources of mathematical problems for K-12 students, the Internet will greatly expand the research capability of both teachers and students. Strategies and teaching approaches which utilize technology have been shown to improve student attitudes, problem solving ability, ability to visualize mathematics, and overall performance. Here, possibly more than anywhere else in this Framework , we need to be open to new ideas and receptive to new approaches. K-12 Development and Emphases Many specific suggestions for appropriate uses of calculators, computers, and manipulatives are given in the following pages and, indeed, throughout this Framework . The point to be made here, though, is that the frequent, well-integrated use of these tools at all levels is essential.
Young children find the use of concrete materials to model problem situations very natural.
Indeed they find such modeling more natural than the formal work they do with number sentences and equations. Older students will realize that the adults around them use calculators and computers all the time to solve mathematical problems and will be prepared to do the same. Such opportunities do exist, however, and new approaches and tools are being created all the time. In summary, mathematical tools play an ever-more important role in today's mathematics. References National Council of Teachers of Mathematics.