• Students should be provided opportunities to work independently of the teacher both individually and in pairs or groups.

• When homework is assigned for the purpose of developing skill, stu dents should be sufficiently familiar with the skill and the tasks so that they are not practicing incorrect procedures.

In the discussion above, we mention the special role that calculators and computers can play in learning algebra. But they have many other roles to play throughout instruction in grades pre-K-8. Using calculators and computers does not replace the need for fluency with other methods. Confronted with a complex arithmetic problem, students can use calculators and computers to see beyond tedious calculations to the strategies needed to solve the problem. Technology can relieve the computational burden and free working memory for higher-level thinking so that there can be a sharper focus on an important idea. Further, skillfully planned calculator investigations may reveal subtle or interesting mathematical ideas, such as the rules for order of operations.

A large number of empirical studies of calculator use, including long-term studies, have generally shown that the use of calculators does not threaten the development of basic skills and that it can enhance conceptual understanding, strategic competence, and disposition toward mathematics. For example, students who use calculators tend to show improved conceptual understanding, greater ability to choose the correct operation, and greater skill in estimation and mental arithmetic without a loss of basic computational skills. They are also familiar with a wider range of numbers than students who do not use calculators and are better able to tackle realistic mathematics problems.

Just like any instructional tool, calculators and computers can be used more or less effectively. Our concern is that, when computing technology is used, it needs to contribute positively:

• In all grades of elementary and middle school, any use of calculators and computers should be done in ways that help develop all strands of stu dents’ mathematical proficiency.