In the view of many Americans, our schools have failed to produce literate graduates. Although some people always have held this view, the launching of Sputnik in 1957 gave it national and international exposure. From that time forward the "failings" of our schools repeatedly have been the subject of media attention. These failings include failing to teach respect; graduating students who cannot read, write, or spell adequately; producing students who are not literate in geography, history, the sciences, or mathematics; and the list continues. This discussion concentrates on the area of mathematics. Internationally our students are ranked near the bottom in comparative studies of mathematics achievement. The business community finds this appalling and demands a workforce that is better educated, possesses greater skill in mathematics, is more familiar with the technology necessary to conduct business_ and to communicate in today's world, and, above all, has "common sense" in making decisions. There is increasing concern that America is relinquishing its role as a leader in technological advancement. As a consequence, the schools are experiencing increasing pressure to solve these problems. The discussion here examines one aspect of a potential solution to the problem of poor mathematics achievement. We focus on specific research findings in the area of forgetting, and examine the implications for year-round schooling. The implications, of course, go far beyond the mathematics curriculum.

No abstract

The subject of geometry in the curriculum continues to be an area of concern among mathematics educators. The gap between standards expectations and actual textbook content continues to reflect the need for substantial change. In this study, the geometry language introduced in K‐6 textbooks was carefully examined and compared to the language used in the Curriculum and Evaluation Standards for School Mathematics (National Council of Teachers of Mathematics, 1989), Principles and Standards for School Mathematics (NCTM, 1999), and New Standards Elementary School Mathematics Performance Standards (National Center for Education and the Economy, 1997). The. logic followed was that the language in textbooks reflects the content presented in the textbook, and the language in the standards reflects what should be presented. The results of the study clearly indicate that there is a substantial misalignment between the geometry presented in the textbooks, the. geometry expected to be taught by groups such as NCTM, and the geometry being assessed in student performance measures as suggested by NCEE. Specific areas of misalignment are identified, along with implications, and some areas in which the curriculum should be revised are identified.

Teachers have a constant challenge to find ways of making new concepts meaningful. Mathematics is not exempt from this challenge. The analogy is a much used technique in other subject areas. Certainly there are dangers in the use of an analogy, but the astute teacher will recognize most difficulties that arise in using analogy and will provide proper corrective procedures.

In the view of many Americans, our schools have failed to produce literate graduates. Although some people always have held this view, the launching of Sputnik in 1957 gave it national and international exposure. From that time forward the "failings" of our schools repeatedly have been the subject of media attention. These failings include failing to teach respect; graduating students who cannot read, write, or spell adequately; producing students who are not literate in geography, history, the sciences, or mathematics; and the list continues.This discussion concentrates on the area of mathematics. Internationally our students are ranked near the bottom in comparative studies of mathematics achievement. The business community finds this appalling and demands a workforce that is better educated, possesses greater skill in mathematics, is more familiar with the technology necessary to conduct business_ and to communicate in today's world, and, above all, has "common sense" in making decisions. There is increasing concern that America is relinquishing its role as a leader in technological advancement. As a consequence, the schools are experiencing increasing pressure to solve these problems.The discussion here examines one aspect of a potential solution to the problem of poor mathematics achievement. We focus on specific research findings in the area of forgetting, and examine the implications for year-round schooling. The implications, of course, go far beyond the mathematics curriculum.