Not since the post-Sputnik era of the early 1960s has the United States government placed such emphasis, and indeed money, on mathematics and science education. At that time, the thought of being second to Russia in these areas spurred such activity as National Science Foundation summer institutes and Academic Year Institutes (AYIs). It was also at this time when President J. F. Kennedy said that America would have a man on the moon before the end of the decade, and we did. This gave the United States a renewed sense of superiority and self-confidence. The main concentration of the government efforts turned towards the raging Vietnam war. By 1975, teacher institutes and emphasis on science and mathematics education was a thing of the past.
In the early 1980s, international testing of overall achievement in mathematics education at grade levels 8 and 12 was initiated by a number of countries. Tables 1 and 2 show the results.
There were a number of analyses of this testing in the individual areas of mathematics and the results were similar. It was suggested that while the United States looked as though it ranked poorly, perhaps there was not really a significant difference in the scores. Table 3 indicates that the United States scored a full 35% worse than Hong Kong and Japan in 12th grade advanced algebra [9].
For a short time, many mathematics educators continued to look for excuses for the poor showing. Among these were the following.
Upon comparison with the Japanese school system in regard to the above, the following facts were noted.
It became abundantly clear that one must look elsewhere for reasons that the United States performed so poorly on international testing. Closer and more exhaustive investigation of the American system pointed to a number of shortcomings, among them being the following.
A great deal of documentation has been obtained to show that these factors have contributed significantly to the low scores in testing. As an example of the first factor, how often have you heard a person say ``Oh, I was never very good in math'' and it is perfectly acceptable? On the other hand, how many people would admit to ``Oh, I never could read very well''? There is a very large attitudinal discrepancy which needs to be overcome.
The technological advances of the 1980s underlined the pervasiveness of mathematics. Almost every non-science academic discipline started requiring some level of mathematical understanding. This, together with the feeling that the United States was losing its international scientific edge, prompted the National Council of Teachers of Mathematics (NCTM) in 1986 to establish a Commission on Standards for School Mathematics. The standards were drafted during 1987 and revised in 1988 by members of four working groups, each representing a cross section of mathematics educators, including classroom teachers, supervisors, educational researchers, teacher educators and university mathematicians.
The document, referred to as The Standards [2], was published in 1989 and contained a set of standards for mathematics curricula in North American schools (K-12) and for evaluating the quality of both the curriculum and student achievement. The Standards is a vision of what the mathematics curriculum should include in terms of content priority and emphasis. The grades are divided into the three groupings K-4, 5-8 and 9-12. The body of the text makes specific recommendations as to content that should be emphasized and that which should be deemphasized in each of these groupings. There are some dissenters from the Standards but virtually every mathematics and science organization has endorsed this effort.
Changing what and how mathematics should be taught in the United States is an enormous task. The autonomy among states and within state school districts made it clear that if anything was to change, support of and encouragement by the federal government was necessary. Shortly after the Standards were made available nation wide, the National Research Council (NRC) established the Mathematical Sciences Education Board (MSEB) whose sole responsibility was to encourage each of the fifty states to adopt and implement the Standards. To help accomplish this goal, the board made \$10,000 available to each of the states to establish mathematics coalitions. It was not until 1994 that each state had a coalition together with a director and some type of steering committee. The activities and strength of the coalitions vary from state to state but their purpose remains unaltered.
The main activity for the first two years or so for each coalition was the public relations exercise of convincing the main players that change is not only needed but crucial. There were three main groups to deal with: the teachers, the administrators, and the clientele, the parents. The group that was viewed as being the most onerous to convince, the teachers, turned out to be the most receptive. They were very aware of the need to change and for the most part added their voice to help convince the other groups. The acceptance of the administrators is coming but much more slowly. This is understandable. They are accepting a real financial burden on their district when they acknowledge the need to introduce the Standards. This stems from the need to buy new materials at each grade level, send teachers to regional as well as national meetings, conduct and support in-service training, consider alternative assessment techniques, and participate in convincing the parents that all of this is necessary. Many of the parents of today's school children are still suffering from the ``new math'' shock of the '70s.
There is a great deal more to be said about the need for new instructional materials. Many of these are being developed right now. Much more needs to be done about assessment. National tests such as the Scholastic Achievement Test (SAT) and the American College Testing (ACT) are being scrutinized carefully to see if they are really a reliable measure.
At present, there is still a great deal to do and it will be at least ten years before significant change will be noticeable. Some of the activities that various coalitions are involved in are: newsletters for regional and national mathematics meetings and workshops, Family Math, summer workshops, in-service training, speakers bureaus to explain the Standards to civic groups, small industrial grants to provide more computers or new instructional materials, networking science and math educators, school/business extern programs, Mathematics Awareness Week, portal schools, and much more. The Mathematics Coalition concept is very viable at this point and has recently formed its own national organization, the National Association of State Science and Mathematics Coalitions (NASSMC).
A large number of publications in regard to the Standards have been produced to help make the public aware of the need for change. One of the first was Everybody Counts --- A Report to the Nation on the Future of Mathematics Education [4]. This publication detailed the need for change in several areas. It pointed out the opportunities many students were missing, the need to invest in human resources, develop mathematical power, mobilize for curriculum reform, and the action necessary before we could move into the 21st century. Most importantly it pointed out the shortcomings of our current system. Since then, many other publications worth reading have evolved. Among them are Moving Beyond Myths: Revitalizing Undergraduate Mathematics [5], A Call for Change: Recommendations for the Mathematical Preparation of Teachers of Mathematics [1], Professional Standards for Teaching Mathematics [3], Improving Math and Science Teaching [10], Counting on You: Actions Supporting Mathematics Teaching Standards [6], Measuring What Counts [7], Measuring Up: Prototypes for Mathematics Assessment [8], and others.
More support from the national level was initiated in 1990 when the National Science Foundation (NSF) solicited proposals from the states for Statewide Systemic Initiatives (SSI) in Science, Mathematics and Engineering Education. These grants were for two million dollars a year for five years and the state had to come up with matching funds in some way. The purpose of the grants was to remove the barriers between the sciences, mathematics and engineering, the idea of connections, and it had to be done in a systemic way, that is wholistic from K through 12. So far twenty seven states have received such grants, ten awarded in 1991, eleven in 1992, six in 1993. The program appears to be over. Every state made application in some form or another and those which were not funded must seek help elsewhere. There was some criticism of the program when you consider the fact that ten million dollars has a different meaning in Wyoming as compared to California and also it was reported that politics started to play a role in who received the grants.
Also in 1989 the Dwight D. Eisenhower Mathematics and Science Education Act, Title II was enacted. The intent of this law was to provide funding to improve mathematics and science instruction in grades K-16. Funds are distributed to the individual state departments of education on a per capita basis and they in turn evaluate various proposals submitted for funding. A large number of very worthwhile activities are undertaken in each of the fifty states because of this funding. It may be a workshop on assessment, training Family Math teachers, or upgrading the background of high school teachers in some topic recommended by the Standards. The breadth of the undertakings is very broad. Proposals are submitted yearly but are looked upon as a three year proposal to insure some long-term funding for some projects. Two three-year programs have just been completed. Because of the viability of the funded projects over the last six years, the federal government is now going to expand funding to include many of the social sciences and arts and literature while maintaining the same former level of support for mathematics and science.
There has never been a flourish of activity to this degree in mathematics and science education in the United States. No one knows how long money will be made available for the myriad of projects that are being undertaken. It is felt however that this age of technology and communication is asking more of the educational institutions than ever before and funding must be made available if our students are to be able to compete in tomorrow's global job market.
Department of Mathematics
University of Wyoming
Laramie, WY 82071. USA