included policy issues, social issues, and instruction in other curriculum areas--such as those that focus on reading, writing, or the sciences.
My purpose in writing this chapter is to describe what I feel are the several prices we as a society pay for using nonpublicly available instruments for the assessment of the effectiveness of mathematics learning and teaching in our schools. Our society is profoundly undereducated and incapacitated in dealing with public policy matters that have quantitative dimensions, that is, all public policy. Our school systems either do not have the freedom or do not believe they have the freedom to challenge students to think inventively and creatively about mathematics. Finally, teachers and parents feel torn between the desire to educate youngsters richly and imaginatively and the need to prepare them to demonstrate their competence on examinations that are deeply flawed.
All the ills of the present methods of accountability assessment in mathematics are not due to the nonpublic nature of the instruments, but I believe that many of them are. Moreover, I believe that many of the ills that do not result directly from the secrecy of the instruments are nonetheless indirect consequences of the secrecy and are substantially exacerbated by it. Finally, because the field of assessment has seen more than its share of complaints about the ills and evils of educational testing, I shall sketch what I believe to be a viable and pragmatic alternative approach to assessment that does not seem to be flawed in the ways that our present methods of assessment of mathematics teaching and learning are.
Most state departments of education and local school boards depend heavily on the results of standardized multiple choice tests to decide how well their systems are educating students mathematically. Even the federal Department of Education must use of the results of such instruments. In fact, much of the current public concern about U.S. students' mathematical incapacity is due to reports in the press and electronic media about poor performance on such instruments.
A remarkable feature of the reports that reach the public's attention is that the public cannot usually see the questions that are asked. The media do not publish the questions; rather, they publish reports about students' performance on the questions. In fact, the media are not able to examine the test instruments either. To some extent, the media are to blame