Educators in elementary and secondary schools across the nation are struggling to improve and redesign mathematics and science education so that all students are well-prepared for the beginning of a new millennium. Policymakers are confronted with growing determination that a solid foundation in mathematics, science, and technology is essential not only to the economic but also to the social well-being of the nation. Indeed, a task for today's policymakers, parents, and communities is to ensure that all students are graduated from high school with a quality education that will enable them to contribute productively to society. Toward this end, the United States has set, as a matter of national policy, the goal of its students being first in the world in mathematics and science achievement by 2000.
However, national and international indicators of educational progress suggest that the country is still far from its goal, despite a growing reform movement aimed at achieving excellence and equity in education. Unresolved issues concerning the performance of students and teachers, the quality of instructional materials and teaching, and access to quality education for all students are matters still very much at the center of local, state, and national education agendas. Nevertheless, indications of forward movement abound: students are taking more advanced courses in science and mathematics, teachers are more aware of the need to change their conceptions of teaching and learning, and student achievement in mathematics and science has largely returned to or exceeded the levels set in the 1970s.
The spark for much of the current reforms came from early work in setting standards performed by professional associations of mathematics and science educators. In mathematics, the National Academy of Sciences laid out the broad outlines of mathematics reform in Everybody Counts: A Report to the Nation on the Future of Mathematics Education (MSEB 1989). The National Council of Teachers of Mathematics (NCTM) followed with two reports that made more specific recommendations-Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) and Professional Standards for Teaching Mathematics (NCTM 1991).
During this same period, consensus on new directions for science education was beginning to develop, though actual national standards were some years away. By 1993, the American Association for the Advancement of Science had issued two publications, Science for All Americans (AAAS 1989) and Benchmarks for Science Literacy (AAAS 1993), and the National Science Teachers Association produced Scope, Sequence and Coordination of Secondary School Science (NSTA 1992). These reports, as well as others, led to a national dialog on science standards resulting in the National Academy of Sciences' National Science Education Standards (NRC 1996).
The standards for mathematics and science education share many core ideas: high expectations for all students; in-depth study and understanding of core concepts; emphasis on hands-on tasks that promote active engagement with the subject matter; and a strong focus on reasoning, problem solving, and the ability to apply learning within broader contexts.
The standards in both subjects view teachers as the critical agents that enable students to meet these more demanding levels of performance. However, a large proportion of current mathematics and science teachers were trained when conceptions of teaching and learning were very different from today. Consequently, both sets of standards emphasize the importance of professional development for teachers. Previously offered as a sporadic set of brief workshops to train teachers in specific skills, professional development is now portrayed as a career-long process of continuously updating teachers' mathematics and science knowledge and teaching skills (Darling-Hammond 1994a). And although some school systems, schools, and teachers have begun to adopt practices consistent with the standards, mathematics and science educators recognize that full implementation of standards-based reform will take much more time (Jones et al. 1992; Lindquist, Dossey, and Mullis 1995; and NSF 1996).
Like professional development, equity remains an important challenge for educational reformers in mathematics and science education. At its base, equity means that each and every student has access to quality education regardless of background, race, ethnicity, or location. Some of the building blocks for equity are:
One of the critical issues currently facing educators is how to achieve equity and excellence amid the complexities born of an increasingly diverse national makeup. Of the 45 million children enrolled in elementary and secondary schools in 1994, approximately 15 million are ethnic or racial minorities and 6 million come from homes where English is not the primary language spoken (NCES 1996b).
There are still more challenges: how to make effective use of the information technologies that are now commonplace in homes and workplaces as tools for reforming education and improving teaching and learning productivity; how to ensure consistency in approach and quality among instructional materials, teaching, assessment of student learning, and policies formed at district or state levels; and, finally, how to continue learning how to improve-and what works and doesn't work in improving-the quality of education.
Clearly, the role education plays in our personal lives and in the nation's well-being has grown over the years. And the challenges in mathematics and science education-and in all school subjects, for that matter-are before us as educators, students,
parents, and community members. And although these challenges may differ from those of years past, it is not clear that there are necessarily more of them, nor is it certain that they are any more daunting than they once were. It may be that we are
more concerned and know more about mathematics, science, and technology education in this nation than we did 20 or 30 years ago. As shown in this chapter, what is certain is that we have a stronger research base and a deeper, more far-reaching set of
national and international indicators of performance than ever before. (See "Measuring the Performance of the Education System.") [Skip Text Box]
Few countries have a truly unitary national education system. Many are aggregations of smaller (e.g., regional) subsystems coordinated by an overall national entity. Most of the 49 countries that participated in TIMSS, for example, have fewer than five subsystems. In the case of some nations-such as the United States-these subsystems (i.e., states) are more or less autonomous, with only indirect influence exercised at the national level (Schmidt, Raizen et al. 1997).
Schmidt, Raizen et al. point out that policymaking is affected by the degree of complexity within the national education system. Countries with a unitary system can make policy about curriculum and decisions about system performance measurement with greater ease than countries with more complex, decentralized systems (Schmidt, Raizen et al. 1997).
The U.S. educational "system," then, is more accurately a multiplicity of systems that can be described from numerous perspectives. It is useful to keep various dimensions simultaneously in mind when thinking about how to measure its performance. Decisions about learning practices are made and affected by networks of practitioners, researchers, policymakers, parents, and community and business leaders, as well as by students. Decisions about what to teach are reflected in curriculum frameworks and materials, instructional practices, teachers' professional development, and student performance assessments. Decisions about resource use are shared by several levels of government: federal, state, and local-within which are school districts, schools, grade levels, and classrooms-across a country of 268 million people.
The states are the primary agents of education as delegated by the U.S. Constitution. However, a long tradition of local decisionmaking authority about what and how to teach is distributed among parent and teacher groups and school boards for each autonomous school district. No matter how the system is portrayed, the difficulty in measuring it is based in its complexity-a web spanning the nation woven within the boundaries of individual states and communities in the form of people, places, behaviors, and ideas.
Compared with countries around the world, the U.S. education system is distinguished by its size, organization, and-above all else-the diversity of the students it serves. In the 50 states and 11 territories, there are over 14,000 school districts and 87,000 public schools (NCES 1996b).
While trends in student performance and coursetaking, characteristics of curriculum and instruction, and preparation and qualifications of teachers may describe the condition of various elements of the system, they do not necessarily encapsulate the performance of the elements as they interact, work in tandem, or change across the system. How much and in what direction the system components move together (or co-vary), is an indicator of systemwide change (Chubin 1997).
The demand is increasing for valid and reliable indicators in accounting for the use of public resources and in sharing knowledge with parents, educators, and policymakers.
Many of these "systemic" features are affective or qualitative, such as system leadership, partnerships, alignment of policies and practices, and student and teacher creativity. Such systemic qualities have not yet been adequately operationalized into acceptable indicators of a system's performance.
Consistent with this systems notion, the Consortium for Policy Research in Education has developed a potential model for evaluating systemwide change in the context of a Philadelphia reform project sponsored by a large collection of public and private funders. The evaluators have created a scorecard that allows them to make judgments about the degree of change across various elements of the Philadelphia reform, thus enabling them to portray the movement of the system as a whole (CPRE 1996).
New approaches to measurement and measurement tools will be needed to investigate the synergy (or lack thereof) among system components. What is needed are indicators of how these various elements work together or apart, what factors characterize the system, and what their effects are on student achievement. Indeed, NSF has funded several research studies that support these new measurement directions. One such study, performed by Cohen and Hill (1997), has examined the interrelationship among teacher professional development, the use of curriculum materials, and the assessment of student performance in fourth and eighth grade mathematics classes in the state of California. What they found supports the power of measuring the combined effects of system components.
Cohen and Hill found that teachers who participated in professional development based on curriculum materials relevant to reform goals were much more likely than other teachers to report teaching practices aligned with these goals. Moreover, their results suggest that "when educational improvement is focused on learning and teaching academic content, and when curriculum for improving teaching overlaps with the curriculum and assessment of students, teaching practice and student performance are likely to improve" (Cohen and Hill 1997). In other words, Cohen and Hill have begun to measure the synergy among system elements as they relate to instructional materials-and have found evidence that such synergy results in improved student performance.
In general, the U.S. curriculum is not consistent with those of other countries that performed well on the TIMSS assessment. When compared with other countries, U.S. mathematics and science curricula are less focused and include far more topics than is common internationally. The topics-especially in mathematics-tend to remain in the curriculum for more grade levels than is the practice in other countries (Schmidt, McKnight, and Raizen 1997).
The Cohen and Hill study, TIMSS, and other studies supported by NSF are indicative of the research that is needed to address systemic issues. Indeed, much of the TIMSS data is yet to be analyzed, and the richness of the study holds forth the promise of more lessons to be learned. More research on systemwide change in larger and different settings is needed to advance and refine these findings.
This chapter begins to move in the direction of examining systems, both national and statewide, of mathematics and science education at the elementary and secondary level. The various measures of student performance, however imperfect, provide some evidence of system outcomes. There are still many more indicators to be developed that will aid local decisionmakers, state and federal policymakers, educators, parents, and their community partners. Although we do not yet have all of the desirable information, we have much more than we once did, more in mathematics and science than in other subject areas, and more at the elementary and secondary levels than at the postsecondary level and beyond.
This chapter is organized into three main parts: first, a detailed description of student achievement in mathematics and science is provided; second, curriculum and instruction are examined; and third, teachers and teaching are addressed. These latter two parts are presented because they are the components of the education process thought to have the greatest direct influence on student achievement. The chapter concludes with a summary of trends in these three areas and an interpretation of what this may mean for educational progress.
Under the student achievement section, the performance of U.S. students in both national and international contexts is examined in order to address the following questions:
The second major section of this chapter, on curriculum and instruction, focuses on the following questions:
The third major section of the chapter examines the background of U.S. mathematics and science teachers in national and international contexts. The discussion centers on these questions:
Many national and international data sources-all based on national probability samples-have been mined in writing this chapter. The first section of this chapter can be examined from a number of perspectives using a variety of data sources. The discussion here draws on three primary sources: the National Assessment of Educational Progress (NAEP), the Third International Mathematics and Science Study (TIMSS), and the High School Transcript Studies. NAEP is a reliable indicator of achievement for U.S. students. Since the early 1970s, NAEP has conducted trend assessments every two years covering mathematics, science, reading, and more recently, writing. These assessments draw on nationally representative samples of 9- 13-, and 17- year-olds. To date, eight trend assessments have been conducted in mathematics and nine in science.
NAEP also conducts subject matter assessments periodically on a wider range of subjects including history, geography, civics, computer competence, art, and music. Subjects are covered on a rotating basis so that in one assessment, the focus may be on mathematics and science, and in the next, on history and social studies. These assessments draw on nationally representative samples of students in grades 4, 8, and 12 rather than the age groups used in the trend studies. Items in the periodic subject matter assessments are revised from time to time to incorporate new assessment strategies and reflect prevailing professional judgments about what students in a particular grade should be learning. The items used in trend assessments are fixed, so that performance in basic areas of skill and knowledge can be traced over time, even as curriculum emphases change. Results of these two kinds of NAEP assessments are not directly comparable because of these sampling and content differences.
The second source of student performance data used in this chapter, TIMSS, compares the mathematics and science achievement of elementary and secondary students in the United States with the achievement of students in other countries. TIMSS was conducted in 1994-95 by members of the International Association for the Evaluation of Education. It is the largest and most ambitious undertaking of its kind. Forty-five nations took part in TIMSS at the middle school level (seventh and eighth grades), and 27 at the elementary school level (third and fourth grades). Achievement data and background information were collected from students in each country. Teachers and principals supplied information about instructional resources, practices, staffing, course content, and views of mathematics and science teaching. Curriculum guides and textbooks from 46 nations were analyzed to provide information on the content and skills students in different countries are expected to learn in each grade. Mathematics lessons were videotaped in a sample of eighth grade classrooms in the United States, Japan, and Germany to document differences and similarities in the content presented and the instructional approaches used.
TIMSS results have been published in several reports. Results of curriculum studies are presented in three reports: A Splintered Vision: An Investigation of U.S. Science and Mathematics Education (Schmidt, McKnight, and Raizen 1997) and two volumes-one for mathematics and one for science-that present international comparisons, Many Visions, Many Aims (Schmidt, McKnight et al. 1997; and Schmidt, Raizen et al. 1997). International achievement and survey results are available in four volumes, one for each subject by grade (Beaton, Mullis et al. 1996; Beaton, Martin et al. 1996; Martin et al. 1997; and Mullis et al. 1997). Results from the survey of eighth grade U.S. teachers are presented in Mathematics and Science in the Eighth Grade (Williams et al. 1997). Syntheses of U.S. findings from component TIMSS studies are published in two volumes of Pursuing Excellence, one for fourth grade (NCES 1997c) and one for eighth grade (NCES 1996c).
A third major source of information about student performance is the 1994 High School Transcript Study, which is based on the records of over 25,000 seniors who graduated from high school that year. The transcript study reports information such as the mean number of credits earned in each subject field and the percentage of students earning a given number of credits in particular subjects (NCES 1997e).
The discussion of curriculum and instruction is based largely on data from the TIMSS curriculum analyses, video observational studies, and teacher questionnaires. The technology portion of this section is drawn from a recent survey on the status of advanced telecommunications in public elementary and secondary schools (NCES 1997a).
The third section of this chapter, on teachers and teaching, is based on comparisons of data from the TIMSS teacher questionnaires with results from the National Survey of Science and Mathematics Education (NSSME) conducted during the 1993/94 school
year (Weiss, Matti, and Smith 1994). NSSME, which was initiated in 1977 and updated in 1985, is one of the most comprehensive sources of detailed information on the preparation and classroom practices of mathematics and
science teachers. The discussion of teacher qualifications is supplemented by data from questionnaires administered as part of the 1993/94 Schools and Staffing Survey. (See NCES 1996a.) Information on teachers' efforts
to implement educational standards in their classrooms is drawn from a school reform survey conducted in spring 1996 (NCES 1997d).