The National Council of Teachers of Mathematics' standards and the National Research Council's science standards present new visions of what should be taught, as well as when and how it should be taught. Standards in both subjects call for teachers to introduce and develop topics that, in the past, were reserved for later grades and to orchestrate instruction in ways that are not commonly observed in today's classrooms. At present, few teachers possess both the knowledge of teaching and learning and the knowledge of content necessary to meet these expectations for the effective teaching of mathematics and science.

Until recently, attempts to link student achievement to teacher qualifications focused on degrees earned and major or minor fields of study. These attempts have not been altogether successful; few, if any, consistent effects were found. This was a sensible research strategy at the time because teacher certification requirements were specified in those terms. But more contemporary findings suggest that additional coursework in specific areas may not only increase teachers' knowledge of subject matter, but may also expand the range of teaching and learning approaches a teacher is likely to use in the classroom-and expand student achievement.

Recent studies are using more refined ways to measure teacher qualifications and, as a result, have established that the number and kind of courses taken by mathematics and science teachers do influence student performance. Higher student test scores have been related to teachers who have had more advanced courses in mathematics and science and in other educational areas. Taking additional coursework in unrelated subjects had no-or sometimes even a negative-effect on student learning (Monk 1994).

In addition, students whose teachers have completed more course credits in their field (and those with higher grade point averages) achieve at higher levels than other students. In a study conducted by Chaney (1995), teachers who had taken courses in mathematics at above calculus level coupled with courses in mathematics education were found to have students who less frequently scored in the lower achievement grouping and more often demonstrated advanced levels of performance. (See appendix table 1-26.) In addition, these better prepared teachers were more likely to expose their lower level mathematics students to college preparatory subjects such as algebra in regular mathematics classes (Chaney 1995).

Still other studies examining the knowledge base and preparation of teachers have identified important differences in instruction. Several of these studies showed that when covering topics on which they were well-prepared, teachers more often encouraged student questions and discussion; spent less time on unrelated topics; permitted discussion to move in new directions on the basis of student interests; and generally presented the topics in a more coherent, organized fashion. When covering unfamiliar topics, teachers discouraged active participation by students, kept discussion under tight rein, relied more on presentations than on student discourse, and spent more time on tangential issues such as study skills and cooperative effort (see, e.g., Carlsen 1991, and Smith and Neale 1991).

An increasing number of states are requiring that teachers have a college major or a minimum number of credits in the subjects they plan to teach. Twenty-nine states now require, at least at the middle and high school levels, that teachers have a degree in a specific subject area other than education. Nine of these states also require this of elementary school teachers (CCSSO 1996). (See appendix table 1-20.)

As of the 1993/94 school year, 1 percent of elementary school teachers possessed a mathematics degree, 2 percent had a science degree, and only 5 or 6 percent more had either majored or minored in mathematics or science education in college. The vast majority of elementary school teachers earn college degrees in education rather than in specific disciplines or disciplinary areas of education. High school teachers were much more likely to possess mathematics and science degrees. Of high school mathematics teachers, 41 percent had earned a degree in mathematics compared with just 7 percent of middle school teachers. In science, 63 percent of high school, and 17 percent of middle school, science teachers possessed some form of science degree. (See text table 1-4.)

The professional associations have made specific recommendations for the preparation of mathematics and science teachers. (See "Are Teachers Knowledgeable About the Standards?") The NCTM standards recommend that middle school
mathematics teachers take college courses in abstract algebra, geometry, calculus, probability and statistics, and applications of mathematics/problem solving. An even more detailed list of coursework is recommended for high school mathematics
teachers (Weiss, Matti, and Smith 1994). **[Skip Text Box]**

## Are Teachers Knowledgeable About the Standards?
In a 1995 survey of teachers, 85 percent of eighth grade mathematics teachers reported being "fairly" or "very" familiar with the There are indications that U.S. teachers believe they are implementing some aspects of standards-based instruction. A 1996 survey asked teachers to report on the kind of reform activities they are implementing in their classrooms. The seven-item list of activities included assisting students to reach high standards, using curriculum materials aligned with standards, and using authentic assessments. (See figure 1-18.) Except for using authentic assessments and telecommunications to support instruction, in the majority of cases, mathematics and science teachers at all three levels of schooling believed they were implementing each of the activities included in the survey (NCES 1997d). |

Many middle school mathematics teachers fall short of these recommendations. Only 7 percent of middle school mathematics teachers have taken courses in all of the areas recommended by the standards, and about one-third have taken none. High school teachers are generally better prepared. About one-third have completed courses in at least 9 of 10 recommended areas, and only 2 percent have completed just one course or none of the recommended coursework. Virtually all elementary school teachers have completed some courses in mathematics education or mathematics for elementary teachers: 42 percent have completed college algebra/trigonometry, or elementary functions, but only 12 percent have completed calculus (Weiss, Matti, and Smith 1994).

The National Science Teachers Association recommends that elementary school teachers have one course each in the biological, physical, and earth sciences as well as coursework in science education. Just about half of elementary teachers have satisfied this requirement. Middle school science teachers are encouraged to take at least two courses in each area as well as teacher training in their field (Weiss, Matti, and Smith 1994). Only 42 percent of middle school science teachers (grades 5 to 8) and 57 percent of junior high school (grades 7 to 9) science teachers meet the Association's recommendations in full. Recommended courses for the prospective high school teacher are quite detailed in each of the three areas of science, and there is a considerable range in the number of teachers meeting those recommendations. Less than half of earth science teachers, compared with 90 percent of biology teachers, had taken six or more credits in their respective subject areas (Weiss, Matti, and Smith 1994).

How teachers go about their work in classrooms depends to some extent on their views about the nature of their academic disciplines and about teaching and learning in their fields. Research in the last 10 years supports this claim (Dwyer 1993a and 1993b). Teachers who see science as a static collection of facts tend toward instructional approaches that rely on "teacher-talk" and direction, and on student practice and memorization. Teachers who see science as a process of empirical discovery are more comfortable with hands-on learning and open-ended tasks (Carlsen 1991, and Smith and Neale 1991). Others have made similar observations about the views and practices of mathematics teachers (Dossey 1992 and Thompson 1992).

The majority of teachers have fairly practical views of mathematics and science. Close to 80 percent of teachers in both subjects see their fields as providing "formal ways of representing the real world," and close to 90 percent as a "structured guide for addressing real situations." Only 31 percent of mathematics teachers and 18 percent of science teachers view their subject as an abstract conceptual system.

A number of teachers have views that run counter to the general directions set by standards. Close to 80 percent of mathematics teachers believe that some students have a natural talent for mathematics while others do not, and 35 percent think that mathematics should be learned as a set of algorithms or rules. In science, teachers sometimes hold similar views. Almost two-thirds of science teachers believe that some students have a natural talent for science and others do not. About three-quarters believe that students should be given prescriptive and sequential directions for doing experiments; only 32 percent thought focusing on rules might be a bad idea. (See figure 1-19.)

There is substantial agreement between mathematics and science teachers on the aptitudes and skills students need to succeed in learning mathematics and science. Over 80 percent of mathematics and science teachers consider it very important for students to understand concepts, to understand how the subjects are used in the real world, and to be able to support their results and conclusions.

There are some areas of difference in these views. Fewer mathematics teachers (65 percent) than science teachers (73 percent) consider creative thinking very important. However, the biggest difference in views centers on the importance of students remembering formulas and procedures. Over 40 percent of mathematics teachers believe that it is important for students to memorize formulas, compared with 26 percent of science teachers. (See figure 1-20.)

Information about the academic preparation of the teaching force and their views and attitudes toward teaching and learning do not tell the complete story of teachers' qualifications. All too frequently, teachers are assigned to classes outside their fields (Ingersoll 1996). The problem is particularly acute in mathematics. In the 1990/91 school year, students were less likely to have a qualified teacher in mathematics than in any other core subject. About 27 percent of students in grades 7 to 12 had a mathematics teacher without at least a minor in mathematics or mathematics education compared with 21 percent in English, 17 percent in science, and 13 percent in social studies. Out-of-field teaching is more common at middle and junior high schools than in senior high schools. In 1991, 32 percent of students in 7th grade science classes had teachers without a major or minor in science or science education, while only 13 percent of 12th graders did. (See appendix table 1-24.)

There are large differences across states in the proportions of mathematics and science teachers who have degrees in these subjects. The percentage of secondary mathematics teachers with a major in mathematics ranges from under 45 percent in Alaska, Delaware, and Washington to over 80 percent in Pennsylvania and the District of Columbia. Similarly, fewer than half of secondary science teachers in Nevada and Louisiana majored in science in college compared with 80 or more percent in 10 states (Blank and Gruebel 1995).

There are also equity issues involved with out-of-field teaching which is more prevalent in high-poverty schools, in low-achieving classes, and in low-track classes (Chaney 1995; Gamoran 1986; and Oakes, Gamoran, and Page 1992). For example, more than one-quarter of students enrolled in secondary school science classes in which students were judged to be low achieving had a teacher without at least a minor in science or science education, compared with fewer than 1 in 10 students in high-achieving classes. Thirty-six percent of students in classes with high minority enrollments had a mathematics teacher without a major or minor in mathematics or mathematics education, compared with 23 percent of students in low minority classes. In addition, students who attend school in high-poverty areas are much more likely to have mathematics and science teachers without at least a minor in these fields than students attending schools in low-poverty areas. (See figure 1-21.) In effect, students who need the most support are left with the teachers least qualified to help them (Darling-Hammond 1994a; Oakes 1990; and Weiss, Matti, and Smith 1994).

Many efforts in the last decade to bring about systemic, standards-based changes in schools have focused on the professionalization of teaching. The logic underlying this approach is that upgrading the profession will increase teachers' commitment and motivation. This will in turn result, it is believed, in better teaching, with the final outcome being improved student learning. A variety of proposals have been offered for improving the status and professional credentialing of teachers. The most ambitious of these proposals seek changes in how teachers are prepared, licensed, and supported throughout their careers (see, for example, Carnegie Forum on Education and the Economy 1986, and National Commission on Teaching and America's Future 1996).

The National Commission on Teaching and America's Future, for example, recommends:

- organizing teacher education and professional development programs around the standards;

- developing extended graduate level teaching programs that offer year-long internships, similar to those offered in the medical profession, to provide closely supervised practice that is tied to coursework; and

- creating stable, high-quality professional development services to support teachers.

Efforts are under way to bring about each of these changes. Some of these initiatives have focused primarily on teacher preparation. The Holmes Group, which was formed by college deans of education, proposed that prospective teachers be required to devote four years of undergraduate study to academic content in their chosen major, and that professional preparation in teaching be postponed to a fifth or sixth year (Holmes Group 1986). Year-long internships, two-year induction periods, and professional development schools are all variations on this basic idea aimed at providing prospective teachers with both better academic preparation and more classroom experience before licensing.

Other efforts have focused on development of standards to guide the profession. The National Board for Professional Teaching Standards has developed standards for accomplished teaching, created performance-based certification exams to identify accomplished teachers, and established a professional board to oversee operation of the system (NBPTS 1991). The Interstate New Teacher Assessment and Support Consortium (INTASC), which was formed by a consortium of state education agencies, higher education institutions, and national educational organizations, has focused on the other end of the continuum: new teachers. INTASC has begun to develop standards and performance-based assessments useful for judging competent entry-level teaching and for guiding the professional development of early career teachers (INTASC 1991).

Both sets of teachers' standards are compatible with each other, and both are directly linked to the national standards for student performance in specific content areas. The standards for new teachers developed by INTASC have been adopted or adapted for use by 14 states and are being used in several additional states as a basis for evaluating their systems for licensing (INTASC 1994).

Policy efforts also have been initiated to infuse standards-based conceptions of teacher preparation into higher education and teacher training institutions. Many educators view the process of program accreditation as the most effective lever for
bringing about desired changes. The National Council for the Accreditation of Teacher Education, which has accredited teacher education programs for many years in cooperation with state agencies, has taken steps in this direction. Recently, it has
incorporated performance standards developed by the aforementioned INTASC in the program approval process (Darling-Hammond 1994a).

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