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Educating Teachers of Science, Mathematics, and Technology: New Practices for the New Millenium 1 Introduction and Context Nearly everyone can drive a car. But can everyone drive a tractor-trailer or fly an airliner? What minimum qualifications and background are required to carry out these demanding tasks competently? How does one define an “expert” in each of these categories? How much training and experience would travelers want the truck driver or pilot to have had? These kinds of questions were raised recently in an article comparing methods used around the world for the training of commercial airline pilots for United States and foreign carriers (Mangan, 2000). Pilots for the U.S.-based airlines go through training over a six-year period that includes a four-year college degree (or military piloting experience). They then move through the ranks from flight instructor to pilot of a regional carrier. By contrast, new pilots for many foreign carriers are given one year of rigorous training and instruction. Which training method is preferable? The foreign carrier pilots do not appear to have more accidents, but they also do not have the experience and flexibility that results from a longer-term training program. Like pilots who fly aircraft and are responsible for cargo, crew, and passengers, teachers have demanding jobs, with responsibilities that can have long-term impacts on their students, communities, and society in general. Thus, as with the skills required of airline pilots, one might reasonably ask, “Can every-one teach?” The answer to this is likely “Yes!” That is, virtually everyone has taught something to someone else, even if it was as a parent or friend. “Teaching as telling” is a common human behavior. But what does it require to be a highly competent teacher in a classroom? In the prevailing cultural norms in the United States, there seems to be an assumption that certain professions do
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Educating Teachers of Science, Mathematics, and Technology: New Practices for the New Millenium not require all that much background—that anyone can be a professional writer, for example, or teacher, with the relative outcomes the same regardless of education, experience, or professional development. But as this report will show, highly knowledgeable, highly skilled teachers do make a difference in terms of student learning. And, therefore, if for no other reason, careful attention must be paid to how they are educated and professionally supported and nurtured throughout their careers. THE REFORM MOVEMENT IN EDUCATION: CURRENT CHALLENGES Although education has been a central focus of concern for the U.S. public for many years, the first contemporary national expression of concern was issued in 1983, in a U.S. Department of Education-funded report entitled A Nation at Risk (National Commission on Excellence in Education). That report warned of a “rising tide of mediocrity” that threatened the United States both economically and militarily. At the time, the nation was especially concerned with the rise of Japanese economic power and Soviet military might. Sixteen years later, the United States stands as the world’s sole economic and military superpower, but our nation still remains concerned about the academic performance of U.S. children on national (e.g., National Assessment of Educational Progress—NAEP) and international (e.g., the Third International Mathematics Science Study—TIMSS) The key difference between the current and previous calls for reform in teacher preparation is a focus on strategies that coordinate the preparation of high quality teachers with improvements in K-12 student achievement. Rodriguez, 1998 assessments compared with the academic performance of students in many other countries. What might these poor performances bode for our future international and economic stature? Are schools accomplishing what we want for our children? For all of our children? Following publication and national discussion of A Nation at Risk, a spate of other reports appeared. Those reports offered criticisms of and proposed solutions for the entire landscape of K-12 education (e.g., reviewed by Darling-Hammond, 1997). In science and mathematics, the American Association for the Advancement of Science (AAAS) initiated its comprehensive
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Educating Teachers of Science, Mathematics, and Technology: New Practices for the New Millenium project, “Project 2061”1 in 1986. Project 2061 resulted in the publication of Science for All Americans (1989), which articulated AAAS’ vision for scientific literacy. Benchmarks for Science Literacy, which offered goals and objectives for what U.S. students should know and be able to do in science, appeared in 1993. In 1986, the National Council of Teachers of Mathematics began its work on K-12 content standards for mathematics, which were released in 1989 and subsequently revised in 2000. By the end of the 1980s, the National Science Teachers Association (NSTA) had started crafting a new approach to teaching science (Scope, Sequence and Coordination), which recommended that students in grades 9-12 be exposed to every science subject each year (NSTA, 1996). In 1991, the National Research Council was asked by the president of the NSTA and other scientific organizations, the U.S. Department of Education, the National Science Foundation, and the co-chairs of the National Education Goals Panel (a project supported by the National Governors’ Association) to coordinate the development of national science education standards. These voluntary standards, published in 1996, reflected input from thousands of scientists, mathematicians, and science and mathematics educators. The National Science Education Standards addressed not only content but also critical related issues, such as the professionalism of teachers, the roles of colleges and universities in preparing teachers to implement and teach curricula that are consistent with the content standards, appropriate assessment of knowledge, and the educational infrastructure that would be needed to support these new approaches to teaching and learning.2 The development of these national standards reflected the concern that U.S. students needed to become much more knowledgeable about science and mathematics than they had been in the past. The national standards presaged a growing researched-based consensus about how people learn and should be taught (summarized in NRC, 1999d,e). All 50 states are now at varying stages of developing and implementing their own curriculum frameworks and learning outcomes for students in grades K-12 (Education Commission of the 1 “Project 2061” was so named because it was launched in 1986, the year that Halley’s comet made its most recent close pass by Earth. The next time that the comet returns will be in 2061. The title serves as a metaphor for what AAAS views as a generation of change for fundamentally new approaches to teaching and learning science. 2 In mathematics, the National Council of Teachers of Mathematics issued a separate set of recommendations for teacher education (NCTM, 1991) two years after the release of its content standards for mathematics.
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Educating Teachers of Science, Mathematics, and Technology: New Practices for the New Millenium States, 2000). Many of these state initiatives are based at least in part on the national standards. Thus, a growing consensus is emerging about the science and mathematics content that all students in grades K-12 should know, understand, and be able to do to prepare themselves for living and working in the 21st century. While there continues to be a recognized need to improve the content of science and mathematics education for K-12 students, a near revolution in understanding human learning has been taking place through the emerging field of cognitive science. This research, summarized recently by a study committee of the National Research Council (1999d), indicates that teachers should incorporate content-appropriate methods of teaching that improve their students’ chances of knowing and understanding content in areas such as mathematics. This new understanding, coupled with research that substantiates the importance of guiding beginning teachers so that they learn to employ a variety of instructional practices, implies the need for and benefit of sound preparation in both subject matter and pedagogical training for prospective teachers (Stoddard and Floden, 1995; Ball, 1997). Concomitant with the reform of content in K-12 science and mathematics and knowledge about how people learn, there have been calls for restructuring teacher preparation and professional development. The leading proponents of education reform have argued that the attainment of high standards for students—standards that demand understanding and the ability to perform—will be unlikely until teachers are educated in ways that enable them to implement and teach curricula that are consistent with the vision, goals, and content of the national standards. If children are to be able to engage in inquiry and problem solving as they learn science and mathematics, then surely their teachers also need to experience and practice inquiry and problem solving in their own education (NRC, 2000a). Three other recent reports have served to catalyze attempts to improve teacher education: In 1996, the Council of Basic Education (CBE) cited several problems that it claimed compromised the education of teachers. These problems included inadequate and poorly supervised school-based practicum experience, the mediocre academic credentials of students who enroll in teacher education programs, and the questionable quality of faculty in the schools of education who prepare those students (Rigden, 1996). In the same year, a report from the
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Educating Teachers of Science, Mathematics, and Technology: New Practices for the New Millenium National Commission on Teaching and America’s Future (NCTAF, 1996) admonished educators of teachers for not attending to problems of uninspired teaching in their own courses, a curriculum that lacks both substance and depth, and a lack of coherence and articulation in teacher education programs between schools of education and other disciplines. Although critical about how teachers are prepared, the NCTAF report also pointed to research data showing that the United States labors with fatal distractions in its reform efforts, including the misguided beliefs that 1) anyone can teach, especially if they have adequate content knowledge, and that 2) teacher preparation programs contribute little to the production of qualified teachers and high-quality teaching. In a second report, NCTAF (1997) cited 12 partner states that have begun far-reaching sets of reforms that could affect virtually all aspects of teaching. In North Carolina, for example, the state’s Excellent Schools Act of 1997 enacted “nearly all of the recommendations of the National Commission that were not already in place in the state,” including increasing teachers’ average salaries by 33 percent over four years; improving teacher education by establishing school-university partnerships to create clinical school settings and requiring special education training for all newly prepared teachers; enhancing mentoring of beginning teachers by setting standards for the selection of mentor teachers and providing funds to professionally prepare and compensate mentors; and the funding of professional development tied to state content standards for students. Mundry et al. (1999) noted the lack of focus and coherence in teacher education programs. That study also highlighted the failure of teacher educators to establish a “coherent set or ‘continuum’ of career-long learning experiences for all K-12 teachers of science and mathematics, primarily to improve teaching and learning in the classroom.” Significant effort is needed to bridge the gap between preservice and inservice teacher education. However, the authors noted that a “disconnect” in teacher education programs actually stems from a major problem that teacher educators face. In the current education system, most teachers do not have access to high-quality, ongoing opportunities for professional development. Thus, schools of education attempt to prepare prospective teachers for the demands of the present system of K-12 education as well as for both probable and unanticipated changes to the education system in the future. Partly as a result of these attempts to cover such broad ground in teacher preparation programs, many
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Educating Teachers of Science, Mathematics, and Technology: New Practices for the New Millenium graduates and their supervisors report that their teacher preparation programs were inadequate, idealistic, or too theoretical. Too often, teacher preparation programs are characterized by a lack of coherence and articulation across the general education, science education, and professional education curriculum strands. In each of these three areas, expectations typically are defined by a list of courses. These courses in turn usually are defined by a body of basic knowledge within the respective disciplines without major attention to the nature of the investigative modes that produced them. Similarly, few courses address the application of this knowledge to societal issues or other matters—dimensions that the Standards say need significant attention in K-12 education in science. National Research Council, 1997b In the past decade, the criticism of teacher preparation programs also has extended to content preparation. Numerous reports, including those from the American Association for the Advancement of Science (1990) and the National Research Council (1989, 1991, 1995, 1999h) have criticized the nearly exclusive use of lecture-based teaching that prospective teacher candidates experience in many of their undergraduate science and mathematics courses. As noted in the National Science Education Standards (NRC, 1996a), science is not something that is done to students, it is something that students do. If teachers are to implement standards-based teaching approaches, then they too must experience these models of instruction in their undergraduate classes. Furthermore, prospective teachers need to experience science and mathematics learning through inquiry, problem-based approaches, and direct, hands-on experiences in the classroom, laboratory, and field (e.g., Howard Hughes Medical Institute, 1996; NRC, 1999h). Although calls for reform persist, teacher educators at some major research universities have been working for many years to reform teacher education. Representatives from many of these universities banded together in 1986 to produce the hallmark Holmes Group Report (Holmes Group, 1986). This report was to be the first in a series of efforts to deal with the reform and revitalization of teacher education. The Holmes report called for prospective teachers to acquire a solid background in the liberal arts as undergraduates and then to engage in substantive post-
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Educating Teachers of Science, Mathematics, and Technology: New Practices for the New Millenium Teaching science through inquiry allows students to conceptualize a question and then seek possible explanations that respond to that question. For example, in my field of cell biology, cell membranes have to be selectively permeable—they have to let foodstuffs like sugars pass inward and wastes like carbon dioxide pass out, while holding the many big molecules that from the cell inside. What kind of material could have these properties and yet be able to expand as the cell grows? It is certainly easy to remember another and more familiar type of science teaching from my childhood. In this approach—which remains depressingly common today—teachers provide their students with sets of science facts and with technical words to describe those facts. In the worst case, this type of science teaching assumes that education consists of filling a student’s head with vocabulary words and associations, such as mitochondria being “the powerhouses of the cell,” DNA being the “genetic material,” and motion producing “kinetic energy.” Science classes of this type treat education as if it were preparation for a quiz show or a game of trivial pursuit. This view of science education has many problems. Most students are not interested in being quiz show participants. They fail to see how this type of knowledge will be useful to them in the future. They therefore lack the motivation for this kind of “school learning.” Most important, this kind of teaching misses a tremendous opportunity to give all students the problem-solving skills that they will need to be effective workers and citizens in the 21st century. Bruce Alberts Excerpted from the Foreword in National Research Council (2000b)
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Educating Teachers of Science, Mathematics, and Technology: New Practices for the New Millenium baccalaureate work that would allow them to apply their knowledge and pedagogical skills in school settings. The Holmes report also urged that teacher education take place at “teaching centers” linked to major universities, a strategy parallel to the reform of medical education in the early 1900s following publication of the Flexner Report (1910). A major study by Goodlad (1994) served as further impetus for restructuring teacher education. Goodlad highlighted significant problems, such as the lack of “connectedness” among schools of education, university liberal arts programs, and the K-12 education sector. Goodlad also cited as problematic the low status accorded to teacher education programs and schools of education on university campuses. He recommended strengthening the connections between reform efforts taking place in schools of education (teacher preparation) and those in K-12 education (e.g., implementation of content standards). Both the Holmes Group and Goodlad reports encouraged development of Professional Development Schools and other forms of university and K-12 partnerships. More than 300 schools of education responded to these reports to create programs that go beyond the traditional four-year degree programs to include more extensive study of subject matter and more extensive clinical training in K-12 schools (Darling-Hammond, 1997). In 1998, Abdal-Haqq reported that over 600 PDS models had been developed in the United States, with some of these institutions exploring several different models for improving teacher education. More than 1,000 such schools exist today (Abdal-Haqq, personal communication). Professional Development Schools are described in greater detail later in this report. ROADBLOCKS TO CHANGES IN TEACHER EDUCATION Murray (1996) emphasized that a significant barrier to the reform of teacher education results from a long-standing belief among many people that teaching is a natural human endeavor. Parents teach their children, and friends and colleagues teach each other. Even people with few personal connections or similar interests may teach each other. However, in most of these cases, the act of teaching almost always occurs among people of like minds, backgrounds, education, or beliefs and centers around tasks or problems that the teacher and learner have in common. It is strikingly different from what typically occurs in schools. The notion that anyone can teach clearly is ingrained in the contemporary
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Educating Teachers of Science, Mathematics, and Technology: New Practices for the New Millenium culture of the United States, and it can be seen in how university professors are prepared and selected (Merseth, 1993; Murray, 1996). The typical doctorate program emphasizes research, not teaching. Yet many of these researchers take positions at colleges or universities where they also must teach. Many reports in recent years have called for paying more attention to teaching, especially of undergraduates (reviewed in NRC, 1999h; Rothman and Narum, 1999). These notions that “teaching is telling” and that “anyone can teach” also are seen in the design of many alternative teacher education programs that emphasize content background and deemphasize lengthy pedagogical preparation. These programs might, for example, actively recruit college graduates, provide a highly abbreviated “training” period on pedagogy, and then immerse the novice teachers in the culture of the classroom, sometimes with a mentor and sometimes not. Sadly, the belief that anyone can teach also seems to be reflected in some traditional teacher preparation programs. This notion or belief that everyone can teach can lead to overly simplistic approaches to teaching and teacher education. The design of such programs seems to presume that all teacher candidates have some level of natural teaching ability, that teaching is largely “telling,” and that the primary role of teacher educators is to acquaint their students with procedural rules that will ensure success in the classroom. Thus, some teacher education programs stress to their students “basic principles of teaching” and then help these teacher candidates learn, practice, and implement them (e.g., Goodlad, 1990; Howey, 1996). Such approaches also can lead to the espousal of “simple” solutions to problems such as maintaining classroom discipline rather than to broader, deeper examination of what may be the underlying causes for disciplinary problems—failed instruction. Thus, those programs may lack program coherence or a comprehensive philosophical framework. They may not integrate preparation in subject content and pedagogy. Field components of the program may be instituted primarily to comply with state regulations for certifying teachers or for accreditation of the program itself. All of the aforementioned attributes of some traditional preparation programs may help explain why the preparation of teachers historically has been described as teacher “training” rather than teacher “education” (Goodlad, 1994; Howey, 1996; Mundry et al., 1999). Career-long professional development for teachers has suffered a similar lack of coherence, integration, and continuity. In the current system, school
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Educating Teachers of Science, Mathematics, and Technology: New Practices for the New Millenium districts typically have assumed primary responsibility for inservice education. These programs too often are presented in the form of short (typically one-day) “workshops” that may not be sufficiently focused or grounded in practice to be useful to teachers. Or, teachers are sent to a teachers’ convention where they may attend or participate in sessions on a variety of related or unrelated topics, collecting teaching ideas that school officials hope they will be able to implement shortly after returning to their classrooms or share with teacher colleagues. If their content and pedagogical preparation has modeled teaching as a simple, straightforward enterprise—“teaching as telling”—then these teachers’ students may not be better off as a result of these kinds of inservice experiences. More than small changes, what is needed are fundamental changes in teachers’ content and pedagogical preparation and ongoing professional development (Ball, 1997; Loucks-Horsley et al., 1998). INCREASING EXPECTATIONS FOR TEACHING AND LEARNING The paradigm for teacher education outlined above was developed in and may have worked during an era when students and classes were more homogeneous and when the level of knowledge required of students was more basic. The approaches to teacher preparation described above and the patterns of inservice programs met the needs of a largely agrarian society and also worked later when schools were expected to prepare “citizen-students” to function as workers in an increasingly industrialized society. But current learning goals include expectations for much higher levels of knowledge and understanding about science (AAAS, 1993; NRC, 1996a), mathematics (NCTM, 1989, 2000), and technology (ITEA, 2000). In addition, these standards emphasize understanding as well as knowing content and the ability to undertake activities that are related to these disciplines. For example, the National Science Education Standards (NRC, 1996a)3 call for teachers of science to plan inquiry-based programs for their students. guide and facilitate learning. engage in on-going assessment that is appropriate for the new expectations for learning. design and manage learning environments. develop communities of science learners. 3 An elaboration of these six teaching standards can be found in Appendix A.
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Educating Teachers of Science, Mathematics, and Technology: New Practices for the New Millenium actively participate in the ongoing planning and development of the school science program. Similarly, the NCTM’s Professional Standards for Teaching Mathematics (1991)4 envision teachers as decision-makers who must bring to their classrooms the following: A deep content knowledge and understanding of mathematics beyond the mathematics they are teaching. An understanding of students as learners and their previous and current knowledge about the subject area. Carefully selected learning goals. Knowledge of a variety of pedagogical strategies, including the use of modeling and simulation. Experience knowing how to frame questions, choose activities to address misunderstandings they know students have, and assess student learning appropriately. According to the new Principles and Standards for School Mathematics, effective mathematics teachers use strategies and approaches that range from extended student explorations in small groups to direct teaching. As student needs change, teachers make deliberate shifts among these strategies. Teaching mathematics well “takes deep insight about mathematics, about teaching, and about learners, coupled with a sound and robust mathematics curriculum and thoughtful reflection and planning” (NCTM, 2000). Linked with these standards for teaching is changing expectations about what should receive greater emphasis in science and mathematics instruction. Table 1-1 is an example from the National Science Education Standards that illustrates these differences. Both the science and mathematics standards call for teachers to ensure that all students have learning opportunities in science and mathematics that result in measurable learning outcomes (NRC, 1996a; NCTM, 2000). However, today’s K-12 student population in the United States is much more diverse, in terms of different languages, cultures, and ethnicities, for example, than it was just a few decades ago, and teaching standards-based science and mathematics to this new generation of students can pose great educational challenges for teachers. Expectations for increased performance by K-12 students have shifted dramatically during the past 10 years with the development and publication of standards and curriculum frameworks of individual states, many of which are 4 An elaboration of these standards can be found in Appendix A.
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Educating Teachers of Science, Mathematics, and Technology: New Practices for the New Millenium TABLE 1-1 Changing Emphases and Expectations in Science Education The National Science Education Standards envision change throughout the system. The teaching standards encompass the following changes in emphasis: Less Emphasis on More Emphasis on Treating all students alike and responding to the group as a whole Understanding and responding to individual student’s interests, strengths, experiences, and needs Rigidly following curriculum Selecting and adapting curriculum Focusing on student acquisition of information Focusing on student understanding and use of scientific knowledge, ideas, and inquiry processes Presenting scientific knowledge through lecture, text, and demonstration Guiding students in active and extended scientific inquiry Asking for recitation of acquired knowledge Providing opportunities for scientific discussion and debate among students Testing students for factual information at Continuously assessing student understanding the end of the unit or chapter Maintaining responsibility and authority Sharing responsibility for learning with students Supporting competition Supporting a classroom community with cooperation, shared responsibility, and respect Working alone Working with other teachers to enhance the science program based at least in part on the national statements of learning goals in science and mathematics. In increasing numbers of states, calls for higher student understanding of and achievement in science and mathematics has been coupled with high-stakes standardized tests, placing even greater pressure for effective teaching performance on teachers. These changing expectations are making clear that teaching no longer can be seen as an activity that
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Educating Teachers of Science, Mathematics, and Technology: New Practices for the New Millenium anyone can do, nor is it primarily “teaching as telling.” Rather, these developments must compel those who educate prospective and currently practicing teachers to redesign their programs to meet the needs of teachers in this new educational environment (Goodlad, 1994; Darling-Hammond, 1997). ORIGINS OF THE STUDY As part of a grant from the National Science Foundation (NSF), the National Research Council (NRC) commissioned in 1998 the Committee on Science and Mathematics Teacher Preparation (CSMTP).5 This study committee has undertaken a series of projects and activities to examine ways to improve the education of teachers of science, mathematics, and technology for grades K-12. The Executive Committee of the NRC’s Governing Board approved the following Statement of Task to define the nature and scope of the committee’s purview and responsibilities: The [study committee] will identify critical issues emerging from existing practices and policies for teacher preparation. The project report will synthesize existing research relevant to teacher preparation in science, mathematics, and technology. The process will include collecting and summarizing comprehensive recommendations that have been developed by professional societies for science, mathematics, and technology teacher preparation. These three components of the project report will be interwoven, so that the resulting report provides an analysis of the ways in which research, recommendations from professional societies, and practice might be integrated to improve the teacher preparation process in mathematics, science, and technology. (1998) In response, this report of the committee explores the landscape of teacher education in general, and then focuses on issues that can be seen as specific or unique to the teaching of science, mathematics, and technology. It synthesizes and builds on the research literature and current calls for reform of K-16 science and mathematics education as well as on more general principles of effective teacher education that are derived from analysis of actual classroom practice. Research about what is 5 As noted throughout this report, this study undertaken by the members of the Committee on Science and Mathematics Teacher Preparation has led to the conclusion that teacher preparation (which often is equated with the education of prospective teachers, or preservice education) cannot be addressed adequately by itself. Instead, teacher preparation must be viewed as a component of a much more integrated approach to improving the education of teachers at all stages of their careers. Thus, while the study committee was designated as the Committee on Science and Mathematics Teacher Preparation, this report stresses teacher education in its entirety rather than separating teacher preparation from professional development (also known as inservice education).
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Educating Teachers of Science, Mathematics, and Technology: New Practices for the New Millenium currently known about effective teacher preparation and career-long professional development undergirds the report’s discussion, conclusions, and recommendations. The main topics and issues contained in the report’s chapters are The broader context and issues surrounding teaching and teacher education that led to the NRC’s establishment of a Committee on Science and Mathematics Teacher Preparation (this chapter); The current status of education for teachers of science, mathematics, and technology, including stresses on current systems of teacher education and the teaching profession that are exacerbated by the urgent need in many localities for many new “qualified” teachers, especially in science, mathematics, and technology (Chapter 2); The critical importance of well-prepared teachers for improving student learning and achievement (Chapter 3); Descriptions of how teacher preparation might be redesigned in light of research, new knowledge about how teachers learn the content and art of their profession, and, based on recommendations from higher education organizations and the disciplines themselves, how expectations for the professional quality of teachers and teaching, especially for science and mathematics, are likely to change in the near future (Chapter 4); Descriptions of and vignettes from exemplary and promising current practices for improving teacher education in science, mathematics, and technology, including the establishment of close local or regional partnerships between school districts and teacher educators, scientists, and mathematicians in institutions of higher education (Chapter 5); The study committee’s vision for improving teacher education in these disciplines (Chapter 6); Specific recommendations for implementing the committee’s vision for the improvement of education for K-12 teachers of science, mathematics, and technology (Chapter 7); and Information about national standards for K-12 science and mathematics for teacher development, course and curriculum content, and teaching practices (Appendixes A-C); statewide programs that offer ongoing professional development for both novice and experienced teachers of K-12 science and mathematics (Appendix D); examples of formal partnerships between institutions of higher education and schools or school districts (Appendix E); and a glossary of terms specific to the profession.
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Educating Teachers of Science, Mathematics, and Technology: New Practices for the New Millenium The CSMTP’s vision for improved teacher education (Chapter 6) and general as well as specific recommendations (Chapter 7) not only are grounded in research and reports of best practice in teacher education programs and classrooms but on advice from professional societies and organizations, as well. Therefore, committee members are confident that the report will prove useful to the many dedicated people who are working to improve the quality of the education of teachers of K-12 science, mathematics, and technology. The report also should help increase the numbers of teachers who are teaching in ways that allow their students to understand and appreciate the wonders of science, mathematics, and technology and the relevance of these disciplines to virtually every aspect of people’s lives in the new millennium.
Representative terms from entire chapter: