Teachers are the key to improving mathematics education. What teachers know how to do and what they choose to do when delivering instruction in their classrooms determine what content students learn and which students learn that content. The preparation, certification, and ongoing professional development of teachers define what they are able to do with theit students. Two important facets shape teacher preparation: (1) what mathematics. the teachers need to know to teach and (2) how they learn to teach that mathematics. Ensuring that well-prepared and competent teachers are in every mathematics classroom means considering the following questions:
What should teachers of mathematics know and be able to do?
How do teachers need to learn this material and these skills?
What is the nature of coursework that will prepare prospective teachers to be efective teachers of mathematics?
How can schools and school systems institutionalize a system of ongoing preofessional development?
How can schools and school systems create a prefessional working environment to make teaching more attractive?
Before It's Too Late: A Report to the Nation from the National Commission on Mathematics and Science Teaching for the 21 st Century, chartered by the United States Secretary of Education, 2000.
Educating Teachers of Science, Mathematics, and Technology: New Practices for the New Millennium, development by the National Research Council's Committee on Science and Mathematics Teacher Preparation, 2000.
The Mathematical Education of Teachers, development by the Conference Board of the Mathematical Sciences, 2001
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Page 19 4 What Preparation and Support Do Teachers Need? Teachers are the key to improving mathematics education. What teachers know how to do and what they choose to do when delivering instruction in their classrooms determine what content students learn and which students learn that content. The preparation, certification, and ongoing professional development of teachers define what they are able to do with theit students. Two important facets shape teacher preparation: (1) what mathematics. the teachers need to know to teach and (2) how they learn to teach that mathematics. Ensuring that well-prepared and competent teachers are in every mathematics classroom means considering the following questions: What should teachers of mathematics know and be able to do? How do teachers need to learn this material and these skills? What is the nature of coursework that will prepare prospective teachers to be efective teachers of mathematics? How can schools and school systems institutionalize a system of ongoing preofessional development? How can schools and school systems create a prefessional working environment to make teaching more attractive? RESOURCES AVAILABLE Before It's Too Late: A Report to the Nation from the National Commission on Mathematics and Science Teaching for the 21 st Century, chartered by the United States Secretary of Education, 2000. Educating Teachers of Science, Mathematics, and Technology: New Practices for the New Millennium, development by the National Research Council's Committee on Science and Mathematics Teacher Preparation, 2000. The Mathematical Education of Teachers, development by the Conference Board of the Mathematical Sciences, 2001
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Page 20 OVERVIEW OF THE RESOURCES These three resources address the issues of who is going to teach mathematics (and science), how they should be prepared, and how they should be supported professionally once they are in the classroom. Before It's Too Late suggests that the lack of well-prepared mathematics and science teachers are a critical national issue. It argues that to improve our students' proficiency in mathematics and science, we must improve mathematics and science teaching. Educating Teachers makes the case, based on research, for well-prepared teachers and calls for restructuring teacher preparation and professional development. Finally, The Mathematical Education of Teachers describes the mathematics a teacher needs to know and what mathematics programs should look like to deliver that knowledge. Before It's Too Late Before It's Too Late is the report of the National Commission on Mathematics and Science Teaching for the 21st Century (the Glenn Commission), which was charged with “(1) reviewing the current state of American K–12 mathematics and science education with a focus on the challenges of teacher recruitment, preparation, retention, and professional growth and (2) articulating the steps needed to strengthen the classroom practice of math and science teachers” (p. 46). Before It's Too Late is predicated on four premises: “At the daybreak of this new century and millennium, the future well-being of our nation and people depends not just on how well we educate our children generally, but on how well we educate them in mathematics and science specifically.” (p. 4) “It is abundantly clear from the evidence already at hand that we are not doing the job that we should do—or can do—in teaching our children to understand and use ideas from these fields.” (p. 4) “The most powerful instrument for change, and therefore the place to begin, lies at the very core of education—with teaching itself.” (p. 5) “Committing ourselves to reach three specific goals—going directly to the issues of quality, quantity, and an enabling work environment—can go far in bringing about the basic changes we need.” (p. 5) Summarizing what happens in most classrooms, the report notes that: “If the core of mathematics and science is about inquiry, then too many of today's mathematics and science classrooms come up short. Students are crippled by content limited to ‘What?' They get only a little bit about the ‘How?' (or ‘How else?') and not nearly enough about the ‘Why?' Missing almost entirely is
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Page 21 ‘Why should I care?' It is hard to imagine that students in these classes are gaining the conceptual and problem-solving skills they need to function effectively as workers and citizens in today's world” (p. 21). This scenario is contrasted with the following vision of high-quality teaching (p. 22): High-quality teaching requires that teachers have a deep knowledge of subject matter. The ability to teach, contrary to myth, is not “something you're born with”; it can be learned and refined over time…through training, mentoring, collaboration with peers, and practice. The process of inquiry, not merely “giving instruction”, is the very heart of what teachers do. A good science or mathematics teacher encourages students to try new possibilities, to venture possible explanations, and to follow them to their logical conclusions. High quality teaching fosters healthy skepticism. High quality teaching has the deepest respect for students as persons, and builds on strengths, rather than trying to stamp out weaknesses. Teaching is grounded in a careful and thorough alignment of curriculum, assessment, and high standards for student learning. Practice is continually reshaped by supportive institutional structures, such as professional development, continuing education, and the effective use of technology. Effectiveness is evaluated by student performance and achievement. Asking why high-quality teaching is not universal, the report makes the following observation: For teachers to deliver high-quality teaching, they must be empowered to do so. Generating this kind of teaching means that school boards, administrators, parents, and policymakers must be willing to stand up for teachers as the primary drivers of student achievement. Teachers must be given the time they need within the school day to keep up with new developments in their fields, teaching aids, materials, and technology. Teachers must be encouraged to contribute knowledge back to their disciplines. They need the time and the feedback necessary to reflect on their teaching, so they can get better at it. Teacher empowerment also means according teachers the respect they deserve for their judgments about learning, rewarding their professionalism, and yes, paying them what they are worth. (p. 23)
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Page 22 Before It's Too Late proposes three goals or recommendations and sets forth 14 action strategies by which to implement the goals: “Establish an ongoing system to improve the quality of mathematics and science teaching in grades K–12” by (p. 24): – Immediately conducting a full needs assessment. – Establishing summer institutes. – Developing school- and district-level inquiry groups. – Providing leadership training. – Creating an Internet portal for teachers. – Forming a nongovernmental Coordinating Council for Mathematics. – Initiating reward and incentive programs. “Increase significantly the number of mathematics and science teachers and improve the quality of their preparation” by (p. 29): – Identifying exemplary models of teacher preparation. – Finding ways to attract additional qualified candidates into teaching. – Creating 15 Mathematics and Science Teaching Academies. “Improve the working environment and make the teaching profession more attractive for K–12 mathematics and science teachers” by (p. 32): – Instituting focused induction programs to acclimate beginning teachers to the profession. – Developing district/business partnerships to help create more professional working environments. – Providing incentives—in the form of cash awards, salary increases, support for further education, or community-wide recognition to encourage teachers to remain in teaching. – Making salaries—especially for mathematics and science teachers—more competitive. Educating Teachers of Science, Mathematics, and Technology: New Practices for the New Millennium Educating Teachers was developed by a National Research Council committee charged with identifying “critical issues emerging from existing practices and policies for teacher preparation” (p. 27). The report includes a detailed analysis of the problems and issues relating to teacher education and the teaching of science, mathematics, and technology; a
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Page 23summary of current recommendations concerning these issues; and recommendations for a systemic approach to improving teacher education. Among the teacher education issues raised (pp. 31–34), the report notes the following: Research is demonstrating that good teaching does matter. Many of the nation's teachers are not adequately prepared to teach mathematics and science using standards-based approaches and in ways that bolster student learning and achievement. The preparation of beginning teachers often does not meet the needs of the modern classroom. Accreditation standards and licensing examinations often do not reflect recent changes in expectations for teachers or for students. Professional development for continuing teachers too often consists of a patchwork of courses, curricula, and programs and may do little to enhance teachers' content knowledge or the techniques and skills they need to teach science and mathematics effectively. Examining results from emerging research, the study committee concluded that a teacher must have conceptual understanding of mathematics. It also argues that pedagogical content knowledge is an important subset of content knowledge (p. 119). The report also presents a broad set of issues related to teaching in today's classrooms (pp. 35–39) and compares teaching with other professions. The report indicates that the teaching profession falls far short of the expectations, rewards, and working conditions found in other professions. Significant systemic improvements are needed to provide the following: Access to adequate career advice from college-level faculty in the sciences, mathematics, or engineering. Rigorous and appropriate content courses for prospective teachers. Oversight of teacher education programs by professional organizations. A continuum of professional development. Adequate mentoring of new employees; targeted professional development programs; encouragement and incentives for continuing education within the profession; and expectations for credentialing of professionals. The involvement of teachers in decision- and policy-making. The vision for improving teacher education and the teaching profession that emerges in the report is built upon six guiding principles (p. 88): “The improvement of teacher education and teaching in science, mathematics, and technology should be viewed as a top national priority;
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Page 24 Teacher education in science, mathematics, and technology must become a career-long process. High quality professional development programs that include intellectual growth as well as the upgrading of teachers' knowledge and skills must be expected and essential features in the careers of all teachers; Through changes in the rewards for, incentives for, and expectation of teachers, teaching as a profession must be upgraded in status and stature to the level of other professions; Both individually and collectively, two- and four-year colleges and universities must assume greater responsibility and be held more accountable for improving teacher education; Neither the higher education nor the K–12 communities can successfully improve teacher education as effectively in isolation as they can by working closely together. Collective, fully integrated efforts among school staff and administrators in individual schools and districts, teacher unions, faculty and administrators of higher education, policymakers, from local colleges and universities, and parents are essential for addressing these issues; and Many more scientists, mathematicians, and engineers, must become well informed enough to be involved with local and national efforts to provide the appropriate content knowledge and pedagogy of their disciplines to current and future teachers.” Educating Teachers offers three general recommendations (p. 109): “Teacher education in science, mathematics and technology be viewed as a continuum of programs and professional experiences that enables individuals to move seamlessly from college preparation for teaching to careers in teaching these subject areas; Teacher education be viewed as a career-long process that allows teachers of science, mathematics, and technology to acquire and regularly update the content knowledge and pedagogical tools needed to teach in ways that enhance student learning and achievement in these subjects; and Teacher education also be structured in ways that allow teachers to grow individually in their profession and to contribute to the further enhancement of both teaching and their disciplines.” These general recommendations are reinforced by a set of specific recommendations for government, for collaboration between institutions of higher education and the K–12 community, for the higher education community, for the K–12 education community, and for professional and disciplinary organizations. As a whole, these recommendations advocate building a far more coherent, collaborative and professional system of teacher education. The report highlights the following specific activities, among others:
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Page 25 Building partnerships and other forms of collaboration between institutions of higher education and K–12 school districts to improve teacher education. Increasing reliance on the professional development school model of teacher preparation. Establishing collaborative beginning and experienced teacher support programs. Restructuring which organizations have primarily responsibility for the various components of teacher education. Enhancing links between research and practice at all levels of the system. The Mathematical Education of Teachers The Mathematical Education of Teachers is designed “to be a resource for mathematics faculty and other parties involved in the education of mathematics teachers. It is a distillation of current thinking on curriculum and policy issues affecting the mathematical education of teachers, with the goal of stimulating efforts on individual campuses to improve programs for prospective teachers”. It is also meant to stimulate “efforts on individual campuses to improve programs for prospective teachers” (p. xi). Accordingly, the report “calls for a rethinking of the mathematical education of prospective teachers within mathematical sciences departments at U.S. two- and four-year colleges and universities. It offers principles to assist departments in this process, along with specific suggestions for mathematics courses for prospective teachers.” Moreover, the report “seeks to convince faculty that there is more intellectual content in school mathematics instruction than most realize, content that teachers need to understand well” (p. 3). The report has been prepared by the Conference Board of the Mathematical Sciences, an umbrella organization of 16 professional societies, all of which have as one of their primary objectives the increase or diffusion of knowledge in one or more of the mathematical sciences. The Mathematical Education of Teachers connects the mathematical aspects of teacher preparation with the mathematical content teachers are expected to teach through a set of 11 broad recommendations (and accompanying specifics) for effectively preparing all teachers of mathematics. As noted in the preface: The mathematical knowledge needed for teaching is quite different from that required by college students pursuing other mathematics-related professions. Prospective teachers need a solid understanding of mathematics so that they can teach it as a coherent, reasoned activity and communicate its elegance
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Page 26and power. Mathematicians are particularly qualified to teach mathematics in the connected, sense-making way that teachers need. For maximum effectiveness, the design of this instruction requires collaboration between mathematicians and mathematics educators and close connections with classroom practice, (p. xi) These themes are played out in three sets of recommendations for mathematical content for elementary, middle, and high school teachers. In addition to specific content recommendations at each level, the report's supporting commentaries provide insights into preparing teachers. For example, in the elementary grades chapter, it is suggested that The key to turning even poorly prepared prospective elementary teachers into mathematical thinkers is to work from what they do know—the mathematical ideas they hold, the skills they possess, and the contexts in which these are understood—so they can move from where they are to where they need to go. For their instructors, this requires learning to understand how their students think. The disciplinary habits of abstraction and deductive demonstration, characteristic of the way professional mathematicians present their work, have little to do with the ways each of us initially enters the world of mathematics, that is, experientially, building our concepts from action. And this is where mathematics courses for elementary school teachers must begin, first helping teachers make meaning for the mathematical objects under study— meaning that often was not present in their own elementary educations—and only then moving on to higher orders of generality and rigor, (p. 17) Similarly, in the middle grades chapter, readers are informed that: One way to develop meaning in algebra is to highlight the manner in which algebra is generalized arithmetic, a language that encodes properties of arithmetic operations. A somewhat different way to think of algebra is as an extension of quantitative reasoning in arithmetic situations. If arithmetic word problems are solved by focusing on the quantities in a problem and determining relationships among these quantities before assigning any numerical values to the quantities, it is a reasonable next step to assign variables rather than numbers. Assigning variables to the quantities and setting up equations representing the relationships is then a formalization of reasoning quantitatively about the problem. However, this formalization is not always an easy one. Prospective teachers
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Page 27need practice on solving problems situated in realistic contexts through this type of analysis, which can also help them develop a deeper appreciation of the important role variables play in algebra. (p. 31) In the high school chapter, it is suggested that: Algebraic connections between high school and college courses can be an explicit focus of the capstone sequence for teachers. For example, this sequence could profitably examine the historical evolution of key concepts in number theory and algebra and it could trace the development of key number and algebra ideas from early secondary school through contemporary applications. It could examine the crucial role of algebra in use of computer tools like spreadsheets and the ways that computer algebra system might be useful in exploring algebraic idea. Each facet in such a capstone treatment of number and algebra would provide teachers with insight into the structure of high school mathematics, its uses in science and technology or in the workplace, and the conceptual difficulties in learning number and algebraic concepts. (p. 41) Clearly, this report calls for substantive reform of both the content and the approach to mathematical coursework for prospective teachers as well as a renewed commitment on the part of the mathematics faculty to meeting their mathematical needs. The Mathematical Education of Teachers makes 11 broad recommendations: “Prospective teachers need mathematics courses that develop a deep understanding of the mathematics they will teach.” (p. 7) “Although the quality of mathematics preparation is more important than the quantity, the following amount of mathematics coursework for prospective teachers is recommended: – Prospective elementary grade teachers should be required to take at least 9 semester-hours on fundamental ideas of elementary school mathematics; – Prospective middle grades teachers of mathematics should be required to take at least 21 semester hours of mathematics, that includes at least 12 semester-hours on fundamental ideas of school mathematics appropriate for middle grades teachers; and – Prospective high school teachers of mathematics should be required to complete the equivalent of an undergraduate major in
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Page 28mathematics, that includes a 6-hour capstone course connecting their college mathematics courses with high school mathematics.” (P. 7) “Courses on fundamental ideas of school mathematics should focus on a thorough development of basic mathematical ideas. All courses designed for prospective teachers should develop careful reasoning and mathematical “common sense” in analyzing conceptual relationships and in solving problems.” (p. 8) “Along with building mathematical knowledge, mathematics courses for prospective teachers should develop the habits of mind of a mathematical thinker and demonstrate flexible, interactive styles of teaching.” (p. 8) “Teacher education must be recognized as an important part of mathematics departments' mission at institutions that educate teachers. More mathematicians should consider becoming deeply involved in K– 12 mathematics education.” (p. 8) “The mathematical education of teachers should be seen as a partnership between mathematics faculty and mathematics education faculty.” (p. 9) “There needs to be greater cooperation between two-year and four-year colleges in the mathematical education of teachers.” (p. 9) “There need to be more collaborations between mathematics faculty and school mathematics teachers.” (p. 10) “Efforts to improve standards for school mathematics instruction as well as for teacher preparation, accreditation, and teacher certification, will be strengthened by the full-fledged participation of the academic mathematics community.” (p. 10) “Teachers need the opportunity to develop their understanding of mathematics and its teaching throughout their careers, through both self-directed and collegial study, and through formal coursework.” (p. 10) “Mathematics in middle grades (grades 5–8) should be taught by mathematics specialists.” (p. 11) ACTIONS EDUCATORS MIGHT CONSIDER After a period of collaborative planning and preparation—following the steps proposed in Before It's Too Late (pp. 38–1) and the detailed recommendations in Educating Teachers (pp. 109–130) —teachers, teacher educators, administrators, and policymakers concerned with how teachers learn the content knowledge and skills to teach might do the following: Establish partnerships between K–12 communities and higher education institutions to share the responsibility for preparing and
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Page 29 supporting teachers, using mechanisms like professional development schools. Suggest that the research conducted by universities include the development and execution of peer-reviewed studies that focus on (1) ways to improve teacher education, (2) the art of teaching, and (3) how people of different ages learn. Work for adequate funding for ongoing professional development. Provide teachers with significant professional development opportunities to improve their teaching through in-depth study in the context of inquiry groups and summer institutes. Establish induction programs to ensure that new teachers receive the support they need to be effective. Establish programs and policies that develop teacher leaders who facilitate the continuous learning of their colleagues. Ensure that teachers and other school staff have electronic and other forms of access to the ever-expanding knowledge base about teaching. Work to develop career-long incentives and rewards for effective teachers that encourage them to remain in teaching and to continually upgrade their skills. Encourage students to consider teaching as a profession. In addition, using The Mathematical Education of Teachers as a guide, faculty members, administrators, and policymakers—particularly at institutions of higher education—who are concerned with what mathematics content teachers should know can: Ensure that the courses offered by two- and four-year colleges and universities provide teachers and prospective teachers with strong exposure to appropriate content and model the kinds of pedagogical approaches appropriate for teaching that content. Review certification requirements to ensure sufficient and appropriate coursework in mathematics, particularly courses that focus on teaching and understanding the fundamental ideas of school mathematics. Foster greater collaboration among mathematicians, mathematics education faculty, and K–12 classroom teachers when designing and implementing programs for prospective teachers. Advocate the use of mathematics specialists for all mathematics instruction in grade 5 and beyond.