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This summary of The Mathematical Education of Teachers: Part 11 was prepared by Bob Kansky ([email protected]). It is part of an "occasional" series of uninvited, unfunded, unendorsed summaries offered to business, education, and policy leaders who are pursuing systemic improvement of mathematics and science education. While not attempting to critique the report's assumptions, methods, or conclusions, it does use a standardized format to overview them. Readers should consult the original report for further information.2
Introduction to the Report
The Mathematical Education of Teachers was prepared by leaders in the mathematical sciences and in mathematics education under a grant from the United States Department of Education. The report has two parts. Part 1 (Chapters 1-6) is addressed to departments of mathematics at community colleges, colleges, and universities; single copies are available without charge from the Conference Board of the Mathematical Sciences (CBMS)2. Part 2 (Chapters 7-9) of the report - not summarized here - is directed to "mathematics education faculty and mathematics faculty deeply involved in teacher education." Part 2 may be downloaded from the Internet without charge3; also, Parts 1 and 2 also may be purchased as a single volume4.
All six chapters of Part 1 are recommended reading for members of college/university mathematics departments and are necessary background for mathematics educators who would read Part 2. Subsets of Part 1 are directed to special audiences. For instance, deans and mathematics department heads are urged to read Chapter 1 which describes changing expectations related to mathematical knowledge and to the teaching of K-12 mathematics. Chapter 2 is recommended reading for state and national education policy groups, because its twelve general recommendations to mathematics departments have policy implications.
The authors of The Mathematical Education of Teachers assert that "after reading and writing, mathematics is widely viewed as the most important component of K-12 education to promote future success in college and subsequent careers." The K-12 mathematics curriculum required of all students must be rethought: arithmetic skills and a smattering of algebra no longer is sufficient. Higher expectations for the mathematical performance of all students at grades K-4, 5-8, and 9-12 have been set forth in the Principles and Standards for School Mathematics of the National Council of Teachers of Mathematics. The Mathematical Education of Teachers: Part 1 sets forth concomitant expectations for the preparation of teachers of mathematics for each of these three grade-level groupings and considers the role of technology in K-12 mathematics education.
The recommendations in Part 1 are of three kinds. As previously noted, Chapter 1 suggests who should read what chapters of The Mathematical Education of Teachers (Parts 1 and 2). Chapter 2 presents general recommendations to mathematics departments regarding the content and delivery of a curriculum for prospective teachers of mathematics, cooperation with other groups involved in the mathematical education of teachers, and participation in development of national policy directed at improving mathematics teaching. Chapters 3-5 identify concepts and procedures that constitute required "mathematical knowledge for teaching" at grade levels K-4, 5-8, and 9-12, respectively, and address the role of proof and justification at each level.
Chapter 2: General Recommendations. Of the eleven general recommendations to departments of mathematics, five attend to recognizing teacher education as an important part of the departments' mission. To that end, curriculum should make explicit connections between the content of college courses and the mathematics taught in K-12. Prospective teachers of K-4 mathematics should take 9 semesters of coursework related to the fundamental ideas of elementary school mathematics; mathematics teachers in grades 5-8 should have 21 semesters of similarly-appropriate coursework; the equivalent of an undergraduate degree in mathematics is recommended for teachers of grades 9-12. Although connections between college-level mathematics and K-12 mathematics might be made in "capstone" courses designed for that purpose, the report also suggests special courses for teachers who are "lacking prerequisites". (Core mathematical concepts to be "deeply understood" by teachers at each of these three levels are set forth in Chapters 3-5.) Recommendations 6-8 call for increased cooperation among groups that contribute to teacher education. College/university mathematics faculty and mathematics education faculty need to work closely not only to prepare prospective K-12 teachers but also to develop new PhD programs to meet the growing need for mathematics education specialists. Ties with community college mathematics faculty need strengthening , since many teaching candidates complete their first two years of study at community colleges. Finally, teachers of teachers need to spend time with K-12 practitioners in order to "get helpful perspectives for their instruction of prospective teachers" and to connect college mathematics courses with K-12 practices. Recommendations 9-11 urge mathematicians to participate in the development of policy affecting K-12 mathematics education (e.g., K-12 curriculum standards and standards for the preparation, certification, and continuing education of teachers). Specifically, mathematicians are called upon to promote the policy that middle school students (grades 5-8) should be taught by mathematics specialists.
Chapter 3: Recommendations for Elementary Teacher Preparation. Although the report presents its teacher-preparation recommendations in three grade-level groupings, it does so with the understanding that the mathematical of a student is a seamless garment - albeit a garment that acquires holes that require repair. Moreover, a student's mathematical education begins before entering school. Hence, teachers at any level require in-depth content and pedagogical knowledge that allow them to detect and correct students' mathematical misconceptions and to teach new mathematics in a way that anticipates future learnings. To prepare teachers of grade K-4 for their role in students' mathematical development, it is recommended that teacher-preparation programs focus on four broad areas of mathematics that elementary school teachers are responsible for: numbers and operations; algebra and functions; geometry and measurement; and data analysis, statistic, and probability. The 4-5 fundamental understandings needed in each area are further described in bulleted form and are illustrated in terms of elementary school curriculum.
Chapter 4: Recommendations for Middle Grades Teacher Preparation. Recommendations for the preparation of teachers of mathematics in grades 5-8 assume implementation of the earlier-mentioned policy that such teachers be mathematics specialists. Recognizing that few institutions currently offer programs that target middle school teachers of mathematics, the authors take the opportunity to suggest the uniqueness of such a program by asserting that "Teaching middle grades mathematics requires preparation different from, not simply less than [emphasis added], preparation for teaching high school mathematics, and certainly reflecting more depth than that needed by teachers of earlier grades." While the report notes that coursework for middle grade teachers could overlap that of K-4 teachers in order that middle school teachers might make connections to what has come before, it also notes that middle school teachers need to be prepared to teach full-year courses in algebra and geometry. The recommended coursework for teachers of middle school mathematics addresses the same four broad areas recommended for K-4 teachers but extends content to the middle school curriculum (e.g., number and operations moves from a focus on whole numbers to a focus on integers and rationals) with an emphasis on "reasoning, explaining, and sense-making." The content of each area is refined in terms of 6-8 focal understandings that are connected by examples to the mathematics of grades 5-8.
Chapter 5: Recommendations for High School Teacher Preparation. One general recommendation of Chapter 2 was that teachers of grades 9-12 have the "equivalent of undergraduate major in mathematics." Chapter 5 notes that current college and university programs that simply merge courses of a liberal arts mathematics major with courses that emphasize teaching and learning of mathematics are not attracting sufficient candidates to meet the demand for new high school teachers of mathematics. Moreover, the authors assert their concern that the mathematics coursework of existing programs fails to "provide prospective teachers with the depth and breadth of knowledge need to teach high school mathematics well." The report proposes that the high school teacher-preparation be modified in two main ways: (1) core mathematics courses offered to all students should be redesigned "to help future teachers make insightful connections" between the mathematics they are learning and the mathematics they will teach, and (2) mathematics departments should offer a capstone course sequence for high school teachers "in which conceptual difficulties, fundamental ideas and techniques of high school mathematics are examined from an advanced standpoint."
About the Publisher
The Mathematical Association of America (MAA) is the largest professional society of college and university mathematics teachers in the world. It's mission is to advance the mathematical sciences, especially at the collegiate level. MAA's 30,000 members include college and university faculty, two-year college faculty, high school teachers, government and corporate workers, graduate school faculty, research mathematicians, and graduate and undergraduate students. The MAA office is located at 1529 18th Street NW, Washington, DC 20036-1385. TEL: 1-800-741-9415 or 202-387-5200. FAX: 202-265-2384. WEBSITE: http://www.maa.org.
Board of the Mathematical Sciences. (2001). The Mathematical Education of
Teachers: Part 1. Washington, DC: Mathematical Association of America. 51
to The Mathematical Education of Teachers