Toward Excellence in K-8 Mathematics (1997)

venture is to have a measurable impact. Particularly important is funding for basic research about instructional practice and teacher learning, and about the role of technology.

We recommend, for the next three years, a national focus on the professional development and preparation of grades 5-8 mathematics teachers to ensure that they are adequately prepared and supported to develop student learning at high levels.

Teachers of mathematics at the middle grades traditionally have borne the unique responsibility of helping their students in the transition from the arithmetic-dominated curriculum of the elementary years to readiness for the abstraction of algebra in the secondary school. With the advent of the NCTM Standards, new state frameworks, and new state-level eighth grade assessments, as well newly developed instructional materials, the mathematical responsibilities of these teachers have increased significantly. The recommended curricular topics for the middle grades now include a much greater emphasis on patterns and functions, algebra, and areas of statistics, probability, geometry, and measurement (NCTM, 1989). If the national test follows the NAEP framework, it is likely to also reflect these emphases.

At the same time that curricular demands are increasing, many states do not require certification or specialization at the middle grades ² . The result is often that school districts employ either elementary teachers prepared for the elementary grades (K-6 or K-8), or teachers prepared for the secondary grades ³ (7-12). Neither the elementary nor the secondary preparation has consciously taken into account either the mathematical emphases that are particular to the middle grades, with its cross-disciplinary features and applications orientation, nor the special needs of middle grades learners. Few institutions of higher education actually offer middle grades specializations in mathematics, although such programs have been developed through NSF funding (Stake et al., 1993).

Teachers’ professional development needs are substantial (Darling-Hammond & Cobb, 1995; National Center for Education Statistics [NCES], 1993). The introduction of the national test in mathematics will only heighten and intensify the need for immediate explicit focus at middle grades. A number of reports have emphasized the importance of strong and appropriate content preparation of teachers, such as the MSEB report, The Preparation of Teachers of Mathematics: Considerations and Challenges (NRC, 1996b). Introduction of the national test will make this recommendation even more critical.

To carry out this recommendation, it will be essential to:

• Build national, regional, and state accreditation and certification policies so teachers have the content knowledge and pedagogical expertise to support high standards in mathematics.

All states, over time, should strive to introduce middle school mathematics certification. Such certification should require knowledge and experience with mathematics and pedagogy appropriate to the middle school level. Such experiences would be consistent with the expectations of the National Board for Professional Teaching Standards and the Interstate New Teacher Assessment and Support Consortium. Within higher education, programs for preparing specialists in middle school mathematics teaching could become an integral part of all teacher education programs. In the short term, there should be a compilation of information on states with middle school mathematics certification programs. Such a compilation should include details about standards and relationship to school structure, as well as information about extant middle school mathematics teacher preparation programs in higher education.

• Use and extend the research that clarifies how teachers’ mathematics content knowledge relates to their classroom effectiveness, and how teachers can best learn about mathematics content.

In the long term, there is a need for increased funding for research about teachers’ mathematics learning. More immediately, the NSF and U.S. Department of Education could jointly commission papers about the role of content knowledge in teaching effectiveness and disseminate them widely to teacher preparation institutions.

• Enhance mathematics professional development experiences for preservice and inservice middle grades mathematics teachers.

In the long term, this goal can be accomplished by fostering partnerships among mathematicians, mathematics educators, and teachers that focus on the mathematical emphases and instructional issues of the middle grades curriculum. In the short term, the NSF and the U.S. Department of Education could sponsor a National Professional Development Forum centered on various middle school curriculum materials. There are several types of materials and curricula now available at the middle grades, and teachers need to become familiar with the options, learn from those who have used these materials about what is involved in their successful implementation, and examine the evaluation findings from these projects. It is also important to understand better the shortcomings of such materials. There is growing evidence that curriculum-based professional development—i.e., professional development situated concretely in the student curriculum—correlates significantly with teacher effectiveness (Cohen & Hill, 1997).

Teachers’ opportunity to learn needs to be grounded in practice (NRC, 1996b). By examining and analyzing student work, teachers come to develop shared expectations for student performance. Any national test should be accompanied by a guide for teachers that includes the content framework, sample items, student responses, sample rubrics, and

teaching strategies. Such a guide should be disseminated over the Internet, as a means of generating conversations and professional networking. Additional professional development could be centered around helping teachers understand the nature and scoring of extended response items.

For the proposed national test to be a useful tool, it must be set in a broader assessment context that includes classroom assessment consonant with it, and with the K-8 reforms. Considerable staff development efforts educating teachers about assessment will be necessary, and have been undertaken elsewhere (Stake & Raizen, 1997).

• Engage the mathematics higher education community more centrally in providing high quality preparation and professional development experiences for K-8 teachers of mathematics.

In the long term, this could involve linking all mathematics teacher development to appropriate content-based programs in colleges and universities. In the short term, postsecondary mathematics faculty need opportunities for professional development where they can learn about K-8 mathematics education and how the mathematical content areas recommended for grades K-8 are typically treated through curriculum and instruction. Higher education faculty also could benefit from a focus on the issues in teaching content effectively to prospective and inservice teachers. A first step would be to compile examples of programs and materials used for helping teachers learn mathematics and mathematics teaching. These could be disseminated and reviewed with postsecondary mathematics faculty as well as K-12 professional development practitioners, through conferences or other national networking activities.

We recommend that high-quality instructional materials and associated support mechanisms be available for all schools and for those who prepare and provide professional development for teachers.

Federal agencies should focus attention and resources on raising awareness and facilitating implementation of standards-based curricula in topic areas to be emphasized in the national mathematics test. Since the publication of the NCTM Curriculum and Evaluation Standards in 1989, commercial publishers as well as the Federal government have engaged in substantial instructional development activities, often designed to reflect the emphases of the Standards. Many of these materials are just now becoming widely available. Issues related to mathematics curriculum at the middle grades are complex, as reflected in the diversity of curriculum designs at this level. There are new, innovative materials that are module-based, where teachers and students work on large, cross-cutting themes over extended periods, often with a technology emphasis. There is also a strong movement toward preparing all students to take an algebra course in the eighth or ninth grade; and there is the more typical seventh and