Toward Excellence in K-8 Mathematics (1997)

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

eighth grade sequence emphasizing general topics and culminating in pre-algebra ideas. This array of choices and competing directions places teachers in the difficult position of making judgments and decisions without adequate data or information about the effects of such choices, or the long term impact on student learning and mathematical progress.

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

• Provide guidance to those who make curriculum selections—guidance in judging the quality of materials, and guidance which includes information about the conditions and context under which the materials have been used by others, and the resulting student achievement.

In the long term, there is a need to support ongoing implementation research and revision of curriculum based on teachers’ and students’ experiences. Such research and revision should be coordinated and linked to shifts in the national test and its emphases. The “National Professional Development Forum” mentioned earlier could provide in-depth looks at curriculum, to help people in all schools understand how these materials work and their relationship to the national test. Heightened efforts to disseminate curricular materials and evaluation information should begin immediately. Discussion of the ways in which the classroom assessment tools within these materials will complement the national test, as teachers judge student performance, needs to be introduced.

• Help administrators, school board members, teachers, and the public understand the relationship of curriculum materials to the emphases on better student preparation in mathematics.

The kinds of learning this test will measure will be unevenly available to children in the United States. Mathematics teaching and learning should be structured so that all students are given the opportunity to achieve at their maximum potential. School leaders must recognize what is at stake in their decisions about adoption of instructional materials, professional development, and resources for school mathematics. Districts will need to consider how their resources can ensure that all students have the educational opportunities that will enable them to increase their capabilities in mathematics. Most immediately, there is a need to examine the potential relationship between the national test and the emphases in various curriculum materials. It will be important to have an organized program to reach administrators, especially principals and superintendents, to guarantee that they understand the high standards for students in grades K-8 set forth by the national test, and the implications for their students of various curricular choices.

• Provide curriculum materials for use in teacher preparation and development and for use by higher education faculty and staff development professionals.

There is no coherent or nationally recognized system for reviewing, publishing, sharing, and critiquing the curriculum materials that are used to help teachers learn. Higher education faculty and professional developers frequently create their own materials. Higher education

mathematics faculty responsible for teaching mathematics content to prospective elementary and middle grades teachers need access to appropriate high-quality materials. Staff developers who offer long-term workshops in schools need new materials that focus on the important mathematics of the K-8 grades. In the short term, prototype course modules in mathematics content for use with prospective teachers at undergraduate institutions should be developed and disseminated to faculty in mathematics departments via the Internet and a national colloquium. Similarly, appropriate materials for inservice teacher development should be selected or developed and disseminated for school-based leaders in mathematics education, with involvement by the mathematics teacher professional organizations.

We recommend that technology be made available on an equitable basis for use in improving student learning and enhancing teacher professional development.

Technology includes computers, calculators, and other learning tools that can help students with a diversity of learning needs and preferences. In addition, technological tools provide teachers with an enhanced array of strategies for instruction. Research indicates some promising uses of technology as a means of helping learners understand mathematics concepts more deeply and effectively (Heid, 1988; Hembree & Dessart, 1986), and continued research into the pedagogical implications of various uses of new technology is needed. Such instructional use of technology, to be effective, requires appropriate subject matter understanding on the part of teachers.

A key step here will be for the Federal government to follow through as soon as possible with its commitment to make the Internet available to all schools. The Internet has potential value for networking students and teachers, and for dissemination of educationally valuable materials. At a different level, the technological opportunities for teacher learning, for professional collaboration, and for building of networks around professional interests are burgeoning and promise an end to the traditional isolation of teachers. Literature in professional development is quite clear on the benefits of providing professional development opportunities within a support community (Lord, 1994).

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

• Enable teachers to establish contacts for mentoring, participate in networks, and access a variety of curricular and pedagogical models, via technology.

Over the long term, increased research about how teacher learning and development occurs through innovative technologies will be critical to using these resources most effectively. In the short term, expecting all federally-funded teacher enhancement and professional development programs to have an Internet component would be useful.

• Provide all students with access to appropriate technologies for learning mathematics.