Two Mathematiciansâ Perspectives on Standards:
Interviews With Judith Roitman and Alfred Manaster
Mark Olson and Dawn Berk
Michigan State University
This article summarizes an interview in the spring of 2001 with professional
mathematicians Judy Roitman, University of Kansas, and Alfred Manaster,
University of California, San Diego. Both mathematicians were members of
the Writing Group for the National Council of Teachers of Mathematics Principles
and Standards for School Mathematics.
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Curriculum Materials Supporting Problem-Based
Teaching
Kimberly Harris, Robin Marcus, Karen McLaren, and James Fey
University of Maryland
The vision for school mathematics described by the National Council
of Teachers of Mathematics (NCTM) suggests a need for new approaches to
the teaching and learning of mathematics, as well as new curriculum materials
to support such change. This article discusses implications of the
NCTM standards for mathematics curriculum and instruction and provides
three examples of lessons from problem-based curricula for various grade
levels. These examples illustrate how the teaching of important mathematics
through student exploration of interesting problems might unfold, and they
highlight the differences between a problem-based approach and more traditional
approaches. Considerations for teaching through a problem-based approach
are raised, as well as reflections on the potential impact on student learning.
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Principles and Standards for School Mathematics
and Teacher Education: Preparing and Empowering Teachers
Karen J. Graham Francis (Skip) Fennell
University of New Hampshire Western Maryland College
Teachers and teacher educators play a critical role in the improvement
of mathematics education. Recommendations for appropriate teacher
support can be gained from examining the Teaching Principle in the document,
Principles and Standards for School Mathematics (NCTM, 2000), as well as
earlier recommendations from the Professional Standards for Teaching Mathematics
(NCTM, 1991). This paper discusses implications of the recommendations
for preservice teacher preparation, the continuing professional development
of teachers, and mathematics teacher certification policy.
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The Cyclical Relationship Between Research
and Standards: The Case of Principles and Standards for School Mathematics
W. Gary Martin Dawn Berk
Auburn University Michigan State University and University of New Hampshire
The link between standards and research may not be clearcut.
However, in this article the authors argue that there is a notable
relationship between standards and research, one that is cyclical in nature.
Using the standards for school mathematics developed by the National Council
of Teachers of Mathematics (NCTM) as a case in point, the authors examine
how NCTM's standards have influenced the agenda for mathematics education
research and stimulated research on the impact of those standards. In turn,
this and other research played a significant role in the development of
NCTM's new Principles and Standards for School Mathematics. The authors
conclude with a discussion of ways in which the Principles and Standards
may continue this cyclical relationship in coming years, potentially promoting
investigation of new research areas and systematic research on the impact
of standards.
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