Two mathematicians' perspectives on standards: Interviews with Judith Roitman and Alfred Manaster

School Science and Mathematics, Oct 2001 by Olson, Mark, Berk, Dawn

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.

In 1989, the National Council of Teachers of Mathematics [NCTM] released the Curriculum and Evaluation Standards for School Mathematics (Standards), which represented the first effort by a mathematics education professional organization to develop and disseminate standards. As a first such effort, the 1989 document reflected primarily the views and perspectives of professional mathematics educators -teachers, teacher educators, supervisors, and mathematics education researchers. Indeed, although many of its writers had extensive backgrounds in mathematics and were faculty members in mathematics departments in major universities, the 1989 Writing Group did not include members whose primary professional activity was the production of new research in mathematics.

In the years following the release of the 1989 Standards, members of the professional mathematics community demonstrated increased interest in the goals and state of school mathematics, and indicated willingness to participate more actively in efforts to improve mathematics education. NCTM leaders, in planning for the process of updating the 1989 document, recognized the importance of tapping into this piqued interest and involving all who have a stake in the improvement of school mathematics. Consequently, several efforts were made to ensure that a wider sampling of the various constituencies in the mathematical sciences community had a voice in the development of Principles and Standards for School Mathematics. For example, Association Review Groups (ARGs) were formed by 14 of the member organizations of the Conference Board of the Mathematical Sciences to serve as advisory groups through the standards development process. The American Mathematical Society, the Mathematical Association of America, the Society for Industrial and Applied Mathematics, and the American Statistical Association, each formed an ARG and, thereby, were positioned to channel feedback and advice directly to the Writing Group throughout its process. (For an account of the ways in which mathematicians' views influenced Principles and Standards, see the introduction by Ferrini-Mundy in this issue of School Science and Mathematics.)

One of the most significant ways in which the views and expertise of mathematicians were incorporated into the development of the Principles and Standards was through the inclusion of four mathematicians as members ofthe Writing Group: Judy Roitman, Grades preK2 team; Phil Wagreich, Grades 3-5 team; Jim Sandefur, Grades 6-8 team; and Alfred Manaster, Grades 9-12 team. These mathematicians, through their participation in the development of the Principles and Standards and other mathematics education activity have gained a unique perspective on both the stances taken in the document and on many of the most intensely debated issues in mathematics education today.

In spring 2001 Dawn Berk and Joan Ferrini-Mundy interviewed Roitman, University of Kansas, and Manaster, University of California, San Diego. Here we explore some of the questions that proved to be most challenging for mathematicians and mathematics educators to wrestle with, from the perspectives of Roitman and Manaster. In doing so, it can be seen again that issues in mathematics education are complex and nuanced and that a thoughtful engagement in them requires open and informed discussions. We look in particular at how Manaster and Roitman addressed issues about what should be "core" expectations for all students in high school and about the role oftechnology in mathematics learning.

What Mathematics Is "Core" for High School Students?

Chapter 7 ofthe Principles and Standards presents the standards and expectations for Grades 9-12. In writing this chapter, the Writing Group struggled with enormous challenges. One particularly challenging issue was whether or not to follow the form of the 1989 Standards, which provided, for each standard, a set of expectations for all high school students and then additional expectations for college-intending students. After extended and heated discussions, the group settled on a set of recommendations that comprise a core foundation of mathematical ideas intended for all students - and they make the case that this foundation for all is "no more than is necessary for full quantitative literacy" (p. 288) and "a foundation for the study of more-advanced mathematics" (p. 289).

To better understand the group's decision to focus on a core set of mathematical ideas, one must understand what is meant by "core." Manaster explained,

The core, in our view, was not a collection of basic or rudimentary skills. Rather, "core" refers to a relatively deep understanding of some important mathematical notions. A close reading of Chapter 7 will reveal that the core is quite ambitious, not only because it applies to all students but also because it calls for serious study by each student.