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Multiple Paths to Success

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by Lee V. Stiff, NCTM President 2000-2002
NCTM News Bulletin, January 2001 


Principles and Standards for School Mathematics is a vision, a guide, a tool, and focal point of discussion. It is not a state, national, or international curriculum.


Nevertheless, Principles and Standards is a powerful resource for improving school mathematics programs in Canada and the United States. Principles and Standards provides a focused and coherent vision of what every student should be able to accomplish. Its strength is in helping us make changes in school mathematics that benefit every child.

The document also recognizes that transforming a school mathematics instructional program is a journey whose destination lies at different distances for different school systems--because each school system begins at its own unique point. Principles and Standards is a flexible and adaptable vision that works with and within local and state or provincial frameworks.

This vision enables us to make wise choices--and one of the most important of them is the choice of curriculum materials. Large numbers of mathematics curricula, special projects, and innovative programs claim to reflect the vision of Principles and Standards, and indeed, textbook publishers, curriculum developers, and test writers do look to Principles and Standards for guidance in developing their products.

Although the components of many instructional programs may reflect the goals of Principles and Standards, for an instructional program to be successful, competent and knowledgeable teachers must carefully evaluate the program to determine whether the needs of the students and teachers who will use it will be met. As schools implement new curricula, special projects, or innovative programs based on Principles and Standards, educators must still take into consideration the strengths of teachers, previous instructional programs, and the complete set of students' levels of understanding to avoid creating an improper fit at the outset. Finally, since NCTM purposely does not endorse any mathematics curriculum, textbook, or instructional program, educators must consider the degree to which the vision of NCTM has been met by the programs under consideration.

To help, Principles and Standards includes a detailed Table of Standards and Expectations, which gives some specificity to what the NCTM Content Standards look like at the four grade bands. For instance, the table allows you to follow the expectations for the Algebra Standard all the way from pre-K–2 students being able to describe qualitative change, such as a student growing taller, to grade 12 students approximating and interpreting rates of change from graphical and numerical data.

Yet, in spite of everything that has been accomplished, I still have questions. Should we provide even greater specificity by describing our expectations at each grade rather than just by grade band? Would such details be useful or harmful to the lively, and often fruitful, dialogues that currently take place in the United States and Canada about the quality of mathematics and mathematics instruction at the different grade bands? If, indeed, the many school systems in the United States and Canada are at different places and have different needs, what role would providing greater specificity of our expectations play in serving the needs of teachers and students in these school systems?

Interestingly, our lack of national consensus on curriculum-related questions sets both Canada and the United States apart from the countries that perform highest on international comparisons. In the recent findings of the Third International Mathematics and Science Study–Repeat, 35 out of the 38 participating countries had a national curriculum in mathematics. The expectations of their students, teachers, and society are well defined. In these countries, instructional programs seek to match the goals of their curriculum--not high-stakes tests.

For NCTM, a danger in being too specific is limiting programs in ways we would not intend. However, the danger in not explicitly stating what we expect is not having a way to identify what is inappropriate in programs professing to implement Principles and Standards and having no clear way to describe how different programs may reach the same instructional destination.

In Canada, and especially in the United States, we are comfortable with multiple paths to success. Principles and Standards can help all of us reach our desired mathematics education destination no matter which route we decide to follow. Principles and Standards will continue to promote ongoing conversations at the national, provincial or state, and local levels about school mathematics. For the vision of a high-quality mathematics education for every child to be realized, school systems must work to incorporate change that does not outpace those who must implement it, while guaranteeing that change toward the goals of Principles and Standards steadily takes place. If school systems accept this challenge, they can make the recommendations and guidelines work for their teachers, and most important, for all of the students we serve.

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