by Lee V. Stiff, NCTM President 2000-2002
NCTM News Bulletin, March 2002
In NCTM's Curriculum and Evaluation Standards for School Mathematics(1989), "standards" described the teaching and learning outcomes that were valued. In the updated version of this document, Principles and Standards for School Mathematics (2000), the teaching and learning outcomes that we continue to value are revisited. What we expect students to be able to do and understand is carefully described with rationales and examples. Performance expectations are presented for each of the four grade bands. Overall, the Standards documents serve as a guide to improving the teaching and learning of mathematics. However, with the increased attention being given to assessments and testing, it may be time for NCTM to take another step forward, developing a tool that will provide clearer support to those who construct assessments.
Since 1989, "standards" have been reinterpreted by various audiences and have taken on a meaning often associated with the assessment of students and teachers. They have become a bar that school districts, states, and provinces set in order to gauge the performance levels of students. The need to set the bar for students at higher levels is often discussed in terms of "who" and "how many" will eventually graduate from high school. Although assessments emphasize gauging success, they are less frequently used as tools to collect information about what students have been taught and have understood, or as a source of information that can be used to improve the ongoing teaching and learning of mathematics.
Benchmarking mathematics teaching and learning standards to tests is becoming more common. That is, tests are defining the curriculum without necessarily reflecting the mathematics teaching and learning that is valued. Most agree that analyzing the quality and alignment of mathematics standards and tests is essential to the proper implementation of high-quality mathematics instruction--that standards and assessments must be complementary. But obtaining consensus on the appropriate levels of quality and alignment has proved challenging. The disagreements related to traditional mathematics instruction versus NCTM Standards-based instruction find fertile soil in the fields of assessment.
High-stakes testing has evolved as one approach for making decisions about the quality of the teaching and learning of mathematics in general and about students' future in particular. Of course, the Council opposes the use of such tests to make significant educational decisions about children, teachers, schools, and school districts. It considers the use of a single objective test to make decisions about grade placement, promotion, graduation, and tracking to be an abuse of such assessments.
Of equal concern is the way in which the content and format of high-stakes tests promote the narrowing of curricula and instructional approaches. A danger exists that the objectives of certain tests may not truly reflect the "standards" that we value. Thus, high scores on such assessments may be misleading and not represent high-quality mathematics. In fact, there is a danger that important standards discussed in NCTM's Standards documents--such as developing problem-solving and reasoning skills and connecting mathematics to real-life situations--will largely be ignored in favor of more easily constructed computation-based tests.
NCTM's Position Statement on High-Stakes Testing states clearly that assessment should advance students' learning and help teachers improve their instruction. However, this recommendation has not prevented the creation of tests by those who hope to affect the content of school mathematics. As a result, we must be concerned about a likely mismatch between the NCTM Standards and high-stakes assessments used by states and provinces.
The Standards are the teaching and learning outcomes that we value. We have described them clearly in Principles and Standards for School Mathematics, but we must take them one step farther. Beyond the mathematics learning expectations we have for each grade band, it is now time to demonstrate what such outcomes look like in assessment form.
There are examples of Standards-based assessments. NCTM must now pull together such examples and draw on the experiences of its members to produce a rich collection of Standards-based assessments that can assist test-developers in creating appropriate measures of what students should be able to do and understand. Once more, NCTM must lead the way by demonstrating that we can faithfully measure the Standards we believe students should master.
The challenge is great. Traditional tests emphasize computation because the traditional view of mathematics instruction holds that computational skills must be mastered before application and thinking skills can be engaged. Standards-based instruction recognizes that students can learn basic facts and skills in a context in which the mathematics content is analyzed and applied.
We have to convince parents, community leaders, heads of business and industry, and politicians that traditional computation-based tests are inadequate in assessing standards. The importance of problem solving, communication, and representation, for example, in the understanding of algebra and geometry is rarely addressed in traditional assessments.Standards-based assessments would effectively evaluate process standards.
NCTM must begin the development of assessment tools that are aligned with Principles and Standards--tools that can help our members construct their own assessments. The development of an NCTM assessment tool would help the Council provide clearer support to other organizations and agencies that want to create assessments that meet the demands of parents and schools and society more broadly. NCTM can no longer ignore the need for clear delineation of Standards-based assessments. Nor can NCTM ignore that the meaning of the NCTM Standards has been compromised in the forum of public discussion. It is time to reclaim NCTM Standards and say how we can know that students have mastered them.