by Lee V. Stiff, NCTM President 2000-2002
NCTM News Bulletin, March 2001
Have you ever stepped on the scale and not liked what you saw? Stepped off, and stepped back on again, just to make sure it was right? And maybe stepped back on a few days later, hoping to see the results you wanted? Then embarked on a crash diet--that grueling low-calorie, unsatisfying, and often unhealthy eating regimen that gets relatively fast results ... that don't last? The weight returns because the necessary and difficult but more healthful lifestyle changes needed to get good results weren't made.
Weighing ourselves repeatedly and crash dieting don't really achieve the long-term results we want, as many of us have learned the hard way. Or have we? In a troubling trend, we're applying the same approach to improving mathematics learning in the United States and Canada. We're implementing a series of tests, many of them high-stakes assessments not aligned with curricula and sometimes with goals not clearly conveyed to teachers. And all too often with many types of tests--and especially high-stakes tests that are used to pass, promote, or group students--teachers frequently feel the need to teach to the test to ensure students will pass. This is the educational equivalent of a crash diet and does a cruel disservice to students relative to their long-term mathematical and academic success.
Testing ourselves repeatedly and teaching to the tests won't help us improve mathematics teaching and learning; changing how elementary and middle school teachers are certified in mathematics teaching will. Providing teachers more time to develop better lessons with colleagues and to increase their understanding of mathematics will. Creating working environments in which teachers can study and implement the best teaching practices of master teachers will. And so too will making sure teachers and students have high-quality materials, making sure schools provide disciplined and safe environments, and holding students accountable for trying to learn and reach high standards.
Unfortunately, the use of high-stakes tests has received more support recently than the effort to analyze and remove impediments to improved performance by students in school mathematics. We're placing too much emphasis on developing the ability to determine if students are failing at the expense of refining our ability to determine why students are failing and what we should do to help them become more successful in school mathematics.
We've invested much already to determine the "why" and the "what" in helping all students be more successful in school mathematics. The First International Mathematics Study in 1964 revealed that the performance of students in the United States and Canada did not compare favorably to that of students in other parts of the world. Soon after, renewed attention was given to what a quality mathematics education would look like. Over many years, the mathematics education community has identified teaching and learning standards for the United States and Canada--and those ideas are reflected in NCTM's Principles and Standards for School Mathematics, a guide to establishing curricula, instruction, and assessment that engenders a high-quality mathematics education for every child. Furthermore, one of NCTM's original Standards documents, the Assessment Standards for School Mathematics, carefully describes how multiple assessments should be used to promote students' learning and monitor program improvements.
Tests are an important component in promoting students' success in mathematics, but they must be used carefully. Test results may reveal very little about students' understanding of mathematics if the test's objectives are narrowly focused. Scores can rise without improvements in the broader, usually more important, set of academic knowledge, skills, and understanding essential to being successful in the real world. Scores can fall in spite of true academic progress. And when such tests are used to make major decisions about a child's future, they undermine the quality of education and the equality of opportunity.
A top ranking in mathematics performance among the countries of the world must be seen as the by-product of establishing a sound educational approach to the concerns we all have about our students' performance in school mathematics. Assessment should foster growth toward high expectations; support and resources should help students and teachers meet these expectations. Our nations' students, teachers, and schools deserve substantive teaching and learning. Let's build on the vision of Principles and Standards for School Mathematics to improve, for the long haul, the way we teach and the way students learn mathematics in the United States and Canada. We know what we need to do. Now we must do it.
Note: NCTM and other organizations have taken public positions on high-stakes testing. See NCTM's statement here or the American Education Research Association's position at www.aera.net/about/policy/stakes.htm. The National Research Council's report on high-stakes testing is available online at www.nap.edu/catalog/6336.html.