After setting off dramatic changes in math instruction 11 years ago, the National Council of Teachers of Mathematics this week is planning to unveil its latest version of standards for learning, teaching, and testing the subject.
The standards the group was to release April 12 at its convention in Chicago will place an expanded emphasis on basic skills and list specific tasks that students should accomplish at designated points in their K-12 educations, according to the president of the 100,000-member organization.
Such changes are intended to assuage critics of the 1989 document and its companions published in the 1990s, as well as to refocus teachers on the essence of what teaching mathematics entails, said Glenda T. Lappan, the NCTM president and a professor of mathematics at Michigan State University in East Lansing.
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The original standards, Ms. Lappan said recently, put too much emphasis on new ideas, such as teaching conceptual understanding over basic skills and integrating electronic calculators into instruction.
“That became, in some places and for some teachers, the goal. They missed the main goal: that children become highly skilled in using mathematics,” Ms. Lappan said. “We’ve tried to be very clear [in the revised standards] that mathematics is the goal.”
The final document is significantly different from the proposed revisions that the NCTM circulated for discussion in October 1998, Ms. Lappan said. It includes, for example, a detailed chart explaining what skills students should acquire in each of four grade-level bands and in each discipline of mathematics.
But the messages of the 1989 standards and the 1998 proposed revisions remain the same: Mathematics teachers need to reach all children by offering a variety of instructional strategies that encourage students to learn the concepts that lie under the algorithms they are learning.
“There are no 180-degree changes,” Ms. Lappan said.
The changes, however, are unlikely to satisfy critics who find fault with the 1989 standards themselves, not just the way teachers and policymakers have implemented them. And they may also confuse and frustrate educators who have radically changed the way they teach based on the 1989 standards.
“It’s going to be difficult for the two sides to come together,” said Michael McKeown, a founder of Mathematically Correct, a parent-based group that led the charge for drastic changes in the California standards that once reflected the NCTM’s work.
The NCTM and its critics agree on “platitudes,” said Mr. McKeown, a molecular biologist for the Salk Institute for Biological Studies in San Diego, but they disagree about how much emphasis to put on them.
Mathematically Correct started as a group of critics of the San Diego math curriculum, and its leaders were part of the state panel that rewrote the state’s standards to reflect more traditional teaching methods and content. A similar backlash against the NCTM standards, and curricula based on it, has occurred in Los Angeles, suburban Detroit, and Plano, Texas, as well as in Massachusetts, in recent years.
“If you look at the history of the past 40 or 50 years, whenever a group of educators say they are going to de-emphasize basic skills, you can look at that as a storm warning,” said the education historian Diane Ravitch, who as an assistant U.S. secretary of education in the Bush administration supported the creation of similar standards-setting efforts.
“The general public is perfectly willing to accept creative learning opportunities, but not at the expense of basic skills,” she said.
Renewed emphasis on the basics will reflect what the writers of the original standards actually wanted but failed to communicate as they tried to incorporate new ideas into math classrooms, NCTM supporters say.
“The conceivers had in mind all along that basic skills are very important,” said Jerry P. Becker, a professor of mathematics curriculum at Southern Illinois University Carbondale and a former NCTM board member. “If they pay some more attention to that, it would be very good.”
The Gold Standard
In 1989, the NCTM released its Curriculum and Evaluation Standards for School Mathematics, a unique document at the time that defined what students should know and be able to do in the subject throughout their precollegiate schooling. Two years later, the group unveiled its standards for teaching the subject. It completed a trilogy in 1995, with standards for assessing student progress toward meeting the standards.
The Reston, Va.-based group began the process of revising the standards in 1996, soliciting comments for two years before releasing a draft for comment. (“Math Council Again Mulling Its Standards,” Nov. 4, 1998.)
The math standards helped inspire a flurry of activity to write companion pieces for just about every subject taught in U.S. schools, from English and science to physical education and the arts. Standards for some other subjects were clouded in controversy from the start, especially in English and history, but the NCTM standards were widely accepted before some parents, educators, and policymakers started challenging them in the mid-1990s.
Dramatic changes in the content and methods of math instruction in the nation’s classrooms have resulted from the NCTM standards, according to Ms. Lappan and others.
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“They are not far from the fingertips of almost anybody we deal with in the math community,” said Christopher T. Cross, the president of the Council for Basic Education, a Washington-based organization active in the national-standards movement. “Despite the criticisms, they have established themselves as being very credible. Of all the standards [in various subjects], they by far are the most known, the most accepted, and the most influential.”
“The NCTM standards have certainly reshaped how people talk about mathematics,” said Larry Cuban, an education professor at Stanford University. “There has been tremendous action in terms of districts and states adopting them. When you talk about implementation, you get much more variation. That is not unlike what has happened with every single curriculum reform in the past century.”
Mr. Cuban agrees with Ms. Lappan and others that teachers have been “highly selective” in what portions of the standards they rely on. “A very tiny percentage have” adopted them as a whole, he said.
That has led to problems in several areas, Ms. Lappan acknowledged.
For example, while the 1989 standards say “calculators can be used as an effective instructional tool for teaching computational skills,” they don’t recommend that calculators replace memorizing the multiplication tables, as may have happened in some teachers’ classrooms.
Even some NCTM supporters say the organization has failed to communicate the messages underlying the standards. Many of the criticisms of the standards are “well-founded,” but exaggerated, said Guillermo Mendieta, the director of mathematics education initiatives for the Achievement Council, a Los Angeles nonprofit group trying to increase the number of minority students entering and succeeding in college.
Many of the problems are created because teachers don’t have the understanding of the subject, said Mr. Mendieta, who had threatened a hunger strike if the Los Angeles Unified School District eliminated a curriculum modeled after the standards. Late last month, the district decided to keep the curriculum for next year at least. “We’re fighting policy battles, when it’s implementation that counts,” Mr. Mendieta said.
Impact of State Tests
While the math teachers’ council is likely to find continued opposition from back-to-basics advocates, it also is facing threats from the increasing importance of statewide testing systems, Mr. Cuban said. The standards “are at odds with what the teachers and administrators perceive will be rewarded,” he said. “The NCTM standards are oriented to performance-based assessments and real-world problems.”
