Revised math standards released last week by the National Council of Teachers of Mathematics show a greater emphasis on basic skills and content knowledge.
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Called “Principles and Standards for School Mathematics,” the standards were unveiled in Chicago at the organization’s annual meeting. They reflect the latest research on the teaching of the subject, according to the NCTM, and provide voluntary new national benchmarks for instruction in grades K-12.
The modifications, which list specific tasks that students should accomplish at key grade levels, respond to criticisms that the original standards, released in 1989, put too much emphasis on new ideas over such fundamental skills as arithmetic. (“Math Revisions Add Emphasis on Basic Skills,” April 12, 2000.)
For example, the updated standards specify that students in grades 3-5 “should develop fluency with basic number combinations for multiplication and division and use these combinations to mentally compute related problems.”
Memorization and rote computation were downplayed in the original standards and in the companion documents published in the 1990s.
The revised standards are also more detailed. The NCTM has separated the grade-level standards into four groupings, instead of three, in an attempt to imbue the standards with more content and specificity.
Only one middle school standard in the original document focused on linear equations, for example, while the revised standards discuss linear equations in four different student expectations for grades 3-5.
The updated document also combines the standards for students, teachers, and assessments into a single publication.
The new publication includes:
- Six principles that define the basic characteristics of a high-quality mathematics program;
- A table that explains how the 10 math standards relate to each of the four grade bands; and
- A CD-ROM version of the standards, “E-Standards,” that has interactive features.
‘Not Far Enough’?
The math teachers’ council contends that, despite the revisions, the philosophy behind the standards remains largely unchanged.
The council argues that teachers should use a variety of instructional techniques to ensure that all students learn and enjoy mathematics and mathematical ideas.
“They did listen to their critics and made some incremental changes,” said Tom Loveless, the director of the Brown Center on Education Policy at the Brookings Institution, a Washington-based research organization. But he added: “I don’t think they went far enough. There is still a pretty strong message that basic skills should be de-emphasized.”
As an example, Mr. Loveless noted that the revised standards still advocate the use of electronic calculators for kindergartners.
He and other critics have argued that students should learn basic arithmetic before being exposed to calculators. Such technological aids, they say, should not be used until students are in grades 7 or 8.
Glenda T. Lappan, the president of the NCTM and a mathematics professor at Michigan State University in East Lansing, agreed that some changes to the original standards were needed. “This is an evolutionary process,” she said.
“NCTM believes that children should know arithmetic cold,” she added. “We also believe that crunching numbers isn’t enough, but kids have to understand the underlying concepts in math.”
In an effort to add more content to the standards and mollify some of the professional mathematicians who critiqued the original document, the NCTM elicited comments from a large number of professional groups, including the American Mathematical Society.
How the new standards will affect schools and teachers remains to be seen.
Jerry P. Becker, a professor of math education at Southern Illinois University and a supporter of the standards, said: “It remains problematical, in my opinion, how widely the average classroom teacher will be reached. This is true not only for [the revised standards] but for the earlier standards as well.”
Mr. Loveless agreed. “The standards, the tests, and the stakes that states and localities adopt and attach are far more important than national standards,” he said. “If national standards affect those three things, then [teaching] will change, but time will tell.”
A number of states and districts have based their math standards on the original NCTM documents and now must decide whether to incorporate the recent changes.
Last year, David P. Driscoll, the commissioner of education in Massachusetts, asked a group of experts to revisit his state’s math standards, which were based on the first NCTM documents. He praised the NCTM revisions and said the state would try to “incorporate as much as works for us.”
The state board of education is scheduled to approve revised math standards for Massachusetts next month.
A version of this article appeared in the April 19, 2000 edition of Education Week as Revised Mathematics Standards Provide More Guidance