Note: The National Council of Teachers of Mathematics has released a draft of it's updated standards, entitled "Principles and Standards for School Mathematics." The document is available for review at www.nctm.org/standards2000. The "Principles and Standards for School Mathematics: Discussion" is available for $7.50 (free to members) from the NCTM by calling (888) 220-7952. It can be downloaded from the web. *****************************************************
The National Council of Teachers of Mathematics is proposing changes to its groundbreaking 1989 academic standards that would place a greater emphasis on teaching basic skills while reaffirming the group's belief that students need hands-on experience to help them understand mathematical facts.
Draft revisions released last week will be the subject of extended debate over the next 18 months. The goal of the 110,000-member group is to adopt the revisions formally at its annual meeting in April 2000.
As laid out in the proposal, changes in format and content address some of the criticisms from mathematicians and parents that the NCTM has focused on teaching mathematical concepts at the expense of basic skills and content.
"Kids have to understand addition and subtraction. They have to have automatic recall," Glenda T. Lappan, the council's president and a professor of mathematics at Michigan State University in East Lansing, said last week, after the group started distributing its draft on the World Wide Web.
"While they are accumulating those facts, there have to be problems on the table that lead to deeper understanding," she added.
The new document, "Standards and Principles for School Mathematics: Discussion Draft," partially addresses criticisms leveled at the current standards, but it appears unlikely to appease the severest critics.
"It's not significantly different. It's still the same philosophy," asserted William G. Quirk computer-software developer in New Haven, Conn., and a former college math professor. "They emphasize process skills and continue to be vague about content. NCTM just doesn't want to get specific about content."
Leaders of the math teachers' council were hailed as innovators in 1989 when the NCTM became the first subject-area group to publish, at its own initiative and expense, national content standards. When other disciplines followed, with the federal government underwriting a good portion of the ventures, those later efforts were often found wanting. The math standards generally continued to steer clear of controversy.
Then, in just the past few years, the NCTM standards, too, became a target of criticism, particularly from those who favor a more traditional approach to teaching the core curricula.
"The math wars" is how some have dubbed the debate over how to teach what most people consider to be the second-most fundamental subject behind reading. In California, for example, NCTM backers are at odds with advocates of a traditional curriculum over standards that the state school board has adopted. ("Calif. Education Officials Approve Back-to-Basics Standards in Math," Jan. 14, 1998.)
The California standards differ greatly from the NCTM's existing standards and its strategy to modify them. The state standards mention specific skills students should master, such as memorizing multiplication tables, and they emphasize repetitive problem-solving.
The NCTM, by contrast, encourages teachers to help students understand the concepts behind mathematics tasks such as multiplication by using real-world experiences to illustrate them.
A Merger of Content
The math council's proposed new standards have been in development for almost two years. The draft was written by a committee of 32 professors, curriculum directors, and teachers. Panels from professional groups--including the Mathematical Association of America and the American Statistical Association--advised the writing committees by critiquing the 1989 standards and responding to questions posed by the standards writers.
The comment period moves to a new phase now that the NCTM has published a draft of the changes it proposes. Throughout the 342-page document, also released in printed form last week, the writing committee poses specific questions of readers to gauge reaction. The comments will be used to inform the final proposal.
Nine and a half years ago, the NCTM released its standards to explain what students should learn from kindergarten through the end of high school. Two years later, the group released recommendations on how to teach those standards. In 1995, it explained how to assess student progress toward the standards.
The discussion draft merges content from each of those documents. "What we're trying to do is give teachers one document that covers the whole act of [mathematics] teaching," Ms. Lappan said.
The draft introduces six new principles that should guide teachers and reorganizes the general standards into 10 topics.
The principles call for all students to have access to high-quality math instruction which should be given by "competent and caring teachers."
The standards address geometry, statistics, reasoning, communication, and problem-solving.
They also realign the benchmarks: The new grade breakdowns are preschool-2, 3-5, 6-9, and 9-12 instead of K-4, 5-8, and 9-12.
The proposed standards are consistent throughout the four new grade spans, with content increasing in difficulty as students move through school. In the 1989 version, the standards differed across the grade spans.
In another change, the discussion draft lists standards dealing with content--such as geometry and algebra--before those covering process, such as reasoning and communication.
'Correct Answers Matter'
Throughout the document, the standards writers add specific issues teachers need to address. For example, it suggests that by the end of 5th grade, students should be able to graph fractions such as one-fourth, one-half, and five-eighths on a number line. And the section on high school geometry includes an extended discussion of the Pythagorean theorem.
"A lot of our input suggested that our document needed to be a lot more specific," said Joan Ferrini-Mundy, the chairwoman of the group that wrote the draft and the associate executive director of the center for science, math, and engineering education at the National Research Council in Washington. "There were people who wanted to provide as much food for thought as possible."
At the same time, the draft maintains its focus on teaching children how to learn through solving real-life problems and to communicate their reasoning through pictures, graphs, and prose.
"There can be no doubt that both conceptual understanding and procedural proficiency are important," the draft says. "It is not the primacy of either that we should be considering. Instead, it is the connections between them that are important."
Such statements try to clarify an earlier emphasis on conceptual understanding that many teachers misinterpreted, Ms. Lappan and Ms. Ferrini-Mundy said.
Some went overboard in interpreting the 1989 standards to mean that the communication of problem-solving took precedence over finding the correct answer.
"Teachers shouldn't say the correct answer doesn't matter," Ms. Lappan said. "In our zeal to make sure we're focusing on understanding, we cannot forget correct answers matter."
While few had read the weighty document that became available just last week, some mathematicians suggested that the changes were necessary and welcome.
"They shouldn't go too far afield from what they started in '89," said Thomas L. Moore, an associate professor of mathematics at Grinnell College in Iowa and the chairman of the group from the American Statistical Association that advised the NCTM committee. "The message people got out of the '89 standards means there's some rewriting that needs to be done."
Mr. Quirk and some other mathematicians, however, say that the council is still placing too much weight on process and not enough on basic skills. Children need to learn how to perform basic functions before they can apply them to real-world problems, these critics say.
"Doing precedes understanding," said Frank Y. Wang, the president of Saxon Publishers, a Norman, Okla., company that has bucked the trend of revising textbooks to match the NCTM standards. "You have to do, do, do before you understand."
The proposed standards also don't go far enough to appease those who object to letting young children use electronic calculators. "Students at all levels should have access to calculators and other technology to use as they solve problems," the draft says.
"There's a place for calculators," said David Klein, a professor of mathematics at California State University-Northridge. "They're very good in science labs, but to put them in an arithmetic class is obscene."
************************************************************** Jerry P. Becker Dept. of Curriculum & Instruction Southern Illinois University Carbondale, IL 62901-4610 USA Fax: (618)453-4244 Phone: (618)453-4241 (office) E-mail: JBECKER@SIU.EDU