When It Comes To MATH, Does LESS Equal MORE?
In and around the Nation's Capital, they're debating whether or not the kids are studying too many math topics:
Advocates of new math and old math, back-to-basics math and "fuzzy" math might be shelving their differences to collectively focus on what many consider a more pressing problem: too much math.It seems to me that the old over-worked (and clichéd) EduPendulum may be about to swing yet again.
Maryland math leaders meet today -- and D.C. math educators gather tomorrow -- to discuss Curriculum Focal Points, a new document from the influential National Council of Teachers of Mathematics that could profoundly influence math instruction in the region and nationwide.
It says the typical state math curriculum runs a mile wide and an inch deep, resulting in students being introduced to too many concepts but mastering too few, and urges educators to slim down those lessons.
Some scholars say the American approach to math instruction has allowed students to fall behind those in Singapore, Japan and a dozen other nations. In most states, they say, the math curriculum has swelled into a thick catalogue of skills that students are supposed to master to attain "proficiency" under the federal No Child Left Behind mandate.
The report urges teachers to focus on three broad concepts in each grade and on a few key subjects -- including the base-10 number system, fractions, decimals, geometry and algebra -- that form the core of math education in higher-achieving nations. Some are calling Focal Points the most significant publication in the field since the 1980s.
R. James Milgram, a Stanford University math professor who is among the harshest critics of U.S. math instruction, said the 41-page report aligns teaching "with what is being done with unbelievable success" in other countries. The curriculum would teach a few topics intensely and have students master them and move on rather than teach many topics briefly and repeatedly over several years.
In the fourth grade, for example, Focal Points trims the list to three essential skills: multiplication and division; decimals; and two-dimensional shapes.
Virginia lists 41 "learning expectations" for fourth-grade math students in its statewide Standards of Learning. Maryland lists 67 in its Voluntary State Curriculum. The District has 45 standards.
To meet states' goals, some teachers feel compelled to teach a different topic nearly every day. "And math wasn't meant to be taught that way," said Jonathan Wray, a Howard County math leader who is president-elect of the Maryland Council of Teachers of Mathematics.
Textbooks have ballooned as publishers have tried to include hundreds of overlapping standards from every state.
"I don't see any reason for my grandson, who's soon to be in third grade, to be carting home a 738-page book," said Francis "Skip" Fennell, president of the national math teachers association and an education professor at McDaniel College in Westminster, Md.
Maryland is one of at least 10 states mobilizing to discuss, and possibly adopt, the guidelines, Fennell said. The state math curriculum is up for revision in 2009. To meet that deadline, educators will have to start work now, said Donna Watts, Maryland math coordinator.
Virginia's math standards will be reviewed in the 2008-09 academic year. "Whether we will significantly revise how the standards look, I don't know," said Deborah K. Bliss, state math coordinator.
Sue P. White, director of mathematics in D.C. schools, will meet tomorrow with school-level math specialists for the first District-wide discussion of Focal Points. She doesn't know how the school system will respond to the document, but she agrees with its message.
"You've got to provide clarity to teachers," she said, "so that they can go deep."
Teachers in the region say that although math instruction seems strong overall, they would welcome the chance to study fewer topics in greater depth.
So, it appears, would their students.
Brittney Pinkney, 13, of Silver Spring considers herself good at math, and so does her mother. Yet Brittney is behind in her eighth-grade math class at White Oak Middle School.
"Every three days, it's a new lesson," she said. "You move on to the next lesson without really understanding what happened in the last lesson."
Refocusing the curriculum will help struggling students, mathematicians say, because they need more time to learn the basics. It will also aid math teachers across the elementary and middle grades, many of whom learn comparatively little math in getting their teaching credentials.
"Wouldn't it be nice," Fennell said, "if someone told [them] what's important here?"
He and other math scholars hope the new publication will, as a bonus, bring together the adversarial camps of math instruction.
One group, led by mathematicians, has argued that children must learn a sequence of basic skills, including times tables and some memorization, if they are to have a fighting chance at college-level math study.
The other camp, led by math educators, has urged children to understand the theory behind math problems and to find solutions in their own way.
W. Stephen Wilson, a math professor at Johns Hopkins University, deems Focal Points "probably the most important contribution to mathematics education in a good long time." As states begin to review and revise their math standards over the next few years, "this will be the document that states will look at, and it's a good one," he said.
Math educators in the region point to local and national tests as evidence that, international comparisons aside, math instruction in America is fundamentally sound. The National Assessment of Educational Progress shows no decline, and some improvement, in math ability nationwide during the past 30 years. The SAT math average in the same period has climbed 21 points, from 497 to 518, after adjusting for a recalibration of scores in the mid-1990s.
Math leaders in some Maryland and Virginia school systems say their math curricula accomplish the key goals of Focal Points: organizing and prioritizing what should be taught. In Montgomery County, for example, the expansive state curriculum is synthesized so that "it doesn't look like this long list of things that teachers need to do," said Leah Quinn, mathematics supervisor.
What lies ahead, all agree, is a comparison of Focal Points and state math curricula. Critics of math education hope that process will lead some states to delete entire sections of their lesson plans.
Most of the topics listed in Maryland's math curriculum and Virginia's math standards can be found in the Focal Points document. But Focal Points is far more selective in identifying the essential math topics for each grade.
Maryland's math curriculum recommends study of three-dimensional shapes across the elementary grades. The Focal Points document addresses them chiefly in kindergarten and grade 5. Probability is taught throughout the elementary grades in Virginia, but Focal Points doesn't introduce the subject until grade 7, when students are likely to understand it better.
"Focal Points is saying, 'Teach a few things, and teach them well,' " Bliss said.