More News

Long division separates math program’s backers, critics

Wednesday, Nov. 30, 2005

Click here to enlarge this photo Susan Whitney-Wilkerson⁄The Gazette Class participation helps fifth-graders Luis Paz (left) and Cherrah Barclay learn mathematical concepts by involving them in hands-on exercises. Cherrah displays her answer to a question posed by Denise Galbo. Click here to enlarge this photo Susan Whitney-Wilkerson⁄The Gazette Student teacher Denise Galbo demonstrates how to build a tool to help Piney Branch fifth-graders visualize decimals.

But the Silver Spring resident wants his 10-year-old son, Sam, to be challenged. He is glad that Sam, like more than one-third of all county fifth-graders, is taking sixth-grade math this year at Piney Branch Elementary School in Takoma Park.

‘‘I want my son in a level of math education that will keep him engaged and working hard,” Blattner said.

That’s what school administrators say they want for all students. The school system’s goal is to have 80 percent of all students complete algebra or higher before they enter high school.

Schools are working to increase those numbers by enrolling students not traditionally singled out for above-grade-level courses.

Of the more than 3,800 fifth-graders taking sixth-grade math this year, 42 percent are not labeled gifted and talented, which school officials say proves that challenging instruction is available to all students who want it.

The school system has been lambasted by parents groups critical of the lack of African Americans and Hispanics in gifted and talented and in magnet programs.

Part of the school system’s response to that criticism has been to give more students the grounding they need to tackle higher-level math courses.

Opportunity breeds higher achievement, said Jody Leleck, associate superintendent for curriculum and instructional programs.

‘‘If we give all children the opportunity to take above-grade-level [courses] ... we will get more children demonstrating they are ready for higher-level math,” she said.

The goal is to have more students taking Advanced Placement calculus by their senior year.

To learn more About the school system’s math curriculum, go to the school system's Web site.

So in addition to the school system’s early childhood reading programs, educators in 2001 began changing the math curriculum, with an eye to preparing more students earlier for more advanced courses.

The number of fifth-graders taking above-grade-level math has increased dramatically — from 196 in 2001, with just a few African-American and Hispanic students, to more than 3,800 students in advanced courses this year. Of those, about 500 are African-American and 380 are Hispanic.

‘‘I don’t think we had high enough expectations as a system, or as employees of the system, in regards to all these children,” Superintendent Jerry D. Weast said at a Nov. 8 school board meeting. ‘‘... Now we’re getting into ‘You can do it. We’re going to be with you to help you do it.’ ... I don’t want to point the fickle finger, but it was us.”

Hands-on math

The policy is showing results. Forty-eight percent of eighth-graders completed algebra or higher last school year, according to the school system.

The path begins at schools like Piney Branch, where an accelerated class taught by Lila Tolman is made up entirely of African-American and Hispanic students. The class is small, only 16 students, and instruction is tailored to the students’ pace of learning.

Parents have agreed that their children will forgo social science and science three times a week in order to attend a double period of math.

On a recent morning, Tolman worked with students on decimals. She stretched a clothesline, segmented by dangling strings, across the classroom.

Each segment represented a metric unit. In each unit were one index card with a zero and one labeled with the words milli, centi, deci, deka, hecto or kilo. Another card in the middle read ‘‘unit,” indicating a single measurement, in this case a gram. Ten-year-old Dwayne Baker stood under that card.

‘‘What do you want him to be?” Tolman asked the class.

‘‘A kilogram,” the students answered.

Tolman asked Baker to stand under the ‘‘deka” card.

‘‘When you moved, you became a ... ?” Tolman asked Dwayne.

‘‘10,” he answered.

Tolman then asked Dwayne to move under the ‘‘hecto” card and finally the ‘‘kilo” card.

As he moved down the line, Dwayne handed a zero card to Tolman, who posted it on a dry-erase board so that one gram grew to 10, then 100, then 1,000, or one kilogram.

The students in Tolman’s class are, like most students, concrete learners, meaning they need a more hands-on approach.

‘‘I always try to have an activity where they’re moving around,” Tolman said. ‘‘... Those lessons aren’t in the book.”

Pretend algebra

Not everyone is a fan of how the school system is preparing students for algebra.

The sixth- and seventh-grade math courses, known as Math A and Math B, even when taught in middle school, have been ‘‘dumbed down,” said John Hoven, of Silver Spring, a former president of the county’s Gifted and Talented Association.

It happened in 2001, he said, when the school system decided to align the county’s math curriculum with the state’s, which has lower standards.

Hoven calls the 10th-grade math test that this year’s ninth-graders will be required to pass in order to graduate from high school ‘‘pretend algebra.” It covers only fifth- and sixth-grade concepts, complained Hoven, a proponent of the math curriculum used in Singapore.

‘‘[Hoven] thinks if the Algebra 1 curriculum is aligned with the High School Assessment, we’ve dumbed it down,” said Theresa A. Cepaitis, the school system’s math curriculum supervisor. ‘‘It’s aligned with the HSA, but we’ve gone beyond it ... so students can reach the goal of calculus.”

Hoven said the curriculum adds ‘‘extra fluff” such as statistics instead of algebra.

‘‘They think that a more rigorous curriculum is one that piles on more and more and more,” he said. ‘‘And that’s exactly wrong.”

The state algebra exam limits what it tests to integers, or whole numbers, said Cepaitis, a former calculus teacher.

But the county curriculum covers integers, fractions, and decimals so that students can move beyond algebra, she said.

Critical learning

Teachers are the linchpin in the process, said Francis ‘‘Skip” Fennell, an education professor at McDaniel College in Westminster and president-elect of the National Council of Teachers of Mathematics.

‘‘All things considered, the teacher is the engineer, the pilot, the director, the captain,” he said in an e-mail to The Gazette. ‘‘This assumes deep understanding of important mathematics and the pedagogy associated with it. To me, it is less so about the book being used and more so about the teacher knowing the mathematics — in that book and elsewhere — and being able to frame lessons, every day, that appropriately meet the needs of his or her class.”

The school system trained its elementary school teachers in the sixth-grade math curriculum over the past two summers and provided voluntary training after school last year.

Mandatory training will be given over the next three months.

For Hoven, the training is beside the point.

‘‘If you dumb down all those courses so it’s elementary school math, you do well with elementary school teachers, which is what [the school system] is doing,” he said. ‘‘[It’s] pushing schools all across the county to push kids in to Math A and Math B, ready or not.”

Fennell cautions against pushing students too far too fast, stressing that a good foundation in algebra is most important.

‘‘Of course, algebra is a gatekeeper to higher levels of mathematics, and so we should encourage all students to learn algebra deeply and well,” he said. ‘‘However, rushing some [students] into algebra at an early age may be counterproductive.

‘‘I worry that some very good math students may be pushed into algebra at grade seven without the background or without being fully ready for such experience.”

A Nov. 10 editorial in Silver Chips, the student newspaper at Montgomery Blair High School in Silver Spring, said a premature push into higher-level math is occurring at some point on the way to high school.

‘‘Over a quarter of Blair’s 90 sophomore precalculus students who were accelerated by a year, have since dropped out of the honors program and now take regular precalculus,” the editorial said.

The editorial quoted math teacher Dona N. Dyas: ‘‘We find more and more kids who, when they get to the ninth grade, are not conceptually ready. It’s not that they are not smart; they’re just not ready yet.”

Some parents also wonder if there is much use of pushing children into an accelerated course of study.

‘‘I’m not 100 percent behind the county’s fanaticism about pushing advanced math,” said Blattner, a philosophy professor at Georgetown University. ‘‘At the university level, except for super-elite math students, students have to take calculus again in college anyway.”

But educators see benefits to the effort, especially among students who have not been challenged in the past.

‘‘I believe the teachers’ expectations and the kids’ expectations for themselves are carrying over to other subjects,” said Peggy Kennedy, a Piney Branch guidance counselor. ‘‘... They believe so much in themselves that it goes so far past math.”