State and county math standards hurt student performance

Changes in the Algebra I curriculum brought about by the new Maryland High School Assessment Tests (HSAs) and a push by MCPS to have more middle-school students take algebra have caused many students to be seriously unprepared for higher-level math, according to numerous Blair teachers and administrators.

The Algebra HSA was first instituted by the Maryland State Department of Education (MSDE) four years ago. Since then, it has been widely criticized for its content. "The HSA takes the algebra out of algebra," said University of Maryland Associate Professor of Mathematics Jerome Dancis.

Shortly before the introduction of the HSA, MCPS mandated changes to the Algebra I curriculum to align the course with the tested material. However, the new curriculum has attracted a great deal of criticism. "We don't think the material is what they need to know to be successful," said Blair algebra lead teacher Maria Costello.

Changes in the curriculum are cited as a main cause for students' deficiencies in basic algebra, which are manifesting themselves in higher-level math courses that require an understanding of concepts taught in Algebra I. "Our Algebra II students are worse than ever. Our Pre-Calculus students are worse than ever. It's falling apart as we go up the ladder," said Costello.

Concerned about her students' performance, Pre-Calculus teacher Julie Greenberg asked her colleagues via e-mail about the competency of their current students. Forty teachers responded, 29 of whom indicated that their students were "less competent" than those of their earliest teaching experience. The majority of those 29 cited basic algebra skills as the root of their students' deficiencies.

The problem is not limited to the non-magnet Blair population; magnet coordinator Eileen Steinkraus is worried about the mathematics preparation of many of the current magnet freshmen. "This issue was a concern last year. We thought it was just an anomaly, but that doesn't appear to be the case," said Steinkraus. The freshmen "are not as well prepared…their skills in algebra are weaker," said magnet Pre-Calculus teacher Judith Bishop.

According to Steinkraus, students from the Takoma Park Middle School Math, Science and Computer Science Magnet Program, which does not follow the mandated MCPS Algebra I curriculum, are largely unaffected.

The new MCPS algebra curriculum

One of the main complaints about the new MCPS algebra curriculum is the emphasis on data analysis, a topic that was not included in Algebra I until the introduction of the HSA. Costello considers data analysis to be displacing some of the algebra topics that used to be covered. "The new Algebra I curriculum consists of 45 percent data analysis," said Costello. Fourteen of the teachers who responded to Greenberg "explicitly criticized" the algebra curriculum's emphasis on data analysis.

Data analysis represents one of the seven Algebra I units, and that unit takes less time than most of the other units, said MCPS Mathematics Instructional Specialist Lauren Duff. However, MCPS documentation for the Algebra I curriculum recommends spending six weeks on the "Data Analysis and Probability" unit, more time than on any of the remaining six units in the curriculum.

The inclusion of data analysis in the Algebra HSA grew out of the desire for students to master objectives in algebra, geometry and data analysis, said Maryland State Department of Education (MSDE) mathematics specialist Donna Watts. MSDE only requires two credits of high school mathematics for graduation, and those topics had to be combined into two tests. According to Watts, data analysis was wed to algebra to form the current HSA.

As a result of the curriculum changes, the Magnet has restructured the pre-calculus curriculum to allow for review of more basic algebra concepts, something that non-magnet teachers are not permitted to do under current MCPS regulations.

"The HSA is our first priority"

While the MCPS algebra curriculum is centered around the objectives of the HSA, according to Watts, those objectives represent only fundamental competency levels. "The core learning goals [for algebra and data analysis] do not represent all of algebra. It only represents about 60% of a typical Algebra I course. It's up to the local school system to decide what to add," said Watts.

Although MCPS teaches additional material on top of the core requirements of the HSA, "the HSA is our first priority," said Duff.

Montgomery County Gifted and Talented Association president John Hoven considers the HSA to be the main focus of Weast's mathematics initiatives. "What Weast cares about is that Montgomery County students pass the test in large numbers, so he rewrote the entire [algebra] curriculum to be as close to the Maryland standards as possible," said Hoven.

Coupled with the increased MCPS emphasis on the goals of the HSA, many teachers feel that since they are evaluated based on the HSA scores of their students, they must spend even more time covering and reviewing the material in preparation for the test.

"[It's a] number game…It's all because of the numbers," said Math Department Chairman Barbara Hoffman.

Taking algebra too early

Coupled with changes in the algebra curriculum, many teachers see MCPS initiatives to push more middle-school students into taking algebra as contributing to the decline in student performance.

Eighteen of the 40 teachers who responded to Greenberg also said that many of their Honors students were pushed into algebra before they were either ready to absorb the material or mature enough to handle the workload. Bishop also attributes much of her magnet students' deficiencies to being pushed into algebra too early.

In 1996, 32.8 percent of students completed algebra by the end of their eighth-grade year. That percentage rose to 51.4 percent in 2003. The percentage of students completing algebra by their seventh-grade year rose from 2.3 percent to 12.3 percent during the same time period.

"The superintendent wants more students in Algebra and Geometry in middle school… and kids who are ready to take algebra should take algebra." said Hoffman.

"But it's definitely not half of all students," said Costello.

How should math be taught?

Many believe that this problem is not only limited to Algebra I and other courses with HSA requirements, but that it is a symptom of a larger movement in math instruction that spans K-12.

According to Hoven and Dancis, math curriculum and instruction have been factionalized into two sides of a "math war." One side is represented by the National Counsel of Teachers of Mathematics (NCTM), who, according to Hoven, "wants to emphasize geometry vocabulary and fake data analysis." The other side, according to Dancis, is represented by people like Hoven and magnet Calculus teacher Eric Walstein, who advocate for teaching methods that promote a deep understanding of material. According to Hoven, MCPS has "enthusiastically" embraced NCTM's goals.

Walstein believes that this new instruction is preventing students from learning fundamental math concepts which are needed to understand higher level material. "The kids are not learning the foundations of the material. They're just sitting and memorizing formulas, and they don't have any idea what it means," said Walstein. "It all relates to one word…intuition. The kids just memorize, and they can't intuit anything."

"The things that should come out of their heads automatically are just not there," agreed Costello.

Walstein cited the increased use of calculators in MCPS curriculum as an example of this problem. "If students can just punch things into a calculator, and it spits out the answer, that's not math. They're not learning anything," said Walstein. While Walstein believes that calculators should be used in certain circumstances, they are not a substitute for understanding the material.

"It's a lot easier to teach someone to use a calculator," said Walstein. "But that doesn't mean they're being taught math," he added.

Whose responsibility is it?

The 2001 No Child Left Behind Act provides for the removal of school administrators if students' test scores fail to meet federal standards. MCPS also evaluates teachers based on their students' performance on the HSAs. If students don't perform well, "it's the teacher's fault," joked statistics teacher Karen Klarman.

However, according to Walstein, the role of the student in math instruction should be emphasized as well. One thing that Walstein often tells his magnet students it that "You learn, I help." Walstein believes that while the teacher should cover and explain the material, it is the students' responsibility to spend time practicing it and studying.

Despite the fact that the current curriculum, state policies, MCPS policies and federal place all of the responsibility on teachers, Walstein believes that the students are the ones who are ultimately suffering. "The kids are the victims here," said Walstein.