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Formula for learning

Monday, August 24, 1998

Jane Blotzer, Associate Editor,Post-Gazette

The motto for most middle school math in the United States could easily be “same old same old.”

Most sixth-, seventh- and eighth-graders learn so few new concepts, they could sleep through most of their math classes without missing much.

William Schmidt, professor of education psychology at Michigan State University and the national research coordinator for the Third International Math and Science Study, claims that the damage inflicted by standing still for so long is nearly impossible to overcome.

Algebra and geometry become all the more daunting in ninth and 10th grades because students are suddenly confronted with new concepts on a daily basis.

If there is one overriding message of the Math and Science Study it is that middle school math needs to be rigorous and move beyond basic arithmetic for all students.

Newly developed National Science Foundation-funded middle school math programs push algebra, geometry, probability and statistics down into the middle grades. But this change in approach has to overcome ingrained beliefs of many parents and educators.

The first is that students must master multidigit computations - without a calculator - before they tackle more difficult concepts. The second is that only an elite few are ready for the demands of algebra in the middle school years.

Nationally, about 25 percent of eighth-graders study algebra. Locally, a few districts have much higher percentages of their students in such programs. Some, such as Bethel Park, South Fayette and Quaker Valley, enroll a majority.

A few, including the Pittsburgh, Beaver Area, Greensburg-Salem, Mars Area, Mt. Lebanon and Upper St. Clair districts, provide rigorous math for all middle school students.

Upper St. Clair made the change in 1991 despite the fears of parents and some administrators, according to William White, a district administrator.

Before 1991, White said, about 40 percent of the district’s eighth-graders scored above the 75 percent mark on national standardized tests. Since algebra was opened to all eighth-graders, between 60 percent and 75 percent score at that level.

In Pittsburgh, the change met with resistance, especially from parents of higher-achieving students who felt that the existing system was working for their children. They believed teaching all students what their children were learning could only be accomplished by watering down the subject matter.

But Marianne O’Connor, who is a demonstration teacher helping middle school teachers adjust to the city’s new curriculum called Connected Mathematics, said she’s found otherwise: The program offers so many opportunities for deepening the lessons that students get it on different levels depending on their background knowledge, interest and abilities.

Nancy Bunt, head of the Regional Math/Science Collaborative, believes the evidence is overwhelming on the importance of granting access to all students. She also has personal experience with the dangers of exclusionary education.

When her son was a fifth-grader, he took the test that helped determine placement in sixth-grade pre-algebra. Although he had always scored “A”s in math, he didn’t do well on the test and was not recommended for the class. Bunt played the part of parent advocate and insisted that he should have the opportunity, and the district, reluctantly, agreed.

This year, after getting the highest possible ranking of 5 on an Advanced Placement calculus test, he graduated as valedictorian from Fox Chapel High School.

Bunt believes that all children should have the opportunity that her son had, and it shouldn’t depend on a single test or a parent advocate.

But judging from the organization of most middle school programs, and talks with teachers and administrators, it is clear that view is not universally shared.

A more common view is held by Bob Chiappetta, former principal of Dorseyville Middle School in the Fox Chapel Area District and a former math teacher himself. He believes all children can learn math but thinks it is disastrous to move them ahead too fast without creating the proper foundation. And that means many eighth-graders - more than half at Dorseyville - are not ready for algebra.

Once districts sort out who learns what and when, middle schools must figure out the best way to present the material. Reformers believe that an earlier introduction of advanced content must be accompanied by a fundamental change in the way math is taught.

Like their elementary counterparts, the new middle school programs are designed to challenge students to be active learners, to question and think creatively and to relate math to the real world.

In Connie Finseth’s seventh-grade math class at West Liberty Classical Academy in Pittsburgh, students learn about probability by picking colored blocks out of a drum and predicting what the likelihood of choosing red, yellow or blue blocks would be based on the proportion of the various colors in the drum.

Two weeks into the lesson they are rolling dice to determine the probability of coming up with an even product vs. an odd product.

The concept of probability was new, but the unit provided an opportunity to reinforce earlier learning on fractions, decimals and percentages.

The class was focused and engaged. The group work was animated as students tested their theories and altered their estimates.

They were using the highly regarded National Science Foundation-funded Connected Mathematics program developed at Michigan State.

The classes include all ability levels and implementation of the curriculum is being accompanied by intensive professional development, a combination that makes the city’s middle school math program a leader nationally, said Bunt.

It is too soon to tell whether blazing a new trail in math can overcome other problems endemic to urban districts, like absenteeism and a transient student population, but O’Connor said it has already made a difference in attitudes and that performance is sure to follow.

Connected Math, which is also used by Beaver Area, is the most cutting edge middle school curriculum in use locally, but all new textbooks and programs tend to include student-centered projects.

In Mt. Lebanon, for example, eighth-graders do a boat project in which students use the Pythagorean theorem and right-angle trigonometry and geometric reasoning to design and build a boat out of a milk carton. They predict how much cargo it can carry, experiment to see how accurate their predictions are, then defend their techniques and procedures before a panel of parent questioners.

At the same time some schools are trying such inquiry-based approaches, most districts continue to rely on the more traditional lecture and practice techniques.

Mary Ellen Lippert, a seventh-grade math teacher at Ingomar Middle School in the North Allegheny district, has an easy rapport with her students. And even as she presents a new topic just a few days before school is out for the summer, they pay attention and participate.

The class is working on the “lowest common multiple,” which she carefully defines and writes on the board, so they can copy it into their notebooks. The lowest common multiple of two numbers is the smallest number that both can divide into evenly. Thus the lowest common multiple - or LCM - of 10 and 8, for example, is 40.

Lippert works a problem on the blackboard using prime factors to find the LCM, then explains carefully why this is the most efficient way to reach a solution. Individual students work three more problems out on the board, while the others do them in their seats, and Lippert goes over the results.

With 15 minutes left in class, she assigns homework and has the students begin work on it as she circulates around the room.

Unlike some class periods which jump from topic to topic, Lippert stays focused on one subject and her presentation is clear and lively.

Most educators agree that lectures are a valuable component of math education. How to balance this direct lecture and example approach with a more student-discoverer model is a topic of debate in schools around the country.

It is hardly a new issue. Theodore von Karman, one of the fathers of modern rocketry, described the education his father designed for him in Hungary before the turn of the century:

“At no time did we memorize rules from a book. Instead we sought to develop them ourselves. I think this is a good system of education. . . . How one learns the elements of reasoning in primary school will determine his later capacity for intellectual pursuits.”

While primary math classes look very different than they did a decade ago, and while districts are rethinking what middle school students need to learn, local high school math is undergoing its own transformation. Though not as flashy as the reforms in the earlier grades, some changes are significant.

An increasing number of districts are eliminating general math courses on the belief that “shopkeeper math” - alternately called consumer math or business math - is no longer helpful. This change is in keeping with the proposed state standards that will require all students to have exposure to algebra and geometry and the beginning concepts of calculus.

That does not mean that every student will take calculus, but rather that every student must take a more rigorous math program that prepares him for life and work.

And more schools, including Mt. Lebanon, North Allegheny and Mars, are moving to integrated math.

Schmidt has noted that the highest achieving countries in the Third International Math and Science Study teach math as an integrated whole rather than in the linear fashion that is traditional in the United States: algebra one year, geometry the next, followed by algebra II, trigonometry and calculus. Teaching math the integrated way, proponents believe, helps children make the connections that help math make sense.

All of the NSF-funded programs preach the integrated approach.

No district in the region has approved one of the National Science

Foundation programs at the high school level. Philadelphia, however, has introduced the Interactive Math Program, developed in California.

Joe Merlino at LaSalle University, co-director of the regional center for Interactive Math Program, believes that the curriculum is empowering, and he is unabashedly dramatic in saying so.

“We live in a data-rich world and we need a curriculum to prepare kids to handle this,” Merlino said. “Before, we appealed to the top 3 percent of kids who were math whizzes. But our program works for all kids. We want independent learners. It’s really subversive. It’s what democracy is all about. This is America!”

America is nothing if not eclectic. And while the nation seems to be moving toward changing its approach to math, it is not a straight nor easy path. Local districts that believe a cure is needed have suggested that the only way to reach all students is to begin at the elementary level and have them work their way up.

And even then, some have suggested, real, lasting, systemic change will not occur until those students become the teachers for the next generation.

Copyright, Pittsburgh Post-Gazette, 1998, all rights reserved.

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