Nationwide, about 5 percent of seniors typically take AP calculus, according to Bob McDonough, Midwest director of academic services for the College Board, which administers the program. AP courses are more advanced than freshman courses at many colleges, he says, adding that they’re comparable to what Northwestern and Harvard universities offer.

At Chicago’s Whitney Young Magnet High School, 14 percent of seniors are taking AP calculus this year; at Lane Tech, 5 percent are taking it. At west suburban Oak Park & River Forest High School, the percentage is 18.

The performance of Lake View students on the end-of-course AP tests is improving, but it’s still subpar. Last year, only 18 percent scored high enough to garner college credit; nationwide, the percentage was 60.

Lake View students do not have as strong a background in math as other AP students do, explains Richard Kaplan, chair of the school’s 10-member mathematics department. “In the suburbs, students in AP calculus are at the 90th percentile on standardized math tests,” he says. “At Lake View, students enter at the 30th percentile, but graduate with much higher scores. These aren’t kids who performed brilliantly in math all their lives.”

Kaplan says the goal of his department is to convince students they can handle college-level work and to get them interested in college. “The key is to have non-magnet, inner-city kids take enough math to prepare them for college,” says Kaplan. Most of the 36 Lake View students who took AP calculus last year went on to four-year colleges and universities.

Lake View’s math faculty attributes its success to a hands-on curriculum that seeks first to grab students’ interest and then to provide a variety of opportunities for students to demonstrate math knowledge, besides ending up with a correct answer. In addition, teachers take a demonstrable interest in students’ personal lives.

The school started building its math curriculum in 1990, when it joined several other Chicago public schools and the University of Illinois at Chicago in the College Preparatory Mathematics Program. The program trained teachers to use cooperative learning techniques and sought to increase the time students study math, to replace remedial math with more challenging problems, and to form teams of teachers to create plans to change math education at their schools.

Through this program, Lake View teacher Margaret Small learned of the Interactive Mathematics Program (IMP), a curriculum that weaves together the traditional courses of algebra, geometry, advanced algebra and trigonometry and that is aimed at mixed-ability classes. (See accompanying story.) One of her concerns was that students were being placed into math classes incorrectly because of their scores on placement tests. “Placement tests are like a snapshot of a person’s mathematical ability,” explains Small, now co-director of IMP in Chicago.

Donna Macey, then principal of Lake View, was impressed with IMP and wanted it to reach as many students as possible. To accomplish that, math teachers met with enrolling students and their parents to explain IMP and give them the option of following the IMP path or the traditional path. IMP proved popular, with sections filling up quickly.

Further, math teachers set calculus as a goal for all students, beginning with 8th-graders at neighboring elementary schools. Meeting with the incoming freshmen and their parents, they encourage the students to enroll in summer math classes the school offers.

Teachers continue talking up calculus during freshman and sophomore years. In the junior year, they take students to see the movie “Stand and Deliver,” which is based on the success that a California math teacher had with low-income students. The school also invites bilingual college recruiters to the school—65 percent of Lake View’s enrollment is Hispanic. Seniors who take calculus join the marketing effort, talking to freshmen and sophomores about their experiences and designing their own T-shirt. Students who enroll in calculus are required to attend a summer preparatory course that meets four hours a day for six weeks.

Teachers’ attention extends beyond math. In Kaplan’s classes, for example, students write about their classes and their lives outside school. “We treat our students with respect, and we find that they overwhelmingly come through,” he says.

**‘Fun but hard’**

“Fun but hard” are the words students frequently use to describe the course, which meets 100 minutes a day, five days a week, and includes an hour of homework each night.

“It’s important to have the mind set that you can do calculus before coming to class,” says senior Moises Jerez.

This year, Lake View began phasing out IMP in favor of a new textbook series that integrates social studies, art and literature in the teaching of algebra, geometry and data analysis. The series is to be used in freshman and sophomore classes; juniors will take advanced algebra and trigonometry. Asked why the school is making the switch, Principal Scott Feaman says the new textbook series is better than IMP for helping students meet new state and Chicago academic standards. Not all teachers agree.

Asked whether any math department could accomplish what Lake View’s has, Kaplan says: “Any school can develop an engaging, exciting math program, but the principal and bureaucracy have to empower the teacher.”

]]>**CHICAGO PUBLIC SCHOOLS**

The Chicago Systemic Initiative. A citywide effort involving staff development and school-based teams.

Amount: An estimated $10 million from 1994 through 1999.

**UNIVERSITY OF CHICAGO**

Everyday Mathematics, 4-6. An extension of work in lower grades, this project is designed to develop a complete mathematics curriculum for grades 4,5, and 6, including data analysis, math in everyday situations and math in the natural and social sciences, arts and language.

Amount: An estimated $4.8 million from 1992 through 1997.

**UNIVERSITY OF ILLINOIS AT CHICAGO**

TIMS 95: School University Partnerships for Improvement of Math Teaching & Learning. This project aims to establish university-school partnerships for improving math instruction using standards-based curricula and developing resource materials.

Amount: An estimated $3 million from 1996 through 1999.

UIC-ALL Learn Mathematics. This project aims to improve math understanding and classroom pedagogy of middle-school teachers in Chicago public schools, grades 5-8.

Amount: An estimated $1.8 million from 1995 through 1998.

College Preparatory Mathematics Project. For continued teacher training at the University of Illinois at Chicago and for starting teacher training at the University of Wisconsin-Parkside and DePaul University.

Amount: An estimated $2.4 million from 1993 through 1997.

**NORTHWESTERN UNIVERSITY**

Materials World Modules. A series of science and technology kits designed to reinforce the existing math and science curriculum in high schools.

Amount: An estimated $1.8 million from 1994 through 1997.

The Co Vis Testbed. This project focuses on project-enhanced science learning, collaboration and scientific visualization as a way to reconstruct science education.

Amount: An estimated $3.5 million from 1994 through 1997.

**ARGONNE NATIONAL LABORATORY**

Partial support for a five-year effort by the Department of Energy national laboratories to advance science education in grades K-8.

Amount: An estimated $3.7 million from 1993 through 1998.

**CHICAGO STATE UNIVERSITY**

Chicago Alliance for Minority Participation (CHAMP). A consortium of six Chicago area universities supported by local businesses, national laboratories and local school districts. The mission is to increase the number of minority students earning science, math or engineering bachelor’s degrees and to increase the number of minority students entering graduate school.

Amount: An estimated $3.3 million from 1993 through 1998.

**FIELD MUSEUM OF NATURAL HISTORY**

Life Underground: Foundations of the Biosphere. This exhibit displays the underground ecosystems and the importance of soil.

Amount: An estimated $1.6 million from 1996 through 1999.

]]>On the surface it’s play, but underneath it’s the serious business of learning about money, communications and math, especially math. “This whole class flunked during the regular school year, but now they are all passing,” says Buchanan.

Buchanan’s unusual way of teaching math skills is part of a program that just nabbed a $900,000 grant from the National Science Foundation for expansion in the Chicago public schools. Called the Interactive Mathematics Program (IMP), it is a four-year secondary curriculum used in 178 high schools nationwide. IMP was introduced at Lake View High School in 1992, and spread to another 11 high schools over the past five years through the Institute of Math and Science Education at the University of Illinois at Chicago. The new grant will pay for training and support for 200 teachers in 27 schools.

“This is more active learning, not just memorizing formulas,” says institute director Philip Wagreich.

Buchanan says he prefers IMP to a traditional math program because students “are constantly presenting their work to the class, as opposed to just writing it down and handing it in. They learn to defend their ideas.”

**No answer book**

IMP departs from standard mathematics instruction in several other significant ways. For one, it integrates five core areas—algebra, geometry, trigonometry, statistics and probability—and teaches them simultaneously rather than sequentially. Over time, the lessons become more sophisticated and abstract, building on the skills students already have learned. Further, since the program challenges students to find solutions to real-life problems, there is no answer book for teachers or students.

“To us as math teachers, the most important thing for people to realize is that mathematics is a really powerful tool in solving problems,” says Margaret Small, project co-director. “There’s a certain analytic power to mathematics that’s more than opinion.”

After Lisabelle’s roulette game, Buchanan writes equations showing students how math relates to their probability games. Then students complete a worksheet of five problems based on probability.

As for the gambling part, co-director Anne Horn says, “I believe these probability games teach kids not to gamble. They know what a small chance there is to win at casinos, the race track or even the lottery. The students know this is not a lucrative way to make a living.”

Edgar Allan Poe’s story “The Pit and the Pendulum” provides the springboard for another lesson. Students read an excerpt of the story about a prisoner looking up at a razor-sharp pendulum that threatens to slice him in half. Then comes their challenge: “How much time does the prisoner have to escape?” Students construct their own 30-foot pendulum to test their estimates. In the process, they learn complex mathematical concepts such as standard deviations, normal distributions and functions.

IMP not only has made math more interesting for students, it also has produced gains on basic skills tests. At Lakeview High School, for example, juniors who had taken IMP for three years advanced 2.1 years on the Tests of Achievement and Proficiency between 1995 and 1996. Juniors who had taken traditional math courses advanced 1.5 years.

“There’s a large number of people who agree that what we’re doing in math education needs to change, but how it should change, that always makes people very nervous,” says Small. “One of the reasons U.S. students score lower than other students [on international tests] is that we have a shotgun approach to math in high school.

“We want kids to memorize a million things and test them on it, and nobody remembers anything. Using these new approaches to math instruction is important in Chicago if we are going to successfully have all students pass three years of high school math.”

Beginning with the Class of 2000, which is in its sophomore year, CPS students must take three years of high school math to graduate.

The Reform Board recently approved academic standards that align with state goals; now it is developing end-of-course tests.

Small says IMP covers the state math goals, which include measurement, number sense, geometric thinking, algebraic thinking and probability and statistics. “The end-of-course test will be integrated to test for the five state goals, not strictly algebra or geometry,” she says.

**Schools participating**

1997-98: Clemente, Chicago Vocational, DuSable, Foreman, Future Commons, Lakeview, Richards, South Shore, Wells, Whitney Young and two charter schools, Acorn and Perspective Academy for Communication and Technology.

1998-99: Bowen, Robeson, Simeon, Corliss, Orr, King and Harper.

**For more information:**

Philip Wagreich, director of UIC’s Institute for Mathematics and Science Education: (312) 413-3019

Anne Horn, project co-director Chicago IMP: (773) 535-1098

Margaret Small, project co-director Chicago IMP: (312) 996-2448

Interactive Mathematics Program (IMP) Toll-free: 1-888-628-4467

National Science Foundation: (202) 342-2760

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