Calculus in Inner City High Schools:
Equity and Reform

These first offerings are built on an NSF-developed curriculum (using the CCH text, Calculus), a stress on concepts and good applications, cooperative learning, and regular use of graphing calculators. (Paradoxically, the fact that there was no calculus in place in these schools allowed for the smooth introduction of "reform" calculus.) College math and engineering majors visit the classes regularly to mentor the high school students, and a college faculty member and a high school teacher (who is part-time with the project) collaborate with the teachers through individual conferences, workshops, and classroom visits. The students are enthusiastic about calculus, and go on to college with a background and confidence in mathematics comparable to that of students from private or suburban schools. The teachers are likewise energized, and several have commented that they wish they had first studied calculus the way it is presented in the CCH text.

How did we get to a fundamental shift in the entire system with respect to calculus? Let's go back to the beginning, when the collaboration was formed.

School-University Collaboration
In the fall of 1994, sixteen students met in the first reform precalculus course at Hyde Park High School (it was recognized early in the planning that a reform precalculus must be in place before offering calculus). In a typical class meeting, the teacher, Joanne Saluti, asked the students to form groups and distributed a problem leading them to investigate the comparative growth of exponential and power functions utilizing the graphing calculator. The teacher had just come from a weekly meeting with a Northeastern University faculty member (myself) and Cedric Fletcher and Cassandre Felix, two Northeastern students who were mentors. They had discussed the curriculum for the next several classes along with the progress of students. Now as the groups of students began to delve into the problem presented, the mentors and the teacher circulated, encouraging the students and responding to student questions with other questions, hopefully leading to student discovery.

The college mentors were available for individual tutoring or small group sessions with students, when this could be arranged, and were often from the same racial or ethnic background as the high school students. They quickly became strong role models as the students bonded readily with someone close to their own age. They were also a tangible promise of the high school students' success in mathematics and in college.

After completion of this pilot section, a high school math teacher, Julie Goldberg, was brought in to disseminate the precalculus course to three new high schools in 1995-96. (It was part of the design of the NSF proposal that a high school teacher would coordinate the dissemination of both precalculus and the calculus courses that were being piloted.) It was time to pilot the calculus course.

The First Calculus Class at Hyde Park High School
In the fall of 1995, the first calculus section, consisting of seven students, began at Hyde Park High School with Joanne Saluti as the teacher. The students had had a year's experience with the approaches, the group work, and the mentors' coaching, so they took to the subject with great energy. They were becoming "intellectually addicted" to problem-solving, to making and testing conjectures, and to proceeding at their own level to do what a mathematician does. Evaluations by high school students of their reform calculus course include remarks like: "it really makes you think" and "we get not just the how but the why."

Because the majority of the first reform precalculus class were seniors, the first calculus class was quite small. The firm decision was taken, regardless of the number of students, to make this pilot course a high quality, well-defined entity which could then be disseminated to other schools. A mentor was assigned to the students and the weekly meetings between a University faculty member and Joanne Saluti continued. In fact, the curriculum followed closely the topics of Northeastern's first calculus course, but the high school calendar allowed it to be developed in an appropriately extended way. (During the life of the grant, students who earn a B or better in this course are awarded Northeastern University credit.)

Dissemination of Calculus to Other High Schools
This year, calculus is being introduced at Snowden High School, South Boston High School, and West Roxbury High School. The number of students in these new classes is substantial (averaging about twenty). This addresses a key goal of the project, that of truly expanding the "pipeline" of mathematics education leading to calculus.

Before 1994, the general approach in those Boston schools which offered no calculus was to have one or two students with an unusually strong background and talent sent to a local university during high-school hours to begin their study of the subject. This "pull-out" policy had the damaging effect of leaving the curriculum of the school untouched. This situation is now completely altered, and the goal is systemic change to increase the mathematics capacity of the school itself. This change in direction allows the course's population to reflect the actual makeup of the school itself. Where the student body is largely African-American and Hispanic, the new courses are reflecting these proportions.

Further, even though only a relatively small percentage of a school studies calculus, this project's emphasis on calculus has made it a keystone of reform across the math curriculum. The emphasis on strong challenge and equally strong support bypasses the obsession with remediation that deadens mathematical interest and achievement.

The NSF has been instrumental in carrying out this project, supplying texts, calculators, mentor stipends, funding for teacher workshops, and release time for college and part-time high school faculty. The success of the project suggests elements for a national model for inner-city calculus:

1. An emphasis on collaboration among teachers at the secondary and university level, including the college mentors. This collaboration has been carried out over years on a regular basis, including classroom visits, individual planning sessions, and short courses and seminars. Materials and strategies have been shared both between and across levels.

2. Making a priority the development of a high quality, high-profile pilot course in calculus at one site, and only subsequently seeking its dissemination.

3. Keeping clearly in sight issues that affect the entire population of the school, "pipeline" concerns which result in the actual population of the school, underrepresented minorities, acquiring access.