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March 1995 | Volume 52 | Number 6 Aiming for Higher Standards Pages 30-33
Edward A. Silver
Let X equal mandated algebra instruction and Y equal serious curriculum reform. Is there an equation for combining them—and does it add up to competence for all students?
Algebra is sometimes called a gatekeeper to educational opportunity, for successful completion of an algebra course serves as the passageway to more advanced academic and vocational opportunities. Learning algebra provides more than a particular set of skills in dealing with quantitative relationships. It also introduces students to mathematics as a style or method of thinking, involving modeling, abstraction, and the formalization of patterns and functions. In this respect, mandated algebra instruction shares a common goal with the wider movement for mathematics reform. Both agendas seek to increase the number of students who learn important mathematical ideas, and to deepen their mastery of skills.
Most American students now study algebra in high school for two years, and many states and school districts require the completion of an algebra course for graduation. In recent years, some districts have mandated an algebra course for all students in grade 9. Others require algebra for all students in grade 8 (Olson 1994). In the six school districts participating in the Equity 2000 project, all students take algebra in grade 9 and geometry in grade 10 (Hawkins 1993).
These efforts to mandate algebra for all have developed unevenly—and the results have been mixed, at best. In urban schools, for example, a considerably lower percentage of students take algebra than in suburban and affluent schools. According to data from the National Assessment of Educational Progress, fewer than half the students in urban schools take any mathematics beyond one year of algebra, and one student in five never studies algebra at all (Mullis et al. 1991). This situation led Bob Moses, a noted civil rights activist and mathematics educator, to identify access to algebra as an issue for a new civil rights movement (Jetter 1993).
But in pursuit of the benefits of competence in algebra, policymakers risk resorting to a quick fix with the potential for unintended consequences. Mandating algebra at grades 8 or 9 may lead to massive failure or to grade inflation. Even worse, students may find themselves tracked into courses called “algebra” that deliver something very different. At the same time, extensive curriculum development and teacher education may appear too slow to guarantee access and opportunity for all students.
To provide algebra instruction for larger numbers of students, many districts simply offer more sections of a traditional one-year algebra course. This approach certainly avoids the time-consuming development of new curriculum—but at a price.
Students may, perhaps, derive some benefit simply from an exposure to algebra, regardless of the form in which it comes. Yet there is little evidence that mandated algebra courses lead to real competence for all who enroll in them. Indeed, the track record suggests exactly the opposite.
Among students who voluntarily elect to study algebra or are placed by examination into a traditional algebra course, a failure rate of 40 to 50 percent is typical. Even after two years of algebra, many 12th graders display only a limited mastery of the major concepts—and often are unable to use their knowledge to solve problems (for example, Mullis et al. 1991). The large number of remedial mathematics courses offered by the nation's colleges and universities also attest to a general lack of algebraic competence resulting from traditional algebra courses, even by those fairly successful high school graduates who go on to college.
No less sobering are the data available from early efforts in three of the six school districts involved in the Equity 2000 project. In two of the three districts, more students failed a traditional algebra course after it was mandated; and the percentage of students receiving high grades (A or B) decreased (“Positive Attitudes” 1993). The kinds of supplemental teacher and student support available within the Equity 2000 project will be beyond the reach of most school districts. There is little reason to be optimistic about the benefits of mandated traditional algebra instruction in districts lacking such support.
The problem rests with the content and teaching methods used in traditional algebra courses. Lynn Steen, a prominent mathematician and spokesperson for mathematics education reform, has observed that the traditional algebra course is often worthless:
For most students, the current school approach to algebra is an unmitigated disaster.... First-year algebra in its present form is not essential for a quality mathematics education. This is not to say, however, that algebra is not essential (1992, p. 10).
... first-year algebra in its present form is not the algebra for everyone. In fact, it is not the algebra for most high school graduates today (“Board Approves Statement on Algebra” 1994).
One would hardly expect the situation to improve merely by requiring that the traditional algebra course be taught in grade 8. Yet that is one trend—fueled by a perception of the middle grades mathematics curriculum as a wasteland of needless drill in skills that should have been learned in earlier grades.
Few experts would argue that most students need another year of arithmetic review in grade 8. But algebra is not the only alternative. With algebra mandated as a target course for grade 8, curriculum for the remaining middle grades is spread across only two grades instead of three, so that the range of topics is compacted rather than expanded. Students may lose access to important mathematical ideas and experiences. In this way, mandated algebra instruction in grade 8 can undermine those reform efforts directed precisely at broadening and integrating the curriculum of middle grades by including topics in measurement, geometry, algebra, probability, and statistics.
Mathematics educators recognize and support the effort to incorporate basic algebra ideas throughout the K–8 mathematics curriculum (especially in grades 6–8), rather than segregating them into a one-year course (NCTM 1993). Yet, it seems that the National Council of Teachers of Mathematics' Curriculum and Evaluation Standards (1989) are being ignored in this area—even though they recommend exactly such a broad, integrated curriculum for the middle grades.
In keeping with a broad consensus among mathematics educators, the curriculum must be revised to teach appropriate algebraic ideas, and greater access to algebraic competence must be provided to all students. Likewise, it is generally agreed that teachers must improve instructional strategies. As Seeley (1993) has suggested:
Simply changing the courses in which students are enrolled does not change the fact that most teachers have never been taught how to teach in a way that engages a diverse student population in a variety of interesting and important learning activities structured to develop the inherent critical thinking and problem-solving abilities of all students (p. 43).
Ironically, school districts are mandating traditional algebra instruction at the very time a new vision of algebra teaching and learning is being formulated. Some middle schools—for instance, the six associated with the QUASAR project (Silver, in press)—have been developing and modifying instructional approaches to provide a foundation for algebraic thinking and reasoning in grades 6–8. This task should soon become easier because new curriculum materials to support such instruction should be commercially available in a few years. At present, however, text materials to support a yearlong traditional algebra course are far more readily available than good curricular materials in which algebra instruction is woven into the fabric of the mathematics curriculum for the middle grades.
Despite the tensions between mandated algebra instruction and longer-term mathematics education reform, our experiences in the QUASAR project suggest that they might be combined. At one QUASAR middle school—located in a district participating in the Equity 2000 project—all students were required to take an algebra course in grade 9 during the 1993–94 school year. Prior to this project, the school had a reputation for low-performing students. A change was evident by the end of the first grading period: compared to students at the 20 other middle schools in the district, the QUASAR students had the second highest passing rate. And at the conclusion of the course, QUASAR students passed at a much higher rate than their peers in the district schools that were demographically most similar to them. Undoubtedly, their exceptional performance was due to mathematics instruction in the middle grades that had emphasized thinking, reasoning, communication, and problem solving—all important mathematical goals in the NCTM Standards (1989).
The school district is building on this base to improve mathematics education more broadly. For example, several of the teachers from the QUASAR school have conducted workshops for other middle school teachers. One instructor has met with high school teachers to present successful teaching strategies and curricular ideas. Over the next few years, it is likely that the middle grades mathematics program will be enhanced throughout the district in ways similar to the QUASAR school—and that the algebra course in grade 9 will also be enriched.
There is an important lesson in this experience for everyone concerned about improving access to good mathematics for all students. Without the support of the QUASAR project, which was grounded in the agenda for mathematics instruction reform for all students, the mandated algebra experience likely would have resulted in even higher failure rates at that school. Without the policy mandate for increased attention to universal access to algebra, the QUASAR efforts to enhance instruction would likely have had far less impact throughout the district. As this example suggests, the two reform agendas can support each other for the benefit of students. But it will take attention and commitment.
“Board Approves Statement on Algebra.” (May 1994). NCTM News Bulletin 30, 6: 1, 3, 6.
Chambers, D. L. (1994). “The Right Algebra for All.” Educational Leadership 51, 6: 85–86.
Hawkins, B. D. (1993). “Math: The Great Equalizer: Equity 2000 and QUASAR, Improving Minority Standing in Gatekeeper Courses.” Black Issues in Higher Education 10, 6: 38– 41.
Jetter, A. (February 21, 1993). “Mississippi Learning.” The New York Times Magazine: 28–32, 50–51, 64, 72.
Mullis, I. V. S., J. A. Dossey, E. H. Owen, and G. W. Phillips. (1991). The State of Mathematics Achievement: NAEP's 1990 Assessment of the Nation and the Trial Assessment of the States. Washington, D.C.: National Center for Education Statistics.
National Council of Teachers of Mathematics. (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, Va.: NCTM.
National Council of Teachers of Mathematics. (1993). Algebra for the Twenty-First Century: Proceedings of the August 1992 Conference. Reston, Va.: NCTM.
Olson, L. (May 18, 1994). “Algebra Focus of Trend to Raise Stakes.” Education Week: 1, 11.
“Positive Attitudes, Positive Changes.” (1993). EQUITY 2000 News 2, 2: 5.
Seeley, C. (1993). “Increasing Access or Ensuring Failure? Policy Makers Throw a Hammer into the Wall.” In Algebra for the Twenty-First Century: Proceedings of the August 1992 Conference, edited by National Council of Teachers of Mathematics. Reston, Va.: NCTM.
Silver, E. A. (In press). “The QUASAR Project: The `Revolution of the Possible' in Mathematics Instructional Reform in Urban Middle Schools.” Urban Education.
Steen, L. A. (1992). “Does Everybody Need to Study Algebra?” Basic Education 37, 4: 9–13.
Author's note: Preparation of this paper was supported by a grant from the Ford Foundation for the QUASAR project. The opinions expressed herein are those of the author and do not necessarily express those of the foundation.
Edward A. Silver is Professor and Senior Scientist, Learning Research and Development Center, University of Pittsburgh, 3939 O'Hara St., Pittsburgh, PA 15260.
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