Promoting Equity in Mathematics: One Teacher's Journey

Promoting Equity in Mathematics: One Teacher's JourneyAuthor(s): Alan D. TennisonSource: The Mathematics Teacher, Vol. 101, No. 1 (AUGUST 2007), pp. 28-31Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/20876026 .

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Promoting Equity

in Mathematics:

One Teacher's Journey

Alan D. Tennison

n 2000, the National Council of Teachers of Mathematics (NCTM) released Principles and Standards for School Mathematics. This document contains a vision of mathematics education for all schools:

Imagine a classroom... where all students have

access to high-quality, engaging mathematics instruction-The curriculum is mathematically rich, offering students opportunities to learn impor tant mathematical concepts and procedures with

understanding_Students ... draw on knowledge from a wide variety of mathematical topics, some times approaching the same problem from differ ent mathematical perspectives or representing the

mathematics in different ways until they find meth ods that enable them to make progress_Alone or in groups and with access to technology, they work productively and reflectively, with the skilled

guidance of their teachers. Orally and in writing, students communicate their ideas and results effec

tively. They value mathematics and engage actively in learning it. (NCTM 2000, p. 3)

At the core of this vision is educational equity: the

concept that all students, regardless of their personal characteristics, backgrounds, or physical challenges, must have opportunities to learn mathematics.

Equity does not mean that every student should receive identical instruction; instead, it demands that reasonable and appropriate accommodations be made as needed to promote access to challenging mathematical ideas for all students (NCTM 2000).

28 MATHEMATICS TEACHER | Vol. 101, No. 1 August 2007



Unfortunately, curriculum practices in many schools

prevent a large contingent of students from receiving a quality mathematics education. The most notorious of these practices is tracking, or grouping students by perceived ability level. An eighth-grade class of math ematical "whizzes" may tackle high school algebra or geometry while eighth graders in another class are

still learning how to work with fractions, decimals, and percents (Loveless 1998). Tracking has proven to

be especially harmful for poor and minority students. These students are the ones most likely to end up in the low tracks (Oakes and Wells 1998).

According to the National Research Council

(NRC), low-track classes should help students catch

up (NRC 2001). Students should have opportunities to move out of the low track as quickly as possible. But there is evidence that low-track classes put much less emphasis on the higher-order knowledge and thinking skills associated with future success

(Loveless 1998). Less powerful learning environ ments typically have a poor curriculum, low expec tations, and less experienced teachers, so the dispar ity between students on fast and slow tracks grows over time (NRC 2001; Oakes and Wells 1998).

Tracking is still predominant in our schools, yet there has been a call for high standards for all stu dents. Can tracking coexist with this calling? Oakes and Wells (1998) and Kohn (1998) maintain that there are still deeply held beliefs about intelligence, racial differences, social stratification, and privilege. These are very real obstacles to removing tracking from our schools and for providing a quality mathe matics education for all students. For example, Oakes and Wells (1998) followed the progress of ten sec

ondary schools where personnel were disenchanted with the tracking systems in place. Careful plans to bring low-achieving students up to higher levels

without taking anything away from higher-achieving students were put in place. Many parents of high achieving students, however, reacted negatively, pressuring the schools to maintain separate classes that allowed their children access to more demanding

mathematical content. These parents were concerned

that eliminating low-track classes and bringing in

low-achieving students would water down the classes and that teachers would have to teach a less demand

ing curriculum (Oakes and Wells 1998). The lack of success in ehminating tracking at these schools demonstrates the need for support and cooperation of

teachers, students, administrators, and parents.

IMPACT OF TRACKING IN MY CLASSROOM When I began teaching mathematics in 1988, my first assignment was at a high school in Albuquer que, New Mexico, with a very diverse population of students. I initially taught geometry and basic mathematics. There was a clear distinction between

students in the college-prep geometry classes and the low-track basic mathematics classes. The geom etry students worked hard every day in class and made an effort to complete homework each day as

well. Most of the basic mathematics students were low achievers and apathetic about learning. Home

work was done by only a few students; class work was done poorly, if at all. The curriculum for the basic mathematics students was designed to review the mathematics these students had not mastered in

previous years and consisted primarily of work with

fractions, decimals, and percents. The basic math ematics classes were challenging for me and seemed

pointless for my students. I was perplexed about what to do and did not have any solution at hand.

The next year I transferred to another high school in Albuquerque, where the goal was to pre pare a larger percentage of low-income, underrep

resented students for college. Most of the school's

poor Latino population was tracked into lower level basic mathematics and algebra classes, and there was no mechanism in place to provide opportuni ties for these students to prepare for college. When confronted with this issue, many of the mathemat ics teachers in my department felt more drill and

practice was appropriate for these students and did not consider making the curriculum more chal

lenging and purposeful for them. The aim of the low-level algebra sequence was to slow the pace for these students so they would work through the

equivalent of algebra 1 in two years. If the intent was good, the result was not. Students in these classes still performed poorly, and most eventually dropped out of school. More than 50 percent of the students dropped out of these classes by the end of the year. Many students were capable, but the cur riculum failed to serve their needs.

After a few years of frustration with these

classes, I decided to dedicate myself to making meaningful change at this level. I was convinced that removing tracking was the solution, believing that low-achieving students would be more suc cessful when they had higher-achieving students to serve as role models in their classroom. Many of my colleagues were opposed to such a move and were fearful of the impact these low-achieving stu dents would have on the regular-tracked students. Unable to convince them that the removal of track

ing would benefit all students, I abandoned the

prescribed low-level algebra curriculum and began to incorporate ideas and strategies that aligned with the vision of NCTM. I began using problem-based strategies that provided opportunities for students to generate and collect data and to interpret and

make predictions about the data they collected.

They learned to use graphing calculators to find and explain their solutions. Eventually, during

Vol. 101, No. 1 August 2007 | MATHEMATICS TEACHER 29



the course of the year, students exhibited positive changes in their attitudes about learning mathemat ics. Fewer students dropped out of the classes as

they became more engaged in their mathematics

learning. But this was not enough. Many of these students were still locked in the low track that had been designated for them and simply returned to the routine of drill and practice the following year.

I remained determined to enhance the mathemat ics learning for as many of these students as pos sible. After a few years, Standards-based curricula became available. These curricula were designed around the vision of the NCTM's Curriculum and Evaluation Standards for School Mathematics:

Students should be exposed to numerous and various interrelated experiences that encour

age them to value the mathematics enterprise, to develop mathematical habits of mind, and to understand the role of mathematics in human

affairs;... they should be encouraged to explore, to guess, and even to make and correct errors so they gain confidence in their ability to solve

complex problems;... they should read, write, and discuss mathematics; and ... they should

conjecture, test, and build arguments about a

conjecture's validity. (NCTM 1989, p. 5)

One of these curricula was written in the spirit of these NCTM Standards by advocating for a het

erogeneous learning environment, or classrooms

without tracking. Developed as a collaborative effort by mathematicians and teacher educators, this Standards-based, four-year curriculum was

field-tested during 1989-1994 (Green 1997). In

1997,1 convinced my administrators that our school should pilot this curriculum, which made it possible to integrate the low-track algebra students with stu dents of different mathematical maturity and devel

opment levels in the same classroom and provided an opportunity for students to collaborate with each other on challenging mathematics problems.

In this curriculum, students explore complex, central problems organized into units. Each unit

integrates the use of graphing calculators with alge bra, geometry, trigonometry, and other mathematics

topics in ways that allow students to learn impor tant mathematical concepts and skills in addition

Table 1

Pilot Results _

Standards-Based Students Traditional Students

60% enrolled in a fourth-year 10% enrolled in a fourth-year mathematics class mathematics class

Average ACT score: 19.9 Average ACT score: 16.9

to various problem-solving strategies (Alper et al.

1996). Because the units combine multiple branches of mathematics, students can see how important ideas are related to each other. Since many of the central problems of the units may take six to eight weeks to solve, students undertake several smaller

problems along the way. These central problems may have connections with history, science, and literature. Many are based on practical, real-world

problems such as maximizing profits for a business or studying population growth. Others are more

fanciful and may involve a baseball pennant race or a circus act. Solving problems such as these provides opportunities that are often lacking in traditional curricula (Alperet al. 1996; Green 1997).

Several positive results came from piloting this curriculum. First, I observed that students of differ ent ability levels could explore open-ended problems together and actually learn from one another's ideas and solution strategies. Second, it became apparent that many of the students in the pilot program who

would have been enrolled in low-track algebra classes

engaged in the study of mathematics and enrolled in more mathematics classes. A greater percentage of these students continued taking mathematics classes

through their senior year than did students enrolled in the traditional algebra 1-geometry-algebra 2

sequence (see table 1). Third, average ACT scores of eleventh graders were higher in the Standards based curriculum than in the traditional curriculum.

Finally, a strong parental base formed and began to advocate for the curriculum and for the children. As a result, parents initially resistant to the curriculum

began to examine it more carefully. Since the 1997 pilot year, student enrollment in

this curriculum has increased steadily. From two classes offered during the pilot year, more than a

dozen classes were offered in the fall of 2003. In

2005, six schools in the Albuquerque area and a

dozen more throughout New Mexico offered this

program to their students.

FINAL REMARKS The question about tracking is still on the table. Does student learning and achievement increase when schools opt for heterogeneous classrooms? One thing is certain: When schools opt for heterogeneous group ing in classrooms, it is important to utilize a curricu lum designed for that purpose. A heterogeneous class room coupled with a curriculum written to engage all students is the ideal, as it promotes access to genuine

mathematics for a larger pool of students than does a

system based on ability-level tracking. The pilot cur

riculum implemented at my school has a richness that will challenge the brightest student, yet the concrete ness of the curriculum allows all students to do mean

ingful mathematical work.

30 MATHEMATICS TEACHER | Vol. 101, No. 1 August 2007



Educators must make prudent decisions that will

begin to honor student diversity as well as academ ics. All students should be allowed to demonstrate their "genius within" by being expected to partici pate in challenging and rigorous mathematics. No student in high school should be doomed to two

years of arithmetic with little opportunity to do

anything substantial. What are the true benefits of heterogeneity in our

classrooms? Put simply, it may be the life experiences students can share with one another that are not just valid but valuable. Students get less of an education when they segregate themselves for the purpose of academic enrichment. Perhaps it is just a question of time before more and more teachers, administrators, and parents begin to question and challenge the pre dominant, inequitable curriculum that exists in our schools. Only then will the vision of a quality math ematics education for all be realized.

REFERENCES Alper, Lynne, Dan Fendel, Sherry Fraser, and Diane

Resek. "Problem-Based Mathematics?Not Just for

the College-Bound." Educational Leadership 53, no.

8 (1996): 18-21.

Green, Lori. Teaching Handbook of the Interactive Math ematics Program. Berkley, CA: Key Curriculum

Press, 1997.

Kohn, Alfie. "Only for My Kid: How Privileged Par ents Undermine School Reform." Phi Delta Kappan (April 1998): 569-77.

Loveless, Tom. "The Tracking and Ability Group ing Debate." Fordham Report 2 (July 1998): 1-27.

Available at www.edexcellence.net/foundation

/ publication/publication. cfm?id=127. National Council of Teachers of Mathematics

(NCTM). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: NCTM, 1989.

-. Principles and Standards of School Mathematics.

Reston, VA: NCTM, 2000. National Research Council. Adding It Up: Helping

Children Learn Mathematics. Washington, DC:

National Academy Press, 2001.

Oakes, Jeannie, and Amy Stuart Wells. "Detracking

for High Student Achievement." Educational Lead

ership 55, no. 6 (1998): 38-41. oo

New Mexico, Albuquerque, NM

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