Equity or Quotas in the Secondary Mathematics Classroom
Equity is not a new term nor is it a new issue, but attention to
this aspect of the teaching of mathematics and other disciplines has seemingly
grown exponentially in recent years. As enrollment in schools rose in the
1900s and mandatory attendance became law, the issue of education for all
was debated along with mental discipline and practical utility.
The document, An Agenda for Action, published
in 1980 by the National Council of Teachers of Mathematics(NCTM) showed
evidence of this concern. It discussed the need for the proper selection
of instructional materials within the recommendation for the success of
mathematics programs. It also stated that student learning should be evaluated
by a wider range of measures other than just conventional testing. There
must be a concerted effort to try and prevent instructional materials from
having sexist and/or ethnic biases. These recommendations also included
the need for more mathematics to be required by all students and a flexible
curriculum with a greater range of options be designed to accommodate the
diverse needs of the student population.
Secondary mathematics classrooms of the 1980s have been filled in the upper
grades with college intending students. As the needs of society have changed
towards more skilled jobs, the lack of mathematics has denied many individuals
from finding employment and more importantly, many employers from finding
qualified applicants. Attending college is no longer the sole route to job
satisfaction, prestige, power, or financial security. Mathematics for all
does not translate into the same mathematics for all, yet that is one interpretation
argued in the community.
The recommendations in 1980 stated that "recognizing the diversified
individual interests and needs entails devising programs that are tailored
for particular categories of students. Differentiated curricula must incorporate
the special needs in mathematics of students with handicaps, including physical
or learning difficulties. These programs need to move away from the idea
that everyone must learn the same mathematics and develop the same skills."(An
Agenda for Action , p. 18)
The student that still seems to be most neglected in the typical classroom
is the gifted student of mathematics. Outstanding mathematical ability is
a very precious resource and by the gifted student not reaching his or her
potential, it is becoming very rare as well as precious.
NCTM published the Curriculum and Evaluation Standards in 1989, and it also
addresses the need to correct some social injustices in schooling practices
of the past. Current statistics in 1989 showed that women and most minorities
study less mathematics than their white male peers. Equity has become an
economic necessity as women and minorities are becoming the majority, and
mathematical illiteracy cannot be tolerated any longer. The task is to develop
courses and programs that will allow equal opportunities for all to succeed.
Too often, this gets translated into the practice of the equal opportunity
to fail. Students are placed into courses to satisfy numbers only. Too often,
no regard to preparation or motivation was addressed, yet schools claim
the equity issue has been implemented. The job is not to just place students
in courses in equal numbers, but develop courses that show meaning to the
majority of the student population in terms of mathematical knowledge and
the need for mathematical literacy.
Research has revealed that there are differences in mathematics achievement
by race, sex, and socioeconomic status. There is evidence that white male
students are achieving at a higher level than female students. Other evidence
indicates that white students' mathematics achievement scores are above
black students and there is a correlation between socioeconomic status and
mathematics achievement. It appears that the correlation is positive, which
means that as socioeconomic status increases, the mathematics achievement
appears to increase. One must be careful not to view these classifications
in isolation, as all these variables are present within schools and are
interwoven in a very complex weave.
One model that attempts to explain these differences was published by Laurie
Hart Reyes, University of Georgia, and George M. A. Stanic, University of
Georgia, in 1988. Relationships are described among several groups of variables,
including societal influences, school mathematics curricula, teacher attitudes,
student attitudes and achievement-related behavior, classroom processes,
and student achievement. These variables are found within schools and classrooms,
outside the schools, and within the characteristics of the individuals.
The first area mentioned was the societal influence. This influence may
send different messages to and about students that differ in nature. Examples
of societal influences are the family, the community in which the student
lives, religious institutions and the mass media. These influences can and
do change, and equity in the classroom must be acceptable within this framework
to be consistent and more permanent. The problem is the inability to measure
and monitor this area, except in the indirect manner.
The second area is teacher attitudes about the aptitudes of students and
the appropriateness of their achieving at a high level in mathematics. This
also may differ based on the race, sex, and socioeconomic status of the
students. There seems to be evidence that things said and done by teachers
can intentionally or unintentionally send signals to the different groups.
There have been cases where females have been made to feel inferior and
begin to doubt themselves. Testimony at the college level stated that females
have in fact began to doubt themselves. Videotapes of classroom interaction
have found several unconscious biases. They are that 1) women are interrupted
more than men, 2) faculty members make eye contact with male students more
often than with female students, 3) faculty members are more likely to know
and use the names of their male students than of their female students,
and 4) female students are often asked fewer or easier questions than male
While each of these is not a big issue in and of itself, the cumulative
effect could be very damaging to the female student's self-esteem. This
was at the college level, but there may be similar incidents occurring at
the secondary level. People have been talking about special programs to
encourage women and minorities, but we must ensure first that the current
programs are free of this type of discouragement.
The third area is school mathematics curricula. The courses offered at the
secondary level can greatly affect the attitudes of the students, parents,
and teachers. Within the last five(5) years, a lot of secondary schools
have examined this area and have made some very important changes. Traditionally,
the secondary school would offer a progression of mathematics courses for
the college bound student and busy work or more of the same drill and practice
mathematics for the other students. Consider the following finding in 1984:
As the proportion of black students in the school population increases,
the likelihood of the mathematics curriculum containing lower level courses
increases; as the proportion of white students in the school population
increases, the likelihood of higher level mathematics courses increases.
While graduation requirements in the state of Georgia remained at two(2)
mathematics courses to graduate, this tendency seemed to occur. Several
movements in the nation and the state of Georgia have helped alleviate this
problem. The state of Georgia changed the graduation requirements from any
two(2) mathematics courses to a minimum of three(3) with Algebra I or its
equivalence necessary. In addition, the Schools that Work movement has redefined
non-college bound courses to mean different, not lower. Non college bound
students tended to take mathematics courses that continued to drill and
practice skills that have been covered during the first six(6) years of
their education. Both teacher and student were bored with the continual
repetition and frustration of not mastering manipulation and rote memory
skills. Fortunately, schools are starting to eliminate these general mathematics
classes with success. The NCTM standards of allowing students to experience
higher mathematics concepts rather than stagnant a student based on non-mastery
of manipulation and memorization has finally begun to emerge.
The fourth area is student attitudes and achievement-related behavior. As
stated earlier, all areas are interwoven, and this one especially relates
to the last one discussed. Examples of student attitudes toward the subject
are confidence in learning mathematics, perceived usefulness of mathematics,
beliefs about the appropriateness of mathematics as an area of study, and
attributions of success and failure in mathematics. Examples of student
attitudes toward the social are attitudes toward other students and toward
teachers. Some examples of achievement-related behavior are persistence,
independence, and deciding to enroll in optional mathematics courses.
Confidence in learning mathematics dealt with how sure a student is of his
or her ability to learn and perform well in mathematics. Confidence is important
because it has a significant positive correlation with mathematics achievement,
because it is one of the strongest attitudinal predictors of mathematics
course taking, and because sex differences in confidence are usually associated
with sex differences in mathematics achievement. Technology has played a
major part in this area. Students have been given the power to obtain answers
quicker and with speed that has given them a confidence never seen before.
Calculators in the classroom have made it possible for the students that
do not memorize well to have the same speed as those who were quick at recalling
and reciting mathematics facts. Technology has helped boost the confidence
level of the students almost to a degree that is dangerous. Students tend
to have too much confidence through the technology, and the task of learning
how to check for reasonableness of an answer becomes a higher priority.
Some of the "better" students actually see the technology as a
threat to their ability to stand out in a mathematics classroom, as speed
is no longer their advantage. Other students can come up with answers just
as quick and sometimes quicker, and since technology helped them arrive
at the solution, they are very willing to share the solution without fear
of being incorrect. This is due to the their perception that the technology
got the answer and not them.
Students also vary in how useful they view mathematics to be, both for their
current needs and for the future. Again technology has helped equalize students
in this area as skills using technology is a growing vocation, and students
are very aware of the technology revolution. The redesigning of the courses
taken by students based on their future goals have helped alleviate the
tracking concept of smart, dumb, and dumber. Real changes have been attempted
to have the mathematics meet the needs of college-bound, vocational-bound,
and work-bound. The courses are not designed with the goals of watering
down the content but ensuring students are given the tools to be useful
mathematics users in the pursuit of further education and employment. Along
with the redesign of courses came the large task of educating the public.
A student that chooses not to attend college should not have any negative
stigma attached to his or her academic ability. This corresponds with the
societal influences mentioned earlier.
Another essential part of the model is the classroom processes. Classroom
processes include interactions between teachers and students and between
fellow students. Teachers seem to form a small group of "target"
students within their classrooms, intentionally or otherwise. The teacher
tends to call on this group whenever an attempt is made to form important
connections between topics. Moreover, teachers are often unaware that they
have concentrated on a "target" group and that it was usually
dominated with males. This was because the process of classroom interaction
is unconscious, and teachers respond automatically to students that demand
attention. Males demand more attention, complain more that they are not
receiving enough, and their teachers and female peers expect them to get
Evidence exists that males and females tend to approach learning from different
perspectives, although the reasons for the differences continue to be debated.
In the classroom, females prefer a conversational style that fosters group
consensus and builds ideas on top of each other; the interrelationalship
of thoughts and actions is paramount. Males, conversely, learn through argument
and individual activity. While it has been discussed that most classroom
discourse is organized to accommodate male learning patterns, this is changing
through the development of block schedules and cooperative learning. This
shifting of classroom practice of collaborative thinking helps female learning
as the importance that women place on mutual support, building collaborative
knowledge, and applying it practically is being emphasized and the importance
of individual expertise and debating abstract concepts is being de-emphasized.
In an effort to promote equal access to mathematics achievement, a first
step is attitude change. If parents believe that their daughters can succeed
in mathematics and master technology, they will provide them with toys that
promote mathematics learning readiness and will encourage them to sustain
their perseverance in mathematics courses. If teachers understand and respect
female learning styles, they will alter classroom discourse to accommodate
girls' participation and provide a message to both males and females that
no single learning behavior is superior to another.
Equally important are concrete changes in teaching methods and curricula.
Cooperative learning that promotes collegiality between male and female
students is one approach. Structuring lessons around the thinking processes
needed to arrive at answers to questions rather than focusing solely on
the answer itself is another. Mathematics problems can reflect girls' experience
(although they should not be limited to stereotypically female concerns,
such as cooking and sewing) and can emphasize practical, real life applications.
In one effort to improve equity in the classroom, the College Board's EQUITY
2000 districtwide K-12 education reform model has hit more than 2000 teachers
with its powerful staff development. Dramatic changes in teachers' and counselors'
attitudes toward students' capabilities and opportunities to learn were
revealed in surveys following staff training. After three years of implementing
the program demonstration, it seems that staff development has begun to
make a difference.
Examining the material reveals success in making sixth and seventh graders
believe they can excel in college-prep classes through the use of extensive
support systems. The support comes from a variety of supports - such as
early morning tutoring, encouraging asking questions in class, finding someone
to be a study buddy, and personal pep talks given by the teachers periodically.
The documents refer to providing support necessary for each individual
student. A schedule is blocked out so a student has a teacher or counselor
nearby at all times. The school gave him an extra period to work. Basically,
the school arranges the student schedule to help him be successful. Through
the literature, it appears that taking geometry and the higher college-prep
mathematics courses is the measure of equity. The question that needs to
be answered seems to be "Why must success academically only be measured
by college-prep courses?". I am not sure I agree society should strive
for an educational system that defines equity by supporting each student
to the degree necessary to go to college. Attending college does not necessarily
equate to success, and rather than continually trying to think of our educational
system as factory that produces college-bound students, I think it would
serve the students better to give them the support necessary to achieve
their maximum potential.
In conclusion, educational reform and equity have accomplished great feats
in the recent years. NCTM and the publications published by that organization
have given the educational community an excellent source to help measure
the classroom teacher's ability to allow all students to excel. Assessment
has become the most recent frontier that equity has begun debate. Teachers
are studying and self-evaluating the tools presently being used for assessment.
Teachers are examining them as instruments that accurately measure student
understanding without having built-in biases that hinder equity. I recently
conducted research using the results of the Georgia Graduation Test of the
students at Elbert County Comprehensive High School. The analysis was to
determine if there was any evidence of a difference in academic achievement
between the males and females. The evidence showed that there was no statistically
significant difference between the groups. Further study is needed to determine
if there would be a difference based on race and/or socioeconomic status.
Even with this information, I hope to begin collecting personal classroom
data to determine and evaluate my efforts to promote equity. The only way
true equity will ever occur is by having each teacher start in his or her
classroom and reflect on all aspects of interaction between the student
and teacher and student with peers that promote equity of opportunity and
not quotas of numbers.