1) The document discusses the story of Calvin, an African American male student who excelled in mathematics but was denied entry into a pre-algebra class due to concerns about his behavior from his teacher. 2) It summarizes the NCTM's Equity Principle which calls for high expectations, worthwhile opportunities, and accommodating differences for all students. 3) It provides perspectives from several African American male students who were successful in mathematics, discussing the importance of teacher expectations and additional academic support programs.

1. R O B E R T Q. B E R R Y I I I
The Equity Principle through the
SPOTLIGHT
ON THE
PRINCIPLES Voices of African American Males
ALVIN IS A SIXTH-GRADE AFRICAN ers identified students eligible to take a mathemat-
C American male student in a school district in
the southeastern United States. As an elemen-
tary school student, Calvin earned the highest
level of achievement on his state’s standard-
ized mathematics test in grades 3, 4, and 5. In addi-
tion, he scored in the 98th percentile on the Iowa
Test of Basic Skills in mathematics. On all objective
ics placement test to gain entry into an upper-level
prealgebra mathematics course for sixth graders.
Calvin was upset because he was not selected and
because others that he considered not as “good at
math” were selected to take the test. Calvin’s
mother inquired about the selection criteria for
taking the placement test and discovered that
measures in mathematics, Calvin performed well Calvin met all criteria except one—the teacher rec-
and, in most cases, excelled. In addition, he earned ommendation. Calvin’s fifth-grade teacher indi-
A’s and B’s consistently in mathematics. Calvin cated that although Calvin scored well on assess-
stated that mathematics is his favorite subject and ments, his behavior and his inability to sit still
that mathematics comes naturally to him and is would not make him a good candidate for prealge-
easy. He loves challenging mathematics problems bra in sixth grade. In a conference with the middle
and mathematics puzzles. school guidance counselor, Calvin’s mother asked
Calvin’s mother acknowledges that her son is in about prealgebra placement. The guidance coun-
need of a variety of types of stimulation to prevent selor responded that she would not want to place
boredom. She also stated that Calvin needs to feel Calvin in a class that he could not pass. The coun-
that his teachers are interested and care about him selor assumed that Calvin would not pass the class
to be productive in class. Both Calvin and his and did not consider his previous performance.
mother admit that he can be a handful in class. His The principal at the middle school evaluated
behavior is not always that of a model student; how- Calvin’s situation and argued that prealgebra is a
ever, they believe his behavior is well within accept- rigorous course for sixth-grade students and that
able classroom norms. only disciplined students are capable of passing
At the end of fifth grade, Calvin was excited this course. Even though Calvin had performed
about going to middle school. At that time, teach- well in mathematics throughout his schooling,
school personnel focused their attention on behav-
ROBERT Q. BERRY III, rqberry@odu.edu, is an assistant pro- ior rather than achievement when evaluating his
fessor of mathematics education at Old Dominion University, academic potential. When the sixth-grade school
Norfolk, VA 23529. He is interested in equity issues in mathe- year began, the prealgebra class contained no
matics education and mathematics as a social construct. African American male students (Berry 2003).
Unfortunately, Calvin’s story is not unique.
Edited by JENNIFER BAY-WILLIAMS, jbay@ksu.edu, who African American males are often confronted with
teaches undergraduate and graduate mathematics education lowered expectations even when they have shown
courses at Kansas State University, Manhattan, KS 66506. that they are capable of high achievement. If
teachers, administrators, and school districts are
“Spotlight on the Principles” focuses on the six overarching serious about understanding the needs of all stu-
Principles for grades 6–8 found in NCTM’s Principles and dents, then they should critically assess possible
Standards for School Mathematics (2000). The articles systemic beliefs that impede access of African
discuss how these principles relate to middle grades mathe- American male students to challenging and upper-
matics and suggest ways that teachers might incorporate level mathematics courses. The NCTM acknowl-
them into their instruction. edges that African American students have been
100 MATHEMATICS TEACHING IN THE MIDDLE SCHOOL
Copyright © 2004 The National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved.
This material may not be copied or distributed electronically or in any other format without written permission from NCTM.

2. • Equity requires accommodating differences to help
everyone learn mathematics (NCTM 2000, p. 13).
• Equity requires resources and support for all
classrooms and all students (NCTM 2000, p. 14).
Equity Requires High Expectations and
Worthwhile Opportunities for All
HIGH EXPECTATIONS IN MATHEMATICS LEARNING
are communicated in the ways that school person-
nel interact with students through their words and
actions (NCTM 2000). High expectations are com-
municated in the ways that teachers interact with
students during instruction, through the comments
they write on students’ assignments, and through
the support they provide for high levels of achieve-
ment. When asked, “How does a mathematics
teacher show that he or she cares about you?” Bilal
and Darren recognized that the positive interaction
they had with their respective mathematics teach-
ers had a positive impact on their mathematics per-
formance. Bilal’s comments follow:
One teacher that really stands out is Ms. Williams. Unlike
other teachers, Ms. Williams always stayed on me about
getting my work done. If I didn’t apply [myself] or didn’t
do [my work], she would tell me that I could do better.
She demanded nothing but my best. She really cared
about me.
Darren expressed these thoughts about his
teacher:
underserved in school mathematics (NCTM 1989, My teacher, Ms. Blaine; she cared about all of us. She
1991, 1995, and 2000). The focus of this article is to would bend over backwards to help us when we needed.
spotlight the NCTM’s Equity Principle through She really helped me; she talked to me and told me that
the voices of middle school African American she realized that I had a lot of potential in mathematics
males who have been successful in mathematics. and that I really need to use this to help me in life to get
All the voices in this article are either seventh- or further. [She thought] I was capable of doing a lot in
eighth-grade students in an urban school district mathematics. That’s what really motivated me.
located in the southeastern United States. All
names of individuals are pseudonyms. The students refer to caring not only as an affective
Principles and Standards for School Mathematics connection between teachers and students but also
(NCTM 2000) highlighted equity by making it the as the willingness of the teacher to help students,
first principle for reform of school mathematics: the positive classroom interactions between teach-
“Excellence in mathematics education requires ers and students, and the belief that teachers com-
equity—high expectations and strong support for all municate to students that they are capable of per-
students” (p. 12). Although the focus of this article is forming well in the mathematics classroom. All of
on African American male students, the Equity Prin- these are strong indicators that the teachers had
ciple acknowledges that “all students, regardless of high expectations for their students.
their personal characteristics, backgrounds, or High expectations can be achieved by making
physical challenges, must have opportunities to mathematics instruction relevant and interesting for
study—and support to learn—mathematics” students. By doing this, students may be motivated
(NCTM 2000, p. 12). Principles and Standards offers to do well in mathematics and see the utility of con-
a broad view of what it takes to accomplish equity: tinued mathematics study for their own futures
(NCTM 2000). When asked to talk about his mathe-
• Equity requires high expectations and worth- matics class, Phillip discussed how his teachers
while opportunities for all (NCTM 2000, p. 12). made mathematics interesting, relevant, and fun:
V O L . 1 0 , N O . 2 . SEPTEMBER 2004 101

3. Mr. Wallace, he basically explains things so that you can un-
derstand it and he gives you a lot of examples and a lot of dif-
JERSEY HEIGHT IN FEET HEIGHT IN FEET
ferent situations. He uses everyday life situations; the news-
NUMBER PLAYER AND INCHES (USE DECIMALS)
paper, anything he could find at his house, and sports. Most
of the time, he likes to use basketball [see fig. 1]. I like my
sixth-grade math teacher, Ms. Burns, she did the same
thing. . . . Ms. Burns used pictures to teach some math con-
cepts. . . . Both of them [teachers] made it exciting and fun.
Equity Requires Accommodating Differences
to Help Everyone Learn Mathematics
ACCOMMODATING FOR DIFFERENCES MEANS
recognizing that all students should have access to
an excellent and equitable mathematics program
that is responsive to their prior knowledge, intellec-
tual strengths, and personal interests (NCTM
2000). Consequently, students having trouble in
mathematics need additional learning opportunities
and resources, such as after-school programs. Like-
wise, students with a special interest or exceptional
talent in mathematics may need enrichment oppor-
tunities to challenge or engage them. Jabari dis-
cusses how his mathematics teacher is always avail-
Directions: able to meet the needs of her students:
Go to the NBA Web site (www.nba.com/).
Click on “Teams” to find the listing of NBA teams; choose When the students need help, she takes time out of her
busy schedule to help tutor. She is available after-school
Philadelphia.
and sometimes she gets to school early to tutor kids. A
Click on “Players,” then “Roster” to find data about each
couple of months ago, she used to come to school on the
Philadelphia 76er. weekends to help tutor. She stopped because she started
Complete the chart above. taking a class every Saturday.
1. What is the height of the shortest Philadelphia 76er’s Additional academic support beyond the classroom
player? (This number is the minimum.) _______________ can contribute to the development of positive learn-
2. What is the height of the tallest Philadelphia 76er’s player? ing habits and serve as an indicator that teachers
(This number is the maximum.) __________________ care about students’ learning and understanding
3. Find the difference in heights between the shortest and mathematics. Additional learning opportunities in
tallest players. (This number is the range.) _____________ mathematics help prepare students to gain access
4. Organize the heights of the players from shortest to tallest. into upper-level mathematics courses. Below, Jabari
5. What height occurs the most? (This number is the mode.) discusses the additional learning opportunities he
__________________ had with a precollege program:
6. What height is in the middle of your organized list? (This I have been a precollege student since the sixth grade. I
number is the median and the second quartile.) _________ like being in the program, but sometimes it is hard for me
to get up early for Saturday Academies. During the sum-
7. Divide your organized list into halves.
mer after my seventh-grade year, I participated in the pre-
8. What height is in the middle of the top half of your orga- college program’s Middle School Summer Scholars
nized list? (This number is the third quartile.) __________ (MSSS) program. The MSSS focused on mathematics and
9. What height is in the middle of the bottom half of your or- science. We visited a chemistry laboratory, did laboratory
ganized list? (This number is the first quartile.) _________ experiments, and participated in a mathematics bowl.
10. Find the sum of the heights of the players. _____________
11. Since there are 15 players, divide the sum of the heights Participation in programs such as the precollege
by 15 to find the mean height of a Philadelphia 76er. program described by Jabari can serve as a motiva-
__________________________ tor. Such programs could broaden African Ameri-
can males’ involvement with mathematics. In addi-
tion, it could broaden the pool of students in
Fig. 1 Finding the mean, median, and mode heights of the Philadelphia 76ers upper-level mathematics courses.
102 MATHEMATICS TEACHING IN THE MIDDLE SCHOOL

4. Equity Requires Resources and Support as a kind of intellectual and behavioral vibrancy
for All Classrooms and All Students evidenced by engagement in high-energy activi-
ties and having an affinity for change and stimula-
“ACHIEVING EQUITY REQUIRES A SIGNIFICANT tion. To deal with verve, teachers need to plan op-
allocation of human and material resources in portunities in mathematics for students to move
schools and classrooms” (NCTM 2000, p. 14). around physically in the classroom, to work in
Teachers need help to understand the strengths groups, to share their thinking, and to provide op-
and needs of students who come from diverse cul- portunities that challenge the students’ thinking.
tural backgrounds (NCTM 2000). Professional de- Calvin’s story suggests that his behavior was not
velopment for teachers is a resource that can in- respected in the mathematics classroom. Fortu-
form teachers of the cultural style and learning nately, Calvin had a parent and a teacher who
preferences of African American students and can served as advocates and were willing to challenge
help them learn how to operate within the urban his course placement. Subsequently, Calvin
classroom. Understanding how African American gained entry into the prealgebra class the second
students learn is an important variable of effective week of the new school year.
teaching. Research on the learning preferences of Although Calvin is an African American male stu-
African American students suggests that mathe- dent, many other students in mathematics class-
matics instruction for these students needs to be rooms share his experience. The Equity Principle
embedded in their everyday contexts (Ladson- provides a vision that all students are met with high
Billings 1997). Teachers need to understand their expectations in the mathematics classroom. This
students’ interests and background; conse- means that teachers must make accommodations
quently, this may mean doing things with stu- for the diverse student population they teach. In ad-
dents that are not mathematics—interviewing dition, teachers must be provided with the neces-
them, having them write autobiographies, and dis- sary resources and support to provide an equitable
cussing their interests. This information can help mathematics experience for all students. Creating
teachers develop mathematical links with their mathematics classrooms in which all children re-
students’ daily lives and interests. Akil’s response ceive high-quality mathematics instruction is an at-
to the question “How does a mathematics teacher tainable goal if the Equity Principle is intercon-
show that he or she cares about you?” suggests nected with the other areas of Principles and
that his teacher had taken an interest in his expe- Standards (NCTM 2000).
riences and background:
Seventh-grade class was the one I like the best because References
[of] the teacher and the students. It was an advanced
class and there were a lot of students in there who had the Berry, R. Q., III. “Voices of African American Male Stu-
same abilities and that pushed me to try to do well. At the dents: A Portrait of Successful Middle School Mathe-
beginning of the school year, she had lunch with groups matics Students.” Unpublished PhD diss., University
of students so that she could know us . . . she asked us of North Carolina at Chapel Hill, 2003.
questions about things we like to do. Boykin, A. W. “The Triple Quandary and the School of
Afro-American Children.” In The School Achievement
Revisiting Calvin’s Story of Minority Children: New Perspectives, edited by U.
Neisser, pp. 57–91. Hillsdale, N.J.: Lawrence Erlbaum
CALVIN’S STORY IS AN EXAMPLE OF HOW EDUCA- Associates, 1986.
tional gatekeepers set up barriers to limit the op- Ladson-Billings, Gloria. “It Doesn’t Add Up: African
portunities of African American students. Unlike American Students’ Mathematics Achievement.” Jour-
the other voices in this article, Calvin was met nal for Research in Mathematics Education 28 (Decem-
with lowered expectations and with people who ber 1997): 697–708.
lacked interest in his background. The use of a National Council of Teachers of Mathematics (NCTM).
teacher’s recommendation as a major factor for Curriculum and Evaluation Standards for School Math-
placement in mathematics courses presents seri- ematics. Reston, Va.: NCTM, 1989.
ous limitations because the teacher may not have ———. Professional Standards for Teaching Mathematics.
a strong understanding of a student’s background Reston, Va.: NCTM, 1991.
and may not respect a student’s cultural ways of ———. Assessment Standards for School Mathematics.
knowing, or may be considering behavior as a re- Reston, Va.: NCTM, 1995.
flection of ability. Calvin possessed what Boykin ———. Principles and Standards for School Mathematics.
(1986) describes as verve. Boykin describes verve Reston, Va.: NCTM, 2000.
V O L . 1 0 , N O . 2 . SEPTEMBER 2004 103