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• 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. She1991, 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 thatthe voices of middle school African American she realized that I had a lot of potential in mathematicsmales who have been successful in mathematics. and that I really need to use this to help me in life to getAll the voices in this article are either seventh- or further. [She thought] I was capable of doing a lot ineighth-grade students in an urban school district mathematics. That’s what really motivated me.located in the southeastern United States. Allnames 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 ofon African American male students, the Equity Prin- these are strong indicators that the teachers hadciple acknowledges that “all students, regardless of high expectations for their students.their personal characteristics, backgrounds, or High expectations can be achieved by makingphysical challenges, must have opportunities to mathematics instruction relevant and interesting forstudy—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
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 inFig. 1 Finding the mean, median, and mode heights of the Philadelphia 76ers upper-level mathematics courses.102 MATHEMATICS TEACHING IN THE MIDDLE SCHOOL
Equity Requires Resources and Support as a kind of intellectual and behavioral vibrancyfor 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 moveschools and classrooms” (NCTM 2000, p. 14). around physically in the classroom, to work inTeachers 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 notvelopment 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 whopreferences of African American students and can served as advocates and were willing to challengehelp them learn how to operate within the urban his course placement. Subsequently, Calvinclassroom. Understanding how African American gained entry into the prealgebra class the secondstudents 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 Principleembedded in their everyday contexts (Ladson- provides a vision that all students are met with highBillings 1997). Teachers need to understand their expectations in the mathematics classroom. Thisstudents’ interests and background; conse- means that teachers must make accommodationsquently, 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 equitablecussing their interests. This information can help mathematics experience for all students. Creatingteachers 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 andthat 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 AchievementRevisiting Calvin’s Story of Minority Children: New Perspectives, edited by U. Neisser, pp. 57–91. Hillsdale, N.J.: Lawrence ErlbaumCALVIN’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: Africanportunities 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