Achieving success with African American learners: a framework for culturally responsive mathematics teaching.

For decades, one of the biggest challenges facing the United States has been that of providing equitable education for all students. Today, more than 50 years after the famous Brown vs. Board of Education Supreme Court decision, which legally ended school segregation based on race, urban schools are more segregated than ever (Ladson-Billings, 2004). Large numbers of minority students in impoverished neighborhoods endure the greatest injustices. The school buildings often are dilapidated and have fewer resources than those in wealthier neighborhoods, and the schools experience lower student achievement and higher dropout rates. Each year, these schools receive fewer qualified teachers, and seem to become more invisible to the school system (Kozol, 1995, 2005). Student achievement data show the effects of this negligence, illustrating that students of color, particularly African American males, are falling behind in nearly every academic category (Ferguson, 2000; Noguera, 2003), regardless of their socioeconomic status.

Within schools, dominant norms and ways of teaching are often based in white culture, mirroring Euro-centric norms. The resulting practices contribute to cultural incongruities in classrooms and schools, leading students of color to perform below their potential. In turn, teachers assume deficits in students of color (Delpit, 1992) and, over time, varied ethnic practices and ways of learning are deemed inappropriate. These negative beliefs may be validated, reinforced, and even exacerbated among colleagues, as the majority of the teaching force, particularly at the elementary level, is white, female, and middle class (Howard, 2006), and most have limited interactions with individuals from diverse backgrounds (Nieto, 1999).

Inconsistencies in school versus home culture (e.g., how learning is assessed, how information is acquired) contribute to students' academic struggles (Boykin, 1986; Spindler, 1987). As such, teachers must consider that poor "test scores and grades [among students of color] are symptoms, not causes, of achievement problems" (Gay, 2000, p. 16).

In response to low achievement among particular groups, inequitable tracking practices are adopted. Students who do not conform to a particular set of cultural behaviors are often placed in the lowest tracks. This trend is evidenced by the overrepresentation of students of color in special education (Gay, 2002), increased drop-out rates among students of color (Montecel, Cortez, & Cortez, 2004), and growing achievement gaps that exist between these groups and their white (European American) counterparts. These gaps are particularly marked in mathematics (Howard, 2006), and mathematics instruction to students of color is often tarnished by lowered expectations, actions that reinforce racial stereotypes, and generally ineffective teaching methods (Irvine & York, 1993). Indeed, "The mathematics classroom is one of the most segregated places in America" (Stiff, 1990).

CULTURALLY RESPONSIVE TEACHING

Successful teachers of African American students have been shown to "bring diverse family histories, value orientations, and experiences to students in the classroom, attributes often not found in textbooks" (Pang & Gibson, 2001, p. 260), helping students to bridge the home-school cultural gap. These educators have strong ties to the black community (Ladson-Billings, 1994) and maintain a strong academic focus while helping students to develop self-awareness, self-confidence, and leadership skills (Foster, 1987). African American children have been shown to respond in a positive manner to "warm demanders" (Ware, 2006), or those teachers who engage students through the use of high expectations, firm and authoritative classroom management, and culturally familiar communication patterns (Ross, Bondy, Gallingame, & Hambacher, 2008). Identifying these attributes is helpful; however, it has remained difficult to describe the whole practice of a culturally responsive teacher in the context of mathematics.

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AN ILLUSTRATION OF CULTURALLY RESPONSIVE MATHEMATICS TEACHING

This article presents a working theory meant to help teachers and teacher educators conceptualize culturally responsive mathematics teaching (CRMT). Grounded in the work of Ms. Johnson (a pseudonym), a highly effective mathematics teacher in a largely African American, high-poverty school, this theory can guide teacher efforts to help students of color succeed in mathematics classrooms. Given the complexity of mathematics classrooms, it is difficult to capture every detail of teacher practice. Major themes in Ms. Johnson's teaching and practice, which were extracted through observations, interviews, and artifact collection, have been organized into the following graphic (Figure 1) in an effort to capture the complex and fluid nature of CRMT.

Knowledge

Clearly, teachers must have vast funds of knowledge. In mathematics, pedagogical content knowledge is essential. Ms. Johnson exhibits a deep understanding of mathematics, making it possible for her to deconstruct difficult concepts, analyze student errors, and contextualize important mathematical ideas. Moreover, this knowledge is often accessed "in action," and mathematical knowledge is activated in the course of teaching (Ball & Bass, 2000) in appropriate ways that allow for student-driven changes in direction and maximum student understanding.

Also evident in Ms. Johnson's knowledge base is a clear and profound understanding of her students' lives, cultures, and interests. It has been shown that successful teachers of African American students often use their cultural knowledge to refer to metaphors and family ties when presenting material, indicating a strong, almost familial, relationship with their students (Foster, 1997; Ladson-Billings, 1994). A product of the neighborhood in which she teaches, Ms. Johnson is able to relate mathematics to student lives in a non-superficial manner. For example, when describing to students how to find a least common multiple or denominator, she refers to the two numbers in question as "big brother" (8, for example) and "little brother" (4, for example). She then relays a story about big brother coming to the school to pick up little brother and the two walking home together. "When you see them coming down the street" she says, "who do you see first?" The children respond in unison, "Big brother!" She continues, "So what is the LCM?" to which the children respond, "8!" She probes the students for reasoning, asking, "How do you know?" to which the students respond, "Because they are related!" When asked for a specific strategy that shows how they figured out that the two numbers are related, the students chant, "When you count by 4s you say 8!"

Ms. Johnson has tapped into several cultural realities of her students' lives. First, in this neighborhood, the older siblings frequently care for the younger siblings. She has based her story on an understanding of a familial tie that is central to many of these children's lives. Connecting related numbers to related family members is effective for this population, and strategy repetition helps students to make this connection. Furthermore, Ms. Johnson has employed a call-response structure, engaging the whole class at once and maintaining a clear academic focus.

Communication

Ms. Johnson's cultural knowledge allows her to effectively communicate ideas to students. She uses a specific vernacular when speaking with students, and employs familiar patterns of interaction in her mathematics les sons. This helps to lessen the cultural disconnect that many African American students face in school. As demonstrated in the above example, use of chants and call-response techniques can be effective. Ms. Johnson also uses rhythms, music, and dance in her teaching, helping students to remember mathematical concepts in culturally relevant ways. In order to choose music for her lessons, Ms. Johnson consults with students to determine what songs are currently popular. "If they can sing along with the radio and learn all those songs," she says, "they can learn math in the same way." This interconnection of culture and cognition is believed to lead to academic success and empowerment (Allen & Boykin, 1992).

Deeper societal issues are also communicated in Ms. Johnson's classroom. It is clear to each student in her class that she genuinely cares for them and has their best interests in mind. Her caring attitude is complemented by a demanding and strict environment. This type of instruction is often referred to as "warm demander pedagogy" (Ware, 2006), and has been shown to be highly effective in evoking positive responses from African American students. These communication patterns mirror those that students experience in their own homes. It is clear from the first day of school that Ms. Johnson has high expectations for her students. She begins teaching from the back of the book so that students will encounter the most difficult concepts first. Students who are not striving for excellence are immediately set straight. If a student in Ms. Johnson's class forgets his math journal, for example, she immediately walks the child to the office to call home and gives the student a choice. If they know where the binder is, they must ask someone to come bring it to the school. If they do not, they must tell their parent that they came to school unprepared and then hand the phone to Ms. Johnson.

Students respond to this type of demanding behavior because they realize that Ms. Johnson believes that they can do more and can excel. In turn, students begin to believe it of themselves. This corroborates the idea that a teacher's belief that his or her students can achieve success in making sense of complex ideas has a positive effect on students' long-term achievement (Love & Kruger, 2005). Ms. Johnson's students clearly gain confidence throughout the school year, and often leave 5th grade as empowered learners and individuals. Such transformations are hallmarks of culturally responsive teaching (Gay, 2000).

Relationships/Trust

Over time, Ms. Johnson has built relationships in the community surrounding the school. She has taught several generations from some neighborhood families, and often visits student homes. She is also very active in her church, which draws from the same population. Moreover, her record of success has brought a new sense of empowerment to the community. After learning with Ms. Johnson, students who had been placed in lower tracks throughout their education are suddenly in honors classes, and students who have never spoken in class before are singing and chanting along with Ms. Johnson. She demands a lot from her students, but the pride she shows in them in return alters their self-perceptions.

Successful practices in the classroom, coupled with community involvement and familial relationships, have resulted in an immensely trusting relationship between the neighborhood and Ms. Johnson. Parents trust that Ms. Johnson will do whatever is necessary to help the children succeed, and they know that their students will emerge from the demanding environment as stronger individuals and learners. Ms. Johnson ensures that students will be able to get help with math homework at home by holding evening classes for parents. She teaches the parents using similar mathematical strategies so that they will be on the same page as their children when working at home. Further, parents gain essential knowledge that they might not otherwise have had access to, creating a more academic focus in individual homes.

Relationships are built with students at various points as well. Each year, Ms. Johnson is in charge of the 5th-grade play, which she writes, directs, and choreographs. She also has created a rite-of-passage event called the Evening of Elegance. Students are asked to dress formally, and each is presented to parents and community members by their homeroom teacher. A large meal is shared and students often perform their class song. Ms. Johnson understands that such rituals are important to students, and she enjoys the pride they show when involved. Since many students at the school are from low-income families, Ms. Johnson provides dresses or suits to those in need.

Constant Reflection and Revision

Successful teachers are always looking for new and improved ways to make mathematics accessible to students, and Ms. Johnson is no exception. The rate at which this reflection and revision process takes place is astonishing; the process is constant and ongoing. For example, Ms. Johnson might try out a strategy with her first class of the morning. If she feels the pulse of the group is positive and responsive, she might deem the strategy a success, but slightly tweak it for the second class. By the end of the day, she has perfected her technique and shares the revisions with her early classes the following day. On other days, she makes adjustments on the spot. If she tries out a certain rhythm, for example, but the students are not fully connected, she will adjust the rhythm or strategy until she feels their full engagement.

Standardized test scores and teacher-made assessments are also utilized in this revision process. If Ms. Johnson notes during grading work that many students have missed a concept that she taught in a particular way, she will go back and re-teach until she discovers a method that makes the concept accessible to all students. The strategy may change from class to class or year to year, but her commitment to the children drives her to continuously engage in this process. In Figure 1, this piece of Ms. Johnson's instruction is captured through the connectors and arrows that have been used to indicate constant movement.

The Cycle of Pedagogy and Discipline

When observing in Ms. Johnson's classroom, it is nearly impossible to tease out discipline and instruction as distinct entities. The two are so intertwined that they become indistinguishable. Essentially, Ms. Johnson's culturally based teaching techniques largely control discipline, and any issues that arise are immediately addressed. This cycle is central to her practice, and, as indicated by the graphic, is focused on the needs of the students.

In classroom practice, this cycle allows Ms. Johnson to maintain a strict academic focus in her classroom, instilling in her students a drive to succeed. One hallmark of her instruction that contributes to the cyclical nature of her practice is constant concept review. Each day, Ms. Johnson teaches a new mathematical idea, and then she orally (using call-response, chants, movement, etc.) reviews many of those that have been covered in previous days. At any point in the class, she might ask students for an old definition or for the solution to a problem relating to any of the past concepts they have covered, keeping all content at the forefront. Students might learn the concept of decimal addition on a given day, then briefly review mixed numbers, area, and perimeter, only to end class by doing the geometry dance. This continuous review process allows students to immediately and internally access information at any time, which is especially important when preparing for high-stakes tests. When students are taking such assessments, an observer may see a student bobbing his head in order to remember a rhythm or another student moving her hands slightly to remember a concept taught through movement. Student results on such assessments have been some of the best in the state for many years.

The various arrows in Figure 1 are meant to show movement and connections. As indicated, the student is at the center of Ms. Johnson's practice, with the cycle of pedagogy and discipline most immediately affecting the learner. The student is constantly engaged in some portion of this continually moving cycle. The outer "layer," which houses the cornerstones of communication, relationships, knowledge, and reflection, represents the larger environment created by Ms. Johnson. In this setting, students continually encounter cultural familiarities and may experience a change in self-concept. These cornerstones keep students engaged in the cycle of learning.

SETTING THE STAGE FOR CRMT

It would be impossible for any teacher to exactly emulate Ms. Johnson, and the goal of this research is not to simply clone someone who is successful with a particular population. Rather, this beginning theory about CRMT can help teachers to find their own teaching styles and practices, keeping in mind the overarching ideals that create responsive and academically focused mathematics classrooms in largely African American schools. Such guidelines might help educators to bridge gaps between home and school that exist for students of color. Moreover, given the complicated, fluid nature of culturally sensitive mathematics classrooms, it is imperative that we put forth what such environments (and the educators who create them) might look like in action.

Ultimately, the theoretical underpinnings of CRMT allow teachers to recognize cultural incongruities as a cause of the achievement gaps, thus providing appropriate interventions. Too many current pedagogical solutions in schools focus on standardized testing as the root of the problem and result in prescribed curricula focused around these assessments. When we consider the cultural discrepancies at the heart of the problem, it becomes clear that dictated pedagogy and curricula may actually exacerbate the achievement problems of students of color. In altering current practice, however, we may begin to bring equity back to mathematics classrooms.

References

Allen, B. A. & Boykin, A. W. (1992). African American children and the educational process: Alleviating cultural discontinuity through prescriptive pedagogy. School Psychology Review, 21(4), 586-596.

Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), Multiple-perspectives on the teaching and learning of mathematics (pp. 83-104). Westport, CT: Ablex.

Boykin, A. W. (1986). The triple quandary and the schooling of African-American children. In U. Neisser (Ed.), The school achievement of minority children: New perspectives (pp. 56-88). Hillsdale, NJ: Lawrence Erlbaum Associates.

Delpit, L. D. (1992). Education in a multicultural society: Our future's greatest challenge. Journal of Negro Education, 61, 237-249.

Ferguson, A. (2000). Bad boys: Public schools in the making of black masculinity. Ann Arbor, MI: University of Michigan Press.

Foster, M. (1987). Effective black teachers: A literature review. In E. R. Hollins, J. E. King, & W. C. Hayman (Eds.), Teaching diverse populations (pp. 225-242). New York: SUNY Press.

Foster, M. (1997). Black teachers on teaching. New York: The New Press.

Gay, G. (2000). Culturally responsive teaching: Theory, research, and practice. New York: Teachers College Press.

Gay, G. (2002). Culturally responsive teaching in special education for ethnically diverse students: Setting the stage. Qualitative Studies in Education, 15(6), 613-629.

Howard, G. R. (2006). We can't teach what we don't know: White teachers, multiracial schools. New York: Teachers College Press.

Irvine, J. J., & York, D. E. (1993). Teacher perspectives: Why do African American, Hispanic, and Vietnamese students fail? In S. W. Rothstein (Ed.), Handbook of schooling in urban America (pp. 161-173). Westport, CT: Greenwood Press.

Kozol, J. (1995). Amazing Grace: The lives of children and the conscience of a nation. New York: Crown Publishers.

Kozol, J. (2005). Theshame of the nation: The restoration of apartheid schooling in America. New York: Crown Publishers.

Ladson-Billings, G. (1994). The dreamkeepers: Successful teachers of African American children. San Francisco: Jossey-Bass.

Ladson-Billings, G. (2004). Landing on the wrong note: The price we paid for Brown. Educational Researcher, 33(6), 3-13.

Love, A., & Kruger, A. C. (2005). Teacher beliefs and student achievement in urban schools serving African American students. The Journal of Educational Research, 99(2), 87-98.

Montecel, M. R., Cortez, J. D., & Cortez, A. (2004). Dropout-prevention programs: Right intent, wrong focus, and some suggestions on where to go from here. Education and Urban Society, 36(2), 169-188.

Nieto, S. (2002). Language, culture, and teaching: Critical perspectives for a new century. Mahwah, NJ: Lawrence Erlbaum.

Noguera, P. A. (2003). The trouble with black boys: The role and influence of environmental and cultural factors on the academic performance of African American males. Urban Education, 38(4), 431-459.

Pang, V. O., & Gibson, R. (2001). Concepts of democracy and citizenship: Views of African American teachers. The Social Studies, 92(6), 260-266.

Ross, D. D., Bondy, E., Gallingane, C., & Hambacher, E. (2008). Promoting academic engagement through insistence: Being a warm demander. Childhood Education, 84, 142-146.

Spindler, G. D. (Ed.). (1987). Education and cultural process: Anthropological approaches (2nd ed.). Prospect Heights, IL: Waveland.

Stiff, L. (1990). African-American students and the promise of the curriculum and evaluation standards. In T. J. Cooney (Ed.), Teaching and learning mathematics in the 1990s (pp. 152-158). Reston, VA: National Council of Teachers of Mathematics.

Ware, F. (2006). Warm demander pedagogy. Urban Education, 41(4), 427-456.

Emily P. Bonner is Assistant Professor, Curriculum and Instruction, Department of Interdisciplinary Learning and Teaching, University of Texas at San Antonio.