ACHIEVING EQUITY IN THE CLASSROOM: IMPLICATION FOR STANDARDS 2000
                                                    by Jamison Hughes


    The Principles and Standards for School Mathematics: Discussion Draft (Standards Draft) covers the issue of equity fairly sufficiently. The Equity Principle in the Discussion Draft states that "Mathematics instructional programs should promote the learning of mathematics by all students" (NCTM 1998, p.23). By "all students", NCTM meant 1) students who have been denied access in any way to educational opportunities as well as those who have not; 2) students who are African American, Hispanic, American Indian, and other minorities as well as those who are considered to be part of the majority; 3) students who are female as well as those who are male; 4) students who have not been successful as well as those who have been successful school and in mathematics (NCTM, 1989). The idea that stronger instructional mathematics programs exist for every student in every school would eliminate inequity is appropriate. As the Equity Principle mentions, higher expectations, recognizing diversity, and more positive role models seem to be key aspects in ridding schools of inequity. These, along with more competent teachers, are important issues that must deal with in order to make mathematics classrooms more equitable.

    While improved teaching and recognizing diversity is critical, we should also accept that students, because of that diversity, may learn differently. Because the learning of mathematics involves making mathematics meaningful to a student, we must realize that what is meaningful to one student may not be as meaningful to another student. We should adapt instruction to take into account diverse life experiences that different students have.

    Now that we have established what needs to happen, we must now ask ourselves how to achieve the necessary implementations in the schools with students that are suffering the most from inequity. We can look to the Equity Principle for some initial ideas, however, we must examine some issues deeper before we can discover any solutions.

The Problem

    There are many students who could be considered victims of inequity. However, many would argue that urban districts, and in particular African American students, are among those with the need for the most equity reform. A major part of the problem in urban school are the teachers. In urban schools up to 30 percent of teachers are not teaching in their certified field. In urban high schools, an amazing 40 percent of math teachers lack even a minor in mathematics (Dougherty and Barthe, 1997). NCTM (1998, p. 25) itself recognizes the fact that:

Schools in middle- and high-income communities are typically able to attract better qualified mathematics teachers than schools in low-income communities, and teachers in more affluent communities are more likely to have access to a variety of instructional material and good professional development opportunities. Teachers and student in middle- and high-income communities often have ready access to role models who can demonstrate the value of schooling in general and mathematics education in particular.     While the suggestions that the entire Standards Draft proposes for teaching would no doubt improve teaching, urban teachers may revert back to what is comfortable or never try what the standards document suggest. In spite of a broad range of options, there is a typical form of teaching that has become accepted as basic in urban schools (Haberman, 1998). This basic style includes giving information, asking questions, giving directions, making assignments, monitoring homework, reviewing assignments, giving tests, reviewing test, assigning homework, reviewing homework, settling disputes, punishing noncompliance, marking papers, and giving grades (Haberman, 1998). These acts are what teachers do and what students expect. In addition, this is what parents, the community, and the general public assume teaching to be (Haberman, 1998).

    Haberman (1998) wrote that there are essentially four reasons that support this type of instruction. Their "logic" runs something like this.

1) Teaching is what teachers do. Learning is what students do. Therefore, students and teachers are engaged in different activities;

2) Teachers are in charge and responsible. Students are those who still need to develop appropriate behavior. Therefore, when students follow teachers' directions, appropriate behavior is being taught and learned.

3) Students represent a wide range of individual differences. Many students have handicapping conditions and lead debilitating home lives. Therefore, ranking of some sort is inevitable; some students will end up at the bottom of the class while others will finish at the top.

4) Basic skills are a prerequisite for learning and living. Students are not necessarily interested in basic skills. Therefore, directive pedagogy must be used to ensure that youngsters are compelled to learn their basic skills.

     There are those that would argue that this system would work if the students would just accept it and work at it. But in fact, students do accept it and work at it (Haberman, 1998). If a teacher were to attempt to proceed with an assignment that involves genuine learning and disregard the preceding steps (i.e. giving information, giving directions, etc.) he or she would be met with resistance from the students. While teachers who followed this direct pedagogy would be rewarded with silence or compliance (Haberman, 1998).

    With this system in place, students actually control the behavior of their teachers. Students reward teachers by complying, and they punish by resisting (Haberman, 1998). In urban districts teachers are never characterized as incompetent when their students, who are considered deprived or disadvantaged, don’t learn. They are considered incompetent when they cannot control their students or get them to comply. Teachers, although not sensitive to it, believe that are responding to student needs, when in fact they are responding to students tactics of compliance or threats of disruption (Haberman, 1998). This type of learning exist in most schools to some extent, however, poor and minority students receive a steady unrelenting diet of mind-numbing assignments. Also, they may not have the resources in their lives to make up for the sheer boredom of these lessons (ENC, 1998 Equity).

    In short, the mathematics pedagogy for poor and minority students is restrained by the following conditions of their school experiences: 1) persistent tracking, 2) less access than other students to the best qualified teacher of mathematics, and 3) fewer opportunities to use technology in school mathematics (Piller, 1992). Each of these obstacles affects the nature of mathematics communication for the African American learner. Ultimately, the African American student is given fewer opportunities to deal with higher levels of mathematics (Secada, 1992).

Diversity among students

    Many would maintain that "good teaching is good teaching" regardless of the differences between students (Nelson-Barber and Meier, 1990). Some people feel that admitting that diverse students are different is like declaring that these students are inferior to the dominant norm (Secada, 1992). However, we must take into account the different experiences of an urban student. Many bring special problems, such as nutritional health and all of the other things that make it hard for the urban child to come to school ready to learn (ENC, 1998 Future Teachers). There are also environmental barriers that stand in the way of poverty stricken students. These include high rates of mobility, high incidences of severe emotional damage, low staff morale, and inadequate facilities (ENC, 1998 Equity).

    Through all this, there are a variety of skills that these children have that go unrecognized at school (ENC, 1998 Future Teachers). This potential barrier to mathematics communication is more directly linked to a teacher’s decisions and the teacher’s conceptions of appropriate mathematics. Stiff and Harvey (1988) argue that attempts by African American students to interject their voice in mathematics classes are often dismissed as "extraneous" matters. Also the communication process is impeded by mathematics instruction that looks to disconnect the learner from the mathematics (Ernest, 1991). Some teachers, in an effort to be color- blind, don’t acknowledge the experiences and thinking of African American Students (Tate, 1995). Teachers view color-blind instruction as fair and objective. A teacher will say, "I don’t see black or white, I only see students." While this appears to be fair and impartial, the opposite may actually be true. Assuming that students are the same presumes that student differences and inadequacies are equivalent (Tate, 1995). This may result in missed opportunities to build on experiences of students. While this practice may seem equitable, it may, in fact, produce inequality.

    Lythcott and Stewart (1995) argue that mathematics that is absent of reference to the human experience is very similar to passing down a family artifact to a ten-year-old child. Initially, the child is thrilled. After a while the child finds that very little is remembered about the importance of the artifact. In the world today, the artifact is seemingly out of place. The child is not able to place the artifact in a real experience, and as a result it does not relate to his or her life. The original meaning and importance are not there. Symbolically speaking, traditional mathematics teaching is like passing down an artifact.

    A small example can help to illustrate this point. Tate (1995) explains one situation where a teacher assumed that all students had certain experiences that were "normal." The teacher realized that it was important to develop problems that were relevant to the students’ experiences. However, she did not initiate a conversation with the students about possible problem parameters. The teacher assumed that it was normal for all students to have pumpkin pie at Thanksgiving. The teacher’s lesson plans indicated that she had spent a few days discussing the history of Thanksgiving. She constructed her mathematics lesson to include Thanksgiving and pumpkin pie as a way of joining her instruction to the student’s reality. The teacher presented her class with the following problem:

Joe has five pumpkin pies. Karis has six pumpkin pies. How many do they have all together?     Tate (1995) explains that on the exterior, the problem seems neutral, however the student response to the problem indicated otherwise. The White students in class were busy solving this, and other similar problems, using manipulatives. These students were focused on the process of obtaining mathematics knowledge with cultural context. On the other hand, an African American student in the class was quiet and seemed indifferent. There are many potential reasons why the student was not participating in the communication process. One that the teacher should have anticipated was the "plurality of difference" that each student brings to class (Tate, 1995). The teacher constructed the lesson using a cultural reference- Thanksgiving pumpkin pie. This reference was foreign to the African American student. His Thanksgiving dinner did not include pumpkin pie. Instead his family ate sweet potato pie. This teacher to recognize and build on the experience of the African American student. While this seems as though it is a minor oversight, this seems to communicate to both White and African American students about the role of mathematics in their life.

    Likewise, educators from middle class backgrounds may not be aware of the class and cultural differences that working class and poor people face in school. They may attribute students’ behavior to lack of intelligence, motivation or self-control. Often times education is focused on what disadvantaged students lack, making it impossible to see the strengths of individual students and their communities (ENC, 1998 Equity).

Solutions

    While some schools have managed to have urban students improve their scores on standardized tests, some discount this by saying that teachers were teaching to the tests and how to take these tests (Haberman, 1998). Furthermore, little knowledge was gained. The goal of equity is to help every child master high levels of skill and knowledge. The measure should be whether every child regardless of race gender, ethnicity, learning style, socioeconomic status, language, or disability does, in fact, achieve at high levels in math (ENC, 1998 Introduction). Students who have traditionally lagged behind in mathematics, will be facing new and challenging standardized test(Dougherty and Barthe, 1997). The way that minorities have been traditionally taught will not prepare them for these new and rigorous exams. Furthermore, they will be compared with their suburban counterparts who have learned in a different way since kindergarten (Dougherty and Barthe, 1997).

    Research shows that African American students bring to the formal classroom setting the same basic intellectual competencies in mathematical thought and cognitive processes as their White counter-parts (Ascher, 1983). By the time African American students reach kindergarten, they are prepared to succeed in the mathematics they will encounter in school (Stiff, 1988). The difficulty that African American students face does not reveal itself before there formal schooling starts. Therefore, the problem is attributable to the experiences that African American face in school (Stiff, 1988). This seems important because it lets us know that we can work with students who come from adverse conditions and that these students are capable of learning. Once we recognize this, we can proceed to look at some individual aspects of achieving equity.

Higher Expectations

    The Equity Principle calls for teachers to expect more from all students. Certain students, such as females, and non-white students have been casualties of low expectations (NCTM, 1998). When differences in student achievement is associated with factors such as gender, race, or economic status, we should suspect that there are biases involved in how we serve those students. Besides low expectations, there are some other biases that can adversely affect students. Giving less attention and restricting certain student from taking courses needed for college is another way in which we detrimentally affect students (ENC, 1998 Introduction). It is though these small acts of omission that we make it tougher for some students to consider themselves competent. Stiff and Harvey (1988) assert that middle school and junior high are a key time for student in their study of mathematics. This is the time teachers frequently indicate what the mathematical future holds for students. Opportunity is gained or lost based upon the decisions about courses that will or will not be taken. A poor achieving African American 17-year-old can be explained only in part by the math that he or she studied in high school. However, as explained, course enrollment in high school depends on those enrollment decisions made in middle school or junior high. The Standards Document, as a whole, if implemented, would greatly assist in raising the level of expectation for African American students. Researchers suggest alternative curricula that emphasize understanding of the math concepts, reduce emphasis placed on computational skills, support in-depth coverage of a broader range of mathematics topics, provide frequent opportunities to apply mathematical ideas and skills, and reduce the redundancy in mathematics content across the grade (Nelson-Barber and Meier, 1990). This appears to reflect the desire of the Standards Document completely.

Recognizing Diversity

    NCTM (1998) calls for teachers to "recognized and reward" strengths that diverse students bring to the classroom. We must begin to make schools work for every student. We must be familiar with a child’s diverse strengths as well as identify and eliminate that child’s inequities. Children enter the classroom with varying perspectives, values, learning styles as well as ways of showing them (ENC, 1998 Introduction). We must identify and utilize those diverse values and perspectives. While teachers and students need not share a cultural background, studies show that the degree of cultural congruence between them can have be a significant factor in student success (Ladson-Billings 1989, Nelson-Barber 1985). These studies also suggest that teachers who have succeeded with non-mainstream students often convey content specific knowledge in cultural ways. Equity requires drawing on resources that arise from such diversity, along with addressing deficits in our current methods that result in inequity.

    Furthermore, minority youths may not understand how mathematics will be of use to them in the future jobs or schooling (Stiff and Harvey, 1988). Some African American students do not know how to go about achieving their goals. They very much want to make money, however, they may not know how to go about making it.

Positive Role Models

    Not all differences in achievement can be accounted for by increased participation in higher level courses by minority students (Stiff, 1988). For example, most mathematics educators believe it is important for African American students to see examples of African Americans involved in scientific pursuits. Educators believe that African American role models will help African American students to understand that careers in science and technology are not only possible, but desirable (Stiff, 1988). Most African American students do not see themselves as scientist or mathematicians. In fact, on study showed that even Black students identified as high achievers in math by their teachers, still expressed an interest in sports, entertainment, or other non-mathematical careers (Stiff, 1988). Perhaps these careers seem more accessible to African American students because of the many role models that already exist in those fields.

    More minority teachers are needed. Despite the fact that more than one-third of America's schoolchildren are now members of minority groups, an overwhelming majority of teachers are white. In fact, 70 percent are white women. Only 13 percent are minority. Some 16 percent of the nation's public school population is African-American, but only 7 percent of its teaching force (Ruenzel, 1998).

    There is some cause for hope in this area. The number of minority students enrolling in teacher preparation programs has begun to rise for the first time in decades (Ruenzel, 1998). Beginning in the 1970s and continuing through most of the '80s, the number of African-American students interested in becoming teachers plummeted, as more lucrative professions opened their doors to blacks. But 20 percent of the students now preparing to be teachers are members of minority groups, up from 15 percent just a few years ago. African-American enrollment in teacher training programs jumped an astonishing 39 percent between 1989 and 1995 (Ruenzel, 1998).

    The reasons for the surge can be traced in part to salary improvements, intensified recruitment efforts, and a renewed societal respect for teachers and teaching. It seems as though there is a shift among young people from an individual to a more community oriented ethic. A new generation of teachers is eager to work in those communities most in need (Ruenzel, 1998).

Competent Teaching

    In order to achieve strong mathematical programs, capable teachers are a necessity. The Standards Draft itself is a prescription for teachers to follow in order to become more proficient. There are certain universal aspects of learning mathematics that are available to all children, such as learning math through understanding, and modeling strategies (Carey, Fennema, Carpenter, and Franke 1995). When connections are seen by children between intuitive and informal knowledge with formal knowledge, children learn math with understanding (Carey, et al 1995). These ideas, along with the many other suggestions presented in the Standards Draft, should equip teachers with the proper knowledge to reach all students. Competent teaching includes recognizing and including diversity in the classroom.

    In order to combat direct pedagogy and fight the habits of traditional teaching, Haberman (1998) suggest several actions that might be considered good teaching. These include getting students involved with issues they regard as vital. Help students to see major concepts, big ideas, and general principles and are not merely engage in the pursuit of isolated facts; getting students actively involved; involving students directly in a real-life experience, involving students in heterogeneous groups; asking students to think about an idea in a way that questions common sense or a widely accepted assumption, that relates new ideas to ones learned previously, or that applies an idea to the problems of living; involving students with the technology of information access. And finally, involve students in reflecting on their own lives and how they have come to believe and feel as they do. These ideas seem to mirror those of the Standards document, and if achieved, could produce more equitable classrooms.

    In summary, we must expect those who have traditionally not succeeded in mathematics to do more. We must not only recognize that all students can learn, but also recognize diversity. And with the recognition of diversity comes the realization that, because of this diversity, we must expect that students might learn and understand in diverse ways. The prospect of a new vision of mathematics education for those students traditionally left out depends on the ability of teachers, administrators, parents, and the community to support a pedagogy that allows those students to draw on, and relate, experiences from their own social environment to the mathematics learned in the classroom.

    With the realization that diverse students need to learn in diverse ways, some language could not necessarily be change, but expanded. For instance on page 26, line 28-30 (NCTM, 1998):

"Instructions programs that address both the challenges and strengths that students bring with them to the classroom are more likely to be successful." After, insert the lines: "With the acknowledgment of these diverse qualities that students bring to class, it is important to recognize the different perspectives, values, and learning styles that students retain with respect to their culture. We must adapt instruction to allow students to draw on experiences from their own social environment and relate them to mathematics."
 
 


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