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Tensions Faced by Mathematics Professional Developers



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Tensions Faced by Mathematics Professional Developers

I recently worked on a research project in which I was the facilitator of a middle school mathematics professional development course, InterMath Rational Numbers, and part of a research team examining InterMath through a National Science Foundationfunded project, Does It Work?: Building Methods for Understanding Effects of Professional Development (DiW). In my position as one of the InterMath facilitators for the DiW project, I took a leading role in tailoring the original InterMath syllabus to meet the needs of the DiW project and the participating teachers. While the course was a great experience for me, it also brought up several tensions that, I suspect, often exist in mathematics education at all levels. In particular, there were several goals in the course that did not appear to be in opposition, yet led to many tensions in my actual practice. After describing my experience I will pose several questions to the mathematics education community about the interwoven, yet sometimes conflicting, goals we often have for our classes. Four common recommendations for effective professional development (PD) include a focus on mathematical content, the use of activities that actively engage teachers in learning, planning for sustained time to learn, and developing a community of learners (e.g., Garet et al., 2001; Guskey, 2003; Sowder, 2007). However, little has been written about the tensions that arise for the mathematics professional developer who is attempting to balance content coverage with elements of effective PD. I felt that the InterMath (IM) syllabus gave me the time and opportunity to balance all four PD recommendations. Hence, my goal was to be as true to the modified syllabus as possible. Nonetheless, as the weeks passed, the pressure to examine all of the content topics started to come into conflict with my desire to balance the other elements of effective PD. I wanted the course to be successful not only for the participants, but also for the DiW research project. This meant I wanted to ensure quality content coverage for the DiW research project, make the course engaging, and support the development of a community of learners for the teachers. In this commentary, I use literature and personal experience to describe the tensions between the different PD goals and pose questions to the mathematics education community for consideration about PD aimed at building teachers’ mathematical content knowledge.

Effective Professional Development

Many studies have shown the need to meet with teachers multiple times to have the greatest impact on teacher learning and change in teaching practice. Garet et al. (2001) found time span and contact hours were important features in PD because both of these measures had a positive influence on opportunities for active learning and focus on content knowledge. Garet et al. found “professional development is likely to be of higher quality if it is both sustained over time and involves a substantial number of hours” (p. 933). Additionally, Banilower, Heck, and Weiss (2007) found the effects of PD to be the greatest when contact hours were high. Their results suggested that if contact time was between 32 and 80 hours teachers would gain the most from the PD. Besides contact hours, this recommendation implies activities designed for teachers should be high quality (focusing on active engagement with content knowledge). Guskey (2003) noted, “although effective professional development clearly requires time, it also seems clear that such time must be well organized, carefully structured, and purposefully directed” (p. 12). Thus, the challenge for professional developers is to ensure that sufficient time is being spent on each mathematical concept. While the IM course included 40 contact hours, well within the recommended 32 to 80 hours, I still struggled with how to distribute the time allotted to various mathematical content. An important guideline for PD is to focus on specific content (Guskey, 2003; Sowder, 2007). Garet et al. (2001) reported that PD focusing on content knowledge “is more likely to produce enhanced knowledge and skills” (p. 935). Research has also supported the notion that focusing on improving teachers’ content knowledge in PD has the potential to Rachael Eriksen Brown is a mathematics program officer at the Knowles Science Teaching Foundation. Her research interests include community building and professional development. positively impact student learning (Hill, Rowan, & Ball, 2005). Cohen and Hill (2000) found empirical evidence to support content knowledge as the focus of PD in changing teachers’ practices, noting, “It seems to help to change mathematics teaching practices if teachers have even more concrete, topic-specific learning opportunities” (p. 312). Rational numbers is an important topic in middle grades mathematics in the United States, and research has shown teachers’ understandings of these concepts are generally not strong (e.g., Ma, 1999; Post, Harel, Behr, & Lesh, 1998). Because of this, the DiW team focused the IM course on this topic. The assumption was that an increase in teachers’ mathematical knowledge for teaching would translate into a positive impact on their teaching practices and their students’ understanding of mathematics. The team decided on three themes for IM: referent unit, drawn representations, and proportionality.1 Thus, consistent with recommendations for effective PD, IM explicitly focused on mathematical content. For the professional developer, focusing on content means planning activities where mathematics is the focus, and supporting and encouraging teachers as they engage in the mathematics that they teach. For example, Kazemi and Franke (2004) studied a group of teachers who used students’ written work as a springboard for discussing their students’ responses to a problem provided by the facilitator. The facilitator’s role was to press teachers to focus on student strategies and propose strategies the teachers did not suggest. They observed that the facilitator was able to help guide the direction of the meetings and assist the group in maintaining a focus on students’ mathematical work. My goal was to press the teachers to remain focused on mathematics and actively engaged in the selected mathematical tasks while also keeping them engaged on working to develop community. The need for PD to help activate knowledge in the participants, not to deliver knowledge, was a common theme in Wilson and Berne’s (1999) review of PD literature. Active learning in PD includes working together, sharing ideas and strategies, and becoming reflective practitioners. In IM, teachers worked in pairs and as a whole group on cognitively demanding tasks focused on rational numbers. By using these tasks, we were addressing many of the PD recommendations: having the teachers engage with mathematically demanding problems, work collaboratively, and do so over a sustained period of time. Professional developers “engage them [teachers] as learners in the area that their students will learn in but at a level that is more suitable to their own learning” (Wilson & Berne, 1999, p. 194). Thus the professional developer has to support teachers in acknowledging their lack of understanding on material they are responsible for teaching, while motivating them to engage with the mathematics they are to learn. Without teachers being willing to engage as learners, IM would have been a failure because the design of the course was dependent on the teachers working together on tasks with little to no direct instruction from me. Borko and Putnam (1995) noted successful PD provides “opportunities for teachers to construct knowledge of subject matter and pedagogy in an environment that supports and encourages risk taking and reflection” (p. 59). This characteristic includes developing an intellectual space where teachers can make public their understandings, as well as misunderstandings. Community building activities are common experiences in PD that supports meaningful interactions between participants and the facilitator, and building community is an important component of effective PD. In Kazemi and Franke’s (2004) study, the teachers began to develop norms about what it means to teach and learn from each other based on their examination of student work. This development of norms was related to the community building of the group and their active engagement in examining students’ mathematical work. Active learning lends it self to creating a community of practice as teachers are given opportunities to explain, compare, and contrast mathematical strategies for solving tasks as a group. Because of my passion for community development, this was important to me as I planned IM. The design of the modified syllabus for the IM Rational Numbers course was especially important because the pacing and tasks allowed me time and opportunity to build a community. For example, there was time at the beginning of the course for me to lead a discussion about the expectations participants had about IM, myself as the facilitator, and themselves as participants. In addition, I felt passionate about all the tasks and the sequencing of the concepts. When learners are producing high-quality materials and are engaged in mathematical discussion, the facilitator is, at least implicitly, working to build a community. I felt confident that the syllabus would allow for both adequate time on mathematically-focused activities and community building, hence balancing all four recommendations.

Tensions

As the facilitator I felt a constant tension between my intentions of increasing participant’s mathematical content knowledge (the explicit goal of IM) and building a mathematical community of practice (my personal goal as facilitator). Balancing community building and pushing the participants’ mathematical knowledge was a challenge. I also felt tremendous responsibility to keep the teachers satisfied with the experience in order to continue to motivate them to engage deeply with the mathematics together. For me, part of the satisfaction would be to continually relate what they were experiencing to their own classroom practices. This meant being explicit about how my actions could be replicated in a classroom of middle grades students. Finally, the pacing of the PD and my knowledge of teachers’ understanding provided a tricky dilemma for me to navigate. One of the principal ways I tried to build community was by fostering productive conversations as we debriefed our mathematical work on tasks in the whole group setting, but I rarely had enough time for all the tasks and conversations I had planned. Thus, I was faced with making decisions about doing more tasks to meet the goal of developing content knowledge versus doing fewer tasks and having longer conversations about them to meet my goal of building community. The tension between building the teachers’ mathematical knowledge and building community was overwhelming at times and made me feel like I was unable to be successful on either front. In one of my journal entries I wrote, “There is so much that we needed to talk about and do but we didn’t have time. I’m concerned because we move on to division of fractions next. I feel like I’m leaving many participants with holes in their knowledge.” Because of the time crunch and the tug I felt between debriefing the mathematics and debriefing our conversations, I never explicitly addressed my community building efforts with the participants. Although I praised the group at the conclusion of a good conversation, we never discussed what made those conversations special in terms of either building a community or developing mathematical knowledge. Despite my efforts to balance building content knowledge with building community, there were times when one goal dominated my decision-making in our class meetings. This leads to another tension I faced about how explicit to be about what I was asking them to do as the facilitator and the success we were having in learning about rational numbers. Clearly, I struggled to do this related to community. But the time limits also impacted how often we could discuss how what they were experiencing could be implemented in their classrooms. This was important to me because I saw it as a component of active learning. For example, the National Council of Teachers of Mathematics (NCTM) has been promoting a vision of the ideal mathematics classroom as one where teachers “establish and nurture an environment conducive to learning mathematics through the decisions they make, the conversations they orchestrate, and the physical setting they create” (NCTM, 2000, p. 18). One goal of mine was to provide an example of learning in this environment. How explicit should I be about how I did this? In the end, there was little time during class to have these conversations. By not finding the time to discuss our own practices as a community, the teachers were unable to reflect as a group on the behaviors and actions that supported our development of a nurturing, mathematical environment. When working with the teachers in small groups, I would ask about their classrooms and students and suggest that what I was doing could be done in their classrooms. Reflection components were part of the course; teachers were asked to do a ticket out the door after each class meeting and were interviewed by a researcher each week about the course. Through these reflections, teachers did think about my role as the facilitator. For example, one teacher said, “She has the approach that you know the answers, there are no right or wrong answers. But everyone should be able to learn from each other. And she tries to make sure that she is not the center focal point, is the center focal point, that it is on us, the students” (King, Week 8). The teachers, however, rarely made connections between what they were experiencing and their own classrooms in the phone interviews or in our class discussions. IM engaged teachers in exploring high cognitive demand tasks related to rational numbers, and at times these tasks pushed the participants to their mathematical limits, which was often uncomfortable. This discomfort was not surprising, as research has shown that exploring rational number concepts is often an uncomfortable enterprise (Armstrong & Bezuk, 1995; Ma, 1999). The discomfort had the potential to inhibit our work together because participants might have been reluctant to expose the gaps in their knowledge to their peers, particularly because those peers taught in the same district. The participants, however, worked through this discomfort and grew to expect it when working together in IM. For example, one task the teachers were asked to work on had a lower cognitive demand. The participants noticed the change in the nature of the task because they expressed concern that the task felt too easy, and they were sure they had missed something. The tension I then faced was determining whether to continue to follow the syllabus despite my growing awareness of teachers’ misconceptions about rational numbers and their willingness to continue to engage deeply with the mathematics. This tension speaks to the recommendation for sustained time to learn. If I forged ahead, how would that affect the quality of our mathematical work? If I remained focused on the same content, would the teachers continue to be actively engaged in the material? This tension was complicated by the fact that the PD was being offered as part of a research project and the district had been promised a specific course. Thus, as a larger team, the decision was made to continue following the pace of our syllabus.

Concluding Remarks

Despite the tensions I felt as the facilitator, IM was a success. Not only did the teachers report being happy with the experience, but the increase in the average score on the pre-assessment and the post-assessment of their mathematical knowledge for teaching rational numbers was statistically significant. More specifically, nine participants had a significant increase in their scores. In addition to the quantitative data, there was qualitative evidence that teachers grew in their understanding of the three themes of IM— referent unit, drawn representations, and proportion— and that the class was able to form a community of practice. Further analysis is being conducted on other aspects of teacher learning in IM. I was able to learn more about myself as an educator and about the challenges faced by facilitators as they attempt to focus on increasing mathematical knowledge and community building. The tensions faced by the professional developer who is balancing the development of mathematical knowledge and following guidelines for effective PD are not trivial. I would like to challenge the mathematics education research community to seriously consider the potential tensions faced by the mathematics educator who finds herself managing these dual, sometimes opposing, goals. I pose the following questions for consideration: 1. How does this tension influence the professional development experience? 2. What can we learn about teaching, in general, from our experiences as facilitators? 3. What can we learn about community building? 4. What does the facilitator learn through this experience? How does it impact how she conducts the PD? 5. How can these understandings be translated to classroom teachers’ experiences? As our understanding of PD grows (including learning of teachers, fidelity of programs, and essential features for effectiveness), we need to consider how the simple decision to facilitate the PD being examined influences all who are involved in the experience.



Acknowledgments

The work reported here is supported by the National Science Foundation under grant number DRL 0633975. The results reported here are the opinions of the author and may not reflect those of NSF. I wish to thank the Does It Work team for their support and particularly Chandra Orrill, Soojin Lee, and Andrew Izsák for help with collecting data and supporting instruction. Additionally, I would like to thank Denise Spangler Mewborn, Sandra Geisler, Katy Ulrich, and Allyson Hallman for their help with earlier drafts of this commentary.



References

Armstrong, B. E., & Bezuk, N. (1995). Multiplication and division of fractions: The search for meaning. In J. T. Sowder & B. P. Schappelle (Eds.), Providing a foundation for teaching mathematics in the middle grades (pp. 85–120). Albany, NY: State University of New York Press. Banilower, E. R., Heck, D. J., & Weiss, I. R. (2007). Can professional development make the vision of the standards a reality? The impact of the National Science Foundation’s local systemic change through teacher enhancement initiative. Journal of Research in Science Teaching, 44, 375–395. Borko, H., & Putnam, R. T. (1995). Expanding a teacher’s knowledge base: A cognitive psychological perspective on professional development. In T. R. Guskey & A. M. Huberman (Eds.), Professional development in education: New paradigms and practices (pp. 35–65). New York: Teachers College Press. Cohen, D. K., & Hill, H. C. (2000). Instructional policy and classroom performance: The mathematics reform in California. Teachers College Record, 102, 294–343. Garet, M. S., Porter, A. C., Desimone, L., Birman, B. F., & Yoon, K. S. (2001). What makes professional development effective? Results from a national sample of teachers. American Educational Research Journal, 38, 915–945. Guskey, T. R. (2003). Analyzing lists of the characteristics of effective professional development to promote visionary leadership. NASSP Bulletin, 87(637), 4–20 Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42, 371–406. Kazemi, E., & Franke, M. L. (2004). Teacher learning in mathematics: Using student work to promote collective inquiry. Journal of Mathematics Teacher Education, 7, 203– 235. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachersunderstanding of fundamental mathematics in China and the United States. Mahwah, NJ: Erlbaum. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author. Post, T., Harel, G., Behr, M., & Lesh, R. (1988). Intermediate teachers knowledge of rational number concepts. In E. Fennema (Ed.), Papers from first Wisconsin symposium for research on teaching and learning mathematics (pp. 194– 219). Madison, WI: Wisconsin Center for Education Research. Sowder, J. T. (2007). The mathematical education and development of teachers. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 157– 223). Charlotte, NC: Information Age Wilson, S. M., & Berne, J. (1999). Teacher learning and the acquisition of professional knowledge: An examination of research on contemporary professional development. Review of Research in Education, 24, 173–209. Referent unit referred to the whole for a given quantity. Drawn representations included array models, area models, single number lines, double number lines, tables, and graphs. These representations were intended to be used to reason about a given problem, not just as a picture of the solution. Proportionality referred to multiplicative reasoning in fraction and decimal operations as well as situations involving direct and inverseproportions.


  • Inequity in Mathematics Education: Questions for Educators

Many years ago I encountered a diagram (Figure 1) that may be familiar to you. It was used to help teachers understand that student learning depended upon the relationship between the teacher, the student, and mathematics. Although I found it helpful in thinking about my teaching, I eventually realized that there are many more triangles that affect student learning. One can draw triangles with students, teachers, parents, school board members, legislators, etc. Figure 1. The relationship between the teacher, the student, and mathematics. Figure 2 is another way of acknowledging that there are many factors that affect student learning and the well-publicized acheivement gap between students from different ethnic and socio-economic groups. The student/teacher/mathematics triangle is located in a classroom, in a school, in a district, in a community that is situated in a larger society. People in this community and in the larger society hold beliefs, attitudes, values, and often deep emotions about a variety of issues—teaching, learning, assessment, the nature of mathematics, the nature of schools in a democratic society, race, class, gender, sexual orientation, culture, and language—to name a few. In this article I will pose some questions and offer some thoughts about how some of these beliefs, attitudes, values, and emotions affect inequity in mathematics education.1 The first question concerns mathematics and culture. Is mathematics culture free? Some people say that mathematics is a set of eternal truths that humans discover. Others maintain that it develops from human social interaction—as all other forms of knowledge do. For example, Paul Ernest points out, “The basis of mathematical knowledge is linguistic knowledge, conventions and rules, and language is a social construction” (1991, p. 42). It is not my intent to settle this dispute in this article. If mathematics is not culture free, however, then one might wonder: Would mathematics be different if male European culture had not become the dominant force in the world? Since mathematics develops in part to solve the problems of society, the culture of a society at least influences the course of mathematical development. Although this influence may seem far removed from the classroom, as soon as we start talking about mathematics problems, we are close to classroom issues. I think immediately of the distinguished mathematician George Polya (1887–1985), a strong advocate for developing a pedagogy of mathematical problem solving. He wrote “An essential ingredient of the problem is the desire, the will and the resolution to solve it. The problem that you are supposed to do and which you have quite well understood is not yet your problem. It becomes your problem, you really have it when you decide to do it.” (1962, p. 63) This comment as useful to solve problems that are important to them, I lose a powerful motivational tool—and often lose lots of students. Since I do not want to lose students, I ask: How do teachers and curriculum developers present problems that are likely to become the students’ problems? This question is closely related to culture, because the culture you grow up in affects what problems engage you. As Steig Mellin-Olsen put it, the probability that a topic “is recognized as important by a pupil is dependent on how he relates it to matters influencing his total life situation” (1987, p. 35). Mellin-Olsen gives three criteria for facilitating the development of this relationship: (See Weissglass, 1991, for a review of Mellin-Olsen’s book.) 1. Mathematics is presented both with regard to the individual history of the student and the history of the culture from which the student comes. 2. Learning a skill occurs in the context of a wider project of interest to the learner. 3. Learning occurs within the context of cooperation. The gains of the individual feed the gains of the group. Although young people are inherently curious about mathematics when they enter school, most do not maintain this curiosity. So we can ask: How do educators’ culture, class, and gender affect their ability to develop and communicate problems so that students desire to solve them? Herein lies a major challenge. Growing up in U.S. society often causes white middle class children to be misinformed or ignorant about history and the lives of people with different backgrounds than themselves. Since most curriculum developers come from this pool, the concerns of racial and ethnic minorities are often ignored in curriculum. Even the most progressive curricula usually do not relate mathematics to the concerns of students who are living in poverty. Curriculum developers often choose problems that are “safe” and uncontroversial, routinely neglecting issues related to social justice. As Kastberg pointed out in a previous issue of this journal, the writers of the NCTM Principles and Standards for School Mathematics (2000) “ignore the power that mathematics can have in debate and discussion of issues critical to the elimination of social and economic inequities in the United States” (Kastberg, 2001, p. 18).

CLASSROOM

SCHOOL

DISTRICT

SOCIETY

BELIEFS, ATTITUDES, VALUES, EMOTIONS ABOUT TEACHING LEARNING ASSESSMENT RACE CLASS GENDER ROLE OF SCHOOLS MATHEMATICS COMMUNITY LANGUAGE CULTURE . . . SEXUAL ORIENTATION

Figure 2. The many factors that affect student learning. 36 The leads me to another question: How does a student’s culture, class, and gender affect whether the problem becomes her or his problem? The first time I taught a class in mathematics for future elementary teachers, I chose a book that used counting problems to motivate the study of number systems. Many of the examples consisted of counting the number of different poker hands. These problems did not interest my students, 95% of whom were female. Mathematically the book was very sound, but it did not work for my students. The lesson for me was that just because I think a mathematical problem is fascinating does not mean that my students will find it so. If I do not enable my students to see mathematics Julian Weissglass is Professor of Education at the University of California Santa Barbara. He received his Ph.D. in Mathematics from the University of Wisconsin, Madison and was a member of the UCSB Mathematics department for over 30 years. He is currently director of the National Coalition for Equity in Education and is most interested in developing leadership for educational equity. Sometimes students are told blatant falsehoods. For example, attempting to situate an algebra lesson in a historical situation, the authors of a highly-regarded eighth grade mathematics text wrote, “When Mexico ceded California to the United States in 1848, California was a relatively unexplored territory with only a few thousand people” (Lappan, Fey, Fitzgerald, Friel, & Philips, 1998, p. 5). In fact anthropologists estimate that there were approximately 150,000 indigenous people in California at that time. Furthermore, to say that “Mexico ceded California to the United States” without mentioning that the U.S. military was encamped outside Mexico City ready to conquer the whole country is misleading. It is akin to saying that in the 17th century large numbers of Africans came to North America to help grow cotton, without mentioning slavery. Because I suspect that curriculur materials might change if the community of curriculum developers were more diverse, we can also ask the following: How do we increase the percentage of people of color in curriculum development groups? Responding to this question is beyond the scope of this article, but I conjecture that it will require an effort similar to the one I recommend later for schools. If you accept that culture, class, and gender affect teachers and students in the math classroom, then you are ready for the next question: How do racism and classism affect the school experiences of students? Since racism and classism are words that have different meanings for people, let me define what I

mean by them.2 Racism is the systematic mistreatment of certain groups of people (often referred to as people of color) on the basis of skin color or other (real or supposed) physical characteristics. This mistreatment is carried out by societal institutions or by people who have been conditioned by the society to act, consciously or unconsciously, in harmful ways toward people of color. Similarly, classism is systematic mistreatment based on socioeconomic status. This mistreatment includes prejudice, discrimination, disrespect, or neglect of rational needs (food, clothing, shelter, communication, opportunities to learn, etc.) The racism and classism pervasive in U.S. society influence the attitudes that people develop. Teachers carry these attitudes with them into their classroom. For example, they may have different expectations for individuals from different groups. But the situation is more complex than that. I cannot, in this article, fully explain how racism and classism and other forms of systematic mistreatment work in schools, but let me at least point out that they can be blatant or subtle, personal or institutionalized, conscious or unconscious. The perception of whether an act is blatant or subtle will vary from person to person. If a teacher or a textbook author limits themselves to problems or situations that avoid social justice issues, someone might say that that is subtle classism. On the other hand, a person who is suffering the effects of classism might see that action as a blatant. Similarly, a policy at the institutional level can contribute to the systematic mistreatment of a group even though no one consciously attempted to hurt them. For example, California implemented a class size reduction policy a few years ago. It caused an immediate teacher shortage and many experienced teachers from inner cities in California took jobs in the suburbs, probably because they thought it was easier to teach there. The result was that students in inner city schools were being taught by less experienced teachers. The effects on poor students and students of color were severe—an example of unconscious institutionalized racism/classism. There is a general principle at work here. Whenever policy deliberations do not include an informed consideration of how racism/classism operate in society, the policy developed will probably not be for the long-range benefit of people of color and people in poverty and will often work to their disadvantage. There are many examples of the blatant racism in the history of the United States—slavery, lynching, segregation, discrimination in housing. It was perfectly respectable for academics (including eminent scientists) in the 1920s and 1930s to join the eugenics movement, which was based on an ideology of racial superiority (See Gould, 1981; Tucker, 1994). For example, Edward East, a Harvard geneticist, wrote: “Gene packets of African origin are not valuable supplements to the gene packets of European origin; it is the white germ plasm that counts” (1927, p. 199). But these pseudoscientific ideas have not disappeared. In a well-publicized book in 1994, the authors wrote “Putting it all together, success and failure in the American economy and all that goes with it, are increasingly a matter of the genes that people inherit” (Herrnstein & Murray, p. 91). While discussing this book a mathematics professor told me, “Anyone who is intelligent has made his way out of the working class.” We like to think things have gotten better, and I believe that in many ways they have—but I am white and middle class. Two examples from California, separated by almost 70 years, suggest that perhaps racist practices and policies have just become subtler. In a 1923 address to the Los Angeles Unified School District principals the Superintendent, Susan B. Dorsey, said “We have these Mexican immigrants to live with and if we can Americanize them, we can live with them.” (García, 2001, p. 51). In 1991, a superintendent of a school district in northern California said, “We’ve got to attend to the idea of assimilation and to make sure that we teach English and our values as quickly as we can so these kids can get in the mainstream of American of life” (p. 51). Many people have a different perspective on culture. César Chávez, for example, said, “Preservation of one’s own culture does not require contempt or disrespect for other cultures” (Chicano Studies Research Library, 1996). Racist/classist practices do not have to be overt. Ignoring issues of race and class are widespread. For example, at the National Summit on the Mathematical Education of Teachers (co-sponsored by the National Science Foundation [NSF], the Exxon Mobil Foundation, and the Conference Board of the Mathematical Sciences) in November 2001, only one of the titles and abstracts made even a passing reference to the challenges of teaching “algebra for all”. None mentioned the challenges of teaching mathematics to a culturally diverse student population or to language minority students. None addressed how teachers’ expectations and belief systems affect the teaching and learning of mathematics, or any of the other issues that are related to the achievement of under-represented students in mathematics. Were these omissions subtle or blatant, conscious or unconscious? From my point of view, the silence was deafening. Evaluation (assessment) methods are another area where racist/classist practices may not be overt. I wonder: How much of the assessment system is driven by (unconscious) race and class bias? Ubi D’Ambrosio, the Brazilian mathematics educator, points out, “… mathematics has been used as a barrier to social access, reinforcing the power structure which prevails in the societies (of the Third World). No other subject in school serves so well this purpose of reinforcement of power structure as does mathematics. And the main tool for this negative aspect of mathematics education is evaluation.” (1985, p. 363) Many mathematics educators find this statement puzzling. How can evaluation (assessment) be used as a barrier to social access? Consider the following: 1. The nature of the instrument may incorporate cultural values and practices—such as being able to respond quickly on timed tests or being good at figuring out how to eliminate answers in multiple choice questions. 2. Previous experiences with being asked questions and riddles and being rewarded for the right response, might be valued in upper-class and middle-class homes more than it is in working class or poverty-stricken homes. 3. The test-taking environment might work to the disadvantage of students from different cultural and class groups by causing different levels of anxiety. In regard to the third point, social psychologists have shown that the performance of members of nearly any stereotyped group can be negatively affected by manipulating (sometimes very subtly) the conditions of the testing environment (through instructions or questions given to the test-takers) to bring to consciousness or sub-consciousness one’s membership in that group. For example, Steele and Aronson (1995) found that African American college students performed significantly worse than Whites on a standardized test when the test was presented as a diagnosis of their intellectual abilities, but about as well as Whites when the same test was presented as a non-evaluative problem-solving test. Other researchers (Croizet & Claire, 1998; Shih, Pittinsky, & Ambady, 1999) produced similar results with different groups. Social psychologists use the term stereotype threat to describe this phenomenon. I prefer the term internalized oppression—the phenomenon of people believing in the messages they receive from society and, as a result, acting in hurtful ways to themselves. A Latino principal talking on a Personal Experience Panel at an institute conducted by the Equity and Mathematics Education Leadership Institute (EMELI, n.d.) sheds some light on the process: …it happened slowly and you know what’s going on but you can’t understand it. …like the SRA, the reading classes. …there’s different colors [for different levels]. I was always in the lower one. I was treated a little bit different again because I was in this lower group and I started noticing a lot of my buddies were in the same group I was in and a lot of the other kids that were usually quiet were in the higher groups and you start kind of feeling a little bit less. You start feeling less about yourself. …as I went into high school, they have the tracks A, B, and C. And C is just one step above Special Ed. And again, I was in the C group and my buddies were in the C group with me. You know…people treat you differently. As I got into college I always felt inadequate, not being capable to do these things. Experiencing racism (or other forms of mistreatment) outside of school can also affect school performance. A Japanese American teacher speaking on a Personal Experience Panel recounted a memory when the parents of a white girl he met did not allow her to date him. He continued: That’s pretty much the age when my whole attitude toward achievement changed. Before then I had been very competitive…striving to be the top student by taking at least eight classes a day and going to special GATE type programs on weekends and summers. I was president of many extracurricular clubs. I ran for student body offices, played in the jazz band, did athletics, and gave speeches in every oratorical contest I could find. A year later, my final schedule consisted of coming to school at 11 AM for two classes and basketball practice. I went out with the boys every evening and weekend. …I was very lucky not to be expelled for drinking (as my two buddies were). (See Weissglass, 1997, for the more complete story.) So I ask: Can we change racist/classist practices in schools and eliminate (or at least alleviate) the effects of racism and classism on students? I think we can, but good intentions, hard work, excellent curriculum, or research, will not be sufficient. Significant change in people’s beliefs, attitudes, and practices only comes through a complex process of sense-making, reflection, and re-evaluation of existing practices and understandings. This process of reevaluation is facilitated by being listened to and releasing emotions about the experiences that formed our beliefs, attitudes, and behavior patterns. Shirley Chisholm points out, “Racism is so universal in this country, so widespread and deepseated, that it is invisible because it is so normal” (1970, p. 133). Therefore, we need school communities where it is safe enough for the invisible to be made visible—where Whites can listen to people of color talk about how they and their ancestors have experienced racism and where people of color can listen to Whites talk about how seeing racial prejudice has affected them. Listening to each other’s stories and emotions helps people identify what needs to change within their institutions and themselves. Being listened to will help them heal from the hurts of racism. Professional therapists are not necessary, nor are there enough of them to do the job. It is one of our responsibilities as educators to heal ourselves from the damage racism has done. However, there is a tendency among educators to dismiss healing from hurt as too “touchy-feely” to belong in academic institutions.3 But consider that this country has spent hundreds of millions (perhaps billions) of dollars in the last two decades on attempts to decrease the differential success in mathematics between students from different ethnic groups without any major change on the national level. It is clearly time to risk new approaches. The National Coalition for Equity in Education (NCEE, n.d.) has developed a theory and a set of structures and approaches that help educators productively address racism, classism, and other forms of bias.4 Three (of the twelve) assumptions underlying the work of NCEE are: · No one is born prejudiced. · All people are deeply hurt by growing up in a racist and classist society. · Many of the assumptions, values and practices of people and institutions hinder the learning of students of color and students from low-social economic classes. Let me emphasize the first assumption. I believe that human beings are good. No one would hurt another person or participate passively in a hurtful system unless they had been hurt. Nevertheless, unequal access to resources, violence and threats of violence, miseducation, lies, stereotypes, and disrespect (some of which are carried out, and others accepted, by educational institutions) cause great harm to people of color and people living in poverty. If we avoid facing this we are silent bystanders—contributing by our silence to the perpetuation of racist and classist practices. I propose that we adopt a new paradigm for our schools: schools as healing communities. People in such schools will undertake a wide range of anti-bias work. Educators will identify how their unconscious bias is affecting their students and challenge any low expectations they or their colleagues hold. Parents and teachers will work together to support children’s learning. Members of the community will identify how bias is institutionalized in policies and practices and they will work for change. Teachers will question their curriculum and pedagogy and make it more engaging to students of different cultures. Schools will teach the history of how oppressed peoples have been treated in this country. They will support students and their families to challenge internalized oppression. Students will talk about and heal from how they experience unfairness and discrimination. A healing community will have as its highest priority people caring about students and their learning. True learning, as contrasted with rote memorization for rapid recall, will increase. Achieving such communities will require leadership—a different kind of leadership than in other reform areas. The issues related to racism, classism, and other forms of bias are complex and emotional. Some people, for example, will not recognize racism or classism. Some may deny that they interfere with their relationships (“I don’t see color”; “I treat everyone the same”) or affect institutional or governmental policies. People of color may feel hopeless or cynical about the possibility of change. They may be skeptical of Whites making a commitment to combat racism. Students and teachers may be fearful of talking honestly about racial or class issues. Leaders will need to understand the personal, social, and institutional roots of inequities. They will be able to raise controversial issues while building unity, relate well with people from different backgrounds, help people recover from hopelessness and powerlessness, and deal constructively with their own and others’ emotions. These skills and knowledge are not routinely developed in schools or colleges or in professional development. Creating healing communities will require resources. Not allocating these resources will be even more costly in the long term. It is easier for educators to hold a workshop celebrating diversity, develop curricula, buy “test-prep” programs, pressure teachers, or write reports and vision statements than to talk about personal experiences with race and class. But any reform effort attempting to reduce the achievement gap that does not get at the roots of racism/classism will not be likely to succeed over time. If, as a nation, we develop healing communities where people can speak honestly about racism/classism and heal from their hurts, we can change biased practices, attitudes, and policies. If we can communicate caring to students, and help them recover from racism/classism, they will be able to achieve their full human potential. If we do all this, we will accomplish more than reducing the achievement gap in mathematics. We will create a better society.

REFERENCES



Chicano Studies Research Library. (1996, June). Sï Se Puede! Cesar E. Chavez and His Legacy. Retrieved from http://clnet.ucr.edu/research/chavez/quotes/cult.htm Chisholm, S. (1970). Unbought and unbossed. Boston: Houghton Mifflin. Croizet, J. C., & Claire, T. (1998). Extending the concept of stereotype threat to social class: The intellectual underperformance of students from low socioeconomic backgrounds. Personality and Social Psychology Bulletin, 24, 588-594. D’Ambrosio, U. (1985). Ethnomathematics and its place in the history and pedagogy of mathematics. For the Learning of Mathematics, 5(1), 44-48. East, E. M. (1927). Heredity and human affairs. New York: Scribners. Equity and Mathematics Education Leadership Institute [EMELI]. (n.d.). What is EMELI? Retrieved October 20, 2002, from http://emeli.education.ucsb.edu Ernest, P. (1991). The philosophy of mathematics education. Bristol: The Falmer Press. García, E. E. (2001). Hispanic education in the United States: Raíces y alas. Lanham: Rowman & Littlefield. Gould, S. J. (1981). The mismeasure of man. New York: W.W. Norton. Herrnstein, R. J., & Murray, C. (1994). The bell curve: Intelligence and class structure in American life. New York: Free Press. Inverness Research Associates [IRA]. (2001, February). Educators for equity: The work of EMELI leaders. Retrieved from http://www.inverness-research.org/reports/ab_emeli.html Kastberg, S. (2001). Problem context in the Standards: What is the message? The Mathematics Educator, 11(1), 15-19. Lappan, G., Fey, J., Fitzgerald, W., Friel, S., & Philips, E. (1998). Frogs, fleas, and painted cubes: Quadratic relationships. Menlo Park: Dale Seymour Publications. Mellin-Olsen, S. (1987). The politics of mathematics education. Dordrecht: D. Reidel. National Coalition for Equity in Education [NCEE]. (n.d.). Mission. Retrieved October 20, 2002 from http://ncee.education. ucsb.edu National Council of Teachers of Mathematics [NCTM]. (2000). Principles and Standards for School Mathematics . Reston, VA: NCTM. Polya, G. (1962). Mathematical discovery, Vol. 2. New York: John Wiley & Sons. Shih, M., Pittinsky, T., & Ambady, N. (1999). Stereotype susceptibility: Identity salience and shifts in quantitative performance. Psychological Science, 10(1), 80-83. Steele, C. M., & Aronson, J. (1995). Stereotype threat and the intellectual test performance of African Americans. Journal of Personality and Social Psychology, 69(5), 797-811. Tucker, W. H. (1994). The science and politics of racial research. Urbana, IL: University of Illinois Press. Weissglass, J. (1990). Constructivist listening for empowerment and change. The Educational Forum, 54(4), 351-370. Weissglass, J. (1991). Reaching students who reject school: An essay review of The Politics of Mathematics Education. Journal of Mathematical Behavior, 10(3), 279-297. Weissglass, J. (1997). Ripples of hope: Building relationships for educational change. Santa Barbara, CA: Center for Educational Change in Mathematics and Science. Weissglass, J. (2000). No compromise on equity in mathematics education: Developing an infrastructure. In W. Secada (Ed.), Changing the faces of mathematics (pp. 67-78). Reston, VA: NCTM. 1 If you are reading this article with a group of people, or you have someone nearby, I suggest that you pair up and each spend a few minutes talking about the beliefs, attitudes, values, and emotions about the topics in Figure 2 that most affect you in your work. 2 If you are reading this article with a group of people, I suggest that you pair up and give each person get a chance to talk for two or three minutes about how she or he feels when she or he hears the word racism. 3 I discuss why the culture of schools does not respect emotional release in Weissglass (1990). 4 The theory and approaches, as well as examples of stories told by educators on Personal Experience Panels, are described in Weissglass (1997). The way the theory and structures is used in equity work is described in Weissglass (2000). The evaluation of a project based on this approach

(IRA, 2001) is available on the web.

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