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Running Head: Discrete versus Integrated Perspectives

Integrated versus Discrete Perspectives: Characterizing the Dispositions of Mathematics Teachers towards Culture, Power and Mathematics Learning

Keywords: Mathematics Education; Teacher Practice; Equity; Critical Theory; Situated Learning; Dispositions

Victoria Hand University of Colorado, Boulder 249 UCB Boulder, CO 80309 [email protected] Ph: 303.492.7738 Fax: 303.492.7090

 

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Discrete versus Integrated Perspectives

Abstract The US-based National Council for the Accreditation of Teacher Education (NCATE) recently took a bold step in calling for a social justice approach to teaching. This change in policy marks a significant shift in the positioning of equity with respect to core teaching practices. However, teacher professional practice programs both in the US and internationally hold vastly different conceptual underpinnings for the relations between cultural processes, sociopolitical structures, and learning outcomes. This paper attempts to characterize these differences to better orient discussions of what it means to teach secondary mathematics equitably. I theorize that approaches to equitable mathematics teaching can be roughly characterized along a continuum of discrete versus integrated perspectives on the interrelations between culture, power and mathematics learning. I draw on a conceptual framework to detail what mathematics teachers might be disposed to do in their practice given their location along this continuum. I emphasize the need to recast teacher dispositions within a situated perspective and to employ it as a means of predicting teachers’ responses to classroom mathematical activity.

 

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I’m her teacher [and] I have to find something that will help me interact with her in order for to her to understand mathematics…not necessarily as a teacher, but more of a human…How can I make sense that [my students] will become better people by knowing the math that we’re learning and what comes from it? …It’s more going out there and taking up their space. I don’t mean that everybody should choose to become a neurosurgeon…But, it’s like being able to have the tools to say, “If I could do this, I will become anything. I will get out there and take up my space”. That’s what I think is my goal: for students to realize that they have the actions, they have the means to have the knowledge, and they can make the choice. (Interview, secondary mathematics teacher, May, 2002)

Attention to the achievement gap in the US in mathematics (Ball & Moses, 2009; National Center for Educational Statistics (NCES), 2009) and to the need for secondary teachers to be versant in equitable teaching practices (National Center for Educational Statistics (NCES), 2009; National Council for Teachers of Mathematics (NCTM), 2000) has been steadily increasing for the last twenty years. Until recently, the language found in official policy documents has largely reflected a colorblind and power-mute philosophy towards equity in mathematics education (Martin, 2003). In 2007, however, the US-based National Council for the Accreditation of Teacher Education (NCATE) took a bold step in calling specifically for a social justice approach to teaching (National Council for Accreditation of Teacher Education (NCATE), 2008). This change in policy marks a significant shift in the positioning of issues of equity with respect to best teaching practices. However, the US lags behind other countries in making explicit the need for teachers to be prepared to grapple with educational injustice on a systemic level. For

 

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example, among western European countries, the Netherlands was first in advocating for a longitudinal approach to educational policy to facilitate the integration of non-dominant groups into mainstream Dutch society. Developed in the early 1980’s, this federal initiative targeted the “proportional participation” of minority and migrant children in early education by distributing greater resources to schools and programs that served these youth (Rijkschroeff, ten Dam, Duyvendak, de Gruijter, & Pels, 2005). Similarly, equity has been a central concern of the New Zealand government since 2001, when the Ministry of Education initiated a program called Te Kōtahitanga designed to create a culturally responsive approach to the underachievement of the Māori students (R Bishop, Berryman, Cavanagh, & Teddy, 2007; Russell Bishop & Glynn, 1999). The turn towards making explicit issues of power, culture, language and history in the distribution of opportunities to learn for groups of students is welcomed by many mathematics education researchers who argue that to ignore them slows progress towards addressing persistent inequities for marginalized groups of people (R. Gutiérrez, 2007; Nolan & de Freitas, 2008; Tate, 1994). Yet, while these mandates share a vision of teaching as a means of uprooting injustice, their assumptions about the relation between cultural processes, sociopolitical structures and learning outcomes vary widely. I am interested in characterizing these differences in ways that serve to orient discussions of what it means to teach secondary mathematics equitably. I theorize that approaches to equitable mathematics teaching can be roughly characterized along a continuum of discrete versus integrated perspectives on the interrelations between culture, power and mathematics learning. Drawing on a conceptual framework my colleagues and I developed to explicate these interrelations (Nasir, Hand, & Taylor,

 

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2008), I discuss how mathematics teachers might be disposed to teach towards equity given their location along this continuum. Recasting teacher dispositions within a situated perspective, I propose that teachers’ moment-to-moment teaching decisions are a function of the perspectives they bring to the classroom, and the features of the classroom itself. I draw on this interpretation to theorize what teachers will notice and respond to in moments and broader levels of mathematical activity with respect to issues of equity. 1 Interpretations of Teaching for Social Justice The fact that the field of education is fraught with different meanings of, processes for, and policies around educational justice is consistent with a sociocultural view of human activity (Cole & Engeström, 1993; Vygotsky, 1978; Wertsch, 1991). As a social justice agenda emerges in dominant educational narratives (North, 2006) communities advocate for particular framings that mark locally constituted trajectories of activity and participation in broader sociocultural Discourses (Gee, 1990). It is not surprising, then, that multiple meanings are ascribed to commonplace terms like “culture” and “justice”. North (2006) argues that maintaining the hybridity and friction among these disparate meanings honors the constructed and subjective nature of social life. However, she does settle on an important theme among these interpretations in the concept of dialogical understanding (Bakhtin, 1981; Britzman, 2003). North draws on Britzman’s (2003) interpretation of dialogical understanding as: “the ways talk, practice and understanding are mediated by difference, history, point of view, and the polyphony of voices possessed by those immediately involved and borrowed from those who become present through language” (p. 237). The positioning of education, teaching, teachers and groups of learners within broader social contexts and historical processes is also inherent

 

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in Cochran-Smith’s (2010) theory of teacher education for social justice. Here, she calls for “connect[ing] the key ideas of distributive justice, which locates equality and autonomy at the center of democratic societies (Howe, 1997, 1998), with current political struggles for recognition, which challenge the school and knowledge structures that reinforce disrespect and oppression of social groups (King, 2006; Young, 1990)” (p. 13). Prominently figured in this statement is the role of education in interrogating predominant storylines (Harre & van Langenhove, 1999; Nolan & de Freitas, 2008) about ways of knowing and coming to know that privilege or oppress cultural groups. Instead of accepting differences in participation and achievement among groups of students as the status quo, as quoted by the mathematics teacher earlier, teaching should aim at helping students who might not otherwise take up their space in and beyond the classroom. For mathematics education, this orientation entails grasping the discursive and mediated nature of our interpretations of mathematics, doing mathematics, and learning mathematics both in school and other places. While this perspective--what I call an integrated perspective on the relations between culture, power and mathematics learning-is prevalent in critical and feminist perspectives, it has not yet taken root in mainstream mathematics education theory, which tends to reinforce what I call a discrete perspective. I am not suggesting that conversations about mathematics learning are devoid of attention to power and culture, but they rarely treat them as reflexive in nature (Freire, 1970; Garfinkel & Sacks, 1970; Giroux & McLaren, 1989). I draw from mathematical definitions of discrete versus integrated elements to provide a metaphor for the relations between power, culture and mathematics learning as

 

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either separate and distinct, or an interrelated whole. Such a metaphor supports the characterization of different approaches to mathematics teacher professional practice. In this paper, I elaborate upon the proposed continuum by examining perspectives embedded in historical interpretations of equitable mathematics teaching, and by contrasting the NCATE call for social justice teaching with the Te Kōtahitanga program for Culturally Responsive Pedagogy of Relations. 1.1 Predominance of the discrete perspective In the 1980’s, a multicultural approach to education took root in the US and promoted the inclusion of practices and artifacts of minority groups in classroom teaching (Banks, 1979; Cazden & Leggett, 1981). For mathematics learning, this meant increased representation of individuals from non-dominant ethnic, racial and cultural groups in the contexts of math problems, in broader recognition of non-Western contributions to mathematics and science, and in acknowledgement of myriad conversational styles in diverse mathematics classrooms. This intervention-based approach marked a commitment in teacher practice to make explicit and address the cultural diversity in mathematics classrooms. However, culture was framed in static ways—as divorced from its interplay in classroom moments and broader timescales--which fostered superficial approaches to equitable teaching and stereotypical (and deficit) perspectives of minority ethnic and racial groups (Nasir & Hand, 2006). A different conception of culture evolved as mathematics education researchers sought to understand the role of discursive and linguistic structures in students’ perspectives of and routines for doing mathematics. It was characterized in terms of the norms, practices and activities of mathematical communities and classrooms (Lampert,

 

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1990; Lerman, 2001; Solomon, 1989; Yackel & Cobb, 1996). It was argued that particular cultural arrangements supported and hindered students’ engagement in forms of representation, argumentation and reasoning characteristic of the field of mathematics (Yackel & Cobb, 1996). Placing students’ mathematical reasoning at the center of classroom inquiry heightened awareness of the degree to which certain learners (and groups of learners) were involved in classroom discussions. However, the connection between the participation gaps (Hand, 2003) that emerged in classrooms and those institutionalized within larger society was largely under-theorized (Zevenbergen, 1996). A tendency to treat classroom teaching and learning as clearly influenced by, but not directly coupled with, broader sociopolitical processes is also evident in the NCATE (2008) mandate. In it, the achievement gap is linked to teacher quality, and characteristics of teaching for social justice are identified as: (1) possessing strong content and pedagogical knowledge; (2) holding high expectations for all students; and (3) understanding how processes of discrimination and marginalization have and continue to affect educational opportunities of underrepresented students. While this mandate marks a milestone in US teacher education in its common vision for social justice teaching, it does not specify the entailments for teacher practice. It could represent a call for teachers to recognize and account the dominant narratives about “competent” mathematics learners that are shaped by and shape processes of discrimination and marginalization. In contrast, lack of a theoretical framing, and the predominance of colorblind and color-mute (Pollock, 2004) mathematics teaching, could also imply a domino-type understanding, whereby discrimination is perceived as acting

 

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upon cultural groups, and culture upon individual achievement. I contend that it reinforces a discrete perspective on the relations between culture, race and power simply by the fact that it does not challenge it. 1.2 Towards an integrated perspective Concurrent with the US multicultural education movement, a critical pedagogy that made central the cultural and political nature of mathematics education was gaining strength in Europe and South America (D'Ambrosio, 1981, 1999; Skovsmose, 1994a, 1994b). Mathematics was positioned as a tool to explore, model, and reflect on students’ everyday experience, and to scrutinize its role in legitimizing the institutional structures and processes that formed this experience. It was theorized that mathematics education “must discuss basic conditions for obtaining knowledge, it must be aware of social problems, inequalities, suppression etc., and it must try to make education an active progressive social force” (Skovsmose, 1994, p. 38). Calls to question privileged forms of mathematical knowing and reasoning were also led ethnomathematics researchers, who illustrated powerful and unconventional mathematical reasoning by indigenous and non-Western peoples (Abraham & Bibby, 1988; Ashcer, 1991; Borba, 1990). Should these two lines of mathematics education research have taken hold, the implications for mathematics teacher practice may have been significant. The work of mathematics teaching could have been re-envisioned as guiding students in illuminating and interpreting (and possibly responding to) unjust situations mathematically (Freire, 1973; Gutstein, 2005; Skovsmose, 1994a), or at the very least, striving for a classroom culture that mediated the reproduction of sociopolitical hierarchies that inhibited participation by marginalized groups of students (DiME, 2007; R. Gutiérrez, 2008).

 

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To more thoroughly operationalize what I mean by an integrated perspective, I draw on a tripartite framework my colleagues and I developed to explicate the relations between culture, power and mathematics (Nasir et al., 2008). [Insert Figure 1 here] This framework proposes three lenses from which to explore the cultural and political nature of mathematics learning. These lenses include: (1) mathematics knowing as a cultural activity (e.g., structures and forms of different kinds of mathematical activity, for example, in everyday versus school math knowing), (2) mathematics learning as a cultural enterprise (e.g., structural and discursive aspects of various contexts for learning, for example, in the classroom versus students' home and local communities), and (3) mathematics education as a cultural system (e.g., structural and discursive aspects of the field of mathematics education). These three lenses draw attention to the particular ways that school mathematics learning gets structured, taught, and accomplished within the system of mathematics education. For mathematics teachers to be truly versant in issues of equity, they not only need to be able to perceive these relations, but they should also understand how the different aspects interact and interpenetrate each other. This type of relational understanding is the centerpiece of an integrated perspective. An example of a teacher professional development initiative aligned with this perspective is the Te Kōtahitanga program for Culturally Responsive Pedagogy of Relations. In 2001, the New Zealand Ministry of Education called for a broad-based effort to rectify educational disparities between students from the majority culture and the indigenous Māori people. Similar to the NCATE focus on teacher quality, an Effective Teaching Profile (ETP) was developed that operationalized equitable teaching in terms

 

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of: (1) caring for students as culturally located individuals, (2) holding high expectations for all learners, (3) managing the classroom for learning, (4) focusing on the discursive aspects of teaching, (5) accepting a range of strategies for learning (R Bishop et al., 2007). Unlike the NCATE approach, however, the broader system of activity in which this program took shape was carefully considered. Researchers counseling the Ministry of Education argued that prior reform efforts around multiculturalism reflected dominant discourses and that educational reform and justice needed to emerge from among individuals being oppressed (Russell Bishop & Glynn, 1999; Freire, 1970). Interviews with Māori students, parents and communities helped to “operationaliz[e] Māori people’s cultural aspirations for self-determination within non-dominating relations of interdependence” (Russell Bishop & Berryman, 2006, p. 735). These interviews grounded the professional development program, which oriented teachers towards differences between the Māori educational narratives and deficit-laden narratives they themselves held. The program held teachers accountable for exercising agency towards breaking the cycle of failure among Māori children (Russell Bishop & Berryman, 2006). Findings from the Te Kōtahitanga program provide evidence that teacher professional development can foster more socially just education (R Bishop et al., 2007). Given the context in the US, I realize that this is a tall order. As a mathematics teacher educator, I have found that while candidates may accept teaching as an inherently political act, they are often less comfortable aiming their teaching at rectifying social injustice. What motivated the shift in teacher practice in the Te Kōtahitanga program? I surmise that central to the shift was what the teachers became disposed to notice and

 

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explain about the disenfranchisement of their Māori students. I argue it is productive for researchers to examine what it means for a teacher to develop such a disposition (Gresalfi & Cobb, 2006) towards mathematics teaching and learning. In the section that follows, I motivate such a theoretical move in the context of mathematics teacher practice, and conceptualize a disposition within a situated view of knowing.

2 Teacher dispositions as a first step Teachers enter the profession with histories of experiences in particular communities (Lave & Wenger, 1991). A teacher’s trajectory of participation across communities shapes how she attends to the activity going on around her, how she interprets what she notices, and how she responds as a result (Cole, 1996). It affords particular ways of interpreting the world and the classroom that depend both on the social activity that is unfolding in any given moment, and a frame of reference that is negotiated over time (Greeno & Gresalfi, 2008; Wenger, 1998). This situated notion of disposition captures the reflexivity between person and context, and is predictive of what a teacher will be disposed to do when faced with a set of circumstances in his classroom (Gresalfi, 2009). In contrast to conceptions of disposition as trait (Allport, 1966) or habitus (Bourdieu, 1990), Gresalfi (2009) describes dispositions as, "ways of being in the world that involve ideas about, perspectives on, and engagement with information that can be seen both in moments of interaction and in more enduring patterns over time" (p. 329). Similar to the concept of identity, disposition captures our tendencies to view and interact with situations in consistent ways. Unlike it, however, a disposition is constantly negotiated

 

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and transformed as an individual is positions themselves and is positioned within communities that confirm, challenge, or even reject the sense of self they are developing. The notion of a developing dispositions situates teachers’ stories about their students in the social boundaries between local and broader social and cultural communities. For example, mathematics teachers in the US often come from educated, white, middle-class backgrounds. One can argue that this limits their understanding of students from underserved communities. Framing this in terms of dispositions highlights the lack of opportunities for mathematics teachers to participate in the communities from which their students come--communities in which a privileged orientation might be challenged in important ways. I draw on the concept of dispositions to draw attention to not only what teachers do in attempting to teach in equitable ways, but also how what they see and interpret lead to these decisions. This is not a new focus for teacher practice; the study of teacher beliefs has made significant inroads into our understanding of the factors that guide teachers’ classroom moves (Nespor, 1987). A construct that holds promise for capturing the situated nature of beliefs, and what I argue is a key aspect of a disposition, is the concept of noticing. 2.1 Learning to notice The concept of teacher noticing encompasses how teachers attend to and make sense of the events taking place in their classrooms (Sherin, Jacobs, & Randolph, 2011; van Es & Sherin, 2008). Researchers argue that it is a key component of teachers’ work, in that teachers on-the-fly decisions are shaped by what stands out to them, what these features reveal about the state of their classroom or students, and whether and how they can

 

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respond (Jacobs, Lamb, Phillip, & Schappelle, 2009; Santagata, Zannoni, & Stigler, 2007; van Es & Sherin, 2002). van Es and Sherin (2002) argue that significant attention has been devoted to the activities of teaching, while less has been paid to helping teachers recognize what to look for as they are teaching to motivate a choice of activity. Accordingly, this paper examines characteristics of mathematics teacher noticing when teachers are disposed to treat issues of culture and power as part and parcel of the learning process. In the section that follows, I draw on a study of equitable mathematics teaching in an urban high school (Hand, 2003) and the framework on the relations between culture, power and mathematics learning introduced earlier to elaborate upon teacher noticing from an integrated perspective. 3 Noticing from an integrated perspective The study of equitable mathematics teaching discussed here was conducted in an urban high school in California. The mathematics department in this school was committed to taking preventative measures against the potential for marginalization and underachievement of their population of nondominant students. Hence, they formed a shared vision for equitable teaching practices that revolved around an inquiry-based mathematics curriculum and a pedagogical approach based on classroom status treatments (Boaler, 2006, in press; Boaler & Staples, 2008; Cohen & Lotan, 1997) Data from the investigation of teacher professional practice for two of the teachers in this study (one of who is quoted in the introduction) illustrates how integrated perspectives held by these teachers shaped their responses to issues of equity in their classrooms. Findings from this data are presented for each component of the framework.

 

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3.1 Mathematics knowing as cultural activity The mathematics taught today is a historical by-product of negotiations that occurred between communities over time (Grabiner, 1997; Saxe, 1985; Saxe & Esmonde, 2005). That what it means to know something mathematically is fundamentally cultural in nature stems from a rich trajectory of research on the historical development of mathematical forms, functions and goals (Abraham & Bibby, 1988; Ashcer, 1991; Lave, 1993; Nunes, Schliemann, & Carraher, 1993; Saxe, 1985). Researchers have illustrated that mathematical knowing is necessarily bound up in socially organized systems of activity (Bowers, Cobb, & McClain, 1999; Greeno & MMAP, 1998; Hutchins, 1995; Saxe & Esmonde, 2005) embodied as individuals develop gesture, symbols systems, and other communication practices to engage in joint activity (Varela, Thompson, & Rosch, 1991), and reified through the coordination of informational, material, and interpersonal aspects of these systems over time (Cole & Engeström, 1993; Hutchins, 1995; Moll, Tapia, & Whitmore, 1993). It is important for mathematics teachers to understand that school mathematics is a form of mathematical knowing that has been sanctioned over time by powerful stakeholders (e.g., mathematicians, curriculum developers, textbook suppliers, professional organizations). Teachers may have an intuitive sense of this, but fail to recognize the role of broader power structures in shaping how different forms of knowing are positioned relative to each other. For example, they may perceive everyday mathematical problem-solving (for example, in the case of Nasir’s (2000) basketball players) as representative of a “concrete” or “basic” understanding of mathematics, since it does not involve symbolic manipulation (Moschkovich, 2002a).

 

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The teachers in this study who held integrated perspectives on the teaching of reform mathematics approached the cultural nature of mathematics in a different way. They actively sought out the mathematical sense-making in the discourse practices that their non dominant students brought from home and community (Civil, 2001; Gonzalez, Andrade, Civil, & Moll, 2001; Moschkovich, 2002b) and linked these forms of knowing to classroom mathematical inquiry. They did this by noticing the mathematics in students’ classroom utterances, and revoicing (O'Connor & Michaels, 1993) these utterances in ways that connected to classroom mathematical inquiry (but not necessarily the formal mathematical register). They also asked students to mathematize aspects of their everyday lives, which in turn helped students to discover that mathematics is not limited to the form it takes in school. The fact that these teachers were able to solicit students’ mathematical ideas has much to do with the fact that they recognized mathematics learning as a cultural enterprise. 3.2 Mathematics learning as cultural enterprise Research that takes knowing and coming to know mathematics as inextricably wedded focuses the affordances of patterns of mathematical activity for the positioning of learners around math and each other (Gresalfi, Martin, Hand, & Greeno, 2008; Herrenkohl, Palincsar, DeWater, & Kawasaki, 1999; Wagner & Herbel-Eisenmann, 2009). Early research on classroom mathematics learning as a type of cultural enterprise questioned whether the funneling down of norms and practices of the mathematics community to the mathematics classroom fostered broad-based participation by a range of learners (Van Oers, 2001) or privileged certain kinds of mathematical identities (Martin, 2000).

 

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The notion that learners are not only negotiating an understanding of mathematics content, but also a vision of what it looks like to be a successful mathematics learner has significant implications for our accounts of mathematics learning. For example, if the practices of a mathematics classroom are organized around speed and accuracy of mathematical solutions, views of who is mathematically able may fall along these lines, leading to a rigid and well-defined hierarchy of mathematical competence among students (Horn, 2007). Similarly, if norms for competent mathematics learning adhere to a one-size-fits all model, students for whom these norms are foreign or even unpalatable may remain at the margins of the classroom community (Hand, 2010). Historically (and I would argue for most mathematics teachers) mathematical identity has been derived from mathematical aptitude, instead of, as was argued earlier, reflecting the interplay of individual and context. The attribution of mathematical identity to individual ability supports a perspective of motivation as arising “naturally”, as a result of different levels of preparation or giftedness. It follows, then, that the disproportionate representation of non-dominant students in the “unmotivated” category may be justified in terms of the lack of access to resources (e.g., early mathematical experiences, well educated mentors, competent teachers, good schools), or lack of heritable mathematical capacity. The teachers in the study rejected this narrative through their practice and in conversations with students. If only a few of their students were participating in class and group discussions and should the differences in participation reinforce predominant identity narratives, the teachers would deliberately assign competence (Cohen & Lotan, 1997) to non-participating students for contributing substantively to mathematical

 

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inquiry. (This relates back to seeking mathematical meaning making in students’ informal discourse.) These teachers also created space in their classrooms for students to express themselves through their mathematical participation in ways that mattered to them (Nasir & Hand, 2008). Broadly speaking, teachers who hold an integrated perspective will understand the need for the mathematics classroom to embrace multiple and hybrid discourse practices (K. Gutiérrez, Baquedano-López, & Tejada, 2000; Moje, 2007) that shift students’ perspectives on who can be and become a mathematics learner. 3.3 Mathematics education as a cultural system In the sections above, I have outlined an argument for mathematics knowing and learning as inextricably embedded in cultural systems. What counts as doing mathematics in today’s classrooms is continually shaped by decisions made in mathematics education to privilege certain mathematics curriculum, pedagogical and assessment practices, ways of participating in these practices, and corresponding dispositions. Researchers argue that beyond the lack of access to quality mathematics education for some groups of students, it is the fact that mathematics education is located within these “invisible” cultural systems that has made the problem of the achievement gap so intractable (Bourdieu & Passeron, 1977; D'Ambrosio, 1981, 1999; Skovsmose, 1994a; Zevenbergen, 1996). While pre-service mathematics teachers are likely to hear dominant narratives of resource-based inequities among schools in their teacher education programs and through popular media, they are less likely to be exposed to the systemic nature of mathematics education in perpetuating individual and community failure. The teachers in the study carefully scrutinized institutional practices and stories that served to disenfranchise their learners and often laminated new meaning systems

 

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onto them (Goffman, 1974). For example, the teachers met regularly to identify weaknesses in their teaching strategy or curricular approach (Horn, 2002). These weaknesses emerged in moments of teaching when students struggled to understand a mathematical concept; these flaws were made explicit to the students. Similarly, in noticing discrepancies between student participation in class and their test scores, the teachers proposed to students that the test had not necessarily captured what they could do mathematically. In both of these cases, the teachers were revealing the imperfect nature of the tools and practices of mathematical education, with respect to students’ mathematical experiences. The development of alternative storylines and counternarratives stemming from the multiplicity of experiences in mathematics education holds promise for motivating an integrated perspective (Peters & Lankshear, 1996; Stinson, 2006; Wagner & Herbel-Eisenmann, 2009). Mathematics teachers may also notice and attempt to respond to inequity located within the school, district, state and nation, depending on their level of access to these contexts. For example, when it became apparent to the teachers that students regularly missed homework assignments, instead of reinforcing a detention policy, they developed an after-school homework club. When students were concerned that a poor test score would place them into a lower ability group, the teachers explained that they chose not to track students into groups since they felt that this practice was unjust. In each case, the teachers interrogated policies and practices of their department and school to advocate on behalf of their nondominant students. These teachers illustrate that an important aspect of learning to notice the system of mathematics in an integrated way is to examine the degree to which a mathematics

 

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classroom exposes and counters narratives and practices that mask unjust conditions in mathematics education. The purpose of detailing their practices with respect to the framework is not to presuppose a set of strategies for equitable mathematics teaching. Instead, these descriptions help to embody a conception of teaching mathematics for social justice as an orientation towards learners, mathematics classrooms, educational institutions and our stories about them that is marked by constant deliberation and reflection on the humanity of classroom life. 4 Conclusion In this paper, I have argued that mathematics teachers are disposed to treat issues of equity in their classroom and in mathematics education in particular ways, and that these dispositions are continually shaped both by their emerging perspectives on the relations between culture, power and mathematics learning, and by the contexts for social activity in which they participate. In particular, while teachers may link histories of marginalization and oppression faced by students and their communities to differences in participation in the mathematics classroom, they may not view these issues as tightly coupled with the cultural and political nature of the system of mathematics education. A growing number of researchers in mathematics education echo what critical theorists have argued for decades--that this tight yet largely imperceptible coupling shapes the narratives widely circulated about what constitutes mathematics learning and why certain students appear less able than others. Developing a disposition characterized by a profound understanding of the reflexivity of these processes can mean that the participation of an individual student is treated in a nuanced way.

 

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Questions arise, however, in conceiving of learning to teach mathematics for social justice in this way. First, is it possible to support such a dramatic shift in perspective through current models of teacher professional preparation and development? Or, are these activities themselves too deeply embedded in dominant structures and narratives (as was argued by the researchers who developed the Te Kōtahitanga program)? Along the same lines, Cochran-Smith (2010) has argued that producing a teaching force prepared to teach for equity is partially a matter of recruitment. She holds that teacher education programs should target individuals who are already oriented towards teaching for social justice. To me, the assumptions embedded in this perspective inevitably lead to a series of questions for the field of secondary mathematics education: Are individuals from dominant cultural groups who apply for secondary mathematics teacher education programs likely to hold these perspectives, given the fact that they have experienced tremendous success within the current system of mathematics education? Are students from non-dominant cultural groups likely to enter secondary mathematics teacher education programs given the type of opportunities they may have in the workforce with a degree in mathematics? Finally, if by virtue of their histories of participation or imagined futures, secondary mathematics teacher candidates are less likely to enter teacher education programs with these perspective, are mandates like the one from NCATE sufficient for producing a teaching workforce committed to issues of social justice? A second set of questions focuses on the conceptual argument being made for a dispositions-based model. Framing this model in terms of a continuum will be rightly criticized as overly reductionist and uni-dimensional. Given this, what kind of research

 

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do we need to pursue to map out additional dimensions and locations in this space? Broadly speaking, how do we conceptualize different aspects of a developing disposition and its functioning in classroom interaction? This paper offers a direction for our conversations around equity and mathematics teaching and learning. I argue that it is productive and timely given the complexity of this issue and the growing concern that our current systems of mathematics education do more harm than good to children from marginalized communities.

Acknowledgements The author wishes to thank Yvette Solomon and Julian Williams for their helpful comments on earlier drafts of this paper.

 

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