Note on Translation Introduction by Michael Holquist Response to a Question from the Novy Mir Editorial Staff The Bildungsroman and Its Significance in the History of Realism (Toward a Historical Typology of the Novel) The Problem of Speech Genres The Problem of the Text in Linguistics, Philology, and the Human Sciences: An Experiment in Philosophical Analysis From Notes Made in 1970-71 Toward a Methodology for the Human Sciences Index

Speech Genres and Other Late Essays

미국의 “전국 수학 교사 협의회”(National Council of Teachers of Mathematics, NCTM)는 1989년부터 〈학교 수학의 교육과정과 평가 규준〉(1989), 〈수학 가르침(교수)의 전문성 규준〉(1991), 〈학교 수학의 평가(시험) 규준〉(NCTM, 1995), 〈학교 수학의 원리와 규준〉(2000)을 출판하여 미국의 수학 교육 의 전망(목표, 나아갈 길)과 규준(실행 지침)을 제시하였다. 수학 교사들로 구성된 미국의 NCTM은 학생, 학부모, 학교 행정가 등 많은 사람들과 힘을 합하여 모든 학생들에게 수준 높은 수학 교육을 받을 수 있는 여건(환경, 기회)을 조성하는 데 구심점의 역할을 하였다. 한편 많은 관련 단체들은 여러 배경과 능력을 가진 학생들이 전문성을 지닌 교사(특수 교사를 일컫는 밀이 아니다. 수학 교과를 이해하고 수학의 전문성과 특수성을 가르칠 수 있는 일반 교사를 일컫는 말이다.)로부터 미래를 대비해 평등하고, 진취적이며, 지원이 잘 이루어지고, 공학 도구(IT)가 잘 갖춰진 환경에서 중요한 수학적 아이디어를 이해하면서 학습할 수 있는 수학 교실(미국에서는 우리나라처럼 수학 교사가 수학 시간에 학생의 방(교실: Homeroom)에 찾아가지 않고 학생들이 선생의 방(수학 교실: Classroom)을 찾아온다. 전형적인 수학 교실의 사진은 2쪽에 나와 있다.)을 만들기 위해 함께 힘썼다. NCTM에서 출간한 여러 규준들은 우리나라의 제6차와 제7차 교육과정에도 큰 영향을 미쳤다. 이 글에서는 NCTM(2000)에서 제시한 학습 원리를 간단히 살펴본 다음 이를 중심으로 현재 미국 수학 교육의 교수ㆍ학습 이론의 동향을 살펴본다.

미국 NCTM의 Principles and Standards for School Mathematics에 나타난 수학과 교수,학습의 이론

Examines various industries to show how business endows products with evocative meaning. Kramer was one of the most visionary musical thinkers of the second half of the 20th century. In his The Time of Music, he approached the idea of the many different ways that time itself is articulated musically. This book has become influential among composers, theorists, and aestheticians. Now, in his almost completed text written before his untimely death in 2004, he examines the concept of postmodernism in music. Kramer created a series of markers by which we can identify postmodern works. He suggests that the postmodern project actually creates a radically different relationship between the composer and listener. Written with wit, precision, and at times playfully subverting traditional tropes to make a very serious point about this difference, Postmodern Music, Postmodern Listening leads us to a strongly grounded intellectual basis for stylistic description and an intuitive sensibility of what postmodernism in music entails. Postmodern Music, Postmodern Listening is an examination of how musical postmodernism is not just a style or movement, but a fundamental shift in the relationship between composer and listener. The result is a multifaceted and provocative look at a critical turning point in music history, one whose implications we are only just beginning to understand. A timely essay collection on the development and influence of secular expressions of Buddhism in the West and beyond. How do secular values impact Buddhism in the modern world? What versions of Buddhism are being transmitted to the West? Is it possible to know whether an interpretation of the Buddha’s words is correct? In this new essay collection, opposing ideas that often define Buddhist communities—secular versus religious, modern versus traditional, Western versus Eastern—are unpacked and critically examined. These reflections by contemporary scholars and practitioners reveal the dynamic process of reinterpreting and reimagining Buddhism in secular contexts, from the mindfulness movement to Buddhist shrine displays in museums, to whether rebirth is an essential belief. This collection explores a wide range of modern understandings of Buddhism—whether it is considered a religion, philosophy, or lifestyle choice—and questions if secular Buddhism is purely a Western invention, offering a timely contribution to an ever-evolving discussion. Contributors include Bhikkhu Bodhi, Kate Crosby, Gil Fronsdal, Kathleen Gregory, Funie Hsu, Roger R. Jackson, Charles B. Jones, David L. McMahan, Richard K. Payne, Ron Purser, Sarah Shaw, Philippe Turenne, and Pamela D. Winfield. `I judge this book to be something of a triumph. It provides many valuable insights into how social psychologists work within different paradigms and with quite different assumptions.... Throughout, the writing is clear, central issues are constantly reexamined, and sight is never lost of the whole \"task\" of the book... it addresses central issues both adventurously and provocatively. Students who use it are lucky to have such a feast provided, and they are bound to find the material both challenging and stimulating... there is much more about self issues in this text than in any comparable social psychology text. And that, in itself, is a major achievement' Self & Society This accessible, broad-based and a

The Saturated Self: Dilemmas of Identity in Contemporary Life

A. L. Kroeber and Clyde Kluckhohn, "culture: A critical review of concepts and definitions"

Background/Context: School tracking practices have been documented repeatedly as having negative effects on students’ identity development and attainment, particularly for those students placed in lower tracks. Despite this documentation, tracking persists as a normative practice in American high schools, perhaps in part because we have few models of how departments and teachers can successfully organize instruction in heterogeneous, high school mathematics classes. This paper offers one such model through a qualitative and quantitative analysis. Focus of Study: In an effort to better the field’s understanding of equitable and successful teaching, we conducted a longitudinal study of three high schools. At one school, Railside, students demonstrated greater gains in achievement than students at the other two schools and higher overall achievement on a number of measures. Furthermore, achievement gaps among various ethnic groups at Railside that were present on incoming assessments disappeared in nearly all cases by the end of the second year. This paper provides an analysis of Railside’s success and identifies factors that contributed to this success. Participants: Participants included approximately 700 students as they progressed through three California high schools. Railside was an urban high school with an ethnically, linguistically, and economically diverse student body. Greendale was situated in a coastal community with a more homogeneous, primarily White student body. Hilltop was a rural high school with primarily White and Latino/a students. Research Design: This longitudinal, multiple case study employed mixed methods. Three

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Creating Mathematical Futures through an Equitable Teaching Approach: The Case of Railside School

principles and procedures in mathematics. The research on the implementation of social justice tasks in the mathematics classroom has also prompted questions about the difficulty of balancing discussions of complex social issues with the mathematics. For example, Bartell (2006) reports that teachers in her professional development course on social justice in mathematics found it challenging to move flexibly between the mathematics content and conversations about social injustice. Gutstein (2006) also admits that in his class, he had to occasionally forgo opportunities to pursue mathematical investigations to deepen the conversations about social issues. Because students often hold strong perspectives about social injustice and these can trigger emotional responses, it is clearly important for teachers to be able to adeptly and sensitively guide students back to the mathematics at hand. We wonder, then, if teachers are being prepared and have bargained for doing this multifaceted work. Also, can social justice activities stemming from students’ social realities sufficiently drive students’ development of sophisticated mathematics knowing across an extended period of time? Or should they mainly serve as supplemental materials to the existing mathematics curriculum, used to convince students that learning mathematics is relevant and even critical to improving their lives and the lives of others? A second challenge is in thinking about how one might apply these approaches in racially or ethnically heterogeneous classrooms. This is an especially salient issue for Funds of Knowledge and the Algebra Project, as to some degree, these approaches assume a degree of coherence within the communities that are being served. How might these approaches be adapted in classrooms where students are from multiple communities? What might it mean to draw on students’ experiences in such multicultural classrooms? This may be less of an issue with social justice approaches, but it still leaves more to be negotiated with and between students in classrooms where there is a wide range of race, class, or socioeconomic groups represented. How are teachers to deal with kids from communities that do not share a social justice perspective or see social justice in terms of their own philanthropy? Would such students (not from working-class families) buy into the basic premises of this approach? What additional support might they need to do so? Another critical issue with social justice approaches is that the time spent on social justice issues is potentially time not spent on math. What about the middle-class and upper-class parents who are unwilling to sacrifice time for “basic math” and relegate these approaches as appropriate only for those from nondominant groups? Similarly, in considering heterogeneity and culturally relevant pedagogy, it may be more difficult in heterogeneous classrooms and communities to have a sense of the community that students come from; there may be greater differences in achievement and histories with school among the students as well as variety in issues of identity that may need to be attended to. A third challenge involves the constraints imposed by the racial and gender makeup of the teaching force in this country and the structure of the profession. 222 Review of Research in Education, 32 The vast majority of teachers in the United States are White, middle-class women (Howard, 1999; Nieto, 2004). This is potentially a population of teachers for whom the approaches we describe may be particularly difficult, as they likely have the most to learn about their students’ communities. Although mathematics teachers are often marginalized within the broader mathematics community, they may not share the same level of marginalization with their nondominant students. Furthermore, teaching is a profession that is largely underpaid and overworked (Darling-Hammond, 1997). Most teachers, given the structure of the school day and demands on their time, have little time to conduct the kind of in-depth investigations of their students and their communities these approaches suggest. Even more important, in the broader context of increased reliance on standardized testing with high stakes for teachers and schools, these approaches that require more of teachers may be unrealistic. Any approach that argues for particular teaching strategies must take into account these very real constraints. However, despite these challenges, we see great promise in the work of the aforementioned approaches, and we offer these critiques as a way to continue to make progress on ways to support increased equity in math classrooms. It is important to note that these approaches highlight the critical role of teachers in reproducing patterns of inequity. In the next section, we focus on the implications our review may have for the knowledge teachers need to have to best support equity and begin to “blur the lines” between cultural and domain knowledge and work simultaneously at all three levels of our model. Because of space, we do not undertake a full review of the vast literature on teacher professional development that includes a cultural or equity lens (see Sowder, 2007; Wilson & Berne, 1999). Rather, we reflect on the implications for teacher training of the research we have reviewed in this chapter, drawing on some of the relevant work in teacher professional development. Toward this end, we briefly consider two questions. What knowledge do teachers need to know, and what professional development models might prove productive possibilities for sharing that knowledge with teachers? Implications for Teacher Knowledge The work of teachers has grown considerably more complex in the past 10 years (Ball & Cohen, 1999; Cochran-Smith & Lytle, 1999; Cochran-Smith & Zeichner, 2005; Lampert & Ball, 1998; Putnam & Borko, 2000). Standards-based instructional practices require that teachers develop a specialized form of mathematics knowledge for teaching (MKT; Ball, 2005; Hill, Schilling, & Ball, 2004; Hill, Sleep, Lewis, & Ball, 2007) that reflects a particular blend of connected domain understanding with techniques and strategies to facilitate productive classroom interactions. Although the details of MKT are currently being worked out, the domain understanding required for eliciting, evaluating, and building (Carpenter, Fennema & Franke, 1996; Lampert, 1990, 2001; Schifter, 2001) on students’ mathematical ideas reflects a facility with and deep understanding of mathematical concepts and procedures across the terrain of K–12 mathematics (Greeno, 1991; Ma, 1999; NCTM, 1991, 2000). Teachers need to have Nasir et al.: Culture and Mathematics in School 223 the opportunity to develop mathematics knowing in practice through ongoing reflection in the classroom and with their peers through the use of records of practice, video, and other learning materials (Kazemi & Franke, 2004; Lampert & Ball, 1998). As Rochelle Gutiérrez (2002b) argues, however, knowledge of dominant mathematics must also be balanced with knowledge of how to enable students to critique the role of mathematics in society and to “contribute toward a positive relationship between mathematics, people, and society in ways that erase inequities on this planet” (p. 172). Delineating a set of teaching practices that encompasses both dominant and critical perspectives on mathematics is complicated by the fact that some classrooms are becoming increasingly diverse while others slip into hypersegregation (Orfield, Frankenberg, & Lee, 2003). Students themselves are also quite complex, as they negotiate hybrid practices, identities, and time scales through new global technologies that transcend traditional racial, social, and linguistic boundaries (Barab, Hay, Barnett, & Squire, 2001; Delpit, 2002; Gergen, 1991; Moje, Ciechanowski, Ellis, Carrillo, & Collazo, 2004). Thus, as we noted, in this chapter we do not presume to be able to comprehensively outline the knowledge teachers need to teach mathematics effectively and fairly. Instead, we juxtapose recent theoretical shifts that blur the boundaries between mathematics and cultural knowledge, with the implications of the various programs we reviewed above to propose ideas about effective mathematics teaching in classrooms with diverse populations of students. First, the Funds of Knowledge approach would suggest that an important aspect of teacher preparation would support teachers in viewing their students as whole people with rich social and intellectual lives outside of the classroom. Activities for prospective teachers might include spending time with students and families outside of school (Civil, 2002; Foote, 2006) and bringing families into schools to better understand students’ interests and skills outside of the classroom and those that exist as funds of knowledge in their communities. Additionally, professional development activities might include a study of modules developed with students’ and families’ funds of knowledge at the center and might offer models for alternative ways to incorporate family and community members into classroom activities. An important aspect of this work would be to support prospective or current teachers in understanding the value (both for students’ learning and for social justice) of shifting the traditional power relations between families and schools and of opening communication channels. Similarly, the activities of the Algebra Project would also suggest that supporting teachers in understanding the importance of and offering suggestions for how to better get to know the young people they are teaching is a critical focus for teacher preparation. The Algebra Project might also share an orientation for teachers that views math teaching as political activity and sees subverting current patterns of unequal access to higher mathematics as an immediate concern. Moses and Cobb (2001) argue that students need to be taught to

Culture and Mathematics in School: Boundaries Between “Cultural” and “Domain” Knowledge in the Mathematics Classroom and Beyond:

This study had two purposes: (a) to investigate the developmental relationship between students’ uses of fractions notation and their understandings of part-whole relations; and (b) to produce an analysis of the role of fractions instruction in students’ use of notation to represent parts of an area. Elementary students ( n = 384) in 19 classes participated in the study. Pre- and posttests were administered before and after fractions instruction, and key lessons were recorded with videotape and field notes. Students’ written responses were coded in two ways: for the forms of the notations (e.g., use of numerator, denominator, and separation line), and for the concepts captured by the notations (e.g., part-whole, part-part, or other kinds of relations). The lessons captured on videotapes and in field notes were rated with respect to their alignment with principles supported by reform frameworks in mathematics education (e.g., opportunity to build understanding of fractions concepts, ongoing assessment of student understanding). Our analyses indicated (a) notation and reference were acquired somewhat independently, and (b) classroom practices that built on students’ thinking were more likely to support shifts toward normative uses of notation.

Representing Fractions with Standard Notation: A Developmental Analysis.

The purpose of this 2-part study was to explore the mathematical and purchasing competencies present in students' engagement in shopping practices in a low-income African American neighborhood. Study 1 consisted of in situ analyses of children's shopping activities at a local store, revealing the variety of arithmetic tasks that emerged in relation to varied artifacts, shopping routines, social norms, and clerk support. In an effort to reveal competencies that could not be measured through observation alone, Study 2 consisted of individual interviews of 30 first and second graders about tasks that required them to purchase items at a mock store. Analyses revealed both strategies that were frequently and infrequently associated with successful purchasing and the relationship between children's strategy choices and the demands of particular purchases. This research documents the many mathematical competencies children present that may not be captured in traditional school assessments and considers how this ...

The Purchasing Practice of Low-Income Students: The Relationship to Mathematical Development

In this chapter we explore what is required of us, as researchers and educators, to disentangle settled disciplinary knowledge and ways of knowing from colonial matrices of power, and to enable insurgent ways of learning, being, and acting in, with, and across disciplines. We posit three sensibilities that are critical to liberatory forms of disciplinary learning animated by onto-epistemic heterogeneity: multiplicity, horizontality, and dialogicality. Grounded in extended examples, we define these sensibilities, illustrate how they shift both the content and the terms of disciplinary ways of knowing in literacy, science, and mathematics, and articulate key implications for the design of learning and the practice of teaching.

Multiple Ways of Knowing * : Re-Imagining Disciplinary Learning

This study describes the Reflection Connection Cycle professional development designed to support teachers’ use and appreciation of students’ out-of-school practices related to school mathematics. The year-long program incorporated group lesson design, readings, and video analysis for 14 elementary school (ages 5–12) teachers. Analysis of lesson development, written reflections, and analysis of teacher talk revealed important patterns related to the difficulty in writing lessons that built on students’ informal understandings. While initial lessons focused solely on the context of practices like gardening and sports, subsequent lessons show a greater concern for the mathematics in which children were engaged within a practice. A Multi-approach Engagement Framework is presented both as a tool to support further professional development efforts and as a means to describe stability and change in teachers’ efforts to connect in-school and out-of-school mathematical understandings.

Edd V. Taylor

Papers

Culture and Mathematics in School: Boundaries Between “Cultural” and “Domain” Knowledge in the Mathematics Classroom and Beyond:

Representing Fractions with Standard Notation: A Developmental Analysis.

The Purchasing Practice of Low-Income Students: The Relationship to Mathematical Development

Multiple Ways of Knowing * : Re-Imagining Disciplinary Learning

Supporting children’s mathematical understanding: professional development focused on out-of-school practices