Cultural Diversity in the Mathematics Classroom

 

This page is being created for Dr. Larry Hatfield’s History of Mathematics (EMAT 4/6650) class at the University of Georgia in Athens, Georgia.  Our group set out to discover and present material on Cultural Diversity in Mathematics.  We discovered a wealth of resources, including books, articles, websites, lesson plans, and activities, and we have compiled a list of those resources.  The primary purpose of this page is to present research into and explanation of culturally relevant pedagogy, as well as two lesson plans that reflect culturally diverse teaching practices.

 

Contents

Culturally Diverse Pedagogy: Research and Background

Jump_to   Cultural Diversity in Mathematics Education: Current Tendencies

Jump__to Classroom Activities

Jump_to_ Compilation of Resources

 

 

 

 


Culturally Diverse Pedagogy: Research and Background

 

History            Definition_of_CR_Teaching              Elements_of_CR_Teaching          Origins_of_CR_Pedagogy             References

 

History of Culturally Diverse Education

Š      By the year 2050, Caucasian people will lose their majority status to people of color in the United States population (Burns, Keyes, and Kusimo, 2005). 

Š      With a large percentage of teachers falling under one ethnic category, schools should be looking for ways to bridge the gap between teachers and students. 

Š      Culturally relevant teaching practices include the specific methodology that the teacher brings to the classroom to effectively teach students based on their culture. 

Š      The effects of and need to empower school culture is an essential building block for enacting relevant teaching practices for with students.

 

Culturally Relevant Teaching Practices Defined

Š      In 1968, Beauchamp argued that curriculum theory and practice are driven by socio-cultural pressure and political structures instead of thoughtful analysis.  This led way to the idea that curriculum should reflect students’ lifeworlds. 

Š      The term “culturally relevant” began to appear in the 1970s (Ladson-Billings, 1995). 

Š      Culturally relevant can be defined in several different ways. 

o     Some researchers believe that culturally relevant teaching practices can only occur when teachers and students are from the same ethnic background (Grant, 1978).  (This is not a widely held belief because this is not practical or feasible in the educational arena and the world.) 

o     Webster’s dictionary (2003) defines culturally relevant in terms of two ideas.  According to Webster (2003), culture is defined as relating to a specific group or culture. 

o     Relevant is defined as having some bearing on or importance for real-world issues, present-day events, or the current state of society. 

Š      There are several different terms that historically have been used interchangeably to define culturally relevant teaching practices:  culturally relevant pedagogy, culturally congruent, and culturally responsive teaching. 

o     Although the primary terminology is culturally relevant teaching practices, other terms may be used as well. 

o     Specific definitions of culturally relevant and pedagogy vary in respect to the content, methodology, and referent group orientations (Gay, 2003).   

Š      Suzuki (1984) looks at culturally relevant teaching practices as a multicultural education that includes interdisciplinary instructional programs that provide multiple learning environments to meet the individual needs of the student.

Š       In 1986, Parekh referred to culturally relevant teaching as multicultural education. 

Š      Parekh (1986) stated that multicultural education was a refined version of a liberal education which celebrated the plurality of the world.

Š       Parekh (1986) defined culturally relevant pedagogy as ensuring equitable access and treatment for all groups in schools. 

Š      Hulsebosch and Koerner (1993) claim that culturally relevant teaching means that teachers have actively engaged in assimilating themselves into the mainstream culture of their students while searching for tools, strategies and other means to enact culturally relevant pedagogy. 

Š      Banks (1990) believes that multicultural education is a framework for a way of thinking to set the criteria for making decisions that will better serve diverse population. 

Š      Banks (1995) also believes that culturally relevant teaching is a concept that some scholars have come to include as an integral part of multicultural education. 

Š      Nieto (1992) defines multicultural education as a process of comprehensive school reform. 

o     Neito (1992) further states that it “challenges and rejects racism and other forms of discrimination in schools and society and accepts and affirms the pluralism that students, their communities, and teachers represent” (208). 

o     Neito is reinforcing the idea that culturally relevant teaching practices encourage and support the cultural differences that students bring to the classroom and work to include those in the daily teaching practices.

Š      In 2000, Gay defined culturally relevant teaching as the practice of using prior experiences, cultural knowledge, and performance styles of diverse learners to make the curriculum more appropriate and effective for them. 

o     Gay (2003) states that equality reflects culturally sensitive instructional strategies that will lead to maximal academic outcomes for culturally diverse students. 

o     Gay also defined culturally relevant pedagogy as a set of beliefs and explanations that recognizes and values the importance of cultural diversity in shaping individuals identities (2003). 

Š      Grant (1977, 1978), Garcia (1982), Frazier (1987), and Banks (1990) define multicultural education as an education reform movement that is attempting to change the structure of all educational institutions. 

o     This change would involve training teachers to use methods that are effective for individual cultural groups and not follow traditional educational practices.

o     Major goal of multicultural education is to reform educational institutions so that students from diverse backgrounds will experience educational equality (Banks, 1993; Matthews, 2003; Sleeter, 1991; Sadker and Sadker, 1982; Klein, 1985; Grant and Sleeter, 1986).

 

Common Elements of Culturally Relevant Teaching Practice

Į    Three common elements critical to the success of culturally relevant pedagogy in middle school mathematics for African American students that emerge when examining the literature. 

o     The first element is the idea that beliefs of the individual school play a key factor in the implementation of relevant teaching practices (Matthew, 2003). 

§      These beliefs can include, but are not limited to the school’s attitude towards the culture of the student body, the belief that these practices are needed, as well as the belief that culture plays a factor in instruction of students’ mathematics education.    

o     A second element is the level and quality of teacher training with respect to culturally relevant pedagogy (Matthew, 2003). 

§      Most of the schools that have implemented these types of teaching practices have extensive teacher training programs that are on-going. 

§      These programs have many different aspects that are essential to the success of teachers and students.  Included in this is the money required to appropriately and adequately train teachers to be the most effective when teaching mathematics to culturally diverse students. 

o     The third and final element includes on-going assessment of strengths and weaknesses of culturally relevant teaching practices (Matthew, 2003).  As the demographics of schools are changing, relevance must be qualified continually by asking who the curriculum is relevant to and for what purpose (Keane and Malcolm, 2003).

 

Origins of the Construct of Culturally Relevant Pedagogy

Culturally relevant pedagogy has a recent history. 

Į    Ladson-Billings (1990, 1992, 1993, 1994, 1995, and 2000) claimed that culturally responsive teaching methods develop intellectual, social, emotional, and political learning by using cultural referents to impart knowledge, skills, and attitudes.     

Į    A major goal of culturally relevant teaching practices is to reform public schools and other educational institutions so that students from all diverse backgrounds will experience educational equality (Banks, 1993). 

Į    Mathematics has always been the subject that students struggle with them most  (Sleeter, 1997). 

o     There is a disconnect as students go through school that causes them to believe that learning math is not an experience that makes sense (Gutstein, Lipman, Hernandez, and de los Reyes, 1996).

o     This is further compounded by teachers’ belief that integration of culture and content is not something that applies to mathematics teachers (Banks, 1993). 

o     To make the curriculum relevant, it must be defined in terms of the dimensions of relevance and assigning priorities (Keane and Malcolm, 2003). 

o     Material is only considered relevant to the audience, thus it is important to recognize the audience for who they are. 

o     Culturally relevant teaching practices attempt to connect the meaningfulness between home and school experiences as well as academic concepts and social realities (Gay, 2000). 

Į    Teachers need to know how children think in mathematics in order to make appropriate instructional decisions based on what each child knows and can do (Carey, Fennema, and Carpenter, 1995).

Į    Unfortunately, as Keane and Malcolm (2003) point out, it is difficult to determine what the students know about relevant mathematics, because they are constrained by their perceptions of mathematics and school. 

Į    Students need to experience connected, applied mathematics (Ladson-Billings, 2000 b). 

Į    Equitable schools demonstrate this by helping teachers obtain the knowledge and experience needed to connect mathematics in relevant ways to the lives of their students (Murphy, 1996).  

Į    According to Kahle (1987), many diverse students attribute their success in mathematics to a nurturing relationship with an adult who provides high expectations, mentoring, and support. 

Į    Gay (2000) points out that mathematics instruction incorporates every day life concepts, economics, employment, and consumer habits which can be used to help African American students can make connections to their own lives. 

Į    However, Banks (1993) contends that content integration can only occur to the extent to which teachers use examples, data, and information from cultures to illustrate key mathematical concepts. 

Į    Sheppo, Hartsfield, Ruff, Jones, and Holinga (1994) emphasize that technology is an excellent resource to help connect mathematics to middle school culturally diverse students. 

o     Computers allow students to connect mathematics to real issues in their communities. 

o     Interactive software for geometry, algebra, and calculus can empower diverse students to use fundamental ideas, multiple representations, and technology assisted methods to reason mathematics problems and ideas (Heid and Zbiek, 1995).

 

 

References and Resources



 



Cultural Diversity in Mathematics Education: Current Tendencies.

By: Victor Brunaud-Vega, Graduate Student in Mathematics Education, UGA, Athens, GA

 

Introduction         Situated_Perspective      Culturally_Relevant_Perspective              Critical_Pedagogies          References_        

 

1.    Introduction

Culture generally refers to patterns of human activity and the symbolic structures that give such activity significance. There are many different definitions of "culture" and each one of them reflects a different theoretical base for understanding, or criteria for evaluating, human activity. In general, the term culture denotes the whole product of an individual, group, or society of intelligent beings. The term includes technology, art, science, as well as moral systems and the characteristic behaviors and habits of the selected intelligent entities. In particular, it has specifically more detailed meanings in different domains of human activities.

Anthropologists most commonly use the term "culture" to refer to the universal human capacity to classify, codify and communicate their experiences symbolically. This capacity has long been taken as a defining feature of humans. It can be also said that culture is the way people live in accordance to beliefs, language, history, or the way they dress.

For the purposes of this paper we will understand culture as "the ways in which a group of people make meaning of their experiences through language, beliefs, social practices, and the use and creation of material objects" (Gutstein et.al., 1997). Nevertheless, because culture is continually being socially constructed, and because individual identities are constructed through the intersection of racial, ethnic, class, gender, and other experiences, it cannot be reduced to static characteristics or essences (McCarthy, 1995).

The vision of current reform aiming at “academic achievement for all students” requires integrating disciplinary knowledge with knowledge of student diversity (McLaughlin, Shepard, & O’Day, 1995). Unfortunately, the existing knowledge base for promoting academic achievement with a culturally and linguistically diverse student population is limited and fragmented, in part because disciplinary knowledge and student diversity have traditionally constituted separate research agendas (O. Lee, 1999). In mathematics education, although reform documents highlight “mathematics for all” (NCTM, 1989, 2000) as the principle of equity and excellence, they do not provide a coherent conception of equity or strategies for achieving it (Eisenhart, Finkel, & Marion, 1996; O. Lee, 1999; Rodríguez, 1997). The multicultural education literature, on the other hand, emphasizes issues of cultural and linguistic diversity and equity, but with little consideration of the specific demands of the different academic disciplines (Banks, 1993; Ladson-Billings, 1994).

Since mathematics usually tends to be presented as a set of objective and universal facts and rules, these subjects are often viewed as "culture free" and not considered socially and culturally constructed disciplines (Banks, 1993; O. Lee, 1999; Peterson & Barnes, 1996; Rodríguez, 1997; Secada, 1989). Teachers need to understand what counts as knowledge in math/science as well as how knowledge may be related to norms and values of diverse languages and cultures.

Instructional practices have traditionally relied on examples, analogies, and artifacts that are often unfamiliar to non-mainstream students (Barba, 1993; Ninnes, 2000).  Teachers who provide culturally relevant instruction capitalize on student strengths—what they do know instead of what they do not know. For example, the curriculum of the Algebra Project (Silva & Moses, 1990) uses student knowledge of the subway system as a basis for understanding operations with integers. The focus on student strengths contrasts to a remediation model of teaching urban students, where curriculum and instruction are predicated on what students do not know and often emphasize rote skills (Haberman, 1991; Oakes, 1990).

Dealing with integrating diverse cultures in the classroom needs a conceptual framework in order to make coherent decisions as a teacher. Here we present a summary of three well-known and respected approaches in teaching mathematics while integrating diverse cultures.

 
2.    Teaching mathematics in multicultural classrooms: three approaches.

a) The Situated Perspective

In the situated perspective, “learning becomes a process of changing participation in changing communities of practice in which an individual’s resulting knowledge becomes a function of the environment in which she or he operates” (Stinson, 2004).
Consequently, the situated perspective (in contrast to constructivist perspectives) emphasizes interactive systems that are larger in scope than the behavioral and cognitive processes of the individual student.
Mathematics knowledge in the situated perspective is understood as being co-constituted in a community within a context. It is the community and context in which the student learns the mathematics that significantly impacts how the student uses and understands the mathematics (Boaler, 2000b).

Boaler (1993) suggests that learning mathematics in context assists in providing student motivation and interest and enhances transference of skills by linking classroom mathematics with real-world mathematics. She argues, however, that learning mathematics in contexts does not mean learning mathematics ideas and procedures by inserting them into “real-world” textbook problems or by extending mathematics to larger real-world class projects. Rather, she suggests that the classroom itself becomes the context in which mathematics is learned and understood: “If the students’ social and cultural values are encouraged and supported in the mathematics classroom, through the use of contexts or through an acknowledgement of personal routes and direction, then their learning will have more meaning” (p. 17).
The situated perspective offers different notions of what it means to have mathematics ability, changing the concept from “either one has mathematics ability or not” to an analysis of how the environment co-constitutes the mathematics knowledge that is learned (Boaler, 2000a). Boaler argues that this change in how mathematics ability is assessed in the situated perspective could “move mathematics education away from the discriminatory practices that produce more failures than successes toward something considerably more equitable and supportive of social justice” (p. 118).

b) The Culturally Relevant Perspective
Gloria Ladson-Billings (1994) developed the “culturally relevant” (p. 17) perspective as she studied teachers who were successful with African-American children. This perspective is derived from the work of cultural anthropologists who studied the cultural disconnects between (White) teachers and students of color and made suggestions about how teachers could “match their teaching styles to the culture and home backgrounds of their students” (Ladson-Billings, 2001, p. 75). Ladson-Billings defines the culturally relevant perspective as promoting student achievement and success through cultural competence (teachers assist students in developing a positive identification with their home culture) and through sociopolitical consciousness (teachers help students develop a civic and social awareness in order to work toward equity and social justice).
Teachers working from a culturally relevant perspective (a) demonstrate a belief that children can be competent regardless of race or social class, (b) provide students with scaffolding between what they know and what they do not know, (c) focus on instruction during class rather than busy-work or behavior management, (d) extend students’ thinking beyond what they already know, and (e) exhibit in-depth knowledge of students as well as subject matter (Ladson-Billings, 1995). Ladson-Billings argued that all children “can be successful in mathematics when their understanding of it is linked to meaningful cultural referents, and when the instruction assumes that all students are capable of mastering the subject matter” (p. 141).
Mathematics knowledge in the culturally relevant perspective is viewed as a version of ethnomathematics—ethno defined as all culturally identifiable groups with their jargons, codes, symbols, myths, and even specific ways of reasoning and inferring; mathema defined as categories of analysis; and -tics defined as methods or techniques (D’Ambrosio, 1985/1997, 1997). In the culturally relevant mathematics classroom, the teacher builds from the students’ ethno or informal mathematics and orients the lesson toward their culture and experiences, while developing the students’ critical thinking skills (Gutstein, Lipman, Hernandez, & de los Reyes, 1997).

c) Critical Pedagogies.
Rooted in the social and political critique of the Frankfurt School, critical pedagogies perceive mathematics as a tool for sociopolitical critique.
The critical perspective in pedagogy is characterized as (a) providing an investigation into the sources of knowledge, (b) identifying social problems and plausible solutions, and (c) reacting to social injustices. In providing these most general and unifying characteristics of a critical education, Skovsmose (1994) notes, “A critical education cannot be a simple prolongation of existing social relationships. It cannot be an apparatus for prevailing inequalities in society. To be critical, education must react to social contradictions” (p. 38).  Skovsmose (1994), drawing from Freire’s (1970/2000) popularization of the concept “conscientizaćčo” and his work in literacy empowerment, derived the term “mathemacy” (p.48).
Skovsmose claims that since modern society is highly technological and the core of all modern-day technology is mathematics, that mathemacy is a means of empowerment. He stated, “If mathemacy has a role to play in education, similar to but not identical to the role of literacy, then mathemacy must be seen as composed of different competences: a mathematical, a technological, and a reflective” (p. 48).
In the critical perspective, mathematics knowledge is seen as demonstrating these three competences (Skovsmose, 1994). Mathematical competence is demonstrating proficiency in the normally understood skills of school mathematics, reproducing and mastering various theorems, proofs, and algorithms. Technological competence demonstrates proficiency in applying mathematics in model building, using mathematics in pursuit of different technological aims, and reflective competence achieves mathematics’ critical dimension, reflecting upon and evaluating the just and unjust uses of mathematics. Skovsmose contends that mathemacy is a necessary condition for a politically informed citizenry and efficient labor force, claiming that mathemacy provides a means for empowerment in organizing and reorganizing social and political institutions and their accompanying traditions.

 

References

Barba, R. H. (1993). A study of culturally syntonic variables in the bilingual/bicultural science classroom. Journal of Research in Science Teaching, 30, 1053-1071.

Boaler, J. (1993). The role of context in the mathematics classroom: Do they make mathematics more “real”? For the Learning of Mathematics, 13(2), 12–17.

Boaler, J. (2000a). Exploring situated insights into research and learning. Journal for Research in Mathematics Education, 31(1), 113–119.

Boaler, J. (2000b). Mathematics from another world: Traditional communities and the alienation of learners. Journal of Mathematical Behavior, 18(4), 379–397.

D’Ambrosio, U. (1997). Ethnomathematics and its place in the history and pedagogy of mathematics. In A. B. Powell & M. Frankenstein (Eds.), Ethnomathematics: Challenging Eurocentrism in mathematics education (pp. 13–24). Albany: State University of New York Press. (Original work published in 1985)

D’Ambrosio, U. (1997). Foreword. In A. B. Powell & M. Frankenstein (Eds.), Ethnomathematics: Challenging Eurocentrism in mathematics education (pp. xv–xxi). Albany: State University of New York Press.

Eisenhart, M., Finkel, E., & Marion, S. F. (1996). Creating the conditions for scientific literacy: A re-examination. American Educational Research Association, 33, 261-295.

Freire, P. (2000). Pedagogy of the oppressed (30th anniversary ed.). New York: Continuum. (Original work published 1970)

Gutstein, E., Lipman, P., Hernandez, P., & de los Reyes, R. (1997). Culturally relevant mathematics teaching in a Mexican American context. Journal for Research in Mathematics Education, 28(6), 709–737.

Haberman, M. (1991). The pedagogy of poverty versus good teaching. Phi Delta Kappan, 73, 290-294.

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

Ladson-Billings, G. (1995). Making mathematics meaningful in a multicultural context. In W. G. Secada, E. Fennema, & L. Byrd (Eds.), New directions for equity in mathematics education (pp. 126–145). Cambridge: Cambridge University Press.

Ladson-Billings, G. (2001). The power of pedagogy: Does teaching matter? In W. H. Watkins, J. H. Lewis, & V. Chou (Eds.), Race and education: The roles of history and society in educating African American students (pp. 73–88). Boston: Allyn & Bacon.

Lee, O. (1999). Equity implications based on the conceptions of science achievement in major reform documents. Review of Educational Research, 69(1), 83-115.

McCarthy, C. (1995). The problems with origins: Race and the contrapuntal nature of the educational experience. In C. E. Sleeter & P. L. McLaren (Eds.), Multicultural education, critical pedagogy, and the politics of difference (pp. 245-268). Albany, NY: SUNY Press.

McLaughlin, M. W., Shepard, L. A., & O’Day, J. A. (1995). Improving education through standards-based reform: A report by the National Academy of Education Panel on Standards-based Education Reform. Stanford, CA: Stanford University, National Academy of Education.

National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.

Ninnes, P. (2000). Representations of indigenous knowledge in secondary school science textbooks in Australia and Canada. International Journal of Science Education, 22(6), 603-617.

Oakes, J. (1990). Opportunities, achievement, and choice: Women and minority students in science and mathematics. In C. B. Cazden (Ed.), Review of Research in Education, Vol. 16 (pp. 153-222). Washington, DC: American Educational Research Association.

Rodríguez, A. (1997). The dangerous discourse of invisibility: A critique of the NRC’s National Science Education Standards. Journal of Research in Science Teaching, 34, 19-37.

Secada, W. G. (1989). Educational equity and equality of education: An alternative conception. In W. G. Secada (Ed.), Equity in education (pp. 68-88). Philadelphia, PA: The Falmer Press.

Silva, C. M., & Moses, R. P. (1990). The Algebra Project: Making middle school mathematics count. Journal of Negro Education, 59(3), 375-391.

Skovsmose, O. (1994). Towards a critical mathematics education. Educational Studies in Mathematics, 27, 35–57.

Stinson, D. W. (2004). Mathematics as “Gate-Keeper” (?): Three Theoretical Perspectives that Aim Toward Empowering All Children With a Key to the Gate.  The Mathematics Educator, Vol. 14, No. 1, 8-18.

 

 

 



Classroom Activities: Culturally Diverse Lesson Plans

 

Š      Heirloom Geometry :  This activity allows students to bring in an artifact from home with both cultural and geometric significance, discuss the significance of their artifacts with the class, and potentially work with coordinatizing the patterns on the artifacts.

Š      Sweat Shop Math: This activity examines the wages in countries including the United States.  The goal is to help students look at the cost of living in various countries to compare how people live.  Students will work to understand how these wages effect living conditions and life in those countries.  Part of the goal is to promote cultural understanding and tolerance to create a deeper understanding in the classroom.  Students make mathematical connections to data analysis, and statistical inference.

   Sweat Shop Math Teacher’s Notes  taken from:
   Gutstein, E. & Peterson, B. (2005). Rethinking Mathematics: Teaching Social Justice

           by the Numbers. Milwaukee, WI: Rethinking Schools.  (pages 53-61, 160-161).

 

 

 

 

 


NCTM Principles and Standards References

to Equity and Cultural Diversity

The Equity Principle

Excellence in mathematics education requires equity—high expectations and strong support for all students.

Equity requires high expectations and worthwhile opportunities for all.

Equity requires accommodating differences to help everyone learn mathematics.

Equity requires resources and support for all classrooms and all students.

Flores, Alfinio. "Sí Se Puede, 'It Can Be Done': Quality Mathematics in More than One Language." In Multicultural and Gender Equity in the Mathematics Classroom: The Gift of Diversity, 1997 Yearbook of the National Council of Teachers of Mathematics, edited by Janet Trentacosta, pp. 81–91. Reston, Va.: National Council of Teachers of Mathematics, 1997.

Chapter 1: A Vision for School Mathematics

URL:  chapter1/index.htm.
".. and voting knowledgeably all call for quantitative sophistication. Mathematics as a part of cultural heritage. Mathematics is one of the greatest cultural and intellectual .."

 

The Equity Principle

URL:  chapter2/equity.htm
".. help to understand the strengths and needs of students who come from diverse linguistic and cultural backgrounds, who have specific disabilities, or who possess a special talent and .."

4. Standards for School Mathematics: Representation

URL:  chapter3/rep.htm
".. expressions and equations, graphs, and spreadsheet displays—are the result of a process of cultural refinement that took place over many years. When students gain access to .."

5. Grades Pre-K - 2: Communication

URL:  chapter4/comm.htm
".. questions in class (Bransford, Brown, and Cocking 1999). Teachers need to be aware of the cultural patterns in their students' communities in order to provide equitable .."

6. Grades 9 - 12: Representation

URL:  chapter7/rep.htm
".. point against the time from takeoff to landing Mathematics is one of humankind's greatest cultural achievements. It is the "language of science," providing a means by .."

 

 

 

 


Compilation of Cultural Diversity

Resources for Teaching Mathematics

 

 

Books

 

NCTM

 

Articles

Lesson Plans/

Activities

 

Ga Standards

 

Websites

 

 

 

 

 


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Created for Dr. Larry Hatfield’s EMAT 4650/6650 Class, Summer 2007,

By: Kelli Parker, for Special Focus Group: Cultural Diversity Project.

 

 

 

 

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