Cultural Diversity in the
Mathematics Classroom
This page
is being created for Dr. Larry Hatfields 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
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).
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.
Culturally
relevant teaching practices include the specific methodology that the teacher
brings to the classroom to effectively teach students based on their
culture.
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
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.
The term
culturally relevant began to appear in the 1970s (Ladson-Billings,
1995).
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
Websters
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.
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).
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.
In 1986, Parekh referred to culturally
relevant teaching as multicultural education.
Parekh
(1986) stated that multicultural education was a refined version of a liberal
education which celebrated the plurality of the world.
Parekh (1986) defined culturally
relevant pedagogy as ensuring equitable access and treatment for all groups in
schools.
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.
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.
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.
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.
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).
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
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 schools 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.
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.
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).
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).
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).
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.
Students
need to experience connected, applied mathematics (Ladson-Billings, 2000
b).
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).
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.
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.
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.
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).
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_
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, & ODay, 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; Rodrguez, 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; Rodrguez, 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.
In the
situated perspective, learning becomes a process of changing participation in
changing communities of practice in which an individuals 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 (DAmbrosio, 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 Freires
(1970/2000) popularization of the concept conscientizao 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.
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.
DAmbrosio, 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)
DAmbrosio, 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.,
& ODay, 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.
Rodrguez, A. (1997). The
dangerous discourse of invisibility: A critique of the NRCs 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
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.
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 Teachers 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
Excellence
in mathematics education requires equity—high expectations and strong
support for all students. |
Flores, Alfinio. "S
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 .."
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
Thank you for visiting our
Website!!
Created for Dr. Larry Hatfields EMAT 4650/6650 Class,
Summer 2007,
By: Kelli Parker, for Special Focus Group: Cultural
Diversity Project.