**ERIC Identifier:** ED482729

**Publication Date:** 2003

**Author: **Bush, William S.

**Source: **ERIC Clearinghouse for Science Mathematics and Environmental
Education

**Understanding Mathematics and Culture in Rural Contexts.
ERIC Digest. **

Scholarship and writing about culture and mathematics covers a wide
range of topics:
the cultural bases for mathematics, mathematics development in different
cultures, the
historical culture of mathematics, effects of culture on how people
learn about and are
disposed toward mathematics, and the political effects on societies
of mathematics and
mathematics education. This Digest provides an overview of "concepts,"
"writers," and"tenets" associated with the study of mathematics and culture, and
offers researchers a
framework for the field, particularly with regard to rural contexts.

**DEFINING ETHNOMATHEMATICS**

Ubiratan D'Ambrosio, a Brazilian mathematician, coined the term "ethnomathematics"
in the 1980s and offered this definition: "Ethnomathematics is the way
different cultural
groups mathematise (count, measure, relate, classify, and infer)" (D'Ambrosio,
1984). In other words, ethnomathematics examines how different cultural
groups use
mathematics.

In subsequent writing about ethnomathematics, he and others struggled
with the
meaning of the term. While many scholars contributed to that debate,
D'Ambrosio's
evolving definitions reflect the full spectrum of discussions--from
very specific: "The
mathematics which is practiced among identifiable cultural groups such
as
national-tribal societies, labour groups, children of certain age brackets,
and
professional classes." (D'Ambrosio, 1985, p. 45), to very broad: "The
arts or techniques developed by different cultures to explain, to understand,
to cope with their
environment" (D'Ambrosio, 1992, p. 1184).

Barton (1996) grouped discussions about ethnomathematics into two categories:
mathematics and mathematics education. In each category he identified
four primary
topics:

Mathematics

* Cultural nature of mathematics

* Mathematics thought in other cultures

* Cultural history of mathematics

*Politics of mathematics

Mathematics Education

* Mathematics learning in other cultures

* Situated cognition, including language and bilingualism

* Societal effects of mathematics education

* Relationships between mathematics and mathematics education

Barton then synthesized a definition of ethnomathematics intended to
embrace all of
these topics: "Ethnomathematics is a research programme of the way
in which cultural
groups understand, articulate and use the concepts and practices which
we describe as
mathematical, whether or not the cultural group has a concept of mathematics"
(p. 214).

According to Barton, this definition implies that "(a) ethnomathematics
is not a

mathematical study, it is more like anthropology or history; (b) the
definition itself
depends on who is stating it, and it is culturally specific; (c) the
practice which it
describes is also culturally specific; and (d) ethnomathematics implies
some form of
relativism for mathematics" (p. 215).

**CULTURE, MATHEMATICS, AND MATHEMATICS EDUCATION**

Professional discourse and literature relating to culture, mathematics
and mathematics
education can be characterized by the following domains of study: culture
and
mathematics, culture and mathematics education, and the effects of
culture on
mathematics achievement.

Culture and Mathematics

Many scholars believe that mathematics activity is highly cultural.
Topics of study
include:

* The cultural nature of mathematics. Dossey (1992) asserted that mathematicians
do
not agree on the nature of mathematics, debating whether or not it
is bound by culture
("interna-lists") or culture-free ("externalists"). Interna-lists such
as Alan Bishop (1976,
1983, 1986, 1988) believe, in Bishop's words, that mathematics is "a
cultural product
which has developed as a result of various activities" and that counting,
locating,
measuring, designing, playing, and explaining are all part of that
cultural product.
Others, including critics of ethnomathematics are externalists who
believe that

mathematics thought is virtually culture free.

* Mathematical thought in other cultures. A body of anthropological
research focuses
largely on intuitive mathematics thinking developed in largely undereducated
cultures.
These studies examined populations varying from native peoples of Australia,
Africa,
the Pacific Islands, and North America to construction workers in Brazil.
This work is
enumerated and summarized in Barton (1994).

* Cultural history of mathematics. Studies in this area attempt to identify
the historical
mathematical contributions of different cultures across the world.
Early examples
include D'Ambrosio's (1980) review of the evolution of mathematics
and his call for
incorporating ethnomathematics into the history of mathematics (D'Ambrosio,
1985).

* Politics of mathematics. These works, such as Bishop's (1990) essay
on the powerful influence of Western mathematics and D'Ambrosio's (1990) discussion of the role of mathematics in building democratic and just societies,
examine how mathematics has affected non-academic areas of society.

Culture and Mathematics Education

Mathematics education can both reflect and influence the political and
social dynamics
of a culture. Topics under this heading include:

* Mathematics learning in other cultures. This body of writing focuses
on the importance of using culturally specific contexts in teaching and
learning mathematics, including a) using relevant examples from the student's
own culture; and b) exposing students to a variety of cultural contexts (multiculturalism). Examples in the first category include making mathematics
curricula more accessible to Native Americans, African Americans, and Hispanic
Americans. Examples in the second include using multicultural children's
literature to teach mathematics and integrating ethnomathematics principles
in middle and elementary school classrooms.

* Situated cognition including language and bilingualism. This research
focuses on
culture's influence in learning mathematics. Situated cognition refers
to the intuitive
mathematics needed for specific tasks rather than the formalized, codified
mathematics
learned in school. In this vein researchers have studied groups as
varied as Brazilian
candy vendors (Saxe, 1988) and American dairy farmers (Schribner, 1984).
Studies on bilingualism's effect on mathematics learning also falls into
this topic.

* Societal effects of mathematics education. This research includes,
for example, work
examining such issues as how mathematics may be used to create and
reveal power
and oppression--the critical mathematics pedagogy theory of Frankenstein
(1997)--and the Mathematics and Society curriculum of Abraham and Bibby
(1988).

* Relationships between mathematics and mathematics education. Work
on integrating
ethnomathematics and teacher preparation (Presmeg, 1998) and on relationships
between African Americans' perception of mathematics and their motivation
to learn
mathematics (Walker and McCoy, 1997) fall under this heading.

Effects of Culture on Mathematics Achievement

Researchers have sought to identify cultural factors that might explain
differences in
mathematics achievement and attitudes, investigating differences across
lines of
national origin, ethnicity, and gender. This body of research identified
the following
general cultural influences on mathematics performance and dispositions:

* Popular media. Media shape and reinforce popular beliefs about ethnic
and gender
differences in mathematical abilities and achievement (Leder, 1992;
Malloy, 1997).

* Parents. Parent expectations consistently show strong effects on student
performance and attitudes. This is reflected in work that contrast Asian
parents' beliefs that effort results in successful performance with American
parents' belief that innate ability largely affects performance (Stevenson,
1987) and a wide range of other work examining parents' attitudes and expectations.

* Teachers. Cross-cultural comparisons of curricula and teaching routines
show widely
varying expectations of student performance and abilities. To cite
just one example,
Zhonghong and Eggleton (1995) found that mathematics curricula in the
United States
reveal low expectations for performance, while Chinese curricula challenged
its
students. In another vein, Bradley (1984) observed that many Native
American students had extensive knowledge of mathematics deeply rooted
in their culture and traditions; few teachers, however, tapped into this
reservoir of traditional knowledge (Kawagley, 1990; Pomeroy, 1988). Leder
(1992) documented subtle differences in the way teachers interacted with
male and female students in mathematics classrooms.

* Students' own beliefs. Research consistently finds that student attitudes
and beliefs
often differ in ways that reflect varying cultural heritage, an observation
not surprising
considering that cultural heritage and parental beliefs and attitudes
shape students'
beliefs and attitudes.

* Language. Researchers have examined how language differences for Chinese,
(Geary et al., 1996), Spanish-speaking (Valverde, 1984), and Native
American (Moore, 1994) students helped or hindered their learning mathematics
concepts.

**A RESEARCH AGENDA FOR CULTURE AND MATHEMATICS IN RURAL CONTEXTS**

Barton (1996) outlined a classification scheme for research in ethnomathematics
in
three dimensions: time, culture, and mathematics. We might apply his
scheme to our
attempt to understand how mathematics is situated in a rural context
in this way:

* Time: Examples include how early rural settlers used mathematics or
how modern
rural entrepreneurs use mathematics.

* Culture: Examples include the extent to which rural male teens value
mathematics,
whether rural girls are encouraged to pursue careers based on mathematics,
or how
rural teachers incorporate community issues or activities in mathematics
lessons.

* Mathematics: Examples include the formal conceptions of mathematics
held by rural
teachers, their students, and community members or how mathematics
is intuitively
used by rural craftsmen and farmers.

**REFERENCES**

Barton, B. (1996). Making sense of ethnomathematics: Ethnomathematics
is making
sense. "Educational Studies in Mathematics," 31, 201-33.

Bradley, C. (1984). Issues in mathematics education for Native Americans
and
directions for research. "Journal for Research in Mathematics Education,"
15, 96-106.

D'Ambrosio, U. (1984). "The intercultural transmission of mathematical
knowledge:
Effects on mathematical education." Campinas: UNICAMP.

D'Ambrosio. (1985). Ethnomathematics and its place in the history and
pedagogy of
mathematics. "For the Learning of Mathematics," 5, 44-8.

D'Ambrosio, U. (1992). Ethnomathematics: A research programme on the
history and
philosophy of mathematics with pedagogical implications. "Notices of
the American
Mathematics Society," 39, 1183-85.

Geary, D. C., Bow-Thomas, C. C., Fan, L., & Stigler, R. S. (1996).
Development of
arithmetical competencies in Chinese and American children: Influence
of age,
language, and schooling. "Child Development," 67, 2022-2044.

Kawagley, O. (1990). Yup' ik ways of knowing. "Canadian Journal of Native
Education," 17, 5-17.

Leder, G. C. (1992). Mathematics and gender: Changing perspectives.
In D. A. Grouws (Ed.), "Handbook of research on mathematics teaching and
learning" (pp.39-48). New York: MacMillan.

Malloy, C. E. (1997). Including African American students in the mathematics

community. In J. Trentacosta & M. J. Kenney (Eds.), "Multicultural
and gender equity in the mathematics classroom: The gift of diversity"
(pp. 23-33). Reston, VA: National
Council of Teachers of Mathematics.

Moore, C. G. (1994). Research in Native American mathematics education.
"For the
Learning of Mathematics," 14, 9-14.

Pomeroy, D. (1988). "A comparative analysis of Yup'ik and western ways
of acquiring knowledge in the sciences" [working paper]. Fairbanks: University
of Alaska.

Presmeg, N. C. (1998). Ethnomathematics in teacher education. "Journal
of

Mathematics Teacher Education," 1, 317-39.

Stevenson, H. (1987). America's math problems. "Educational Leadership,"
45, 4-10.

Valverde, L. A. (1984). Underachievement and underrepresentation of
Hispanics in
mathematics and mathematics related careers. "Journal for Research
in Mathematics
Education," 15, 123-33.

Walker, E. N. & McCoy, L. P. (1997). Students' voices: African Americans
and
Mathematics. In J. Trentacosta & M. J. Kenney (Eds.), "Multicultural
and gender equity in the mathematics classroom: The gift of diversity"
(pp. 34-45). Reston, VA: National Council of Teachers of Mathematics.

Zhonghong, J., & Eggleton, P. (1995). A brief comparison of the
U.S. and Chinese
middle school mathematics programs. "School Science and Mathematics,"
95, 187-94.