Reaching Mathematics
Learners from
Cultures Other
than Yours
Ed Dickey
SCCTM
College of Education
Instruction &Teacher Education
Diverse Cultures in the US and SC
• The U.S. has always been a “melting pot” of
cultures (Today12.4% African-American, 14.8%
Hispanic)
• South Carolina classrooms include cultural and
economic diversity (29% African-American, 3.5%
Hispanic; 15% below poverty line, 43rd
nationally in personal income)
• Language Diversity: Other than English spoken at
home (US has17.9%, SC has 5.2 %)
Sources: US Census http://quickfacts.census.gov/qfd/states/45000.html
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Education and Equity
• We educate to prepare our students as
citizens and as productive human beings
• Education requires a spirit of mutual respect,
trust, and caring
• “Every child comes with strengths as well as
experiences… Can you identify a strength
of each child in your classroom?” NCTM’s
Equity: All Means ALL!
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Achievement Gap
• The “achievement gap” between white and
students of color is not the result of
deficiencies of intellect
• The gap is real but results from unequal
resources and opportunities
• Bridging the achievement gap requires all
educators to be conscious of cultural
differences and address the diverse realities
that students bring to the classroom
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Equity and Quality
Equity without quality is useless;
quality without equity is unjust”
• “
Guillermo Mendieta, author of Pictorial
Mathematics (www.pictorialmath.com )
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Ideas I want to share…
• Awareness/Sensitivity to Issues of
Culture
• Importance of Inclusion and Acceptance
• Humanizing and Caring Teachers
• Inclusion of visual representations available
on the web that teachers can use to infuse
instruction with materials that are culturally
relevant to their students
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Ed Dickey’s Culture
•Born in Brazil
•American father and Brazilian mother
•Came to the U.S. at age 5
•Elementary and High School Education
thru DoDD Schools in Europe
•Resident of South Carolina since 1973
SCCTM
College of Education
Instruction &Teacher Education
What Is Culture?
• Patterns of Human Activity and Values
Exhibited by People
• Symbolic Structures that give Activities
Significance and Importance
• Constantly in Flux and not always Agreed
Upon
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What Culture is NOT:
• Things: artifacts or materials used by
people
• Lists of traits or facts (stereotypes)
• Biological traits such as race
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Is Mathematics Culture Neutral?
• Mathematics is often thought of as abstract and therefore
free of cultural overtone.
• Möbius Transformations Video
(http://www.youtube.com/watch?v=JX3VmDgiFnY)
• “Pillars” of mathematical thought as European males
• Other cultural perspectives are not as well known:
mathematics teacher Gary Booker’s reference to the
Ishango Bone
(http://www.youtube.com/watch?v=kxh3LDHo7AI)
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Is Mathematics Culture Neutral?
• We teach mathematics using context… this introduces
culture
• Instructional choices are based on values and beliefs
• Because teachers must make choices and decisions,
mathematics teaching can be shaped by political, social,
and cultural forces
• Students in our mathematics classes represent a broad
array of cultures… being neutral to other cultures leads
students to disengage… not try.
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Who Should Teach Mathematics to
African American Children?
(Martin, 2007)
Highly qualified teachers for African American children:
• develop a deep understanding of the social realities experienced
by these students,
• take seriously their role in helping to shape the racial, academic,
and mathematics identities of African American learners,
• conceptualize mathematics not just as a school subject but as a
means to empower African American students to address their
social realities, and
• become agents of change who challenge perspectives that
construct African American children as less than ideal learners and
in need of being saved or rescued from their blackness.
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Mathematics Teachers’ Imperative
• Honor different cultures with the teaching of mathematics
so we can help students construct meaning and see the
value of learning mathematics.
• Demonstrate a sensitivity to the contexts we select and to
the different cultural and community influences involved in
mathematics itself and the teaching of mathematics.
• Avoid a racial stereotypes and cultural bias.
• Care deeply and sincerely about the children they teach.
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Consider Carefully HOW We Teach
• Portray cultural groups as part of instruction
• Employ a historical perspective that is
inclusive
• Respect the mathematics of different cultures
• Respect the learning styles and preferences
of different cultures particularly those
representative of our students
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Portray Cultural Groups as Part of
Instruction
• Benjamin Banneker
– Mathematician and
Astronomer
• Juan Diez
– First mathematics book,
Sumario Compendioso
1556, in the New World
• Grace Hopper
– Computer scientist
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Employ a Historical Perspective that is
Inclusive
• Evolution of the Number System
• Al-Khwarizmi and Algebra
• Pascal’s Triangle and China
• The MacTutor History of Mathematics Archive
(http://www-groups.dcs.st-and.ac.uk/~history/ )
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Math History on the Internet
• Let’s Play Math Blog: “The story of mathematics is
the story of interesting people. What a shame it is
that our children see only the dry remains of these
people’s passion.”
http://letsplaymath.wordpress.com/2008/06/27/ma
th-history-on-the-internet/#mhvaluable
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Respect the Mathematics of Different
Cultures
• Ethnomathematics
– “One of the objectives for an ethnomathematics
program is learning to understand the student’s own
reality and create a pedagogical action in a natural
manner by using a cognitive focus and a cultural basis
for the curriculum.”
• Street Mathematics (T. Nunes, A. Schliemann
and D. Carraher as reported by Keith Devlin in the MAA
Online)
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Street Mathematics
•
•
•
•
“How much is one coconut?"
"Thirty-five," he replies with a smile.
"I'd like ten. How much is that?"
The boy pauses for a moment before
replying. Thinking out loud, he says:
"Three will be 105; with three more,
that will be 210. (Pause) I need four
more. That is . . . (pause) 315 . . . I think
it is 350."
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Street Mathematics
• One of the questions he had been asked at his market
stall, when he was selling coconuts costing 35 cruzeiros
each, was: "I'm going to take four coconuts. How much is
that?"
• The boy replied: "There will be one hundred five, plus
thirty, that's one thirty- five . . . one coconut is thirty-five .
. . that is . . . one forty."
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Street Mathematics
• On the formal arithmetic test, the boy was asked to
calculate 35 x 4.
• He worked mentally, vocalizing each step as the
researcher requested, but the only thing he wrote down
was the answer.
• Here is what he said; "Four times five is twenty, carry the
two; two plus three is five, times four is twenty."
• He then wrote down "200" as his answer.
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Respect the Mathematics of Different
Cultures
• Multiplication
– Roman Numerals XXI times XIII
– Vedic Multiplication 21 x 13 video
http://www.youtube.com/watch?v=Ph2OWUd3rd8
• Abbott and Costello Math
http://www.youtube.com/watch?v=rLprXHbn19I
• Subtraction in Mexico
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Subtraction in Mexico
1
1
963
-369
4
7
5 94
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Respect the learning styles and
preferences of different cultures
• Symbolic and Visual Learning
Preferences
• English Language Learners
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Notation Conventions
• Comparison between U.S. and Latin
American Countries
• Summary by Noemi Lopez (TODOS, 2007)
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Respect the learning styles and
preferences of different cultures
• Draw from the “lifeworld” resources of your students and their
knowledge of the community
– Johnson and her colleagues (2007) describe how to use interest
surveys to connect with rural students and develop culturally
relevant lessons.
• Algebra videos in Spanish
– http://www.youtube.com/watch?v=FRhd1k1gO30
– http://www.youtube.com/watch?v=pMQwRgsJ8IQ
• Questioning Techniques
– Fact-based questions (What is this shape?) vary among and
may be foreign to certain cultures
– Providing time to respond
– LISTENING
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Conclusion
• Respect for Diversity
• Build Respect for Culture
• A closing quotation from Ubiratan
D’Ambrosio, Brazilian, mathematician
and winner of the 2005 Felix Klein
Medal of the International Commission
on Mathematical Instruction
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Conclusion
“The two fundamental objectives of education
(preparing for citizenship and stimulating
creativity) can hardly be achieved, in a
constructive way, by a traditional, formal,
mathematics education, which frequently leads to
individual annihilation, and intellectual, even
material, enslavement, and favors inequality,
bigotry and arrogance.”
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Conclusion
“ For all students to succeed at the highest level
possible, they must know that their teacher
believes that they can do well. With support,
collaboration, and effort, students and teachers
together can reach their goals.”
NCTM New Bulletin , October 2008
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Conclusion
To paraphrase psychologist Hiam Ginott,
as a teacher you have to the power everyday to:
• Torture or Inspire
• Humor, Heal or Hurt
• Humanize or De-humanize
Take this awesome responsibility seriously and
care for the needs of every child in your
class.
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References – Print
• D’Ambrosio, Ubiratan. & Rosa, M. (2008). A Dialogue with Ubiratan
D’Ambrosio: a Brazilian Conversation about Ethnomathematics. Revista
Latinoamericana de Etnomatemática, 1:2, 88-110
• Devlin, Keith (2005). Street Mathematics. MAA Online, Retrieved October 8,
2008 from http://www.maa.org/devlin/devlin_05_05.html
• Johnson, Amy, Baker, A. & Bruer, L (2007). Interdependence, Garbage
Dumping, and Feral Dogs: Exploring Three Lifeworld Resources of Young
Children in a Rural School. Early Childhood Education Journal, 34:6, 371-377.
• Martin, Danny Bernard (2007). Beyond Missionaries and Cannibals: Who
Should Teach African American Children? The High School Journal, Oct-Nov,
6-27
• Strutchens, Marilyn (1994). Mathematical Empowerment and African
American Families. In M.M. Atwater, K. Radzik, & M. Strutchens (Eds.).
Multicultural Education: Inclusion for All, 257-270. Athens, GA: The University of
Georgia.
• Wiest, Lynda R. (2001) Teaching Mathematics from a Multicultural
Perspective, Equity & Excellence in Education, 34:1, 16-25
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References – Web
• Lopez, Noemi (2008). Mathematics Notation Comparisons
Between U.S. and Latin American Countries. Available from
http://data.memberclicks.com/site/toma/operation_description.pdf
• MacTutor History of Mathematics Archive: available at
http://www-groups.dcs.st-and.ac.uk/~history/
• Math History on the Internet. From the Let’s Play Math Blog
available at http://letsplaymath.wordpress.com/2008/06/27/math-history-onthe-internet/#mhvaluable
• Pictorial Mathematics available at http://www.PictorialMath.com
• US Census QuickFacts available at
http://quickfacts.census.gov/qfd/states/45000.html
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References – Video
• Möbius Transformation retrieved from
http://www.youtube.com/watch?v=JX3VmDgiFnY
• Ishango Bone retrieved from
http://www.youtube.com/watch?v=kxh3LDHo7AI
• Learn Mathematics – Aprender Matemática: retrieved from
http://www.youtube.com/watch?v=Ph2OWUd3rd8
• Abbott and Costello 13 x 7 is 28: retrieved from
http://www.youtube.com/watch?v=rLprXHbn19I
• A Jugar Algebra: retrieved from
http://www.youtube.com/watch?v=FRhd1k1gO30
• Introducción al Algebra - Definición de Término: retrieved from
http://www.youtube.com/watch?v=pMQwRgsJ8IQ
• Download Streaming Videos for later use: http://keepvid.com/
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Department of Computer Science and Engineering and the