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College of Education


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Title: College of Education

Reaching Mathematics Learners from Cultures Other
than Yours Ed Dickey
Diverse Cultures in the US and SC
  • The U.S. has always been a melting pot of
    cultures (Today12.4 African-American, 14.8
  • 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//

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? NCTMs Equity All
    Means ALL!

Achievement Gap
  • The achievement gap between white and students
    of color is not the result of deficiencies of
  • 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

Equity and Quality
  • Equity without quality is useless quality
    without equity is unjust Guillermo Mendieta,
    author of Pictorial Mathematics
    ( )

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

Ed Dickeys 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

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

What Culture is NOT
  • Things artifacts or materials used by people
  • Lists of traits or facts (stereotypes)
  • Biological traits such as race

Is Mathematics Culture Neutral?
  • Mathematics is often thought of as abstract and
    therefore free of cultural overtone.
  • Möbius Transformations Video (http//
  • Pillars of mathematical thought as European
  • Other cultural perspectives are not as well
    known mathematics teacher Gary Bookers
    reference to the Ishango Bone (http//

Is Mathematics Culture Neutral?
  • We teach mathematics using context this
    introduces culture
  • Instructional choices are based on values and
  • 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.

Who Should Teach Mathematics toAfrican American
Children?(Martin, 2007)
  • Highly qualified teachers for African American
  • 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.

Mathematics Teachers Imperative
  • Honor different cultures with the teaching of
    mathematics so we can help students construct
    meaning and see the value of learning
  • 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

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

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

Employ a Historical Perspective that is Inclusive
  • Evolution of the Number System
  • Al-Khwarizmi and Algebra
  • Pascals Triangle and China
  • The MacTutor History of Mathematics Archive
  • (http// )

Math History on the Internet
  • Lets 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 peoples passion.

Respect the Mathematics of Different Cultures
  • Ethnomathematics
  • One of the objectives for an ethnomathematics
    program is learning to understand the students
    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)

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."

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

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.

Respect the Mathematics of Different Cultures
  • Multiplication
  • Roman Numerals XXI times XIII
  • Vedic Multiplication 21 x 13 video
  • http//
  • Abbott and Costello Math
  • http//
  • Subtraction in Mexico

Subtraction in Mexico
  • 963
  • -369

1 7 4
1 4 9
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
  • Summary by Noemi Lopez (TODOS, 2007)

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//
  • http//
  • Questioning Techniques
  • Fact-based questions (What is this shape?) vary
    among and may be foreign to certain cultures
  • Providing time to respond

  • Respect for Diversity
  • Build Respect for Culture
  • A closing quotation from Ubiratan DAmbrosio,
    Brazilian, mathematician and winner of the 2005
    Felix Klein Medal of the International Commission
    on Mathematical Instruction

  • 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.

  • 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

  • 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.

References Print
  • DAmbrosio, Ubiratan. Rosa, M. (2008). A
    Dialogue with Ubiratan DAmbrosio a Brazilian
    Conversation about Ethnomathematics. Revista
    Latinoamericana de Etnomatemática, 12, 88-110
  • Devlin, Keith (2005). Street Mathematics. MAA
    Online, Retrieved October 8, 2008 from
  • 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, 346, 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, 341, 16-25

References Web
  • Lopez, Noemi (2008). Mathematics Notation
    Comparisons Between U.S. and Latin American
    Countries. Available from http//data.memberclick
  • MacTutor History of Mathematics Archive
    available at http//
  • Math History on the Internet. From the Lets
    Play Math Blog available at http//letsplaymath.wo
  • Pictorial Mathematics available at
  • US Census QuickFacts available at

References Video
  • Möbius Transformation retrieved from
  • Ishango Bone retrieved from http//
  • Learn Mathematics Aprender Matemática
    retrieved from http//
  • Abbott and Costello 13 x 7 is 28 retrieved from
  • A Jugar Algebra retrieved from
  • Introducción al Algebra - Definición de Término
    retrieved from http//
  • Download Streaming Videos for later use