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 SCCTM 2 10/3/2015 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! SCCTM 3 10/3/2015 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 SCCTM 4 10/3/2015 Equity and Quality Equity without quality is useless; quality without equity is unjust” • “ Guillermo Mendieta, author of Pictorial Mathematics (www.pictorialmath.com ) SCCTM 5 10/3/2015 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 SCCTM 6 10/3/2015 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 SCCTM 8 10/3/2015 What Culture is NOT: • Things: artifacts or materials used by people • Lists of traits or facts (stereotypes) • Biological traits such as race SCCTM 9 10/3/2015 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) SCCTM 10 10/3/2015 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. SCCTM 11 10/3/2015 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. SCCTM 12 10/3/2015 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. SCCTM 13 10/3/2015 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 SCCTM 14 10/3/2015 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 SCCTM 15 10/3/2015 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/ ) SCCTM 16 10/3/2015 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 SCCTM 17 10/3/2015 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) SCCTM 18 10/3/2015 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." SCCTM 19 10/3/2015 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." SCCTM 20 10/3/2015 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. SCCTM 21 10/3/2015 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 SCCTM 22 10/3/2015 Subtraction in Mexico 1 1 963 -369 4 7 5 94 SCCTM 23 10/3/2015 Respect the learning styles and preferences of different cultures • Symbolic and Visual Learning Preferences • English Language Learners SCCTM 24 10/3/2015 SCCTM 25 10/3/2015 SCCTM 26 10/3/2015 Notation Conventions • Comparison between U.S. and Latin American Countries • Summary by Noemi Lopez (TODOS, 2007) SCCTM 27 10/3/2015 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 SCCTM 28 10/3/2015 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 SCCTM 29 10/3/2015 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.” SCCTM 30 10/3/2015 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 SCCTM 31 10/3/2015 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. SCCTM 32 10/3/2015 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 SCCTM 33 10/3/2015 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 SCCTM 34 10/3/2015 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/ SCCTM 35 10/3/2015

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