The Algorithm Collection Project

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The Algorithm Collection Project

• Daniel Clark Orey
• Professor, Mathematics and Multicultural
  Education
• California State University, Sacramento
• http//www.csus.edu/indiv/o/oreyd

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Culture

• Culture is a problem-solving resource we need
  to draw-on, not a problem to be solved.
• Terry Cross

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Culture Creative Class

• Three Ts of a creative societies
• Technology
• Tolerance
• Talent
• see Richard Floridas Cities and the Creative
  Class

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Six New Paradigms

• Curriculum
• Professional Roles and Functions
• Policy and Management
• Professional Growth and Development
• Organizational Unit / Structure
• External Linkages

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Toffler

• A new civilization is emerging in our lives, and
  blind men everywhere are trying to suppress it.
  This new civilization brings with it new family
  styles changing ways of working, loving, and
  living a new economy new political conflicts
  and beyond all this an altered consciousness as
  well. Pieces of this new civilization exist
  today. Millions are already attuning their lives
  to the rhythms of tomorrow. Others, terrified of
  the future, are engaged in a desperate, futile
  flight into the past and are trying to restore
  the dying world that gave them birth The dawn of
  this civilization is the single most explosive
  fact of our lifetime.

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Paulo Freire

• ... our task is not to teach students to think
  -- they can already think but to exchange our
  ways of thinking with each other and look
  together for better ways of approaching the
  decodification of an object.
• Decodification to decode to transform
  into an intelligible form and understand

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What isEthnomathematics?
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Ethnomathematics

• For me, Ethnomathematics forms the intersection
  between mathematics and cultural anthropology and
  mathematical modeling.

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Ethnomathematics

• The theory of ethnomathematics was introduced by
  Brazilian mathematician, philosopher, and
  educator Ubiratan D'Ambrosio. He has explained
  that the concept of ethnomathematics is made from
  three words fro math Greek

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Ethnomathematics

• techne the art or technique
• mathema to explain, to understand, of playing
  in reality
• ethno inside of a proper cultural context

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Ethnomathematics

• Therefore DAmbrosio has defined
  ethnomathematics is the art or technique used to
  explain, to understand, reality inside a proper
  cultural context. Where the concept of culture is
  a broad one and includes

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Ethnomathematics

• Cultural-related learning styles related to
  activities such as arithmetic, measuring,
  classifying, ordering, inferring, and modeling.

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Ethnomathematics

• Historical developments in mathematics and
  technology.

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Ethnomathematics

• Prominent people in various cultural contexts
  who have made contributions to the field of
  mathematics.

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Ethnomathematics

• Cultural applications of nontraditional
  mathematics.
• Various forms of mathematics that may draw upon
  the interests, abilities, and talents of all
  students.

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Ethnomathematics

• Many ethnomathematicans are involved in active
  research, that is the documentation and
  empowerment of people through the mathematics
  that they use or have used in their non-academic,
  or traditional, or day to day lives.

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Ethnomathematics

• In the context of a local school or museum, we
  might do well to engage in the collection and
  exploration of examples of the mathematics in its
  community / region with in the context of the
• Mathematics that once was,
• Mathematics that is here now, and
• Contemplate the mathematics that might be.

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The ACP Vocabulary Collection

• The Algorithm Collection Project uses
  Ethnomathematics to explore the Basic Number
  Sense Acquisition across Cultures

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Algorithm

• After al-Khuwarizmi, the first scholar who
  generalized arithmetic applications and
  calculation

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Algorithm

• An algorithm is a specified sequence of steps
  that lead to a particular goal. The Math Gene
  How Mathematical Thinking Evolved and Why Numbers
  are Like Gossip. Basic Books.  p.10.
• Here we define algorithm in a customary way, as
  a finite, step-by-step procedure for
  accomplishing a task that we wish to complete.
• Usiskin, Z. (1998). Paper-and-Pencil Algorithms
  in a Calculator-and-Computer Age. In the Teaching
  and Learning of Algorithms in School Mathematics
  1998 NCTM Yearbook (Morrow Kenney, Eds.).
  Reston, VA NCTM. p. 7.

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Algorithm

• An algorithm is a step-by-step procedure
  designed to achieve a certain objective in a
  finite time, often with several steps that repeat
  or loop as many times as necessary. The most
  familiar algorithms are the elementary school
  procedures for adding, subtracting, multiplying,
  and dividing, but there are many other algorithms
  in mathematics.
• From Algorithms in Everyday Mathematics
• An algorithm is a precise, systematic method for
  solving a class of problems.
• Maurer, S. B. (1998). What is an Algorithm?
  What is an Answer? In the Teaching and Learning
  of Algorithms in School Mathematics 1998 NCTM
  Yearbook (Morrow Kenney, Eds.). Reston, VA
  NCTM   p. 21.

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The Algorithm Collection Project

• Educators in many countries are surprised to
  find that common day-to-day algorithms often
  differ by culture and by national origin.

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The Algorithm Collection Project - Goals

• A goal of this project is to contribute data to
  enable the development of a viable working model
  for facility with basic mathematics by using
  ethnomathematics and mathematical modeling.
• Data will enable researchers to ask relevant
  questions related to the cognitive consequences
  these algorithms have for children.
• And to make use of the diversity of experience
  and problems solving found in our region.

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Data

• To date we have uncovered four styles or
  patterns in Sacramento
• North American (USA / Marshall Islands)
• Franco-Brazilian (Vietnam and Brazil)
• Russo-Soviet (former Soviet Union Countries)
• Indo-Pakistani ( Southern Asia)

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Context

• In the case of Brazil and the United States, the
  unique mixtures of language and culture have
  contributed to create a mix of new mathematical
  strategies and ideas.
• One of these is ethnomathematics
• The project seeks to study the complex
  interaction between the languages we speak and
  the algorithms we use combine to form unique
  abilities or disabilities with mathematics

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Context

• A unique interaction between ones language
  (both oral and written), suggests that USAan
  children may possess equal difficulty with our
  traditional algorithms due to a link between
  American English language and our traditional
  algorithms.
• Might there be a better way to do figures?

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Research Questions

• Do algorithms we use have cognitive, as well as
  pedagogical significance for their users?
• How does ones mother tongue affect ones
  personal form of cognitive processing especially
  in regards to basic mathematics?
• Some language groups have significantly more
  incidences of dyslexia.
• Native monolingual speakers of French and
  American English.
• (Holtz, R. L. (2001, March 16). "Study Some
  written languages intensify dyslexia.
  Sacramento Bee, p. A20.)

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Curiosities

• Some language groups use the coma for the
  decimal, which can cause some confusion for
  scientists, business people, students and
  educators.
• What comes as a surprise to many educators is
  that there are other methods for calculating and
  communicating answers successfully used in other
  countries.
• The actual form of long division differs slightly
  from group to group.

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O Projeto Coleção de Algoritmos / The Algorithm
Collection Project/ El Proyecto de Colección de
Algoritmos

• Brasil / Brazil / Brasil

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O Projeto Coleção de Algoritmos / The Algorithm
Collection Project/ El Proyecto de Colección de
Algoritmos

• Qyirgystão / Kyrgyzstan / Kyrgyzstan

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O Projeto Coleção de Algoritmos / The Algorithm
Collection Project/ El Proyecto de Colección de
Algoritmos

• As Ilhas Marshall / The Marshall Islands / Las
  Islas Marshalls

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Setting up your own ACP

• How can you go about setting up and do a study
  of your own?
• Construct an language wall - link to counting
  for younger kids, and vocabulary of math units
• Do a survey of languages / cultures at your site
  / in your community. \
• Focus on interesting ways that people use and do
  arithmetic calculations, measure, classify,
  order, infer, and model.
• Look for the mathematics that once was, the
  mathematics that is here now, and connect to the
  mathematics that might be.
• Interview, prod, cajole, nag, find, invite,
  learn, share, do, collect

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Finding

• From my interview data and observations, I can
  say that one generality shouts from my work so
  far
• A multilingual student who uses either a
  Franco-Brazilian or Russo-Soviet long division
  algorithm will have less apprehension in learning
  mathematics.

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Finding

• They are less apprehensive then monolingual kids
  in trying something new
• They also are less likely to give up, they keep
  trying a sense of ganas, a sense of hunger
• I believe this is because at some level, they see
  that, or experience mathematics as another
  language to learn. Monolinguals are deprived of
  this ability.

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Recursos / Resources

• ISGEm
• International Study Group  on Ethnomathematics

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Recursos / Resources

• Culturally Situated Design Tools Teaching Math
  through Culture
• http//www.rpi.edu/7Eeglash/csdt.html

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Recursos / Resources

• GEPEm - Grupo de Estudos e Pesquisa em
  Etnomatematica
• http//phoenix.sce.fct.unl.pt/gepem/

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Recursos / Resources

• Ethnomathematics Digital Library
• www.ethnomath.org

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Recursos / Resources
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Recursos / Resources

• TODOS Mathematics for ALL

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Recursos / Resources
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Etnomatemática

• Um indivíduo, espera, nesta fase da evolução da
  nossa espécie, que toda a arrogância, inveja e
  grande poder ceda lugar ao respeito pelos
  diversos povos, que em solidariedade,
  contribuirão para a preservação do patrimônio
  comum.
• DAmbrosio

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Ethnomathematics

• An individual, hopes in this phase of the
  evolution of our species, that the respect for
  diverse peoples will not be replaced by our
  arrogance, envy and great power and that in
  solidarity, we will be able to contribute to the
  preservation of a common inheritance.
• - DAmbrosio

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http//www.csus.edu/indiv/o/oreyd

• Muito Obrigado!
• Thank You!
• Muchas Gracias!