Math TLC Seminar
March 2010
TLC Vision
In Colorado and Wyoming partnership we will maximize
K-12 student understanding of mathematics by
developing teachers and teacher-leaders with deep
mathematics content knowledge that is culturally
relevant and pedagogically effective, and we will
enhance the culturally competent pedagogical
skills of university teacher-educators
at the University of Wyoming and the University of
Colorado.
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What is culture?
How are math and culture related?
How is math embedded in culture?
How is culture embedded in math?
Now what?
 Culture is a system of beliefs, values, and assumptions
about life that guide behavior and are shared by a
group of people. It includes customs, language, and
material artifacts. These are transmitted from
generation to generation, rarely with explicit
instructions.
 Mathematics is embedded in culture.
 Culture is embedded in mathematics.
(Dr. Powers, personal communication)
 Ethnomathematics
 Cultural elements based on mathematical
constructs
 Walpiri Kin System
 Symmetry in quilt construction
 Mathematical constructs imposed on cultural
elements
 Pythagorean Theorem in button construction
 Mathematical Systems (Bishop, 1988)
 All human cultures develop mathematics
 All mathematical systems contain mathematical
universal truths
 Mathematical systems vary based on
 The set of universal truths included
 The representation of the mathematical ideas
 The values and beliefs associated with the
development, application, and learning of
mathematics
Historical
development
Culture of
mathematics
research and
development
Mathematical
universal
truths
Culture of
teaching and
learning
mathematics
Values and
beliefs related
to the
application of
mathematics
 Counting
Historical
development
 Locating
 Measuring
 Designing
Culture of
mathematics
research and
development
Mathematical
universal
truths
 Playing
 Explaining
(Bishop, 1988)
Culture of
teaching and
learning
mathematics
Values and
beliefs related
to the
application of
mathematics
Counting
Locating
Numbers, number patterns, number
relationships
Position, orientation
Algebraic representation
Coordinate systems
Infinite: small and large
Networks
Events, probabilities, frequencies
Loci
Numerical methods
Transformations
Iteration
Combinatorics
Limits
Measuring
Designing
Comparing, ordering
Properties of objects
Length, area, volume
Shape
Time, temperature, weight
Congruence and similarity
Units and tools of measurement
Ratios
Estimation, approximation, error
Playing
Explaining
Puzzles, paradoxes
Classifications
Models
Conventions
Games, rules, procedures, strategies
Generalizations
Predicting, guessing, chance
Linguistic, symbolic , and figural
explanations
Hypothetical reasoning
Logical connections
Game analysis
Proof
Mathematical structure: axioms,
theorems, analysis, consistency
 Who had the opportunity and credibility to contribute
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

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to the development of mathematics
What areas of mathematics were more or less
developed and applied
What systems of representation and communication
developed
What role did mathematics play in society
How did interactions with other cultures influence the
development of mathematics
Historical
developm
ent
Culture
of
mathema
tics
research
and
developm
ent
Mathema
tical
universal
truths
Culture
of
teaching
and
learning
mathema
tics
Values
and
beliefs
related to
the
applicatio
n of
mathema
tics
 Burton (1999a, 1999b, 2000)
 Mathematics is a creative, exciting, meaningful endeavor
 May be undergoing change; gap between perception and
reality (e.g., collaborative rather than individualistic)
 Mathematicians do not pass on their culture in the
classroom (e.g., use intuition in their work, but do not
discuss or develop it with students)
 Norms for communicating mathematics are cultural
developments and do not support mathematics writing
that is clear, understandable and inviting.
Culture
of
mathema
tics
research
and
developm
ent
Historical
developm
ent
Mathema
tical
universal
truths
Culture
of
teaching
and
learning
mathema
tics
Values
and
beliefs
related to
the
applicatio
n of
mathema
tics
 Mathematics is not relevant in everyday life (Devlin,
2010)
 It is good/bad to use mathematics to develop weapons,
help the IRS, data mine for personal information,
develop complex financial instruments, etc.
 Quantitative literacy can be used to support social
justice
Historical
developm
ent
Culture
of
mathema
tics
research
and
developm
ent
Mathema
tical
universal
truths
Culture
of
teaching
and
learning
mathema
tics
Values
and
beliefs
related to
the
applicatio
n of
mathema
tics
 Mathematics can only be learned by “smart” people
 It is OK to admit weak mathematical proficiency
 Mathematics induces anxiety
 The purpose of learning mathematics is to learn more
mathematics (Gerdes, 1988)
 Mathematics is about memorizing rules and
procedures that do not necessarily make sense
(although they might for “smart” people)
Historical
developm
ent
Culture
of
mathema
tics
research
and
developm
ent
Mathema
tical
universal
truths
Culture
of
teaching
and
learning
mathema
tics
Values
and
beliefs
related to
the
applicatio
n of
mathema
tics
 Mathematics embedded in culture
 Ethnomathematics
 Culture embedded in mathematics
 Historical development
 Culture of mathematics R&D
 Applications of mathematics
 Culture of teaching and learning mathematics
 Content related to teachers’ profession (culture of
T&L)
 Ethnomathematics
 To use in the classroom
 To broaden the picture of who uses mathematics
 Transfer of mathematics R&D culture
 Collaborative exploration
 Shifting the locus of authority
 The culture of mathematics teaching and learning
 Turns off a large number of students from all
backgrounds
 Does not develop people who are aware of the values
and beliefs associated with the application of
mathematics
 Does not develop people who can make sense of and
evaluate quantitative information
 Does not represent mathematics as a creative human
endeavor that is systematic and logical