Math TLC Seminar

March 2010

Math and Culture

TLC VisionIn 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.

Why Math and Culture?

1. What is culture?2. How are math and culture related?3. How is math embedded in culture?4. How is culture embedded in math?5. Now what?

The Map

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.

What is Culture?

Mathematics is embedded in culture.Culture is embedded in mathematics.

(Dr. Powers, personal communication)

Dual Perspective

EthnomathematicsCultural elements based on

mathematical constructs Walpiri Kin SystemSymmetry in quilt construction

Mathematical constructs imposed on cultural elements Pythagorean Theorem in button

construction

Mathematics Embedded in Culture

Mathematical Systems (Bishop, 1988)All human cultures develop mathematicsAll mathematical systems contain

mathematical universal truthsMathematical systems vary based on

The set of universal truths includedThe representation of the mathematical

ideasThe values and beliefs associated with the

development, application, and learning of mathematics

Culture Embedded in Math

Model of Mathematical Systems

Mathematical universal truths

Historical development

Values and beliefs related to the application of mathematics

Culture of teaching and

learning mathematics

Culture of mathematics research and development

CountingLocatingMeasuringDesigningPlayingExplaining

(Bishop, 1988)

Mathematical Universal Truths

Mathematical universal truths

Historical development

Values and beliefs related to the application of mathematics

Culture of teaching and

learning mathematics

Culture of mathematics research and development

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

Counting and Locating

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

Measuring and Designing

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

Playing and Explaining

Who had the opportunity and credibility to contribute 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 Development

Mathematical universal

truths

Historical developme

nt

Values and beliefs

related to the

application of

mathematics

Culture of teaching

and learning

mathematics

Culture of mathematics research

and developme

nt

Burton (1999a, 1999b, 2000)Mathematics is a creative, exciting, meaningful

endeavorMay 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 Mathematics R&D

Mathematical universal

truths

Historical developme

nt

Values and beliefs

related to the

application of

mathematics

Culture of teaching

and learning

mathematics

Culture of mathematics research

and developme

nt

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

Application of Mathematics

Mathematical universal

truths

Historical developme

nt

Values and beliefs

related to the

application of

mathematics

Culture of teaching

and learning

mathematics

Culture of mathematics research

and developme

nt

Mathematics can only be learned by “smart” people

It is OK to admit weak mathematical proficiency

Mathematics induces anxietyThe 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)

Culture of Learning and Teaching

Mathematical universal

truths

Historical developme

nt

Values and beliefs

related to the

application of

mathematics

Culture of teaching

and learning

mathematics

Culture of mathematics research

and developme

nt

Mathematics embedded in cultureEthnomathematics

Culture embedded in mathematicsHistorical developmentCulture of mathematics R&DApplications of mathematicsCulture of teaching and learning mathematics

Summary

Content related to teachers’ profession (culture of T&L)

EthnomathematicsTo use in the classroomTo broaden the picture of who uses

mathematicsTransfer of mathematics R&D culture

Collaborative explorationShifting the locus of authority

Now What?

The culture of mathematics teaching and learningTurns off a large number of students from all

backgroundsDoes 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

The Issue

The End