1. Math TLC Seminar March 2010

2. 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.

3. 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?

4. 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.

5. Mathematics is embedded in culture. Culture is embedded in mathematics. (Dr. Powers, personal communication)

6. 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

7. 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

8. 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

9. Counting Locating Measuring Designing Playing Explaining (Bishop, 1988) 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

10. CountingLocating Numbers, number patterns, number relationships Position, orientation Algebraic representationCoordinate systems Infinite: small and largeNetworks Events, probabilities, frequenciesLoci Numerical methodsTransformations Iteration Combinatorics Limits

11. MeasuringDesigning Comparing, orderingProperties of objects Length, area, volumeShape Time, temperature, weightCongruence and similarity Units and tools of measurementRatios Estimation, approximation, error

12. PlayingExplaining Puzzles, paradoxesClassifications ModelsConventions Games, rules, procedures, strategiesGeneralizations Predicting, guessing, chanceLinguistic, symbolic, and figural explanations Hypothetical reasoningLogical connections Game analysisProof Mathematical structure: axioms, theorems, analysis, consistency

13. 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 Mathema tical universal truths Historical developm ent Values and beliefs related to the applicatio n of mathema tics Culture of teaching and learning mathema tics Culture of mathema tics research and developm ent

14. 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. Mathema tical universal truths Historical developm ent Values and beliefs related to the applicatio n of mathema tics Culture of teaching and learning mathema tics Culture of mathema tics research and developm ent

15. 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 Mathema tical universal truths Historical developm ent Values and beliefs related to the applicatio n of mathema tics Culture of teaching and learning mathema tics Culture of mathema tics research and developm ent

16. 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) Mathema tical universal truths Historical developm ent Values and beliefs related to the applicatio n of mathema tics Culture of teaching and learning mathema tics Culture of mathema tics research and developm ent

17. 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

18. 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

19. 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