1. Exploring Strategies to Close the Achievement Gap Native American Students and and Learning Mathematics

2. Presentation by Dr. Cathy Barkley Mesa State College Mesa State College Grand Junction, Colorado Grand Junction, Colorado cbarkley@mesastate.edu cbarkley@mesastate.edu

3. 19502000 Unskilled6015 Skilled2065 Professional2020 Percentages of Jobs Needed

4. Top Growth Jobs Nursing and health occupations Nursing and health occupations Computer engineers/systems analysts Computer engineers/systems analysts Automotive technicians/mechanics Automotive technicians/mechanics Business operations management Business operations management Networks systems Networks systems Data communication analysts Data communication analysts Teachers Teachers

5. Percentages of Graduation Populations Who Enroll in College 60% Asian Pacific 60% Asian Pacific 42% White 42% White 32% African Americans 32% African Americans 18% Native Americans 18% Native Americans

6. Reform in Native Education 1975 Indian Self-Determination Education Assistance Act 1975 Indian Self-Determination Education Assistance Act 1990 Native Languages Act 1990 Native Languages Act 1991 Indian Nations at Risk Task Force 1991 Indian Nations at Risk Task Force 1992 White House Conference on Indian Education 1992 White House Conference on Indian Education

7. Schools for Native Students 87% public schools 87% public schools 10% BIA schools 10% BIA schools 3% private schools 3% private schools

8. Math Education Reform 1991 NCTM Professional Standards for Teaching & Learning Mathematics 1991 NCTM Professional Standards for Teaching & Learning Mathematics Goals for all students: Goals for all students: Value mathematics Value mathematics Develop confidence in mathematics ability Develop confidence in mathematics ability Become mathematical problem solvers Become mathematical problem solvers Learn to communicate and reason mathematically Learn to communicate and reason mathematically

9. Native Education Reform 1991 Indian Nations at Risk Task Force 1991 Indian Nations at Risk Task Force Goals for Native education: Goals for Native education: Develop parent-based, culturally, linguistically, developmentally appropriate education Develop parent-based, culturally, linguistically, developmentally appropriate education Schools are responsible for promotion of tribal language and culture Schools are responsible for promotion of tribal language and culture Train more Native teachers Train more Native teachers Strengthen tribal and BIA schools Strengthen tribal and BIA schools

10. “Send us employees who can think, reason, and solve problems.”

11. Mathematics Learning Theories Field Dependent Field Dependent Whole to Part Whole to Part Learning facts is an integrated part of a larger whole Learning facts is an integrated part of a larger whole Simultaneous synthesis Simultaneous synthesis Holistic view of mathematics Holistic view of mathematics Field Independent Field Independent Part to Whole Focus on facts as an end result Successive synthesis Building block view of mathematics

12. Factoring a Quadratic Equation Factor the following equation: Factor the following equation: 2x ² - 3x = 35 2x ² - 3x = 35 (2x + 7) (x – 5) The area of a garden plot measures 35 square feet. Length is 7 feet more than twice the width.

13. Five Pedagogical Principles from CREDE Teacher as facilitator Teacher as facilitator Sense-making instruction Sense-making instruction Culturally relevant, problem-based instruction Culturally relevant, problem-based instruction Cooperative instruction Cooperative instruction Time-generous instruction Time-generous instruction

14. Teacher as Facilitator De-centralize the authoritarian role of the teacher De-centralize the authoritarian role of the teacher Teacher’s focus is on listening/guiding Teacher’s focus is on listening/guiding De-emphasize the individual and responses, both positive and negative De-emphasize the individual and responses, both positive and negative Promote autonomous and cooperative learning Promote autonomous and cooperative learning

15. Sense-Making Instruction Translations from Native language to English Translations from Native language to English Proficiency in the language of instruction Proficiency in the language of instruction Preferred learning styles Preferred learning styles Use and value visual discrimination and imagery Use and value visual discrimination and imagery Reflective learners Reflective learners

16. NAEP 8 TH Assessment 2004 60% of 8 th graders answered correctly 60% of 8 th graders answered correctly 1, 9, 25, 49, 81,... 1, 9, 25, 49, 81,... The same rule is applied to each number in the pattern above. What is the sixth number in the pattern? The same rule is applied to each number in the pattern above. What is the sixth number in the pattern? A) 40 B) 100 C) 121 D) 144 E) 169 A) 40 B) 100 C) 121 D) 144 E) 169

17. Culturally Relevant Problem-Based Instruction Context for understanding Context for understanding Levels of contextualization Levels of contextualization Pedagogical Pedagogical Curriculum level Curriculum level Policy level Policy level Ethnomathematics: mathematics embedded within a culture Ethnomathematics: mathematics embedded within a culture

18. Cooperative Instruction Communication patterns of Native children Communication patterns of Native children Role assignments in group work Role assignments in group work Verbal participation in group work Verbal participation in group work Talk about it, re-think it, and then write it Talk about it, re-think it, and then write it

19. Time-generous Instruction Lag time for answers and completion of tasks Lag time for answers and completion of tasks Compartmentalized learning segments Compartmentalized learning segments Visual discrimination and imagery Visual discrimination and imagery Rhythms of activity Rhythms of activity

20. Comparison of Pedagogies Hankes & Fast, 2002 Dominant style Dominant style Teacher disseminates information Teacher disseminates information Students are blank slates Students are blank slates Heavy reliance on textbooks/workbooks Heavy reliance on textbooks/workbooks Blocks of time Blocks of time Part-to-whole Part-to-whole Students work alone Students work alone Assessment occurs through testing, not teaching Assessment occurs through testing, not teaching Native American Native American Facilities, guides through age-appropriate tasks Students-gifts/learning Culturally relevant, situational problems Time-generous Whole-to-part Group learning activities Assessment through performance

21. Native student on testing... “It’s OK but kind of hard. Sometimes you have to know more than the test is willing to say. Tests leave out questions that I know. It seems like you don’t know where to put all you do know. It’s frustrating because you feel bad about it.”

22. Native Student Perspective on Testing “My mother says not to say something or will be.” “It’s best to figure it out for yourself... If you don’t get it right, you can go back and change it...there is a Navajo word that explains it...I am learning, almost is, what I learned and what I am learning.”

23. Attention is given not only to what mathematics are learned, but how they are learned. We are usually convinced more easily by reason we have found ourselves than by those which have occurred to others. –Blaise Pascal

24. Resources Ethnomathematics Digital Library www.ethnomath.org/search/browse.asp?type=subj ect www.ethnomath.org/search/browse.asp?type=subj ect www.ethnomath.org/search/browse.asp?type=subj ect www.ethnomath.org/search/browse.asp?type=subj ect International Study Group on Ethnomathematics www.rpi.edu/~eglash/isgem.dir/links.dir/na.htm www.rpi.edu/~eglash/isgem.dir/links.dir/na.htm www.rpi.edu/~eglash/isgem.dir/links.dir/na.htm Indigenous Peoples of Americas SIG/AERA Indigenous Peoples of Americas SIG/AERA www.coe.missouri.edu/~ipa/links.html www.coe.missouri.edu/~ipa/links.html www.coe.missouri.edu/~ipa/links.html

25. More Resources Ascher, M. Ethnomathematics. NY, NY: Chapman & Hall Publishing, 1991. Ascher, M. Ethnomathematics. NY, NY: Chapman & Hall Publishing, 1991. Burns, M. Math: Facing an American Phobia. Sausalito, CA: MB Education, 1998. Burns, M. Math: Facing an American Phobia. Sausalito, CA: MB Education, 1998. Closs, M. Native American Mathematics. Austin, TX: UTA Press, 1996. Closs, M. Native American Mathematics. Austin, TX: UTA Press, 1996. NCTM. Changing the Faces of Mathematics: Perspectives on Indigenous People of North America. Reston, VA: NCTM, 2002. NCTM. Changing the Faces of Mathematics: Perspectives on Indigenous People of North America. Reston, VA: NCTM, 2002. Zaslavsky, C. Multicultural Mathematics in the Classroom. Heinemann Publishing, 1991. Zaslavsky, C. Multicultural Mathematics in the Classroom. Heinemann Publishing, 1991.