Exploring Strategies to Exploring Strategies to Close the Achievement Close the Achievement

GapGap

Native American StudentsNative American Students

and and

Learning MathematicsLearning Mathematics

PresentationPresentationby by

Dr. Cathy BarkleyDr. Cathy Barkley

Mesa State CollegeMesa State College Grand Junction, ColoradoGrand Junction, Colorado cbarkley@mesastate.educbarkley@mesastate.edu

19501950 20002000

UnskilledUnskilled 6060 1515

SkilledSkilled 2020 6565

ProfessionProfessionalal

2020 2020

Percentages of Jobs NeededPercentages of Jobs Needed

Top Growth JobsTop Growth Jobs

Nursing and health occupationsNursing and health occupations Computer engineers/systems analystsComputer engineers/systems analysts Automotive technicians/mechanicsAutomotive technicians/mechanics Business operations managementBusiness operations management Networks systemsNetworks systems Data communication analystsData communication analysts TeachersTeachers

Percentages of Graduation Percentages of Graduation Populations Who Enroll in Populations Who Enroll in

CollegeCollege 60% Asian Pacific 60% Asian Pacific 42% White42% White 32% African Americans32% African Americans 18% Native Americans18% Native Americans

Reform in Native EducationReform in Native Education

1975 Indian Self-Determination 1975 Indian Self-Determination Education Assistance ActEducation Assistance Act

1990 Native Languages Act1990 Native Languages Act 1991 Indian Nations at Risk Task 1991 Indian Nations at Risk Task

ForceForce 1992 White House Conference on 1992 White House Conference on

Indian EducationIndian Education

Schools for Native StudentsSchools for Native Students

87% public schools87% public schools 10% BIA schools10% BIA schools 3% private schools3% private schools

Math Education ReformMath Education Reform

1991 NCTM Professional Standards 1991 NCTM Professional Standards for Teaching & Learning Mathematicsfor Teaching & Learning Mathematics

Goals for all students:Goals for all students: Value mathematicsValue mathematics Develop confidence in mathematics Develop confidence in mathematics

abilityability Become mathematical problem solversBecome mathematical problem solvers Learn to communicate and reason Learn to communicate and reason

mathematicallymathematically

Native Education ReformNative Education Reform

1991 Indian Nations at Risk Task Force1991 Indian Nations at Risk Task Force Goals for Native education:Goals for Native education:

Develop parent-based, culturally, Develop parent-based, culturally, linguistically, developmentally appropriate linguistically, developmentally appropriate educationeducation

Schools are responsible for promotion of Schools are responsible for promotion of tribal language and culturetribal language and culture

Train more Native teachersTrain more Native teachers Strengthen tribal and BIA schoolsStrengthen tribal and BIA schools

““Send us employees who can Send us employees who can think, reason, and solve think, reason, and solve

problems.”problems.”

Mathematics Learning Mathematics Learning TheoriesTheories

Field DependentField Dependent Whole to PartWhole to Part Learning facts is an Learning facts is an

integrated part of a integrated part of a larger wholelarger whole

Simultaneous Simultaneous synthesissynthesis

Holistic view of Holistic view of mathematicsmathematics

Field IndependentField Independent Part to WholePart to Whole Focus on facts as Focus on facts as

an end resultan end result Successive Successive

synthesissynthesis Building block view Building block view

of mathematicsof mathematics

Factoring a Quadratic Factoring a Quadratic EquationEquation

Factor the following equation:Factor the following equation: 22xx ² - 3 ² - 3xx = 35 = 35

(2(2xx + 7) ( + 7) (xx – 5) – 5)

The area of a garden plot measures 35 The area of a garden plot measures 35 square feet. Length is 7 feet more than square feet. Length is 7 feet more than twice the width.twice the width.

Five Pedagogical Principles Five Pedagogical Principles from CREDEfrom CREDE

Teacher as facilitatorTeacher as facilitator Sense-making instructionSense-making instruction Culturally relevant, problem-based Culturally relevant, problem-based

instructioninstruction Cooperative instructionCooperative instruction Time-generous instructionTime-generous instruction

Teacher as FacilitatorTeacher as Facilitator

De-centralize the authoritarian role of De-centralize the authoritarian role of the teacherthe teacher

Teacher’s focus is on listening/guidingTeacher’s focus is on listening/guiding De-emphasize the individual and De-emphasize the individual and

responses, both positive and negativeresponses, both positive and negative Promote autonomous and cooperative Promote autonomous and cooperative

learninglearning

Sense-Making InstructionSense-Making Instruction

Translations from Native language to Translations from Native language to EnglishEnglish

Proficiency in the language of Proficiency in the language of instructioninstruction

Preferred learning stylesPreferred learning styles Use and value visual discrimination Use and value visual discrimination

and imageryand imagery Reflective learnersReflective learners

NAEP 8NAEP 8THTH Assessment 2004 Assessment 2004

60% of 860% of 8thth graders answered correctly graders answered correctly

1, 9, 25, 49, 81, . . .1, 9, 25, 49, 81, . . .

The same rule is applied to each The same rule is applied to each number in the pattern above. What number in the pattern above. What is the sixth number in the pattern?is the sixth number in the pattern?

A) 40 B) 100 C) 121 D) 144 E) 169A) 40 B) 100 C) 121 D) 144 E) 169

Culturally Relevant Problem-Culturally Relevant Problem-Based InstructionBased Instruction

Context for understandingContext for understanding Levels of contextualizationLevels of contextualization

PedagogicalPedagogical Curriculum levelCurriculum level Policy levelPolicy level

Ethnomathematics: mathematics Ethnomathematics: mathematics embedded within a cultureembedded within a culture

Cooperative InstructionCooperative Instruction

Communication patterns of Native Communication patterns of Native childrenchildren

Role assignments in group workRole assignments in group work Verbal participation in group workVerbal participation in group work Talk about it, re-think it, and then Talk about it, re-think it, and then

write itwrite it

Time-generous InstructionTime-generous Instruction

Lag time for answers and completion Lag time for answers and completion of tasksof tasks

Compartmentalized learning Compartmentalized learning segmentssegments

Visual discrimination and imageryVisual discrimination and imagery Rhythms of activityRhythms of activity

Comparison of Pedagogies Comparison of Pedagogies Hankes & Fast, 2002Hankes & Fast, 2002

Dominant styleDominant style Teacher disseminates Teacher disseminates

informationinformation Students are blank Students are blank

slatesslates Heavy reliance on Heavy reliance on

textbooks/workbookstextbooks/workbooks Blocks of timeBlocks of time Part-to-wholePart-to-whole Students work aloneStudents work alone Assessment occurs Assessment occurs

through testing, not through testing, not teaching teaching

Native AmericanNative American Facilities, guides Facilities, guides

through age-through age-appropriate tasksappropriate tasks

Students-gifts/learningStudents-gifts/learning Culturally relevant, Culturally relevant,

situational problemssituational problems Time-generousTime-generous Whole-to-partWhole-to-part Group learning Group learning

activitiesactivities Assessment through Assessment through

performanceperformance

Native student on Native student on testing . . .testing . . .

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

Native Student Perspective on Native Student Perspective on TestingTesting

““My mother says not to say something My mother says not to say something or will be.”or will be.”

““It’s best to figure it out for yourself. . . It’s best to figure it out for yourself. . . If you don’t get it right, you can go If you don’t get it right, you can go back and change it . . .there is a back and change it . . .there is a Navajo word that explains it . . .I am Navajo word that explains it . . .I am learning, almost is, what I learned learning, almost is, what I learned and what I am learning.”and what I am learning.”

Attention is given not only to Attention is given not only to whatwhat mathematics are mathematics are

learned, but learned, but how how they are they are learned.learned.

We are usually convinced more We are usually convinced more easily by reason we have found easily by reason we have found ourselves than by those which ourselves than by those which

have occurred to others. –Blaise have occurred to others. –Blaise PascalPascal

ResourcesResources

Ethnomathematics Digital LibraryEthnomathematics Digital Library www.ethnomath.org/search/browse.asp?typewww.ethnomath.org/search/browse.asp?type

=subject=subject

International Study Group on International Study Group on EthnomathematicsEthnomathematics

www.rpi.edu/~eglash/isgem.dir/links.dir/na.hwww.rpi.edu/~eglash/isgem.dir/links.dir/na.htmtm

Indigenous Peoples of Americas SIG/AERAIndigenous Peoples of Americas SIG/AERA www.coe.missouri.edu/~ipa/links.htmlwww.coe.missouri.edu/~ipa/links.html

More ResourcesMore Resources

Ascher, M. Ascher, M. EthnomathematicsEthnomathematics. NY, NY: Chapman . NY, NY: Chapman & Hall Publishing, 1991.& Hall Publishing, 1991.

Burns, M. Burns, M. Math: Facing an American PhobiaMath: Facing an American Phobia. . Sausalito, CA: MB Education, 1998.Sausalito, CA: MB Education, 1998.

Closs, M. Closs, M. Native American MathematicsNative American Mathematics. Austin, . Austin, TX: UTA Press, 1996.TX: UTA Press, 1996.

NCTM. NCTM. Changing the Faces of Mathematics: Changing the Faces of Mathematics: Perspectives on Indigenous People of North Perspectives on Indigenous People of North America.America. Reston, VA: NCTM, 2002. Reston, VA: NCTM, 2002.

Zaslavsky, C. Zaslavsky, C. Multicultural Mathematics in the Multicultural Mathematics in the Classroom.Classroom. Heinemann Publishing, 1991. Heinemann Publishing, 1991.