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 [email protected]@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.