Exploring Strategies to Close
the Achievement Gap
Native American Students
and
Learning Mathematics
Presentation
by
Dr. Cathy Barkley
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Mesa State College
Grand Junction, Colorado
cbarkley@mesastate.edu
Percentages of Jobs Needed
1950
2000
Unskilled
60
15
Skilled
20
65
Professional
20
20
Top Growth Jobs
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Nursing and health occupations
Computer engineers/systems analysts
Automotive technicians/mechanics
Business operations management
Networks systems
Data communication analysts
Teachers
Percentages of Graduation
Populations Who Enroll in College
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60%
42%
32%
18%
Asian Pacific
White
African Americans
Native Americans
Reform in Native Education
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1975 Indian Self-Determination Education
Assistance Act
1990 Native Languages Act
1991 Indian Nations at Risk Task Force
1992 White House Conference on Indian
Education
Schools for Native Students
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87% public schools
10% BIA schools
3% private schools
Math Education Reform
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1991 NCTM Professional Standards for
Teaching & Learning Mathematics
Goals for all students:
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Value mathematics
Develop confidence in mathematics ability
Become mathematical problem solvers
Learn to communicate and reason
mathematically
Native Education Reform
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1991 Indian Nations at Risk Task Force
Goals for Native education:
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Develop parent-based, culturally, linguistically,
developmentally appropriate education
Schools are responsible for promotion of tribal
language and culture
Train more Native teachers
Strengthen tribal and BIA schools
“Send us employees who can think,
reason, and solve problems.”
Mathematics Learning Theories
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Field Dependent
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Whole to Part
Learning facts is an
integrated part of a
larger whole
Simultaneous
synthesis
Holistic view of
mathematics
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Field Independent
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Part to Whole
Focus on facts as an
end result
Successive synthesis
Building block view of
mathematics
Factoring a Quadratic Equation
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Factor the following equation:
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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.
Five Pedagogical Principles from
CREDE
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Teacher as facilitator
Sense-making instruction
Culturally relevant, problem-based
instruction
Cooperative instruction
Time-generous instruction
Teacher as Facilitator
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De-centralize the authoritarian role of the
teacher
Teacher’s focus is on listening/guiding
De-emphasize the individual and
responses, both positive and negative
Promote autonomous and cooperative
learning
Sense-Making Instruction
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Translations from Native language to
English
Proficiency in the language of instruction
Preferred learning styles
Use and value visual discrimination and
imagery
Reflective learners
NAEP 8TH Assessment 2004
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60% of 8th graders answered correctly
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?
A) 40 B) 100 C) 121 D) 144 E) 169
Culturally Relevant Problem-Based
Instruction
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Context for understanding
Levels of contextualization
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Pedagogical
Curriculum level
Policy level
Ethnomathematics: mathematics
embedded within a culture
Cooperative Instruction
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Communication patterns of Native children
Role assignments in group work
Verbal participation in group work
Talk about it, re-think it, and then write it
Time-generous Instruction
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Lag time for answers and completion of
tasks
Compartmentalized learning segments
Visual discrimination and imagery
Rhythms of activity
Comparison of Pedagogies
Hankes & Fast, 2002
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Dominant style
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Teacher disseminates
information
Students are blank slates
Heavy reliance on
textbooks/workbooks
Blocks of time
Part-to-whole
Students work alone
Assessment occurs
through testing, not
teaching
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Native American
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Facilities, guides through
age-appropriate tasks
Students-gifts/learning
Culturally relevant,
situational problems
Time-generous
Whole-to-part
Group learning activities
Assessment through
performance
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.”
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.”
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
Resources
Ethnomathematics Digital Library
www.ethnomath.org/search/browse.asp?type=subj
ect
International Study Group on Ethnomathematics
 www.rpi.edu/~eglash/isgem.dir/links.dir/na.htm
 Indigenous Peoples of Americas SIG/AERA
 www.coe.missouri.edu/~ipa/links.html
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More Resources
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Ascher, M. Ethnomathematics. NY, NY: Chapman & Hall
Publishing, 1991.
Burns, M. Math: Facing an American Phobia. Sausalito,
CA: MB Education, 1998.
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.
Zaslavsky, C. Multicultural Mathematics in the Classroom.
Heinemann Publishing, 1991.