Dr. William Allan Kritsonis, Dissertation Chair for Clarence Johnson, Dissertation Defense PPT

1. 1
IMPACT OF HIGH SCHOOL
MATHEMATICS CURRICULA ON THE
MATHEMATICS TAKS EXIT-LEVEL
PERFORMANCE OF AFRICAN
AMERICAN STUDENTS
A Dissertation Defense
by
Clarence Johnson
September 17, 2008
Chair: William Allan Kritsonis, Ph.D.

2. 2
Committee Members
William Allan Kritsonis, Ph.D.
( Dissertation Chair)
Pamela Barber-Freeman, Ph.D. Camille Gibson, Ph.D.
(Member) (Member)
Douglas Hermond, Ph.D. David Herrington, Ph.D.
(Member) (Member)

3. 3
Dissertation Defense Format
I. Purpose of the Study
II. Theoretical Framework
III. Research Questions
IV. Null Hypotheses
V. Pilot Study
VI. Subjects of the Study
VII. Instrumentation
VIII. On-Line Survey Questions
IX. Data Analysis
X. Independent/Dependent
Variables
XI. Major Findings -Quantitative
XII. Major Findings-
Qualitative/Interview and
Related Literature Support
XIII. Implications
XIV. Recommendations for
Further Study
XV. Challenges & Opportunities

4. 4
Purpose of the Study
The purpose of this study was to investigate
the impact that high school mathematics
scores and courses had on the Mathematics
TAKS Exit-Level performance of African
American students. Some middle school
counselors were surveyed to investigate
factors that contributed to African American
students’ passing the Mathematics TAKS
Exit-Level Test.

5. 5
Note
The results of this study may be helpful to
school administrators, teachers, and
parents. The results will help to give
needed attention to students in terms of
proper placement in mathematics courses
along with support in the learning process.

6. 6
Theoretical Framework
Explanatory Mixed Methods Design
Quantitative Data Qualitative Data
Track 1
Scores:
Algebra I,
Geometry,
Algebra II
Track 2 Scores:
Algebra I,
Geometry,
Algebra II
Eleventh Grade:
Mathematics TAKS Exit-Level
Scores
Survey of Middle School Counselors
Factors that Impact Students’
Placement in Track 1 or Track 2
Mathematics
African American Students’ Performance

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Research Questions
Quantitative
1. Is there a difference between African
American students enrolled in track one
or track two eighth grade mathematics
in their performance on the eleventh
grade Texas Assessment of Knowledge
and Skills (TAKS) Exit-Level
Mathematics Test scores?

8. 8
Research Questions
Quantitative
2. Is there a relationship between
mathematics scores in Algebra I,
geometry, and/or Algebra II of African
American students enrolled in track one
or track two in eighth and ninth grades
and their eleventh grade Texas
Assessment of Knowledge and Skills
(TAKS) Exit-Level Mathematics Test
scores?

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Research Questions
Qualitative
3. What factors do counselors identify as
influential in African American students’
placement in track one or track two
mathematics?

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Null Hypotheses
H01:There is no statistically significant
difference between African American
students enrolled in track one and those
in track two eighth grade mathematics in
their performance on the eleventh grade
Texas Assessment of Knowledge and
Skills (TAKS) Exit-Level Mathematics
Test scores.

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Null Hypotheses
H02:There is no statistically significant relationship
between mathematics scores in Algebra I,
geometry, and/or Algebra II of African American
students enrolled in track one or track two in
eighth and ninth grades and their eleventh
grade Texas Assessment of Knowledge and
Skills (TAKS) Exit-Level Mathematics Test
scores.

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Methods
Pilot Study
Pilot Study – Initial Survey with 15 Questions
Reduced to Nine (9)
A panel of experts reviewed the survey:
 An executive director of guidance and
counseling
 Two university professors
 Three middle school counselors
 Two high school mathematics teachers

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Methods
Subjects of the Study
Quantitative – 262 African American
Students from 6 Urban High
Schools in Texas
Qualitative – 16 Counselors from Nine
(9) Middle Schools in Texas

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Methods
Instrumentation
Quantitative – Data Banks of TEA and
School District – SASIxp
Qualitative – On-line Survey

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Methods
On-Line Survey Questions
3a. What factors do you consider when placing students in eighth
grade mathematics?
3b. When advising African American students for mathematics
placement, what is the most important factor?
3c. In your opinion, what could the school do that would reduce the
failure rates of African American students in eighth grade
mathematics?
3d. How often do you meet with students to discuss mathematics
grade placement?
3e. Which factor has the greatest influence on eighth grade
mathematics students’ passing rate in mathematics?

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Methods
On-Line Survey Questions
3f. What is the most important factor that contributes
to the recommendation of African American males
to eighth grade advanced mathematics?
3g. In your opinion, do teachers at this school
frequently meet with African American students
about how they can succeed in mathematics
courses?
3h. What is your opinion of the number of eighth grade
African American students enrolled in advanced
mathematics classes?
3i. How do you rate the counseling department in
dealing with African American eighth grade students
in mathematics?

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Methods
Data Analysis
 Descriptive Statistics
 Correlation Statistics – Pearson r, Multiple
Correlation (R)
 t - test for 2 Independent Samples
 Analysis of Variance (ANOVA)

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Methods
Variables-Independent/Dependent
Independent Variables – African
American Students’ Scores in Algebra
I, geometry and Algebra II
 Track 1
 Track 2
Dependent Variable –TAKS Exit-Level
Mathematics Scores

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Major Findings
Research Question 1
Comparison of Performance in the Mathematics TAKS
Exit-Level Test of African American Students Enrolled in
Track 1 vs. Track 2
Mean % Passed TAKS t Sig.
Track 1 2168.34 76.5 6.857* 0.000
Track 2 2321.69 100.0
*Significant at p ≤ 0.05
Null hypothesis was rejected. (Students in Track 2 scored
significantly higher on the TAKS test compared to students
in Track 1).

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Major Findings
Research Question 2
Relationship Between Scores in Algebra I
and TAKS Exit-Level Mathematics Test
Pearson r Track 1 Track 2
TAKS Scores 0.297* 0.455*
Sig. (2-tailed) 0.000 0.001
*Significant at p ≤ 0.05

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Major Findings
Research Question 2
Relationship Between Scores in Geometry
and TAKS Exit-Level Mathematics Test
Pearson r Track 1 Track 2
TAKS Scores 0.651* 0.475*
Sig. (2-tailed) 0.000 0.001
*Significant at p≤ 0.05

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Major Findings
Research Question 2
Relationship Between Scores in Algebra II
and TAKS Exit-Level Mathematics Test
Pearson r Track 1 Track 2
TAKS Scores 0.503* 0.435*
Sig. (2-tailed) 0.000 0.002
*Significant at p ≤ 0.05

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Major Findings
Research Question 2
Analysis Of Variance (ANOVA) for Track 1
Students Passing the Mathematics TAKS Exit-
Level Test
Sum of Squares df F Sig.
Regression 982241.97 3 45.254 0.000
Residual 1215491.8 168
Total 2197733.8 171
Predictors: Constant, T1Algebra II, T1Algebra I,
T1Geometry
Dependent Variable: T1TAKS

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Major Findings
Research Question 2
Coefficients for Track 1 Mathematics TAKS Exit-Level Test
Unstandardized
Coefficients t Sig.
Constant 1297.279 15.949 0.000
T1Algebra I 0.967 1.188 0.236
T1Geometry 7.770 7.479 0.000
T1Algebra II 2.867 2.769 0.006
Dependent Variable: T1 TAKS
Regression Equation to Predict Value of TAKS Score:
Ŷ = 1297.279 + 0.967X1 +7.770X2 + 2.867X3,
where X1 = Algebra I score, X2 = geometry score, X3 = Algebra II
score and Constant = 1297.279.

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Major Findings
Research Question 2
Analysis Of Variance (ANOVA) for Track 2
Students Passing the Mathematics TAKS Exit-Level
Test
Sum of Squares df F Sig.
Regression 349238.75 3 11.613 0.000
Residual 431032.18 43
Total 780270.94 46
Predictors: Constant, T2 Algebra II, T2 Algebra I, T2 Geometry
Dependent Variable: T2 TAKS

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Major Findings
Research Question 2
Coefficients for Track 2 Mathematics TAKS Exit-Level Test
Unstandardized
Coefficients t Sig.
Constant 1025.724 4.334 0.000
T2 Algebra I 4.760 1.560 0.126
T2 Geometry 6.679 3.277 0.002
T2 Algebra II 4.383 1.879 0.067
Dependent Variable: T2 TAKS
Regression Equation to Predict Value of TAKS Score:
Ŷ = 1025.724+ 4.760X1 + 6.679X2 + 4.383X3,
where X1 = Algebra I score, X2 = geometry score, X3 = Algebra II
score and Constant = 1025.724.

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Number of Years Respondents
Worked as a School Counselor
Years Frequency Percent
1 - 5 6 37.50
6 - 10 1 6.25
11 - 15 4 25.00
16 - 20 3 18.75
21 - 25 1 6.25
26 - 30 1 6.25
Total 16 100.00

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Major Findings
Qualitative Question 3a
What factors do you consider when placing
students in 8th grade mathematics?
Factors Frequency Percent*
Parental input 3 18.75
Previous academic
achievement 15 93.75
School district policy 14 87.50
Teachers’ recommendation 14 87.50
*Due to multiple responses, percentages do not add up
to 100.

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Interview Support
“District policy requires standardized test
scores (primarily Iowa and TAKS) to be
used with grades.”
“District guidelines direct the placement of
students in Algebra in the 8th grade.”
“I follow the same schedule that the
students from the home school enter
with.”

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Related Literature Support
In Principles and Standards for School
Mathematics, the National Council of Teachers of
Mathematics (NCTM, 2000) identified algebra as
one of the central themes in K-12 mathematics.
Many educators perceive algebra as the gateway
to higher mathematics, and many state
graduation requirements include at least 1 year of
algebra (McCoy, 2005).

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Major Findings
Qualitative Question 3b
When advising African American students for
mathematics placement, what is the most
important factor?
Factors Frequency
Percent*
Student’s desire for more
challenging courses 11 68.75
Teacher’s recommendation 4 25.00
Counselor’s recommendation 0 0.00
Family history 0 0.00
*Due to less than total documented responses, percentages do not
add up to 100.

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Interview Support
“The district has a matrix that we follow that guides us in
placing students in Algebra I as an 8th grader. We
examine previous grades and teacher
recommendations to determine placement in our AVID
(college prep) program.”
“Teacher recommendations are important but much less
reliable due to subjectivity.”
“I would consider the students’ desire for a challenge and
then speak with the teacher as well.”
“I follow the same schedule that the students from the
home school enter with.”

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Major Findings
Qualitative Question 3c
In your opinion, what could the school do that
would reduce the failure rates of African
American students in 8th grade mathematics?
Factors Frequency Percent*
More tutorials/remediation 12 75.00
Better trained mathematics teachers 9 56.25
More parental involvement 12 75.00
Change entry level 3 18.75
*Due to multiple responses, percentages do not add up
to 100.

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Interview Support
“The ‘Ethnic Disparity Gap’ is irrelevant
when there are strong supportive
homes.”
“This is in consonance with the
counselors’ claim that parental
involvement has tremendous, effective
influence on students’ success.”

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Related Literature Support
Much of the difference in school
achievement found between African
American students and others is due to
the effects of substantially different
school opportunities, and in particular,
greatly disparate access to high quality
teachers and teaching (Darling-Hammonds,
2000).

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Major Findings
Qualitative Question 3d
How often do you meet with students to
discuss mathematics grade placement?
Timeline Frequency Percent*
One time a year 5 31.25
Bi-annually 8 50.00
Monthly 1 6.25
Parent’s request 5 31.25
*Due to multiple responses, percentages do not
add up to 100.

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Interview Support
“Course selection or qualification for advanced classes is
the only time we meet to discuss placement. ‘District’s
Track’ doesn’t allow a student to enter in higher classes in
8th grade unless enrolled in 7th grade mathematics.”
“I follow the same schedule that the student’s from the
home school enter with.”
“We tell students in the 6th grade when we let them
choose their courses about district mathematics
requirements. We tell them again at orientation night
during the first day of school. We tell them again at open
house, early fall. We tell them again in the GT parents’
meeting held in the fall and spring. We send out letters
late spring.”

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Major Findings
Qualitative Question 3e
Which factor has the greatest influence on 8th
grade mathematics students’ passing rate in
mathematics?
Factors Frequency Percent*
Certified Mathematics teacher 0 0.00
Parental involvement 2 12.50
Teacher’s expectation 5 31.25
Peer group pressure 0 0.00
Student’s attitude 8 50.00
*Due to total documented responses, percentages do not add up
to 100.

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Related Literature Support
Working in an urban Missouri junior high school,
investigators studied what happened when
students of average mathematics achievement
were assigned to an advanced eighth-grade pre-
algebra class. They found that the achievement of
accelerated average students was better than
the achievement of similar students in previous
years who had not taken accelerated
mathematics (Burris, Heubert, & Levin, 2006).

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Related Literature Support
The average-achieving students in the high-track
classes enrolled in more advanced high school
mathematics courses than did students at similar
achievement levels from previous low-track
cohorts. The results of the studies are consistent with the
findings and demonstrated almost no growth among
students placed in low-track, remedial eighth-grade
classrooms, and the conclusions from a study
commissioned by the National Research Council that
documented strong negative effects of low-track classes
(Burris, Heubert, & Levin, 2006).

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Major Findings
Qualitative Question 3f
What is the most important factor that
contributes to the recommendation of African
American males to 8th grade advanced
mathematics?
Factors Frequency Percent*
Athletic coach’s recommendation 1 6.25
Student’s interest 1 6.25
Principal’s/counselor’s recommendation 1 6.25
Achievement scores 12 75.00
*Due to total documented responses, percentages do not add up to
100.

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Interview Support
A counselor repeated the matrix’s
guideline as basis for her action regarding
placement of African American students
in 8th grade mathematics.
Counselor commented: “Once again,
Algebra I placement is determined by a
matrix given to us by the district.”

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Major Findings
Qualitative Question 3g
In your opinion, do teachers at this school
frequently meet with African American students
about how they can succeed in mathematics
courses?
Response Frequency Percent
Strongly agree 0 0.00
Agree 6 37.50
Unsure 7 43.75
Disagree 1 6.25
Strongly disagree 2 12.50
Total 16 100.00

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Related Literature Support
A student’s path in middle school can shape his or
her course in high school, which affects success
in college and thereby determines a career path.
As we look at African Americans in the
workplace, our gaze is necessarily directed back
to their formative academic experiences in
middle school, high school and college, where the
track to their future success is first laid down
(“Report Highlights Importance of Middle School
Math”, 2003).

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Major Findings
Qualitative Question 3h
What is your opinion of the number of 8th grade
African American students enrolled in advanced
mathematics classes?
Reasons Frequency Percent
Advanced Mathematics courses
are not offered at this school 1 6.25
About the right number 5 31.25
Too few 10 62.50
Too many 0 0.00
Total 16 100.00

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Related Literature Support
African American students are twice as
likely to be placed in non-academic track
classes and remedial mathematics
classes. Placement in these classes
exposes students to a less challenging
curriculum and the least experienced
teachers (Rubin & Noguera, 2004).

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Related Literature Support
Berry (2003) stated that African American
students receive mathematics instruction
that is not consistent with mathematics
education reform; furthermore, the
mathematics instruction that many African
American students receive is in opposition
to their culture styles and learning
preferences.

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Related Literature Support
African American students take fewer
algebra and geometry courses than White
students and these courses are often
“gate-keepers” to science and mathematics
degrees and performance on standardized
examinations (Russell, 2005).

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Major Findings
Qualitative Question 3i
How do you rate the counseling department in
dealing with African American 8th grade
students in mathematics?
Rating Frequency Percent*
Outstanding 1 6.25
Above average 6 37.50
Adequate 8 50.00
Poor 0 0.00
*Due to total documented responses, percentages do not add up to
100.

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Interview Support
“We have a large group of student load
and we treat them all the same in
placement and do not single out one
group. We speak to all the same and with
the same information which to encourage
them all.”

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Implications
Berry (2003) points outs that African American students’
mathematics achievement levels are indicative of the
instruction that they receive. Data collected on teachers’
instructional practices indicate differences between African
American students and their peers.
National Assessment of Educational Progress (NAEP) data suggest
that most African American students are not experiencing
instructional practices consistent with the
recommendations suggested by the National Council of
Teachers of Mathematics (NCTM), whereas more White
students are experiencing NCTM standards-based
instruction (Lubienski, 2001).

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Implications
The power and influence of the middle-class,
affluent, and more privileged parents plays an
important role in deciding who will be in “their
kid’s classes.” More often than not, political
pressure from parents coupled with low
expectations for African Americans in the
classroom by teachers, counselors, and
administrators result in homogeneous tracks
and ability groups (Russell, 2005).

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Implications
Ward (2008) pointed out that mathematics achievement
builds to increasing levels of complexity only when the base
is solid, and that base is formed from the earliest days of
elementary school. Too many elementary school teachers,
strong in other subjects and talented in connecting with
children, lack the mathematics background needed to
prepare students for algebra by the eighth grade.
Additional research based training, targeted at the specific
skills needed for effective algebra instruction, will be
critical and costly.

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Implications
The existence of linear regression equations
may become one of the bases for remediation
efforts to assure that students pass the
mathematics high-stakes test. Administrators
and teachers may forestall problems associated
with the State of Texas requirement for
students to graduate from high school.

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Recommendations for Further Study
 A study should be conducted to involve
representative samples from one or
more districts in a similar study to
determine if results can be duplicated.
 A study should be conducted to involve
another group of students (Whites,
Hispanics, Asians, etc.) in a similar
study.

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Recommendations for Further Study
 A study should be conducted to determine
specific activities of the guidance and
counseling department in the placement of
students not only in mathematics but also in
the different core areas of science, English and
social studies.
 A study should be conducted on the quality of
mathematics instruction involved in the
different tracks.

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Recommendations for Further Study
 A study should be conducted to predict
the performance of African American
students in the other core areas.
 A quantitative study should be conducted
with a large random sample of teachers
and school counselors regarding the
impact of high school mathematics
curricula on the mathematics TAKS Exit-
Level performance of students.

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Recommendations for Further Study
 A study should be conducted
regarding remediation practices
done by the school and the home in
preparing students to succeed in the
high-stakes tests given by the State
of Texas, not only in mathematics
but also in the other core areas.

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Challenges & Opportunities
Although African Americans have
increased their participation in
mathematics and the sciences within the
last decade, it is important to note that
these advances are still miniscule when
compared to those of White students
(Russell, 2005).

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Challenges & Opportunities
The attitudes and experiences of many school personnel
need to change, too. I have been on campuses and in
classrooms throughout the state, and it is consistent from
one end to the other: certain students are seen as algebra-
ready, and certain students are not. It’s no mystery: Asian
and White students on one hand; Latino, African American
and poor students of all ethnicities on the other. But they
are not ready. This is the common and perfectly honest
explanation. But it is our job to make them ready. It is work
we have chosen. It is our responsibility (Ward, 2008).

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REFERENCES
Berry, R. Q., III. (2003). Voices of African American male middle
school students: A portrait of successful middle school mathematics
students. Unpublished Doctoral Dissertation. University of North
Carolina at Chapel Hill, Chapel Hill, NC.
Burris, C. C., Heubert, J. P., & Levin, H. M. (2006). Accelerating
mathematics achievement. Educational Research Journal, 43(1),
105-136.
Darling-Hammonds, L. (2000). New standards and old inequalities:
School reform and the education of African American students.
The Journal of Negro Education, 69(4), 263-287.

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REFERENCES
Lubienski, S. T. (2001, April). A second look at mathematics
achievement gaps: Intersections of race, class, and gender in
NAEP data. Paper Presented at American Educational Research
Association, Seattle, WA.
McCoy, L. P. (2005). Effect of Demographic and personal variables on
achievement in eighth-grade algebra. Journal of Educational
Research, 98(3), 131-135.
National Council of Teachers of Mathematics. (2000). Principles and
standards for school mathematics. Reston, VA: NCTM.
Report highlights importance of middle school math (2003). Black
Issues in Higher Education, 20(19), 11.

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REFERENCES
Rubin, B. C., & Norguera, P. A. (2004). Tracking detracking: Sorting
through the dilemmas and possibilities of detracking in practice.
Equity & Excellence, 37, 92-101.
Russell, M. L. (2005). Untapped talent and unlimited potential: African
American students and the science pipeline. The Negro Educational
Review, 56(2/3), 167-182.
Texas Education Agency (2005). Accountability System State Data
Table 2005. Austin, TX: Author. Retrieved January 25, 2006,
from http://www.tea.state.tx.us/perfreport/account/2005/state.html
Ward, R. (2008, July 23).Our expectations for all children. The San
Diego Union-Tribune. p. A18.

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Thank You !!!
For
listening
to
my
presentation!
Have a wonderful day!!!