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8/14/2019 Dr. Clarence Johnson, PhD Dissertation Defense, Dissertation Chair, Dr. William Allan Kritsonis
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IMPACT OF HIGH SCHOOLMATHEMATICS CURRICULA ON THE
MATHEMATICS TAKS EXIT-LEVELPERFORMANCE OF AFRICAN
AMERICAN STUDENTS
A Dissertation Defense
by
Clarence Johnson
September 17, 2008
Chair: William Allan Kritsonis, Ph.D.
8/14/2019 Dr. Clarence Johnson, PhD Dissertation Defense, Dissertation Chair, Dr. William Allan Kritsonis
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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)
8/14/2019 Dr. Clarence Johnson, PhD Dissertation Defense, Dissertation Chair, Dr. William Allan Kritsonis
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Dissertation Defense FormatI. Purpose of the Study
II. Theoretical Framework
III. Research Questions
IV. Null HypothesesV. Pilot Study
VI. Subjects of the Study
VII. Instrumentation
VIII. On-Line Survey
QuestionsIX. Data Analysis
X. Independent/DependentVariables
XI. Major Findings-Quantitative
XII. Major Findings-Qualitative/Interview andRelated Literature Support
XIII. Implications
XIV. Recommendations for
Further StudyXV. Challenges &
Opportunities
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Purpose of the Study
The purpose of this study was toinvestigate the impact that high school
mathematics scores and courses had onthe Mathematics TAKS Exit-Levelperformance of African American students.Some middle school counselors were
surveyed to investigate factors thatcontributed to African American students’passing the Mathematics TAKS Exit-Level
Test.
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Note The results of this study may be helpful to
school administrators, teachers, and
parents. The results will help to giveneeded attention to students in terms of
proper placement in mathematics courses
along with support in the learning process.
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Theoretical FrameworkExplanatory Mixed Methods Design
QuantitativeData
QualitativeData
Track 1Scores:
Algebra I,Geometry,Algebra II
Track 2Scores:
Algebra I,Geometry,Algebra II
Eleventh Grade:
Mathematics TAKS Exit-LevelScores
Survey of Middle SchoolCounselors
Factors that Impact Students’Placement in Track 1 or Track 2Mathematics
African American Students’Performance
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Research Questions
Quantitative
1. Is there a difference between AfricanAmerican students enrolled in track oneor track two eighth grade mathematicsin their performance on the eleventhgrade Texas Assessment of Knowledge
and Skills (TAKS) Exit-LevelMathematics Test scores?
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Research Questions
Quantitative2. 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 andtheir eleventh grade Texas Assessment of Knowledge and Skills (TAKS) Exit-LevelMathematics Test scores?
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Research QuestionsQualitative
3. What factors do counselors identifyas
influential in African Americanstudents’
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 thosein track two eighth grade mathematicsin their performance on the eleventh
grade Texas Assessment of Knowledgeand Skills (TAKS) Exit-LevelMathematics Test scores.
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Null HypothesesH
02: There is no statistically significant
relationship between mathematics scoresin Algebra I, geometry, and/or Algebra IIof African American students enrolled intrack one or track two in eighth and ninth
grades and their eleventh grade TexasAssessment of Knowledge and Skills(TAKS) Exit-Level Mathematics Testscores.
8/14/2019 Dr. Clarence Johnson, PhD Dissertation Defense, Dissertation Chair, Dr. William Allan Kritsonis
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MethodsPilot 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 StudyQuantitative – 262 African
American Students from 6 UrbanHigh
Schools in Texas
Qualitative – 16 Counselors fromNine
(9) Middle Schools in Texas
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Methods
InstrumentationQuantitative – Data Banks of TEA
and School District – SASIxp
Qualitative – On-line Survey
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Methods
On-Line Survey Questions3a. 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 importantfactor?
3c. In your opinion, what could the school do that wouldreduce the failure rates of African American students ineighth grade mathematics?
3d. How often do you meet with students to discussmathematics grade placement?
3e. Which factor has the greatest influence on eighth grademathematics students’ passing rate in mathematics?
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Methods
On-Line Survey Questions3f. What is the most important factor that contributes to
the recommendation of African American males to eighthgrade advanced mathematics?
3g. In your opinion, do teachers at this school frequently
meet with African American students about how they cansucceed in mathematics courses?3h. What is your opinion of the number of eighth grade
African American students enrolled in advancedmathematics classes?
3i. How do you rate the counseling department in dealingwith 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)
M h d
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MethodsVariables-
Independent/Dependent
Independent Variables – AfricanAmerican Students’ Scores in Algebra
I, geometry and Algebra II Track 1
Track 2
Dependent Variable –TAKS Exit-LevelMathematics Scores
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Major Findings
Research Question 1Comparison 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 FindingsResearch 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 FindingsResearch 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 0.000Residual 1215491.8 168 Total 2197733.8 171
Predictors: Constant, T1Algebra II, T1Algebra I, T1Geometry Dependent Variable: T1TAKS
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Major FindingsResearch Question 2
Coefficients for Track 1 Mathematics TAKS Exit-Level Test UnstandardizedCoefficients 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 IIscore and Constant = 1297.279.
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Major FindingsResearch 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 FindingsResearch Question 2
Coefficients for Track 2 Mathematics TAKS Exit-Level Test UnstandardizedCoefficients t Sig.
Constant 1025.724 4.334 0.000 T2 Algebra I 4.760 1.560 0.126T2 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 RespondentsWorked as a School Counselor
Years Frequency Percent
1 - 5 6 37.50
6 - 10 1 6.2511 - 15 4 25.00
16 - 20 3 18.75
21 - 25 1 6.2526 - 30 1 6.25
Total 16 100.00
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Major Findings Qualitative Question 3a
What factors do you consider when placingstudents in 8th grade mathematics?
Factors Frequency Percent*Parental input 3 18.75Previous academicachievement 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 stategraduation requirements include at least 1 year of
algebra (McCoy, 2005).
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Major Findings Qualitative Question 3b
When advising African American students formathematics 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 thecounselors’ claim that parental
involvement has tremendous, effectiveinfluence 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 tothe 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 todiscuss mathematics grade placement?
Timeline Frequency Percent*One time a year 5 31.25Bi-annually 8 50.00Monthly 1 6.25Parent’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 isthe only time we meet to discuss placement. ‘District’sTrack’ 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 thehome school enter with.”“We tell students in the 6th grade when we let themchoose their courses about district mathematics
requirements. We tell them again at orientation nightduring the first day of school. We tell them again at openhouse, 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 8thgrade mathematics students’ passing rate in
mathematics?Factors FrequencyPercent*
Certified Mathematics teacher 0 0.00Parental involvement 2 12.50 Teacher’s expectation 5
31.25Peer group pressure 0 0.00Student’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 whenstudents of average mathematics achievementwere assigned to an advanced eighth-grade pre-
algebra class. They found that the achievement of accelerated average students was better thanthe achievement of similar students in previousyears who had not taken acceleratedmathematics (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 thatcontributes to the recommendation of African
American males to 8th grade advancedmathematics?Factors Frequency Percent*Athletic coach’s recommendation 1 6.25Student’s interest 1 6.25
Principal’s/counselor’s recommendation 1 6.25Achievement 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 schoolfrequently meet with African American students
about how they can succeed in mathematicscourses?Response Frequency PercentStrongly agree 0 0.00Agree 6 37.50Unsure 7 43.75Disagree 1 6.25Strongly disagree 2 12.50
Total 16
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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 theworkplace, 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 PercentAdvanced Mathematics coursesare 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
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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, themathematics 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 indealing with African American 8th gradestudents in mathematics?Rating Frequency Percent*Outstanding 1 6.25Above average 6
37.50Adequate 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 encouragethem all.”
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Implications
Berry (2003) points outs that African American students’mathematics achievement levels are indicative of theinstruction that they receive. Data collected on teachers’
instructional practices indicate differences between AfricanAmerican students and their peers.
National Assessment of Educational Progress (NAEP) datasuggest
that most African American students are not experiencing
instructional practices consistent with therecommendations suggested by the National Council of Teachers of Mathematics (NCTM), whereas more Whitestudents are experiencing NCTM standards-basedinstruction (Lubienski, 2001).
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Implications
The power and influence of the middle-class,affluent, and more privileged parents plays animportant role in deciding who will be in “their
kid’s classes.” More often than not, politicalpressure from parents coupled with lowexpectations for African Americans in theclassroom by teachers, counselors, and
administrators result in homogeneous tracksand 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 FurtherStudy
A study should be conducted to involverepresentative samples from one or
more districts in a similar study todetermine if results can be duplicated.
A study should be conducted to involve
another group of students (Whites,Hispanics, Asians, etc.) in a similarstudy.
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Recommendations for FurtherStudy
A study should be conducted to determinespecific activities of the guidance andcounseling department in the placement of
students not only in mathematics but also inthe different core areas of science, English andsocial studies.
A study should be conducted on the quality of
mathematics instruction involved in thedifferent tracks.
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Recommendations for FurtherStudy
A study should be conducted to predictthe performance of African American
students in the other core areas. A quantitative study should be conducted
with a large random sample of teachersand school counselors regarding theimpact of high school mathematicscurricula on the mathematics TAKS Exit-Level performance of students.
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Recommendations for FurtherStudy
A study should be conductedregarding remediation practices
done by the school and the home inpreparing students to succeed in thehigh-stakes tests given by the Stateof 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: Asianand 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 malemiddleschool students: A portrait of successful middle schoolmathematics students. Unpublished Doctoral Dissertation.
University of North Carolina at Chapel Hill, Chapel Hill, NC.Burris, C. C., Heubert, J. P., & Levin, H. M. (2006). Acceleratingmathematics achievement. Educational Research Journal,43(1), 105-136.
Darling-Hammonds, L. (2000). New standards and oldinequalities:
School reform and the education of African Americanstudents.The Journal of Negro Education, 69(4), 263-287.
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REFERENCES
Lubienski, S. T. (2001, April). A second look at mathematicsachievement gaps: Intersections of race, class, and genderin NAEP data. Paper Presented at American EducationalResearch Association, Seattle, WA.
McCoy, L. P. (2005). Effect of Demographic and personalvariables on achievement in eighth-grade algebra. Journalof 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: Sortingthrough the dilemmas and possibilities of detracking in practice.Equity & Excellence, 37, 92-101.
Russell, M. L. (2005). Untapped talent and unlimited potential: AfricanAmerican students and the science pipeline. The Negro Educational
Review, 56(2/3), 167-182. Texas Education Agency ( 2005 ). Accountability System State DataTable 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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