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IMPACT OF HIGH SCHOOL MATHEMATICS CURRICULA ON THE MATHEMATICS TAKS EXIT-

LEVEL PERFORMANCE OF AFRICAN AMERICAN STUDENTS

A Dissertation Defenseby

Clarence JohnsonSeptember 17, 2008

Dissertation Chair: William Allan Kritsonis, PhD

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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)

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Dissertation Defense FormatI. Statement of ProblemII. Purpose of the StudyIII. Theoretical FrameworkIV. Research QuestionsV. Null HypothesesVI. Pilot StudyVII. Subjects of the StudyVIII. Instrumentation IX. On-Line Survey

Questions

X. Data AnalysisXI. Independent/Dependent

VariablesXII. Major Findings -

QuantitativeXIII. Major Findings-

Qualitative/Interview and Related Literature Support

XIV. ImplicationsXV. Recommendations for

Further StudyXVI. Challenge & Opportunity

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Statement of the Problem Forty-three percent of African

American high school students failed the Texas Assessment of Knowledge and Skills (TAKS) Exit-Level Mathematics Test. The data table showed the failure rate was higher among African American students than any other ethnic groups (TEA, 2005).

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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.

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Purpose of the StudyThe 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 ofproper placement in mathematics courses along with support in the learning process.

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Theoretical FrameworkExplanatory 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 QuestionsQuantitative

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?

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Research QuestionsQuantitative

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 QuestionsQualitative

3. What factors do counselors identify as

influential in African American students’

placement in track one or track two mathematics?

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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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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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MethodsPilot Study

Pilot Study – Initial Survey with 15 QuestionsReduced 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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MethodsSubjects 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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MethodsInstrumentation

Quantitative – Data Banks of TEA and School District – SASIxp

Qualitative – On-line Survey

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MethodsOn-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, 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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MethodsData Analysis

Descriptive Statistics Correlation Statistics – Pearson r,

Multiple Correlation (R) t - test for 2 Independent Samples Analysis of Variance (ANOVA)

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MethodsVariables-Independent/

Dependent

Independent Variables – African American Students’ Scores in Algebra I, geometry and Algebra II

Track 1 Track 2Dependent Variable –TAKS Exit-Level

Mathematics Scores

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Major FindingsResearch 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 Track 1 2168.34 76.5 6.857*Track 2 2321.69 100.0*Significant at p ≤ 0.05Null 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 FindingsResearch Question 2Relationship Between Scores in Algebra Iand TAKS Exit-Level Mathematics TestPearson r Track 1 Track 2TAKS Scores 0.297* 0.242** Sig. (2-tailed) 0.000 0.098*Significant at p≤ 0.05 ** Not

Significant

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Major FindingsResearch Question 2Relationship Between Scores in

Geometryand TAKS Exit-Level Mathematics TestPearson r Track 1 Track 2TAKS Scores 0.651* 0.475* Sig. (2-tailed) 0.000 0.001*Significant at p≤ 0.05

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Major FindingsResearch Question 2Relationship Between Scores in Algebra

IIand TAKS Exit-Level Mathematics TestPearson r Track 1 Track 2TAKS Scores 0.503* 0.435* Sig. (2-tailed) 0.000 0.002*Significant at p≤ 0.05

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Major FindingsResearch Question 2

Analysis Of Variance (ANOVA) for Track 1 Students Passing the Mathematics TAKS Exit-Level Test Sum of Squares df F Sig.Regression 1737541.5 3 68.378 0.000Residual 1821106.7 215 Total 3558648.2 218Predictors: Constant, T1Algebra II, T1Algebra I,

T1GeometryDependent Variable: T1TAKS

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Major FindingsResearch Question 2

Coefficients for Track 1 Mathematics TAKS Exit-Level Test Unstandardized Coefficients t Sig. Constant 1161.918 15.130 0.000 T1Algebra I 2.033 2.474 0.014 T1Geometry 8.137 8.596 0.000 T1Algebra II 3.379 3.449 0.001 Dependent Variable: T1 TAKS

Regression Equation to Predict Value of TAKS Score:Ŷ = 1161.918 + 2.033X1 +8.137X2 + 3.379X3,where X1 = Algebra I score, X2 = geometry score, X3 =

Algebra IIscore and Constant = 1161.918.

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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 327637.4 3 10.375 0.000Residual 452633.5 43 Total 780270.9 46Predictors: Constant, T2 Algebra II, T2 Algebra I, T2

GeometryDependent Variable: T2 TAKS

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Major FindingsResearch Question 2

Coefficients for Track 2 Mathematics TAKS Exit-Level Test Unstandardized Coefficients t Sig. Constant 1227.116 6.208 0.000 T2 Algebra I 0.668 0.515 0.609 T2 Geometry 6.995 3.348 0.002 T2 Algebra II 5.765 2.634 0.012 Dependent Variable: T2 TAKS

Regression Equation to Predict Value of TAKS Score:Ŷ = 1227.116+ 0.668X1 + 6.995X2 + 5.765X3, where X1 = Algebra I score, X2 = geometry score, X3 =

Algebra II score and Constant = 1227.116.

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Number of Years Respondents Worked as a School Counselor

Years Frequency Percent1 - 5 6 37.506 - 10 1 6.2511 - 15 4 25.0016 - 20 3 18.7521 - 25 1 6.2526 - 30 1 6.25Total 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 18.75Previous academic achievement 15 93.75School district policy 14 87.50Teachers’ 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 SupportIn 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 68.75Teacher’s recommendation 4 25.00Counselor’s recommendation 0 0.00Family 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 75.00Better trained mathematics teachers 9 56.25More parental involvement 12

75.00Change 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 SupportMuch 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 31.25Bi-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 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 0.00Parental involvement 2 12.50Teacher’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 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 SupportThe average-achieving students in the high-track classes enrolled in more advanced high school mathematics courses than did students at similarachievement 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

AfricanAmerican males to 8th grade advanced mathematics?Factors Frequency Percent*Athletic coach’s recommendation 1 6.25Student’s interest 1 6.25Principal’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 SupportA counselor repeated the matrix’s guideline as basis for her action

regarding placement of African American students in 8th grade mathematics. Counselors 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, teachers at this school frequently meet with African American

students about how they can succeed in mathematics courses?Response Frequency PercentStrongly agree 0 0.00Agree 6 37.50Unsure 7 43.75Disagree 1 6.25Strongly disagree 2 12.50Total 16 100.00

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Related Literature SupportA student’s path in middle school can shape his orher 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 backto their formative academic experiences in middle school, high school and college, where thetrack 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 courses are not offered at this school 1 6.25About the right number 5 31.25Too few 10 62.50Too many 0 0.00Total 16 100.00

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Related Literature SupportAfrican 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 SupportBerry (2003) stated that African American students receive mathematics instruction that is not consistent with mathematics education reform; furthermore, the mathematics instruction that many

AfricanAmerican students receive is in opposition to their culture styles and learning preferences.

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Related Literature SupportAfrican 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 6.25Above average 6 37.50Adequate 8 50.00Poor 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

andwe 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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ImplicationsBerry (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 AfricanAmerican 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 ofTeachers of Mathematics (NCTM), whereas more White students are experiencing NCTM standards-based instruction (Lubienski, 2001).

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ImplicationsThe 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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ImplicationsTracking in American schools often contained a racial and socioeconomic element. African American students were more likely to be tracked in the vocational curriculum, Hispanic students in the general curriculum, and Asian andWhite students in academic or advanced placement curricula. Essentially, the content, rigor, and teachingstrategies vary markedly among curricula programs,although the course names in each program may often be similar. It was also well documented that African Americanand Hispanic boys were over-represented in special education programs (Futrell & Brown, 2000).

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ImplicationsWard (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 specificskills needed for effective algebra instruction, will be critical and costly.

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ImplicationsThe 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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Challenge & Opportunity Simply put, until African American

students on the pre-college level are participating at the highest levels in more rigorous, challenging science and mathematics courses, the achievement gap will only become more pronounced. Although African Americans have increased their participation in 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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Challenge & OpportunityThe attitudes and experiences of many school personnelneed 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 Americanand poor students of all ethnicities on the other. But theyare 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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Thank You !!!For listening to my presentation!Have a wonderful day!!!

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REFERENCESBerry, 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.

Futrell, M. H., & Brown, W. A. (2000). Should African Americans support the current education reform standards movement? The Journal of Negro Education, 69(4), 288-302.

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REFERENCESLubienski, 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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REFERENCESRubin, 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.