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.



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)



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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.



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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




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Major FindingsResearch Question 2

Relationship Between Scores in Geometry




Sig. (2-tailed) 0.000 0.001

*Significant at p≤ 0.05



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Relationship Between Scores in Algebra II




Sig. (2-tailed) 0.000 0.002




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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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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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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




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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


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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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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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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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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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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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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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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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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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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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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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.

http://www.tea.state.tx.us/perfreport/account/2005/state.html

http://www.tea.state.tx.us/perfreport/account/2005/state.html



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dr. clarence johnson, phd dissertation defense, dissertation chair, dr. william allan kritsonis

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