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

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IMPACT OF HIGH SCHOOL

MATHEMATICS CURRICULA ON THEMATHEMATICS TAKS EXIT-LEVELPERFORMANCE OF AFRICAN

AMERICAN STUDENTS

A Dissertation Defense

by

Clarence JohnsonSeptember 17, 2008

Dissertation Chair: William Allan Kritsonis, PhD



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 Format I. Statement of Problem

II. Purpose of the Study

III. Theoretical Framework

IV. Research Questions

V. Null Hypotheses

VI. Pilot Study

VII. Subjects of the Study

VIII. Instrumentation

IX. On-Line Survey Questions

X. Data Analysis

XI. Independent/Dependent Variables

XII. Major Findings -Quantitative

XIII. Major Findings-Qualitative/Interview andRelated Literature Support

XIV. ImplicationsXV. Recommendations forFurther Study

XVI. 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 Americanstudents than any other ethnic groups(TEA, 2005).



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Purpose of the Study

The purpose of this study was to investigatethe impact that high school mathematicsscores and courses had on the MathematicsTAKS Exit-Level performance of African

American students. Some middle schoolcounselors were surveyed to investigatefactors that contributed to African Americanstudents 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, andparents. The results will help to give

needed attention to students in terms of

proper placement in mathematics coursesalong with support in the learning process.



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Theoretical Framework

Explanatory Mixed Methods DesignQuantitative 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 StudentsPlacement in Track 1 or Track 2Mathematics

African American Students Performance



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Research Questions

Quantitative

1. Is there a difference between African

American students enrolled in track one ortrack two eighth grade mathematics intheir performance on the eleventh gradeTexas Assessment of Knowledge and Skills(TAKS) Exit-Level Mathematics 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

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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Hypotheses

H01:There is no statistically significant

difference between African Americanstudents enrolled in track one and those intrack two eighth grade mathematics intheir 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 trackone or track two in eighth and ninth grades

and their eleventh grade Texas Assessment of Knowledge and Skills (TAKS) Exit-LevelMathematics 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 from6

Urban HighSchools 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 Questions3a. What factors do you consider when placing students in

eighth grade mathematics?

3b. When advising African American students formathematics placement, what is the most important factor?

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 toeighth grade advanced mathematics?

3g. In your opinion, teachers at this school frequentlymeet with African American students about how theycan 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 indealing with African American eighth grade studentsin 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, geometryand Algebra II

Track 1

Track 2Dependent 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 2Mean % Passed TAKS t

Track 1 2168.34 76.5 6.857*

Track 2 2321.69 100.0

*Significant at p 0.05 N ull 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* 0.242**

Sig. (2-tailed) 0.000 0.098

*Significant at p 0.05 ** Not Significant



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Major Findings

Research Question 2 Relationship Between Scores in Geometry



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



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 (A N OVA) 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,

T1Geometry Dependent Variable: T1TAKS



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Major Findings

Research Question 2Coefficients for Track 1 Mathematics TAKS Exit-Level Test

UnstandardizedCoefficients t Sig.

Constant 1161.

91

815.130 0.000T1Algebra I 2.033 2.474 0.014

T1Geometry 8.137 8.596 0.000T1Algebra II 3.379 3.449 0.001

Dependent Variable: T1 TAKS

Regression Equation to Predict Value of TAKS Score: = 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 Findings

Research Question 2 Analysis Of Variance (A N OVA) for Track 2

Students Passing the Mathematics TAKS Exit-Level

Test Sum of Squares df F Sig.

Regression 327637.4 3 10.375 0.000

Residual 452633.5 43

Total 780270.9 46

Predictors: Constant, T2 Algebra II, T2 Algebra I, T2 Geometry




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Major Findings

Research Question 2Coefficients for Track 2 Mathematics TAKS Exit-Level Test

UnstandardizedCoefficients t Sig.

Constant 1227.116 6.208 0.000T2 Algebra I 0.668 0.515 0.609 T2 Geometry 6.995 3.348 0.002T2 Algebra II 5.765 2.634 0.012


Regression Equation to Predict Value of TAKS Score: = 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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N umber of Years Respondents

Worked as a School Counselor

Y ears 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 6.2526 - 30 1 6.25

Total 16 100.00



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Major Findings

Qualitative Question 3a W hat factors do you consider when placingstudents in 8th grade mathematics?

Factors Frequency Percent *

Parental input 3 18.75Previous academic

achievement 1593.

75School district policy 14 87.50

Teachers recommendation 14 87.50*D ue to multiple responses percentages do not add up to

100.



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Related Literature Support In Principles and Standards for SchoolMathematics, the National Council of Teachers of

Mathematics (NCTM, 2000) identified algebra asone 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 W hen advising African American students formathematics placement, what is the most

important factor?Factors Frequency Percent *

Students desire for morechallenging courses 11 68.75

Teachers recommendation 4 25.00Counselors recommendation 0 0.00Family history 0 0.00*D ue to less than total documented responses, percentages do not

add up to 100.



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Interview Support ³The district has a matrix that we follow that guides us in

placing students in Algebra I as an 8th grader. W e

examine previous grades and teacher recommendations todetermine placement in our AVID (college prep)

program.´

³Teacher recommendations are important but much less

reliable due to subjectivity.´³I would consider the students¶ desire for a challenge and

then speak with the teacher as well.´

³I follow the same schedule that the students from the

home school enter with.´



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Major Findings

Qualitative Question 3cIn 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 75.00Change entry level 3 18.75

*D ue to multiple responses, percentages do not add up to100.



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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 qualityteachers 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 6.25

Parents request 5 31.25*D ue to multiple responses, percentages do not

add up to 100.



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Interview Support

³Course selection or qualification for advanced classes isthe only time we meet to discuss placement. µDistrict¶sTrack¶ doesn¶t allow a student to enter in higher classes in

8th grade unless enrolled in 7th grade mathematics.´³I follow the same schedule that the student¶s from thehome school enter with.´³W e tell students in the 6th grade when we let themchoose their courses about district mathematicsrequirements. W e tell them again at orientation nightduring the first day of school. W e tell them again at openhouse, early fall. W e tell them again in the GT parents¶meeting held in the fall and spring. W e send out letters

late spring.´



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Major Findings

Qualitative Question 3e W hich factor has the greatest influence on 8thgrade mathematics students¶ passing rate in

mathematics?Factors Frequency Percent *

Certified Mathematics teacher 0 0.00Parental involvement 2 12.50Teachers expectation 5 31.25

Peer group pressure 0 0.00Students attitude 8 50.00*D ue 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 mathematicsachievement were assigned to an advancedeighth-grade pre-algebra class. They found that the achievement of accelerated averagestudents 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 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 W hat is the most important factor thatcontributes to the recommendation of African

American males to 8th grade advancedmathematics?Factors Frequency Percent *

Athletic coachs recommendation 1 6.25Students interest 1 6.25

Principals/counselors recommendation 1 6.25 Achievement scores 12 75.00

*D ue to total documented responses, percentages do not add upto 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.

Counselors commented:³O

nce again, Algebra I placement is determined by a

matrix given to us by the district.´



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Major Findings

Qualitative Question 3gIn your opinion, teachers at this schoolfrequently meet with African American students

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



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Related Literature Support A students 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 inmiddle 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

W hat is your opinion of the number of 8th grade African American students enrolled in advanced

mathematics classes?Reasons Frequency Percent

Advanced Mathematics coursesare not offered at this school 1 6.25

About the right number 5 31.25

Too few 10 62.50Too many 0 0.00Total 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 challengingcurriculum 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 oppositionto 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 standardizedexaminations (Russell, 2005).



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Major Findings

Qualitative Question 3i How do you rate the counseling department indealing with African American 8th grade

students in mathematics?Rating Frequency Percent *

Outstanding 1 6.25 Above average 6 37.50 Adequate 8 50.00Poor 0 0.00

*Due to total documented responses, percentages do not add up to100.



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Interview Support

³W e have a large group of student load and

we treat them all the same in placementand do not single out one group. W e 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 theinstruction 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 experiencinginstructional 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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ImplicationsThe power and influence of the middle-class,affluent, and more privileged parents plays an

important role in deciding who will be in theirkids classes. More often than not, politicalpressure from parents coupled with lowexpectations for African Americans in the

classroom by teachers, counselors, andadministrators result in homogeneous tracksand ability groups (Russell, 2005).



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ImplicationsTracking in American schools often contained a racial andsocioeconomic element. African American students weremore 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 besimilar. It was also well documented that African Americanand Hispanic boys were over-represented in specialeducation 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 specific

skills needed for effective algebra instruction, will be

critical and costly.



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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 todetermine if results can be duplicated.

A study should be conducted to involve

another group of students ( W hites,Hispanics, Asians, etc.) in a similarstudy.



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Recommendations for Further Study

A study should be conducted todetermine specific activities of the

guidance and counseling department inthe placement of students not only inmathematics but also in the differentcore 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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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 sampleof teachers and school counselorsregarding the impact of high schoolmathematics curricula on themathematics TAKS Exit-Level

performance of students.



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A study should be conducted regardingremediation practices done by the

school and the home in preparingstudents to succeed in the high-stakestests given by the State of Texas, notonly in mathematics but also in the

other core areas.



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Challenge & OpportunitySimply put, until African American studentson the pre-college level are participating atthe highest levels in more rigorous,challenging science and mathematics courses,the achievement gap will only become morepronounced. Although African Americanshave increased their participation in the

sciences within the last decade, it is importantto note that these advances are still miniscule when compared to those of W hite students(Russell, 2005).



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Challenge & OpportunityThe 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. Its 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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Thank Y

ou !!!For

listeningto

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 schoolmathematics students. Unpublished Docto ral Diss ertation .Uni versit y of No rth Ca rolina at Chap el Hill , Chap el Hill , NC.

Burris , C. C., Heubert , J. P., & Levin , H. M. (2006). Acc el eratin gmath ematics achi evement . Educational Res ea rch Jou rnal , 43(1),105-136.

Da rlin g-Hammonds , L. (2000). New standa rds and old in equaliti es: School refo rm and th e education of Af rican Am erican stud ents .Th e Jou rnal of Negro Education , 69(4), 263-287.

Fut rell , M. H., & Bro wn , W. A. (2000). Should Af rican Am ericans suppo rt th e cu rrent education refo rm standa rds mo vem ent ? Th e

Jou rnal 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 inNAEP 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 EducationalResearch, 98(3), 131-135.

National Council of Teachers of Mathematics. (2000). Principles andstandards for school mathematics. Reston, VA: NCTM.

Report highlights importance of middle school math (2003). BlackIssues in Higher Education, 20(19), 11.



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 EducationalReview, 56(2/3), 167-182.Texas Education Agency (2005). Accountability System State D ataTable 2005. Austin, TX: Author. Retrieved January 25, 2006,

from http://www.tea.state.tx.us/perfreport/account/2005/state.htmlWard, R. (2008, July 23).Our expectations for all children. The San

D iego Union-Tribune. p. A18.

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

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