Clarence Johnson, PhD and William Allan Kritsonis, PhD

1
IMPACT OF HIGH SCHOOL MATHEMATICS CURRICULA ON
THE MATHEMATICS TAKS EXIT-LEVEL PERFORMANCE OF
AFRICAN AMERICAN STUDENTS

• A Dissertation Defense
• by
• Clarence Johnson
• September 17, 2008
• Chair William Allan Kritsonis, Ph.D.

2
Committee Members

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

3
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 and
  Related Literature Support
• XIV. Implications
• XV. Recommendations for Further Study
• XVI. Challenge Opportunity

4
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).

5
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.

6
Purpose of the Study

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

7
Theoretical Framework
Explanatory Mixed Methods Design
Quantitative Data
Qualitative Data
Track 2 Scores Algebra I, Geometry, Algebra II
Survey of Middle School Counselors
Track 1 Scores Algebra I, Geometry, Algebra II
Factors that Impact Students Placement in Track
1 or Track 2 Mathematics
Eleventh Grade Mathematics TAKS Exit-Level Scores
8
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?

9
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?

10
Research QuestionsQualitative

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

11
Hypotheses

• H01There 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.

12
Hypotheses

• H02There 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.

13
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

14
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

15
MethodsInstrumentation

• Quantitative Data Banks of TEA and School
  District SASIxp
• Qualitative On-line Survey

16
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?

17
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?

18
MethodsData Analysis

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

19
MethodsVariables-Independent/Dependent

• Independent Variables African American
  Students Scores in Algebra I, geometry and
  Algebra II
• Track 1
• Track 2
• Dependent Variable TAKS Exit-Level Mathematics
  Scores

20
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 0.05
• 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 FindingsResearch 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

22
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

23
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

24
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 0.000
• Residual 1821106.7 215
• Total 3558648.2 218
• 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
• 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
• Y 1161.918 2.033X1 8.137X2 3.379X3,
• where X1 Algebra I score, X2 geometry score,
  X3 Algebra II
• score and Constant 1161.918.

26
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 0.000
• Residual 452633.5 43
• Total 780270.9 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
• 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
• Y 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 Percent
• 1 - 5 6 37.50
• 6 - 10 1 6.25
• 11 - 15 4 25.00
• 16 - 20 3 18.75
• 21 - 25 1 6.25
• 26 - 30 1 6.25
• Total 16 100.00

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Major Findings Qualitative Question 3a

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

30
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.

31
Related Literature Support

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

32
Major Findings Qualitative Question 3b

• When advising African American students for
• mathematics placement, what is the most
• important factor?
• Factors Frequency
  Percent
• Students desire for more
• challenging courses
  11 68.75
• Teachers recommendation 4 25.00
• Counselors recommendation 0 0.00
• Family history 0 0.00
• Due to less than total documented responses,
  percentages do not add up to 100.

33
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.

34
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.

35
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.

36
Related Literature Support

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

37
Major Findings Qualitative Question 3d

• How often do you meet with students to
• discuss mathematics grade placement?
• Timeline Frequency Percent
• One time a year 5 31.25
• Bi-annually 8 50.00
• Monthly 1 6.25
• Parents request 5 31.25
• Due to multiple responses, percentages do not
  add up to 100.

38
Interview Support

• Course selection or qualification for advanced
  classes is
• the only time we meet to discuss placement.
  Districts
• Track doesnt allow a student to enter in higher
  classes in
• 8th grade unless enrolled in 7th grade
  mathematics.
• I follow the same schedule that the students
  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.

39
Major Findings Qualitative Question 3e

• Which factor has the greatest influence on 8th
• grade mathematics students passing rate in
• mathematics?
• Factors Frequency
  Percent
• Certified Mathematics teacher 0 0.00
• Parental involvement 2 12.50
• Teachers expectation 5 31.25
• Peer group pressure 0 0.00
• Students attitude 8
  50.00
• Due to total documented responses, percentages
  do not add up to 100.

40
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).

41
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).

42
Major Findings Qualitative Question 3f

• What is the most important factor that
• contributes to the recommendation of African
• American males to 8th grade advanced
• mathematics?
• Factors Frequency
  Percent
• Athletic coachs recommendation 1
  6.25
• Students interest 1 6.25
• Principals/counselors recommendation 1
  6.25
• Achievement scores 12 75.00
• Due to total documented responses, percentages
  do not add up to 100.

43
Interview Support

• A counselor repeated the matrixs
• 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.

44
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 Percent
• Strongly agree 0 0.00
• Agree 6 37.50
• Unsure 7 43.75
• Disagree 1 6.25
• Strongly disagree 2 12.50
• Total 16
  100.00

45
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 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).

46
Major Findings Qualitative Question 3h

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

47
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).

48
Related Literature Support

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

49
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).

50
Major Findings Qualitative Question 3i

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

51
Interview Support

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

52
Implications

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

53
Implications

• The power and influence of the middle-class,
• affluent, and more privileged parents plays an
• important role in deciding who will be in their
• kids 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).

54
Implications

• Tracking 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 and
• White students in academic or advanced placement
• curricula. Essentially, the content, rigor, and
  teaching
• strategies vary markedly among curricula
  programs,
• although the course names in each program may
  often be
• similar. It was also well documented that
  African American
• and Hispanic boys were over-represented in
  special
• education programs (Futrell Brown, 2000).

55
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.

56
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.

57
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.

58
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.

59
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.

60
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.

61
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).

62
Challenge Opportunity

• 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. 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).

63
Thank You !!!

• For
• listening
• to
• my
• presentation!
• Have a wonderful day!!!

64
REFERENCES

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

65
REFERENCES

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

66
REFERENCES

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