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Student mathermatics performance in relation toselected causal variables and a teaming process forimproving higher order thinking skillsDanielle Sanders BattleClark Atlanta University
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ABSTRACT
EDUCATIONAT, LEADERSHIP
BATTLE, DANIELLE SANDERS B.A. NORTH CAROLINA CENTRAL
UNIVERSITY, 1990
M.A. NORTH CAROLINA CENTRAL
UNIVERSITY, 1995
STUDENT MATHEMATICS PEWOR\qANCE PI RELATION TO SELECTED
CAUSAL VARIABLES AND A 'TEAMING PROCESS FOR
IMPROVmG HIGHER O R n E R m K I N G SKILLS
Advisor: Dr. Ganga Persaud
Dissertation dated May 2009
It was proposed that student mathematics gain scores on the Georgia Criteria
Referenced Competency Test (CRCT], metivation ant1 teacher expectation might be
explained by teacher perceptions of the selected independent variables: Instructional I
leadership, professional development, teachcr methodology, achievement lesson
planning, teacher instructional delivzry and teacher cc\llege preparation.
The correlation design did not include a control group. Thirty-seven of the 48
teachers responded to a 5 1 -item, five-point ordinal sccrllc questionnaire in a metropolitan
Atlanta elementary school. Significant correlations were student CRCT performance;
motivation and teacher expectations were interconelated and all three variables were
significantly correlated with the Achievement Lesson ?laming system (ALPS), college
preparation, instructional supervision, math grouping, and staff professional
development. Higher order thinking skills (HOTS) were only significantly related to
CRCT and teacher expectation. Based on these results. five third grade teachers were
selected for treatment, and were asked to rate their 95 students' ability to respond to
higher order thinking skills in addition to providing teacher and student demographic
information. Based on the results of both sunleys, a treatment was conducted to
counteract the identified causal variables for low studerit responsiveness in teaching of
higher order thinking skills in order to improve student nathematic performance. The
researcher (the principal) trained the third grade teachers to function as a Grade
Achievement 1 e m (GAT) on the Empowerment Management of meeting (EMOM)
model and to utilize the ALPS to plan lessons so as to counteract the causal variables for
low student performance and to teach for higher order illirking skills utilizing the
Observation Based Instructional Assessment System (OBIA).
The results of ANOVA indicated that all teachers made significant gains on the
teaching of HOTS in mathematics. In a factor analysis, HOTS gain scores in
mathematics were loaded in component I inversely only with teacher gender. The results
of regression analysis indicated that student CRCT mattti? performance was significantly
predicted only by their Pre-CRCT score and teacher rating of their math performance. It
was suggested that the principal provided professioi~al development at the Grade
Achievement Team (GAT) level in the Management of Meeting (EMOM) model for
conducting Achievement Lesson Planning System (ALPS) and Observation Based
Instructional Assessment (OBIA) on the teaching of higher order thinking skills (HOTS).
STUDENT MATHEMATICS PERFORMANCE IN RELATION TO SELECTED
CAUSAL VARIABLES AND A TEAMING PROCESS FOR
IMPROVING HIGHER ORDER THINKING SKILLS
A DISSERTATION
SUBMITTED TO THE FACULTY OF CLARK ATLANTA UNIVERSITY
IN PARTIAL FULFILLMENT OF THE REQLUIREMENTS
FOR THE DEGREE OF DOCTOR OF EDUCATION
BY
DANIELLE SANDERS BATTLE
DEPARTMENT OF EDUCATIONAL LEADERSHIP
ATLANTA, GEORGIA
MAY 2009
0 2009
DANIELLE SANDERS BATTLE
All Rights Resewed
ACKNOWLEDGMENTS
I would like to thank God for providing me the strength and endurance to
complete my dissertation.
I am grateful to my entire committee. I extend appreciation to my Chairperson,
Dr. Ganga Persaud, who guided me through this process. I am also appreciative to
Dr. Trevor Turner who served on my dissertation committee and provided insightful
feedback regarding my research. To Dr. Noran Moffett, I am eternally grateful for your
service on my dissertation committee and for providing scholarly feedback and
unwavering support during this process. Your work as a higher education professor and
administrator who has worked in schools as a teacher and administrator facilitated the
implementation of the theory designed for this study. I would also like thank Mrs. Betty
Jo Cooke, administrative assistant in the Educational Leadership Department, for her
positive attitude and making sure I did not miss any deadlines. In addition, a very special
thanks to Mrs. Yvonne Baskin for her professional skills and patience necessary for the
typesetting, editing and formatting of the dissertation several times as I made changes.
I am appreciative to my husband, Laurence, for his understanding and support
through this process. I would also like to thank my siblings for encouraging and
nurturing the zest in me to reach higher.
TABLE OF CONTENTS
PAGE
. . ACKNOWLEDGMENTS ................................................................................................. si
LIST OF FIGURES ........................................................................................................... vi
. . LIST OF TABLES ............................................................................................................ vis
CHAPTER
1 . THE PROBLEM IN CONTEXT ................................................................. 1
Purpose of the Study .................................................................................... 1
Student Mathematics Achievement in the School Setting ........................... 2
Identifying Possible Independent Variables in the School Setting .............. 5
Program Strategies Implemented in School for Student Achievement ....... 9
Problem Statement ....................................................................................... 9
Significance of the Study ............................................................................. 9
I1 . REVIEW OF THE LITERATURE ........................................................... 10
............... Student Achievement (Gain Scores and Teacher Methodology) 10
............................................................................... Student Motivation 1 2
'Teacher Expectations (Teacher Rating of Higher Order
............................................................................... Thinking Skills 13
........................................................................... Instructional Leadership -14
........................................................................ Professional Development 1 9
................................ Lesson Planning and Teacher Instructional Delivery 20
Teacher Qualifications (Perceptions of Mathematics Courses
........................................................................... Taken in College 21
Table of Contents (continued)
CHAPTER
PAGE
................................................................................................... Summary -22
............................................................. I11 . THEORETICAL FRAMEWORK 24
................................................................................. Purpose of the Study -24
................................................... Presentation and Definition of Variables 25
Research Questions .................................................................................... 31
.............................................................. IV . RESEARCH METHODOLOGY 29
Research Design ........................................................................................ 33
............................................................................. Population and Sample -34
.................................................................................................. Treatment -35
....................................................................... Description of Instruments -58
Data Collection .......................................................................................... 58
........................................................................ Method of Analyzing Data 61
.................................................................................. . V DATA ANALYSIS -62
...................................................................................... Survey Instrument 62
......................................... Results of Factor Analysis: Survey Instrument 70
...................................................................... Data Analysis on Treatment 79
...................................................... Results of Factor Analysis: Treatment 87
VI . FINDINGS. CONCLUSIONS. IMPLICATIONS. AND
........................................................................... RECOMMENDATIONS 94
Table of Contents (continued)
PAGE
..................................................................................................... Findings 99
............................................................................................. Conclusions 1 0 1
............................................................................................. Implications 102
................................................................................... Recommendations 1 0 2
.................................................................................................. Summary 106
APPENDIX
........................................................................... A . Teacher Questionnaire 1 0 7
....................................................................................... B . Treatment Plan 1 1 2
C . Student Data ............................................................................................. 116
............................ D . Observation Based Instructional Assessment (OBIA) 118
............................................................................... E . Reliability Analyses 1 2 0
.................................................................................... F . Statistical Tables 1 2 2
................................................................................................................ REFERENCES 144
LIST OF FIGURES
PAGE FIGURE
1. School Organizational Chart in Relation to Supervision, Teaching
Students' Performance, and Parent Variables ............................................. 6
2. Diagrammed Outline of the Variables ............................................................... 26
LIST OF TABLES
PAGE TABLE
.......................... 1 . 'Third Grade GCRCT Matlthernalics Scores for 2006 2nd 2007 3
....................... 2. Second Grade GCRCT Matheinatics Scores for 2006 and 2007 4
3. Pretest Data: Empowerrneni Management of Meeting Model (EMOhl) ..... ..4 1
4. Posttest Data: Enlpowzrment Management of Meeting Model (EMOM).. ... .42
5 . Higb Definitior, Lessor, Planning Form (Pretest Data) Third Grade
........................................................................................... i\/lathernatiss.. -45
6. High Definitio~ 1,esscn P1ming Farm (P~sttest Data): 'fiird Grade
Mathematics.. ........................................................................................... -47
7 . Observation-Based Instructional Assessment (OBIA) System
......................................................................................... (Simple Form) 5 1
3. Scaled Teacher Pezception Items 02 Questionnaire by Cronbach Alpha
Reliabiiitj Coefficient (N = 37) ................................................................. 59
9 Results on Pearson Correlation Analyses . . . .63
1 0. Rotated Factor Matrix in 'Two Components: Teacher Perceptiorls about
................................................................................... rhe Listed Variables 72
1 1. Resu!ts on Regression A~alysis: Teacher Rating of Predicted Student
Gain on the CKCT (Dependent Variable: GNSTCRCT) in
............................... Mathematics by the Sekcted Independent Variables 75
List of Tables (continued)
TABLE PAGE
12. Results of Regression Analysis: Student Motivation as
Dependent with Listed Independent Variables ......................................... 76
13. Results of Regression Analysis: Teacher Expectations for Student
Performance (TCEXPEC) as Dependent with Listed Independent
Variables (N = 37) ..................................................................................... 77
14. Mean Score for Pretest, posttest, and Higher Order Thinking Skills
(HOTS) by Teacher ................................................................................... 83
15. Results of ANOVA: Higher Order Thinking Skills (HOTSGAIN) by
.................................................................................................... Teachers 8 3
16. The CRCT Mean Scores for Pretest, Posttest, and Gain in Math .................... 85
17. Results of ANOVA for the CRCT Gain Scores in Math ................................. 85
18. Results on Pearson Correlations CRCT and Higher Order thinking
Skills (HOTS): Pre, Post, and Gain Scores by Selected
Variables (N = 95) ..................................................................................... 86
19. Results on Rotated Component Matrix: All Selected Variables by
Components as Loaded .............................................................................. 88
20. Results on Stepwise Regression Analysis: Higher Order Thinking
Skills Gain Scores (HOTSGAIN) with Selected Independent
................................................................................................... Variables .90
List of Tables (continued)
PAGE TABLE
21. Results of Stepwise Regression Analysis (Model 3): CRCT
Gain Scores as Dependent wid1 Selected Independent Variables. .. . .. .. . . . .. 9 1
22. Resdts on Stepwise Regression Analysis: TCHRATE as Dependent
and Other Selected Variables as Independent ................................ .......... 92
CHAPTER I
THE PROBLEM IN CONTEXT
Purpose of the Study
The purpose of this study was to identify variation in students' mathematics
performance in a single school and to determine the variables that might significantly
influence student achievement in mathematics in an urban public elementary school in
Metropolitan Atlanta. Based on the results, the researcherlprincipal con-jointly with the
assistant principal collaboratively conducted a treatment with the third Grade chair and
teachers so as to enhance their capabilities to function as a Grade Achievement Team
(GAT) and to work collaboratively in making effective decisions for student achievement
in mathematics. The third grade chair was trained in conducting meetings of the GAT for
effective decision-making on the dimensions of the Empowerment Management of
Meeting (EMOM) model. At the meetings of the GAT, the chair utilized the
Achievement Lesson Planning System (ALPS) in order to plan lessons in relation to
students' social background and experie~lces so as to teach and evaluate learning in
mathematics on higher order thinking skills. The principal also oriented the GAT in the
use of the Observation Based Instructional Assessment Instrument (OBIA) system to
evaluate and nurture the GAT on teaching for higher order thinking skills (HOTS) in
mathematics. It was observed by the McRel Report (2003) that Student achievement in
mathematics might depend upon a nurturing school principal's leadership and other
I
2
variables in a pre-post setting. Further, it was observed that NCLB (2001) requires that
all schools should perform at proficiency level. In this study, some of the other
independent variables that might be related to student achievement in the school setting
are examined so as to counteract the effects in the treatment process. The GAT was
considered as the most effective level for teachers to plan, teach and evaluate lessons for
feedback purposes with respect to students of the sane grade level in mathematics. It was
also considered as an effective operational level for the principal to demonstrate both
nurturing and supervision. If the GAT was effective, then it might be possible for
administrators to conduct staff development on lesson planning, teaching and evaluation
at this level in a school so as to engage change process. The results of this study might be
of interest to superintendents, executive directors, human resources, educational
researchers, and educational leadership professors.
Student Mathematics Achievement in the School Setting
The problem with student achievement in mathematics at an urban elementary
public school setting includes results that suggest scores need to improve to surpass the
state average. With the resources in this district, more students should be meeting and
exceeding state standards. Table 1 reflects the evidence of student achievement on the
state mandated Georgia Criterion Reference Competency Test (GCRCT) for the 2005-
2006 school year and the 2006-2007 school year for third then second grade students in
mathematics.
Table 1
Third Grade GCRCT Mathematics Scores for 2006 and 2007
Quality Core Curriculum Quality Core Curriculum
(QCCs) (QCCs)
Performance Levels 2005- 2006 2006- 2007
DNM (Does Not Meet)
Level 1
M (Meets)
Level 2
E (Exceeds)
Level 3
The percentage of third grade 2006 students who did not meet expected
performance standard in math was 7%. The percentage of third grade 2006 students who
met expected performance standards in math was 72%. The percentage of third grade
2006 students who exceeded expected performance standards in math was 2 1 %. The
total percentage of third grade 2006 students who met or exceeded expected performance
standards in math was 93%.
The percentages of second grade 2006 students who did not meet expected
performance standard in math was 9%. The percentage of second grade 2006 students
who met expected performance standards in math was 68%. The percentage of second
4
grade 2006 students who exceeded expected performance standards in math was 23%.
The total percentage of second grade 2006 students who meet or exceeded expected
performance standards in mathematics was 9 1 % (Table 2).
Table 2
Second Grade GCRCT Mathematics Scores for 2006 and 2007
Qual~ty Core Curriculum Georgia Performance
(Qccs) Standards (GPS)
Performance Levels 2005- 2006 2006- 2007
DNM (Does Not Meet)
Level 1 9%
M (Meets)
Level 2 68%
E (Exceeds)
Level 3 23%
The scores may look pretty good but these students were administered the CRCT
mathematics test based upon the preparation provided in the school setting from the
Quality Core Curriculum (QCC) in the state of Georgia. In 2007, second grade students
who did not meet standards were 18%. The percentage of second grade in 2007 that met
expected performances standards in mathematics was 72%. The percentage of second
grade 2007 students u7ho exceeded expected performance in mathematics was 10%. The
total percentage of second grade 2007 students who meet or exceeded performance
standards in mathematics was 82%. There was a drop in the number of students who
passed the CRCT as well as a decline in the number of students who exceeded the test.
In 2007, students who exceeded the standards declined by half when taking the
CRCT using the new Georgia Performance Standards. In 2008, the third grade students
took the CRCT in mathematics but it will be using the Georgia Performance Standards.
Georgia Performance Standards are more rigors and go deeper into context knowledge.
Identifying Possible Independent Variables in the
School Setting
As a result of the suggested problem in context, the following organizational chart
(Figure 1) is utilized to identify the location of student achievement. This cohort of
students were administered the CRCT mathematics test based upon the preparation
provided in the school setting from the Quality Core Curriculum were first and second
grade students but will be administrated the Georgia Performance Standards will be
administrated to grades one through five in mathematics in 2008.
This school system is a social system set up in a hierarchical tier. Starting from
the bottom of the organizational chart, the parents send their students to teachers who are
ultimately responsible for the education safety and development. The mathematic
performance of students in the third grade is directly affected by instruction delivered and
achievement lesson planning by the classroom teachers. The classrooms are comprised of
students with varying levels of readiness, learning profiles and interest. One challenge
according to Darling-Hammond (2005) is for teachers to have the preparation and skills
to teach students to the highest standards.
Figure I . School's Organizational Chart in Relation to Supervision, Teaching Students'
Performance, and Parent Variables
Board of Education and School Reform Team I11
1 Principal
1 Assistant Principal
1 Instructional Liaison Specialist
1
Students
Kindergarten lSt Grade 2nd Grade 3rd Grade 4th Grade sth Grade
Student Mathematics Achievement and Student Motivation
v - Teachers
Instructional Leadership Professional Development Teacher Methodology Achievement Lesson Planning Instructional Delivery Qualifications
4
v
Parents: Background Variables
b
7
The level above students and teachers is the instructional specialist who provides
resources, support and guidance to classroom teachers. The instructional specialist is
under the direct supervision of the assistant principal and the principal, which monitor
and supervise the daily operations of the school. The assistant principal assists the
principal is ensuring that the school is a safe and orderly place for teaching and learning.
The assistant principal is also charged with monitoring the implementation of the
standards in the classrooms and teacher expectations overall in their deliver of
instruction.
The highest administrative level in the school building is the principal and
receives support from the executive director. The executive director is apart of the
superintendent's cabinet that communicates policy to the principals under hisfher direct
supervision. The duty superintendent of teaching and learning ensures that schools are
implementing the Georgia Performance Standards and is accountable to the
superintendent of schools.
The superintendent is accountable to the Board of Education. The Board of
Education is charged with the responsibility of educating the children of this metropolitan
urban district. Hence, all of these key players inadvertently or advertently perform
activities that are intended to influence mathematics.
Further analysis of this chart shows that the parents from this school come from
varied backgrounds including the majority of the students on free and reduce lunch status.
Thus, students come to school with varied experiences, as well as students from low
socioeconomics status that come to school with low verbal skills (Hess & Shipman). As
8
a result, the next level on the organization chart is locus parentis (the teacher as the parent
and provider of instruction in the school setting). The teachers provided lessons using the
ALPS to ensure students are getting to use their social experiences in order to connect
them to the lessons. Thereafter is the school principal who provides leadership to the
organizational setting where the school climate and culture are defined. The principal
depends on support to implement the organizational ethos though grade level chairs and
assistant principal in the school setting. It should also be noted that the principal reports
to the central office for the systems needs to meet state and federal mandates. These
mandates are not absent of the need to recognize the context for the social experiences of
the learners. The learners come from homes and communities where social experiences
are dominate forces in the lives of the learners. Since there are various backgrounds from
which the learners come to the school setting, the parental education, experiences and
environmental circumstances influence the social experiences of the learners. The OBIA
was designed to capture the social experiences of the learner through the teaching and
learning experience. It is up to the principal to monitor the ALPS as well as visit the
classrooms to ensure the OBIA is being used. Professional development should be
incorporated in the school's plan.
Rosenthal and Jacobson (1 968) found that teacher expectations of students of low
socio economic status and minority children were contributing to the high rates of failure
among these students and the same teachers had higher expectations for middle class
children.
Program Strategies Implemented in School for
Student Achievement
This school uses one of the comprehensive school reforms the superintendent has
required all schools to use over her tenure the last nine years. Despite the use of a reform
model at this urban school, the Spring CRCT results indicate that there is a still
achievement gaps versus the actual outcomes. The No Child Left Behind Law requires
all students to meet or exceed state standards by 2014. Therefore, a study would seek to
identify independent variables that might influence student achievement in mathematics.
Problem Statement
It was proposed to examine the extent to which the school's third grade team
mean CRCT mathematics score, student motivation and teacher expectations would be
related to teachers' perception of are instructional leadership, professional development,
teacher methodology as it relates to grouping of students, lesson planning, teacher
questioning of higher order thinking skills and teacher qualifications as it relates to
college courses in mathematics.
Significance of the Study
Student achievement in mathematics for third grade student was identified as a
problem for this urban elementary school. Eighteen percent of the second graders taking
the new test using the Georgia Performance Standards (GPS) did not meet state standards
in mathematics. It is the school's responsibility for student achievement in mathematics,
hence, the study focused on variables that fell under the leadership of the school
principal.
CHAPTER I1
REVIEW OF THE LITERATURE
The primary intent of this chapter is to review relevant literature related to
students' gain score in mathematics, student motivation and teacher expectations, the
dependent variables in this study. In addition, literature is presented that supports the
independent variables of this study, which are instructional leadership, professional
development, teacher methodology as it relates to grouping of students, lesson planning,
teacher questioning of higher order thinking skills and teacher qualifications as it relates
to college courses in mathematics.
Student Achievement (Gain Scores) and Teacher Methodology
Since the release in 1983 of A Nation at Risk, the pressure for greater
accountability has increased according to (Ginsberg and Berry, 1998). The focus and
emphasis of liability systems has shifted to measuring student performance and assigning
accountability for results (Pipho, 1989). Some districts and states develop their own test
while others rely on commercially available standardized tests (Linn, 2000).
In a study of 2,170 teachers in 141 elementary schools, Ross, Hogaboam-Gray
and Gray (2003) found that prior student achievement in six-grade mathematics
supported collective teacher efficacy, as well as social cognition theory. It found school
processes promote teacher ownership in the school vision.
11
O'Neill(2002) found that through the comparison of looping and non-looping
instructional methodologies, its impact on student achievement can be examined. In
addition to the comparison of academic performance, other indicators within the context
of student achievement were researched to determine the measurable effects of looping
on student attendance and parent-teacher contacts. There are also direct sociological and
psychological correlations to looping including student perceptions of feelings about the
classroom and academic motivation. Overall, the cognitive development of the students
was most visible in language arts, parental involvement within the academic process and
relationship with teachers, and student attitudes towards learning.
Bode (1996) found that grouping students for instructional purposes had a neutral
effect on average students but had a higher effect on high achiever and low achievers.
The conclusion was ability grouping for is beneficial for some student but a detrimental
to others.
A study by Shaver and Walls (1998) found that parental involvement, regardless
of gender and socioeconomic status, had a positive influence on reading and mathematics
achievement. They also suggest schools with economically disadvantaged students
utilize various strategies to promote parental involvement.
Student achievement improved in classrooms where the teachers created more
contact with students (Gibson & Dembo, 1984). Also, student achievement improved in
the classrooms of teachers who believed and had confidence in the effectiveness of
education. On the opposite end, teachers who relied on the principal for support
produced lower student achievement results.
Student Motivation
According to educational psychology, classroom motivation is an integral part of
successful teaching. Grolnick and Ryan (1 992) identified the chief objective in learning
is not limited to the absorption of academic concepts, but rather in the development of
intellectual curiosity and a sense of the child's belief in his or her ability to want to grasp
the concept. Hootstein (1 998) identifies four conditions necessary for student motivation
called the RISE model: relevant subject matter, interesting instruction, satisfied learner,
and expectations of success. Other factors include family support as well as the personal
motivation that is intrinsic to students. According to Fisher (2003), there is a relationship
between attitudes and student grades when the RISE model was built-in. It was found
that a correlation between attitudes and achievement while motivational strategies were
put into practice at the elementary school setting.
Eptein (2007) investigated the effects of cooperative learning in the classroom.
The finding revealed that classes that used cooperative learning in the classrooms,
students' motivation was increased as well as improved student achievement increased
time on task, improved group relations and greater satisfaction with the school.
Yin (2005) connected research on formative assessment, motivation and
conceptual change. The findings concluded that motivation beliefs were not correlated
with students' achievement.
Teacher Expectations (Teacher Rating of Higher Order
Thinking Questions)
The teachers' stereotypes and attitudes affect the classroom environment and
student performance. According to Stinson (2006), the "discourse of deficiency" and its
impact on the perceived deficient culture of African-American students, their school, and
in general, their life experiences are affected by the teachers' attitudes and stereotypes.
School leaders and teachers who participate in this discourse often claim that the lower
academic achievement many African-American students exists because they experience a
high rate of poverty, single-parent homes, unsafe neighborhoods and little to no parent
involvement. The belief can create low student expectations and stereotyping by teachers
and thus have and negative effect on student performances.
According to the American Federation of Teachers (1 999), when done well,
professional development should be equal parts an individual and collective assessment
and continued pursuit of excellence. The writer has found that professional development
should increase confidence in a teacher's abilities to problem solve, to resolve issues, and
to identify the relationship between the concept and the application to realize measurable
achievement, In addition, the professional development of teachers should be aligned to
state standards, speak to the multiple intricacies of teaching, and be intellectually
engaging.
Weiss (2003) points out research that indicates that the socio-economic factors
such as students7 racial and/or economic background, their parents' educational level,
their access to high-quality preschool instruction, peer influences, teachers' expectations
and curricular and instructional quality seem to be related to the achievement gap
between poor minority students and those less disadvantaged students. He also highlights
a report from the Economic Policy Institute (EPI), which indicated that research on the
black-white achievement gap does not focus on a particular breakthrough invention, but
on a series of deliberate changes that schools could implement to close the gap.
Using the basis of Rosenthal and Jacobson's (1 966) research on the Pygmalion
Effect as well as Tauber's (1 997) follow-up research over 30 years later, the researcher
confirms all of the assertions that there is a distinctive connectivity between student
achievement and teacher expectations, though not specifically with student IQ's. The
Pygmalion Effect is little more than a restating of the theory of the self-fulfilling
prophecy, which clearly links belief and behavior. Teachers also tend to assign
expectations to certain classifications of students, which include race, gender, and
previous academic performance.
Instructional Leadership
Supervision of Teachers: a process by which a supervisor assists teachers in the
implementation of high-quality lessons through the utilization of effective plans,
observation and constructive feedback. Clinical supervision is cyclical in nature with
improvement in instructional strategies as the desired result. Using Goldhammer's
research dating back to 1969, as well as Sullivan's Clinical Supervision: A State ofthe
Art Review, the writer will argue that throughout the supervision process, the goal is to
eliminate the teaching strategies that do not produce maximum results while
simultaneously strengthening the more productive areas in a teacher's approach. The
writer will also prove that success within this process is shared and depends upon the
timely development of lesson plans for thorough review by supervisors, and the
supervisors must evaluate the practical application of plans as well as provide analysis of
the teacher's ability to deliver the information to students.
Hess and Shipman (1965) found that a mother's education impacted student
achievement outcomes for low socioeconomic status (SES) students. Since the time of
this study by Hess and Shipman, SES has become an increased cited variable related to
student achievement outcome. In the public school setting, the role of the instructional
leader has become a more recent variable used to measure school achievement factors.
The empirical research on instructional leadership as an independent variable was
collected and reviewed in a study released by Mid-Continental Regional Educational
Laboratory (McRel Report, 2003).
According to Waters, Marzano, and McNulty (2003) in their quantitative analysis
of 30 years of research, effective leadership and leadership responsibilities were
identified as significant variables that correlate with student achievement. The findings
suggested that a review of 5,000 studies produced only 70 that met the research
methodology using the criteria of design, controls, data analysis and rigor. As a result, 21
leadership responsibilities significantly correlated with student achievement as the
dependent variable. These leadership responsibilities are:
Culture: The extent to which the principal fosters shared beliefs and a sense
of community and cooperation.
Order: The extent to which the principal establishes a set of standards
operating procedures and routines.
Discipline: The extent in which the principal protects teachers from issues
and influences that would detract from their teaching time or focus.
Resources: The extent to which the principal provides teachers with materials
and professional development necessary for the successful execution of their
jobs.
Curriculum, instruction, and assessment: The extent to which the principal is
directly involved in the design and implementation of curriculum, instruction,
and assessment practices.
Focus: The extent to which the principal establishes clear goals and keeps
those goals in the forefront of the school's attention.
Knowledge of curriculum, instruction assessment: The extent to which the
principal is knowledgeable about current curriculum, instruction, and
assessment practices.
Visibility: The extent to which the principal has quality contact and
interactions with teachers and students.
Contingent rewards: The extent to which the principal recognizes and
rewards individual accomplishments.
Communication: The extent to which the principal establishes strong lines of
communication with teachers and among students.
17
Outreach: The extent to which the principal is an advocate and spokesperson
for the school to all stakeholders.
Input: The extent to which the principal involves teachers in the design and
implementation of important decisions and policies.
AfJirmation: The extent to which the principal recognizes and celebrates
school accomplishments and acknowledges failures.
Relationship: The extent to which the principal demonstrates an awareness of
the personal aspects of teachers and staff.
Change agent: The extent to which the principal is willing to actively
challenge the status quo.
Optimizer: The extent to which the principal inspires and leads new and
challenging innovation.
Ideals/beliefs: The extent to which the principal communicates and operates
from strong ideals and beliefs about schooling.
Monitors/evaluates: The extent to which the principal monitors the
effectiveness of school practices and their impact on student learning.
Flexibility: The extent to which the principal adapts his or her leadership
behavior to the needs of the current situation and it comfortable with dissent.
Situational awareness: The extent to which the principal is aware of the
details and undercurrents in the running of the school and uses this
information to address current and potential problems.
Intellectual stimulation: The extent to the which the principal ensures that
faculty and staff are aware of the most current theories and practices and make
the discussion of these a regular aspect of the school's culture.
According to a study by Lucas and Valentine (2002), principal seems to be the
primary source of identifying and articulating a vision and providing an appropriate
model. Leadership teams seem to be the primary source of providing intellectual
stimulation and holding high expectations.
In a study by Drago-Steverson (2002), there are three main initiatives practiced by
the principal: teaming, providing leadership roles, and collegial inquiry to support adult
development. Findings illustrated how adult developmental theory might be bridged to
leadership.
According to Acker-Hocevar and Touchton. (200 I), 10 elementary school
principals7 perceptions of the high poverty populated schools in Florida that had earned a
grade of "D" or "F." The findings suggested that four themes emerged from the case
study interview analyses: principals addressed external and internal accountability of
schools' development through effects of poverty, building organizational capacity, high
stakes testing, grading the schools, and recruitment and retention.
Niederrneyer (2003) examined whether a specific leadership style is more
beneficial to improving student achievement and if there is a relationship between
leadership styles and teacher satisfaction, willingness to put forth extra effort, and teacher
perception of principal effectiveness. The findings suggest that transactional leadership
19
made a difference in student learning as measured by student test in low-socio economic
elementary schools.
Professional Development
Drago-Steverson (1 997) studied showed how a particular principal with a well-
informed adult development perceptive actually employed the strategies. Its work
focuses on leadership, adult development, and teacher development while studying the
philosophies and practices of a principal's leadership for supporting adult growth and
development. The findings illustrated how adult development theory might be bridged to
leadership practices aimed at supporting the development of the mind.
Turchi, Johnson, Owens, and Montgomery's (2002) study was drawn from
interrelated research strategies. The study analyzed strategies from six policy
inventories, 24 school case studies and one extensive teacher survey from six southern
states. The findings suggested that teacher's opportunity to learn was based upon those
subjects tested by the state and there was an increased attention to analysis of test results.
Elmore (2002) examined the importance of teacher professional development as it relates
to student achievement.
Lombardi (2008) examined if teachers' perceptions of the influence on
vocabulary performance in their students. The conclusion was professional development;
leadership and differentiation were leading variables that affect student vocabulary
development.
Lesson Planning and Teacher Instructional Delivery
Teacher lesson planning is an important factor when preparing for student
success. Lesson planning alone does not equal student success. According to Ediger
(2004). teachers need to ensure that student receive objectives that are clearly stated, and
focused on the actual topic being taught. In order for students to grasp concepts being
taught first teachers must understand and narrow objectives to a point where both teacher
and students can grasp material that is being taught.
According to Persaud and Turner (2002), cases where teachers are able to prepare
lessons and teach in relation to students' social experience, students' performance mostly
like will improve. Candenas (1 999) described that the second key to success is to provide
lesson plans that grabs the students' attention. He suggested that the lesson begin with a
strong hook and student learning is ensured. Teachers are strongly encouraged to include
all of modalities in which students learn in their planning process, Teacher planning is a
key to student success.
Todd (2006) examined whether essentials of systematic lesson planning was
related to student mathematics achievement. A finding with high-favored implications
was pedagogical training related to producing well-developed lessons for pre-service, and
in-service teacher. The training should focus on mental mathematics activities that
surface students' prior knowledge.
Taylor (2004) investigated if collaborative planning had a direct relationship on
quality lesson plans. The findings suggest that if teachers collaborate, they are more
likely to have lesson plans that are more effective thus impacting their state test.
Iyer (2006) investigated school that had programs, which were based on the
multiple intelligences theory. The findings supported that these schools more frequently
see students engaged in higher order thinking skills, discussions and interacting with the
teacher.
Teacher Qualifications (Perceptions of Mathematics Courses
Taken in College)
Ingersoll(2002) highlighted that the quality of teaching is not only dependent
upon recruiting and training but also upon providing a well-managed work environment
that treats teachers like professionals who have specialized expertise. Ingersoll also
noted that out-of-field teaching undermines quality teaching and learning.
Darling-Hammond (1 999) examined the ways in which teacher qualifications and
other school inputs are related to student achievement across states. The findings of the
study were that policy investments in the quality of teachers might lead to improved
student performance.
Wilkes (2008) examined eight pre-service teachers over a period of one year. The
researcher collected lesson plans, written rationales and completed interviews. The
findings from the study revealed that with the gaining of professional vocabulary and an
understanding of lesson planning and assessment would increase their mental models.
Weber (2005) conduced a study to assess changes in preservice teachers' level of
mathematics anxiety and beliefs about teaching mathematics after completing a
mathematics methods course incorporating a constructivist approach to teaching. It was
22
found that constructivist math methods class decreased math anxiety levels in preservice
teachers.
Rockoff (2003) studied elementary school teachers and students of two school
districts to determine the effects of teacher quality on student achievement in the two
school districts. It was found from the regression analysis omitting the teacher fixed
effects were repeating grade significant on reading vocabulary and reading
comprehension; below split in split-level classroom was significant on reading
comprehension and teachers with masters degrees were significantly one related to
reading comprehension.
Williams and King (2002) studied groups of educational leaders from rural areas
who were interviewed about impediments to student's achievement in their districts. The
findings suggested those school leaders' training and development; specific strategies are
needed for rural school districts, critical teacher shortages and shortage of administrators.
Summary
Instruments to measure instructional leadership and relative outcomes were cited
in the McRel Report (2003) through the identification of 2 1 dimensions. Another
indicator proposed by selected research has been the role of professional development
provided to teachers to improve instruction. Also, the influence of teachers on student
outcome has been studied as the most significant indicator of student achievement
(Darling & Hammond, 2000). However, the manner in which teachers influence student
achievement should be scientifically measured and quantified through selected
dimensions. For example, teacher expectations, teacher lesson planning and teacher
23
method using higher order thinking skills questions (Persaud, 2005). Many state report
cards use teacher qualifications, teacher experience, and teacher attendance and teacher
class size as independent variables that may impact student achievement (Moffett &
Persaud, 2005).
CHAPTER 111
THEORETICAL FRAME WORK
Purpose of the Study
The purpose of this study was to identify the causal variables for variation in
student performance in mathematics in the third grade so as to design a treatment for
controlling or minimizing the effects of such causal variables as the basis for teaching for
higher order thinking skills and improving student performance. Specifically it was
proposed that variations in student performance on the CRCT-teacher expectations-
and their motivation might be influenced by: instructional leadership, professional
development, teacher methodology, achievement lesson planning, teaching for higher
order thinking skills, teacher expectations, and teacher and student demographic variables
as identified. It was also proposed that a treatment conducted to control the essential
causal variables that might be identified would show gains on teacher and students'
performance on higher order thinking skills and student performance on the CRCT.
Specifically, based on the results of a survey to determine the causal variables for student
performance and motivation in mathematics, the principal con-jointly and collaboratively
with the assistant principal conducted a treatment with the third Grade chair and teachers
so as to enhance their capabilities to function as a Grade Achievement Team (GAT) and
to work collaboratively with in making effective decisions for student achievement on the
dimensions on the Empowerment Management of Meeting (EMOM) model. The GAT
24
utilized the Achievement Lesson Planning System (ALPS) in order to plan lessons in
relation to students' social background and experiences so as to teach and evaluate
learning on higher order thinking skills. The principal also utilized the Observation
Based Instructional Assessment Instrument (OBIA) system to evaluate and nurture the
GAT on teaching for higher order thinking and student performance. These variables are
denonstrated in Figure 2 as a guide for their operational definitions.
Presentation and Definition of Variables
Dependent Variables
C'RCT in mathematics as a dependent variable is measured in terms of the
2007and 2008 test scores in order to calculate the gain scores. In this respect, the base
pre-test performance in mathematics on the CRCT by the cohort of students who were
second graders was 2006-2007 and as third graders their scores in 2007-2008 were the
posttest. In other words, the second grade CRCT scores in mathematics were used as the
pre-treatment outcome and the CRCT test scores for third grade were used as the post-
treatment outcome.
Student motivation as well as teacher expectalions in relationship to the higher
order thinking questions skills that are asked by the teacher.
Definition of Dependent Variables
Student achievement is defined as the mean students' scores for the school in
mathematics at the third grade on the Georgia Criterion Referenced Competency Test
(GCRCT) and is measured by the actual record performance.
INDEPENDENT VARIABLES
Instructional Leadership s
Treatment at Third Grade Achievement Team (GAT)
Figure 2. Diagrammed Outline of the Variables
DEPENDENT VARIABLES
Gain Scores in Mathematics on CRCT
Student Motivation
Teacher Expectations
A
Professional Development +
Teacher Methodology --+
Achievement Lesson Planning +
I
Teacher Questioning of Higher Order Thinking Skills +
Teacher Qualification/College Courses in Mathematics
Student performance was also measured by teachers' estimation of students'
performance on the CRCT and class assignments as identified in items on questionnaire
(State items).
Student motivation involves students staying on-task and seeking assistance when
help is needed and is defined as the extent to which: Weak students remains on task,
weak students apply themselves on on-task if given attention, weak students know how to
work collaboratively in groups, and weak student tend to become self-motivated, if
assisted. (Items 40-43)
Teacher expectations refer to teacher beliefs about the capacity of students in
developing higher order thinking skills is defined as the extent to which teacher:
Believes that students in level 1 can move to level 2 or above; believes that level 2
students can move to level 3; believes that students in level 3 can maintain their
positions; believes that all students can learn; believes that a student's CRCT pre-
assessment score (from previous year) is a predictor of performance on the CRCT post-
assessment. Teachers were measured by Items 28-30 of Teacher Questionnaire (see
Appendix A).
Definition oj'lndependent Variables
Instructional supervision is measured as the extent to which the principal has
those administrative traits measured by questions 1-1 0 of the Teacher Questionnaire (see
Appendix A). These items were designed to measure teachers' perceptions on the extent
to which the principal supports the teachers to ensure quality instruction in the classroom.
Teacher perception if administrators makes the decisions and faculty to implement, ask
faculty how to solve problems, discuss with faculty how to improve lesson planning,
utilize faculty opinions to develop lesson planning steps so weak students can achieve at
or above grade level, ask teachers to identify causes for low performance in class or
CRCT, ask teachers how to teach weak students to master HOTS and discuss with
teachers how to develop test to measure HOTS.
Professional development refers to teacher opinions about the effectiveness of the
workshops, seminars, and conferences that teachers attended as provided by the school
system and building level administrators. The teacher's opinions about the effectiveness
of how to enable weak students to exceed, show teacher how to differentiate instruction,
and make flexible groups for mathematics. The teachers were measured by questions 1 1 -
14 of the Teacher Questionnaire (see Appendix A). Staff professional development will
be based upon standards by the National Council of Teachers of Mathematics (NCTM),
Quality Core Curriculum (QCC), and Georgia Performance Standards (GPS).
Teacher methodology was measured by the teacher use of grouping mathematics.
The teacher opinion about grouping of students based upon pre-assessments data,
organizing and managing several groups in a classroom, providing on-going assessment
for students' performance. The teachers were measured by questions 15-1 8 (see
Appendix A).
Teacher lesson planning was measured by Achievement Lesson Planning System
(ALPS) designed to identify and define causes for failure, develop strategies to
counteract causes, constructing objectives in relation to the Bloom's taxonomy and
students' experience, specie questions on higher order thinking skills in reference to
students' experiences and indicating how the answers will be used to demonstrate the
construction of higher order thinking skills, and evaluate for effectiveness and feedback
as measured on the ALPS. The teachers were measured using questions 19-24 in the
Teacher Questionnaire (see Appendix A).
Teacher Higher Order Thinking Skills Questions refers to the extent in which
teachers' perceiving that students have experiences that they are using for learning higher
order thinking skills in response to teachers' methods. The teachers' perceiving if level 3
students can maintain, all students can learn equally well, pre-assessment score on CRCT
is a predictor of post assessment on CRCT, teacher can integrate other subjects matters
into mathematics lesson, using personal experiences that are appropriate for teaching
HOTS. The teachers were measured in questions 3 1-36 of the Teacher Questionnaire
(see Appendix A).
Teacher qualifications were measured by teachers' perceptions about relevance of
college courses to teach math effectively in urban schools, to deal with classroom
management in urban schools, how to differentiate instructional levels in urban
classrooms and teach whole group instruction in urban classrooms. The teachers were
measured by questions 44-47 (see Appendix A).
Justification of Variables
The theory purposed by these dependent variables is based upon the state
mandated curriculum change in mathematics. Hence, it is presumed by the use of
Georgia Performance Standards as the curriculum guidelines for test preparation that an
alignment between curriculum and the CRCT will be accomplished. In order words,
what is taught will be tested? The State Department of Education in Georgia has
indicated that beginning in the year the Georgia Performance Standards are implemented
for a content area, the CRCT will directly align with those GPS.
As viewed by Gretzel and Guba's Model (1957) the organization has to exist to
provide service through inputs and outputs. In this proposed study the input groups were
second grade students mandated to take the math CRCT based upon GPS 2006-2007.
Hence, there scores are dependent on a delivery system. This delivery process seeks to
obtain an outcome. This outcome should improve student achievement as measured by
meeting or exceeding performance targets on the CRCT mathematics test. The
influences on the dependent variables maybe measured through the use of school related
variables, teacher related variables and the process of treatment by the instructional
leader. The instructional leader will utilize selected professional development
opportunities in the areas of improved lesson planning, improved instructional strategies,
increased higher order thinking skills as measured by teacher performance on the OBIA
Instrument (pretreatment results and post treatment results used to map the field of
professional development influence on student achievement).
The instructional leader may have the capacity to influence student achievement
through the motivation of teachers increased growth as deliveries of Achievement Lesson
Planning System-ALPS (Persaud & Turner 2002), lesson planning and improved
motivation towards the use of higher order thinking skills in the teaching and learning
delivery system.
Additionally, research-based variables related to student achievement in the
literature are used because of the following:
e Student achievement is proposed to be related to instructional leadership
because research indicates that teacher satisfaction can lead to willingness to
give extra effort.
Student achievement is proposed to be related to professional development
because research shows that it is imperative that teachers continue to learn as
students are expected to continue to learn.
Student achievement is proposed to be related to teacher qualifications
because research indicates that teacher qualifications can affect student
achievement.
Research Questions
RQ 1 : Is there a significant relationship between teacher expectations and gain
scores on the CRCT mathematics teacher expectations and student
motivation?
RQ2: Is there a significant relationship between gain scores on the CRCT in
mathematics and student motivation?
RQ3: Is there a significant relationship between achievement lesson planning
and teacher expectations; achievement lesson planning and gain scores on
the CRCT in mathematics?
RQ4: Is there a significant relationship between teacher qualifications in
mathematics and teacher expectations; teacher qualifications in
mathematics and gain scores on the CRCT in mathematics and teacher
qualifications in mathematics and student motivation?
RQ5: Is there a significant relationship between instructional supervision and
teacher expectations; instructional supervision and gain scores on the
CRCT in mathematics and instructional supervision and student
motivation?
RQ 6: Is there a significant relationship between teacher methodology and
teacher expectations; teacher methodology and gain scores on the CRCT
in mathematics and teacher methodology and student motivation?
RQ7: Is there a significant relationship between professional development and
teacher expectations; professional development and gain scores on the
CRCT in mathematics and professional development and student
motivation?
RQ8: Is there a significant relationship between teacher instructional delivery
and teacher expectations, teacher instructional delivery, and gain scores on
CRCT and teacher instructional delivery and student motivation?
CHAPTER IV
RESEARCH METHODOLOGY
This chapter contains information relative to the type of research design used a
description of the population, instrumentation, and data collection procedures. The
selected school system granted permission to the author of this study to review the
student achievement data within the district as the researcher is a school principal. The
school system's name is not mentioned to ensure anonymity of the system, school and
individual teachers. Benefits to the teachers, school and school system are expected in
terms of identifying strategies that might positively impact student achievement. The
third grade teachers were informed that they could withdraw from the study at any time.
There were 37 teachers who voluntarily responded to the teacher questionnaire.
Research Design
A correlation design was utilized in this study, since the population was not
randomly selected. According to Tuckrnan (1999), "A co-relational study is when a
researcher collects two or more sets of data from a group of subjects for analysis that
attempts to determine the relationship between them" @. 181). In this design, students'
performances in math in the third grade were correlated with possible explanations for
student performance outcomes. In addition a treatment was conducted with a single
group and selected alternative data on teacher opinions and students' characteristics data
were collected for correlation analyses with student performance data.
Population and Sample
The sample inner city elementary school was located in the Metro-Atlanta area.
The school opened it doors in August 2001. The school served 53 1 students where
approximately 85% of the students qualify for free or reduced lunch making it a Title I
School. The school population consists of 86% African-American; nine (9%) Hispanic;
four (4%) Caucasian; and one (1 %) Other. The School's Comprehensive Reform Model
was Modem Red Schoolhouse. The school has made Adequate Yearly Progress (AYP)
every year it has been in existence.
The theoretical framework proposes the administration of a questionnaire to
determine teacher perceptions of the causal variables of student performance in
mathematics as well as a treatment conducted on all five third-grade students in
mathematics in the same school environment. Specifically, the principal as the researcher
administered a questionnaire to determine the causal variables as perceived by teachers
for student performance. A treatment was conducted by the researcherlprincipal to
counteract the causal variables so as to impact student performance. The state mandated
curriculum in mathematics for second grade in 2006-2007 school year represented the
implementation year for the GPS alignment with the GCRCT. This cohort of second
graders became the 2007-2008 school year and was tested on the GPS for the third grade
GCRCT.
Throughout the research, five third grade teachers were surveyed, videotaped, and
assessed. The teachers were from diverse backgrounds, various states and universities.
The students were mostly African-American with a limited number of Caucasians,
Hispanics, Asians, and African students. The researcher found the average score for
students in mathematics from all the teachers. Students' mathematics results were the
dependent variable while using the teacher experience and using higher order thinking
skills as defined by OBIA.
Two strategies were utilized to control for selection as a bias in sampling. First,
the observer selected a lesson to observe that were based upon the lowest mathematics
domain performed by students from previous test scores (CRCT). Students were selected
on the basis that they represent the low achievement in mathematics. In this case all
students in class represented the actual variation that exists. Second. The demographic
variables of teachers and students were identified and measured to estimate if they made
separate impacts on the dependent.
Treatment
The framework for the treatment phrase was learned at Clark Atlanta University
in a Saturday Cohort Doctoral program designed to enable the candidates involved to
learn practical knowledge, skills and dispositions (a) to conduct meetings collaboratively
with group members through a causal analysis of problems and the selection of
solution(s) to counteract the causal variables as the basis for solving the problems
effectively. The following were the strategies implemented by Persaud (2006-2008) in
several courses (EDA 709: Seminar in strategic leadership, Spring, 2007; and Internship
EDA):
Doctoral candidates were divided into two groups of eight to simulate
exercises on how to conduct effective meetings using Empowerment
Management of Meeting (EMOM) model. The EMOM consists of the
following dimensions in which the chair collaboratively: (a) Procedural
communication in which the chair outlines the procedure for the meeting,
(b) Identifies the failed objectives, (c) Prioritizes and sets new standards for
performance, (d) Identifies and prioritizes causes, (e) Identifies and prioritizes
alternative solutions, ( f ) Selects solutions to counteract the causes of cost
effectively, ( f ) Designs and clarifies implementation plan, (g) Selects
evaluation plan. The chair could be rated in his role in each area as follows:
(a) explaining or telling, (b) asking members for suggestions, (c) obtaining
suggestions from members, and (d) accepting, praising, utilizing members'
suggestions.
Each candidate had to role-play the chair and follow the dimensions of the
EMOM in pretest condition followed by group members and instructors'
critical feedback, and subsequent re-simulation for posttest data. Finally,
profesor conducted several role-play sessions on the EMOM and engaged
marginal candidate role-players for improvement in simulation exercises.
Since all the doctoral candidates in cohort were instructional leaders in some
form, it was expected that we would know how to do conduct meetings using
the EMOM. It is also a critical variable in this study.
The professor utilized the EMOM in conducting meetings with the class to
indicate how grade level chairs could conduct meetings in planning lessons
with a teacher associates. For this purpose the Achievement Lesson Planning
37
System (ALPS) was utilized to organize the meeting in writing demonstration
lessons. The APLS consists of five parts: (a) Needs assessment and research
in which the planner is expected to identified failed objectives/outcomes and
determine causal variables, (b) Set new objectives/outcomes following the
design of the Bloom's taxonomy for teaching higher order thinking skills, (c)
State and articulate the content in terms of the higher order thinking skills to
be taught, (d) State and demonstrate the kind of explanations, questions and
possible use of student answers for the development of higher order thinking
skills during the delivery process, (e) Identify and state the kind of questions
that would assess students' acquisition of higher order thinking skills in the
teaching process, (f) Construction of test items for surnmative evaluation and
feedback into lesson planning as a cyclical process. The professor provided
several sample lessons with poems and comprehension passages.
Each candidate had to demonstrate in practical terms the proof that the
candidates acquired the knowledge, skills and dispositions to conduct the
above activities in meeting sessions with Grade chairs to ensure that the grade
chairs could in turn practice these activities. Each doctoral candidate had to
write a lesson plan and teach the lesson from our lesson plan in class as well
to write a lesson plan in for our targeted students in our schools and teach the
lesson. The lessons were videotaped and feedback and ratings were given to
the doctoral students. Each candidate had to demonstrate this process in the
internship program.
The professor trained doctoral candidates on experiential teaching using
(Dewey, etc.) with diagrams and simulations in classes regularly. A guest
experiential methodologist also conducted group exercises in role-playing,
writing, and model building play-dough and other materials.
Training was conducted on the Observation Based Instructional Assessment
(OBIA) system. The OBIA consists of levels of the Bloom's taxonomy in
terms of Knowledge, and comprehension grouped as Lower Order Thinking
Skills (LOTS) and application, analysis, synthesis and evaluation grouped as
higher order thinking skills (HOTS) in the right columns. Each candidate
expected to view video-tapes and observe teachers so as to be able to identify
and perform these dimensions when teaching by (a) explaining, (b) asking
questions, and (c) using and praising answers to build the over-arching
constructs of a lesson. The content and experiential areas in which these acts
(explaining, asking questions and using answers) were to be performed in (a)
procedural communication, (b) students' experiences, (c) textbook knowledge,
(d) related concepts in same subject area, (e) related concepts in different
subject areas, (f) assessment of performance, and (g) managing social
behavior positively. Each candidate who was a principal video-taped master
teachers identified based on high test scores, and those with lower student test
scores these were replayed in class and rated by all candidates until they were
declared proficient by having inter-rater reliability scores.
To ensure that candidates could demonstrate the knowledge, skills and
dispositions learned as a result of viewing videotapes and rating teacher
performances on videotapes proficiently, the candidates during the internship
program had to demonstrate that they planned lessons following the ALPS
design, taught the lessons according to the OBIA and had their lessons
videotaped, rated and reported in the internship portfolio.
The professor modeled and taught doctoral students how to construct multiple
choice test questions using higher order thinking skills. These were done
utilizing several poems and comprehension passage with Powerpoint
presentation. To ensure that candidates could conduct such tests
independently, each candidate had to submit multiple-choice items on each
dimension of the Bloom's taxonomy. The Summer Ranch passage taken from
a second grade reader by McGRaw-Hill Book Company Inc. was utilized for
this purpose. Feedback was provided for each candidate until proficiency was
reached. The professor then supplied his items for comparison.
The researcherlcandidate having been trained to proficiency level in the
doctoral program, in the role as principal of the selected school engaged the
assistant principal (who was also trained in the doctoral program) in a
collaborative framework in training the grade level chairpersons for the
second and third grades.
The researcher in the internship program conducted the above activities with
grade chairs in the selected school as a pre-condition to conduct this study.
Described below is the treatment for the third grade in mathematics and the
results are reported to demonstrate the outcomes.
GAT EMOM Treatment Phase
Constituents of EMOM and how the design might impact effective decision-
making in the planning, implementation, supervision, and evaluation process are as
follows:
1. Pretreatment: The grade chair conducted a meeting after being trained by
principallresearcher. The researcher rated and had the meeting videotaped as
a pretest measure.
2. Treatment: The grade chair conducted meetings weekly with her team form
November through May and using the EMOM.
3. Posttreatment: The researcher rated and had the meeting videotaped as
posttest measure.
The changes from the pre and post rating are demonstrated in the Tables 3 and 4.
In the pretest table the scores in each task area were lower for the chair and grade
associates (teachers) than in the Posttest data. It would appear that once, members saw
the meaning of each task area and how they were inter-related, they were moved to
improve their participation. Likewise, the chair also improved both in his personal
initiation and in accommodating associates' opinions.
Table 3
Pretest Data: Empowerment Management of Meeting Model (EMOM)
Scale. 1 = None; 2 = 1-2; 3 = 3-4,, 4 = 5-6; 5 = 7 + +
Chair or Chair or.
Observation Categories: Chair tells or members ASK Members offer members use or
LeaderIChair, or members explains for opinions opinions, etc, praise opinions
1 ,. Initiates procedural
communication
2 Identifies failed
objectives
3. Prioritizes objectives &
sets standards for
performance
4. Identifies & prioritizes
causes for identified
problems
5. Identifies and prioritizes
alternative solutions
6. Selects solution to
counteract causes & for
cost effectiveness
7. DesignsIClarifies
implementation plan:
Roles, resources,
timeline, monitoring, etc.
Table 3 (continued)
Scale: 1 = None,, 2 = 1-2; 3 = 3-4,, 4 = 5-6; 5 = 7 + +
Chair or Chair or
Observation Categories: Chair tells or members ASK Members offer members use or
LeaderIChair, or members explains for opinions opinions, etc . praise opinions
8. Selects evaluation plan: 3
Formative, summative:
Roles, resources,
timeline, supervision,
etc.
Table 4
Posttest Data: Empowerment Management of Meeting Model (EMOM)
Scale. I - None; 2 = 1-,2,, 3 = 3-4; 4 = 5-6; 5 = 7 + + --
Chair or
Chair or members use
Observation Categories: Chair tells or members ASK Members offer or praise
LeaderIChair, or members explains for opinions opinions, etc. opinions
- -
1. Initiates procedural 5
communication
2. Identifies failed 5 5 4 3
objectives
Table 4 (continued)
Scale; I = None; 2 = 1-2; 3 = 3-4; 4 = 5-6; 5 = 7 + +
Chair or
Chair or members use
Observation Categories: Chair tells or members ASK Members offer or praise
LeaderIChair, or members explains for opinions opinions, etc. opinions
3. Prioritizes objectives & 4 5
sets standards for
performance
4. Identifies & prioritizes 5
causes for identified
problems
5 Identifies and prioritizes 5
alternative solutions
6 . Selects solution to 5
counteract causes & for
cost effectiveness
7. DesignsIClarifies
implementation plan:
Roles, resources,
timeline, monitoring, etc.
8. Selects evaluation plan: 4
Formative, summative:
Roles, resources,
timeline, supervision,
etc.
It would also appear that the grade chair's score probably increased during the
posttest due to increase in self-confidence and familiarity with the dimensions of the
EMOMM and the process. Essentially, the task areas of the EMOM allowed the chair to
focus explanations and questions in each area, and since the task areas are in alignment,
members were encouraged to participate. Even when rating was not conducted the GAT
appeared to function in conformity with the above posttest rating.
GAT Lesson Planning Phase
Constituents of the lesson planning format might impact effective decision-
making in the planning, implementation, supervision, and evaluation process, especially
with respect to effective teaching for higher order thinking skills. Statements of
outcomes in terms of IIOTS and questions to probe students' experiences on such
dimensions follow.
1. Pretreatment measurement: The third grade team wrote a lesson plan together
using the ALPS. The ALPS was rated by the researcher and used as the
pretreatment for ALPS.
2. During the treatment, the GAT began to use the ALPS in their weekly
planning meetings.
3. Posttreatment measurement: The third grade team wrote a lesson plan using
ALPS. This ALPS was rated by the researcher and used as the posttreatment
for ALPS.
Tables 5 and 6 present the pretest and posttest results.
Table 5
High DeJinition Lesson Planning Form (Pretest Data) Third Grade Mathematics
Scale: 1 = Not in line with Model, or Below standard; 2 = Needs Improvement;
3 = Meets Standard; 4 = Above Standard; 5 = Well Above Standard
Lesson Planning 1 2 3 4 5
A Needs Assessment Assesses Performance and Research
1 Identifies variation in students' performance, or identifies X
number of students below expectation, meet expectation, etc.
(NCATE-PSC)
2 Identifies weak concept areas, etc. (NCATE-PSC) X
3 Identifies causes for failure: Teaching Methods & Materials X
used; SES-social conditions, learning styles, etc.
B Ob~ectives. Outcomes
4 Stated to improve weak concept areas
5 Stated to improve higher order thinking skills -Bloom's
6 Stated in terms of helping low achievers to improve on outcomes
7 Containslidentifies basic knowledge in content
8 Containslidentifies higher order thinking skills-Blooms in
content
9 Indicates/demonstrates facts ideas related to students' contextual
experiences, learning level, learning styles, related knowledge,
etc.
Table 5 (continued)
Scale: 1 = Not in line with Model, or Below standard; 2 = Needs Improvement;
3 = Meets Standard; 4 = Above Standard; 5 = Well Above Standard
Lesson Planning 1 2 3 4 5
D. Delivery-Transaction Process
10 Specifies explanations and questions to convey lower order text
meanings in relation to students' experiences
11 Specifies explanations and questions to probe higher order
thinking skills of text in relation to students' experiences
12 Specifies explanations to show how students' answers will be
utilized to re-construct textbook knowledge (Constructivism)
E. Formative Evaluation for Feedback in Teaching Process
13 Specifies questions to assess performance on full range of
Bloom's taxonomy & Dispositions as identified in
objectives/tests
14 Provides questions to assess performance on full range of
Bloom's taxonomy if experiential and/or f hands-on or group
work
15 Provides questions to assess performance on full range of
Bloom's taxonomy in relation to experiences simulated in use of
technology
Table 5 (continued)
Scale: 1 = Not in line with Model, or Below standard; 2 = Needs Improvement;
3 = Meets Standard; 4 = Above Standard; 5 = Well Above Standard
Lesson Planning
F. Summative Evaluation
16 Multiple choice items, true-false items, or short sentence X
completion tests are constructed based on content as taught and
measured on full range of Bloom's taxonomy & dispositions
17 Essay, or project assignments are constructed to cover full range X
of the Bloom's taxonomy & dispositions as stated in objectives
18 Results on assignments are utilized in needs assessment above X
Table 6
High DeJinition Lesson Planning Form (Posttest Data). Third Grade Mathematics
Scale: 1 = Not in line with Model, or Below standard; 2 = Needs Improvement;
3 = Meets Standard; 4 = Above Standard; 5 = Well Above Standard - -
Lesson Planning
A. Needs Assessment.: Assesses performance & Research
I Identifies variation in students' performance, or identifies X
number of students below expectation, meet expectation, etc.
(NCATE-PSC)
2 Identifies weak concept areas, etc. (NCATE-PSC) X
Table 6 (continued)
Scale: 1 = Not in line with Model, or Below standard; 2 = Needs Improvement;
3 = Meets Standard; 4 = Above Standard; 5 = Well Above Standard
Lesson Planning 1 2 3 4 5
3 Identifies causes for failure: Teaching Methods & Materials X
used; SES-social conditions, learning styles, etc.
B Objectives Outcomes
4 Stated to improve weak concept areas
5 Stated to improve higher order thinking skills -Bloom's
6 Stated in terms of helping low achievers to improve on
outcomes
C. Content/Materials
7 Containslidentifies basic knowledge in content
8 Containslidentifies higher order thinking skills-Blooms in
content
9 Indicatesldemonstrates facts ideas related to students' contextual
experiences, learning level, learning styles, related knowledge,
etc.
D. Delivery-transaction process
10 Specifies explanations and questions to convey lower order text X
meanings in relation to students' experiences
11 Specifies explanations and questions to probe higher order X
thinking skills of text in relation to students' experiences
Table 6 (continued)
Scale: 1 = Not in line with Model, or Below standard; 2 = Needs Improvement;
3 = Meets Standard; 4 = Above Standard; 5 = Well Above Standard
Lesson Planning 1 2 3 4 5
12 Specifies explanations to show how students' answers will be
utilized to re-construct textbook knowledge (Constructivism)
E. Formative evaluation for feedback in teaching process
13 Specifies questions to assess performance on full range of
Bloom's taxonomy & Dispositions as identified in
objectives/tests
14 Provides questions to assess performance on full range of
Bloom's taxonomy if experiential and/or f hands-on or group
work
15 Provides questions to assess performance on full range of
Bloom's taxonomy in relation to experiences simulated in use of
technology
F. Summative evaluation
16 Multiple choice items, true-false items, or short sentence
completion tests are constructed based on content as taught and
measured on full range of Bloom's taxonomy & dispositions
17 Essay, or project assignments are constructed to cover full range
of the Bloom's taxonomy & dispositions as stated in objectives
18 Results on assignments are utilized in needs assessment above
50
The comparison between the pre-post ratings was clearly noticeable from does not
meet standard to at least meet standards. The difference might account for the teachers
becoming familiar with the ALPS throughout this treatment and the knowledge to know
that the plans would be monitored weekly.
GA4 T Lesson Planning Treatment Phase
Constituents of the OBIA system and how the design might impact effective
teaching in terms of higher order thinking skills, as related to the Bloom's taxonomy
through the use of (a) students' experiences, (b) textbook knowledge, (c) integrated
related knowledge, (d) assessment, and (e) use of questions and answers to build higher
order thinking skills were implemented in the treatment process as follows:
1. Pretreatment measurement: Each third GAT was rated using OBIA and
videotaped as a pretreatment.
2. Treatment: Teachers used OBIA throughout the treatment.
3. Posttreatment: Each third GAT was rated using OBIA and videotaped as the
posttreatment.
4. The difference between the pre and post treatment is noted in Table 7. The
average of each of the five teachers is listed for each category.
The comparison between the pre and post rating were noticeable from the does
not meet standard to at least meet standards. The difference accounted for is that I was
more familiar with the Observation Based Instrument Assessment (OBIA) than the
teacher.
Table 7
Observation-Based Instructional Assessment (OBIA) System (Simple Form)
Instructor's Task Areas & Means Teacher and Students' Outcomes
Instructor's categories of diverse tasks in
differentiating instructional process (A to I)
and in each case below:
Means of Delivery: Explains, Asks questions, Uses
answers by teacher and students' lower order and
higher order thinking skills as defined in columns
Rating: 0 = Not observed;
1 -1 to 2 times;
2= 3-4 times
3 = 4-5 tines;
4 = 5-6 times;
5 = 7 or more
A Procedural Communzcatzon (Standard
VI) Means: Explains, Asks questions, uses
answers by praising and elaborating, building
l3 Uses student soczal experzences f'Clznzca1
Experzence III)
Explains concepts using students'
experiences, or uses questions and answers to
obtain students' opinions about experiences
to build the concepts
SPSS Preffost
ECEL Lower order
code thinking:
Recall of
knowledge,
Paraphrasing,
Restating in own
words literal
meanings
PrePost
Higher Order Thinking
Skills: Constructivism.
Applies in different
contexts; Analyzes into
sub-parts; Syntheses or
creates new meanings;
evaluates~judges
Dispositions: Considers:
Right & wrong, fai~ness,
equal treatment,
responsibility for change
process; honesty
1 1 2
Table 7 (continued)
Instructor's Task Aseas & Means Teacher and Students' Outcomes
C Uses currzculum/Syllabus content 4- 5 213 113
Explains, asks questions and uses answers on
the content as displayed in text
D Relates concepts toprevzous lessons - zn
same subject area (Iznkzng & webbzng)
Explains, asks questions and uses answers to
link current lesson concepts to previous
concepts taught
E Relates concepts to dEfferent subject areas
and readzngs
Explains, asks questions and uses answers to
link current lesson to different subjects'
concepts and readings
F Assesses performance on concepts (Standard 10-1 1
IIAssessment) Uses questions to identify
learning outcomes; Uses opinions to explore
possible answers
G Manages Soczal Behavzor positzvely
(Standard VI governance) If using
criticisms, etc. to control (0); IJsing eye
contact, proximity, dialogue to manage and
promote interaction (1-5)
H: Standard VI Use of technologzcal resources 14
Check: Yes-; No-
YesNes
Table 7 (continued)
Instructor's Task Areas & Means Teacher and Students' Outcomes
I: Standard VI: Handsoon; Groups; Role Play 15 No/No
Hands-on; Groups; Role Play: Check:
J: Number of students at Level 1 on GCRCT = 16 20 students 20 students
K: Number of students in class = 1 7 ix Level 1 Six Level I
The recommendation is the more one becomes familiar with and uses the
Observation Based Instrument Assessment (OBIA), the more effective the lessons will
become thus improving student performance on higher order thinking skills as observed.
During the treatment phase, all doctoral students had a master teacher come in and
demonstrate how to conduct writing utilizing students' experiences. We had a simulation
of writing through experiences and test construction. We also had an imaginary writing
on trees, the class then conducted observations of campus trees as a group and writing.
he class reported out and made comparisons. In the doctoral classes, constructivism,
differentiated instruction, learning theories, and experiential learning were ongoing
discussions in the class.
Test construction of multiple choice questions were apart of our regular in and out
of class learning. This would have been an optimal time for me to capitalize on the
constructing multiple choice questions. Teachers in this study were only required to
construction questions once, and therefore their efficacy in constructing such tests were
not examined.
54
The school in this study was located in the inner city of metropolitan inner city in
Georgia. The school consists of grades pre-kindergarten through fifth. Grades
kindergarten through fifth is organized into Grade Achievement Teams (GAT). Each
grade achievement team has a chairperson, a recorder and three team members. The third
grade GAT was selected for this study. The third grade GAT follows a schedule for
collaborative planning each Friday for approximately two hours (8:30-10:40 AM). There
were five teachers on the third grade achievement team and ninety-six students. The
researcher selected third grade for this study because it was the first year that third
graders would take the math CRCT using the Georgia, Performance Standards. The third
grade students must meet state reading standards in order to be promoted to the fourth
grade and not mathematics. It was hoped that the results of this third grade treatment
would provide data for use on the Georgia Criterion Referenced Competency Tests
(CRCT) as the students will need to pass the GCRCT in mathematics in fifth grade in
order to be promoted to the sixth grade.
The treatment phase utilized a collaborative management style. The Social
System Model by Getzel and Guba (1957) is based on the theory that institutional goals
can more likely be met when leadership involves the individual who works in the
institution is involved in the decision making process. According to Vroom (1 964), the
desired results are more likely achieved when individual skills and abilities are paired
with the tasks to be performed. Darling Hammond (2001) found that teachers are more
likely to find information useful when professional development was directly related to
what the teachers are currently teaching. Hence, it was the ultimate goal of the researcher
to empower the third grade GAT chairperson to conduct data-driven meetings using
EMOMM (Persaud & Turner, 2006)' and Turner and Persaud's (2006) Observation
Based Instruction Assessment (OBIA) instrument. It was the desire of the researcher that
the third grade GAT would collect data on classroom observations and improve the
lesson planning process using Achievement Lesson Planning System-ALPS (Persaud &
Turner, 2007). Throughout the treatment, professional development was between the
researcher and GAT chairperson who re-delivered to her fellow teammates.
The introductory meeting was between the researcher and the third grade GAT
took place in late October. Attended by the Director of Field Services for this university,
the meeting was videotaped to be viewed and scored. The researcher also introduced the
group to the Achievement Lesson Planning Model (Turner & Persaud, 2006) for mapping
the field identifying the independent variables which may be causal factors for the
dependent variable, low student achievement in mathematics. It was during the initial
planning session that the third grade GAT prioritized a list of strategies to counteract
failed outcomes.
The framework for the treatment phrase involved the following:
Researcher leading the professional development session on how to conduct
grade level meetings
Videotape a mathematics lesson (Pre-OBIA) by each third grade teacher
Review of Bloom's Taxonomy with grade chair by researcher
OBIA training with grade level chairs with Director of Field Services
Grade level chair lead training on OBIA with grade level
Scoring of Grade level chair Video using OBIA with researcher
Scoring of lesson plans already in use by chairperson and researcher
Professional development session with researcher and grade level chair on
Achievement Lesson Planning (ALP) and constructing of multiple choice
questions
Professional development by grade lesson chair and GAT on ALP and
constructing multiple choice questions
Videotaping of chair and researcher co-teaching a mathematics lesson
Scoring the researcher and grade chairperson lesson
Videotape a mathematics lesson (Post-OBIA) by each third grade teacher
Scoring of Post-OBIA mathematics lesson
Analysis of grade level performance on Post OBIA lead by grade chairperson
Administration of 2008 CRCT
During this first session, the researcher provided the purpose and timeline for the
study. Subsequent sessions were held between researcher and grade level chair who re-
delivered the strategies to the third grade team during weekly collaborative planning
grade level meetings which the researcher attended as an observer. The treatment phase
began in October of 2007 and continued through April 2008 lasting about six months.
According to the No Child Left Behind Law (NCLB, 2001), 100% of the students must
master state standards by 2014. The initial meeting was conducted by the researcher with
the entire third grade team in October 2007. The purpose and the timeline of the study
were shared with the team. Each third grade teacher brought copies of their class's spring
2007 CRCT results. The researcher led the teachers in disaggregating the data by listing
the number of students in Level 1, Level 2 and Level 3. Level 1 represents student who
did not meet standards; Level 2 represents the students who met standards; and Level 3
represents the student who exceeded state standards. The results revealed that 18% of the
current third graders scores Level l ,72% scored Level 2 and 10% scored Level 3 in
mathematics.
During this initial meeting, the researcher led the team in a process called
Achievement Lesson Planning (Persaud & Turner, 2006) which is a three-step process:
(a) Identify the dependent variable, (b) List the independent variables (probable causes
for the failed outcomes), and (c) Suggest strategies for counteracting the failed outcomes.
One dependent variable was mathematics outcomes as measured by the CRCT.
Another dependent variable was teacher rating on the survey instrument. The teachers
brainstormed probable causes for student failure as the researcher listed them on the dry
erase board. Following this, the team discussed the interrelatedness of the probable
causes and then grouped similar causes under one heading. The third grade teachers
suggested strategies for addressing the causes that were listed on the board by the
researcher. The strategies for counteracting the failed outcomes were documented and
ranked for use in the treatment of the student achievement plan.
The teachers were instructed to create an Excel spreadsheet for each of the five
classes. The following data should be contained on each spreadsheet: Student name,
gender, meal status and CRCT 2007 results in mathematics. The spreadsheets were
emailed to researcher before next grade level meeting.
58
The Director of Field Services from the university was present at this meeting and
provided written feedback to the researcher using the EMOM rating sheet. A copy of the
treatment phase with the third grade teachers is located in Appendix B.
Description of Instruments
The teacher questionnaire was constructed to measure the dimensions of the
classroom teaching process as perceived by each teacher. It was administered to 37
teachers and the sample was utilized in a test of validity and reliability utilizing the
Cronbach alpha. The sample of teachers represented five third grade teachers. The
results on the perception variables are indicated in the following table. In the table the
Cronbach alpha vary for eight variables in a range of A270 to .9347 indicating high
reliability. The instrument was considered valid and ready for further analyses using
SPSS programs on correlation, factor analysis and regression (Table 8).
Data Collection
Each teacher was given a consent form to participate in this study. Teachers were
reminded that research participation was strictly voluntary and free of any penalties. The
researcher had the literacy coach give out the survey in her purposeful absence so
researcher would not know which teachers were present to complete the sunley if they
choose to participate or declined.
59
Table 8
Scaled Teacher Perception Items on Questionnaire by Cronbach Alpha Reliability
CoefJicient (N = 3 7)
Scaled (1-5) Teacher Perception Variables by Items as Cronbach Alpha
Per Questionnaire (Appendix A) Reliability Coefficient
1. I N S T R S U P (items: 1 - 10) Teachers' perception A270
of support from principal to ensure quality instruction
2. P R 0 F D E V (items 1 1-14): Teachers' opinions .9130
about the effectiveness of staff development
3. M A T G R O U P ( i t e m s 15-18): Teacheruseof .9156
grouping in mathematics
4. A C H L P L A N (items: 19-24): Achievement 3950
lesson planning system (ALPS) designed to identify
and define causes for failure, develop strategies to
counteract causes, and evaluate for effectiveness and
feedback
5. T C E X P E C (items 25-30): Teacher demonstrates
belief for students' progress by indicating that level 1
students would perform at level 3
Table 8 (continued)
Scaled (1-5) Teacher Perception Variables by Items as Cronbach Alpha
Per Questionnaire (Appendix A) Reliability Coefficient
6. T C H 0 T S (items 31-36): teachers' perceiving that 3958
students have experiences that they are using for
learning higher order thinking skills in response to
teachers' methods
7. S T U M 0 T I V (items 37-43): Extent teachers
perceive weak students as being on task in math
8. C 0 L G P R E P (items 44-47): Teachers perceptions
about relevance of college courses to teach math
effectively in urban schools
9. G N S T C R C T (items 48-50): Teachers rating the
extent to which students who were level 1 performer
on CRCT would move to level 2 or above on actual
CRCT
Teachers were given surveys that extract their perception of their principal as
related to culture/climate of the school, curriculum and instruction and assessment and
overall support of the instructional program as well as other related variables. Data were
collected from teachers via teacher surveys and observations. Additionally, assessment
6 1
data were collected via Georgia Criterion Reference Competency Test (GCRCT) data and
student questionnaire filled out by their teachers.
Method of Analyzing Data
Following the quantitative analysis of third grade data from Spring 2008 GCRCT,
grade level teacher surveys and student data interview form was concluded and
summarized. Recommendations were made based upon research findings in the study.
The research questions asked about relationships were tested using the Cronbach Alpha
Reliability. Other research questions were tested using the Pearson Correlation, t-test for
differences and ANOVA. Surveys and observations of teachers were tallied and
analyzed to triangulate teachers' effectiveness and student achievement relative to
nurturing or non-nurturing principals.
CHAPTER V
DATA ANALYSIS
Survey Instrument
The purpose of this quantitative study was to identify variation in students'
mathematics performance and to determine the variables that may significantly influence
student achievement in mathematics. Also, this study seeks to map the field to identify if
teachers' effectiveness in mathematics as measured by student achievement depends on
having a nurturing instructional leader as a principal as seen in observations using the
Observation Based Instructional Assessment Instrument (OBIA), teacher questionnaire
and teacher related variables.
The analyses of the variables were performed from the data collection. These
variables were arranged in a logical sequence based upon the theoretical framework for
the study. The correlation results are based upon Pearson correlation analysis as follows:
The Pearson correlation analysis was conducted with Teacher perceptions about:
expectations for student performance, student motivation in mathematics classes, and
predicted student performance on the CRCT in relation to teacher perceptions about:
Leadership instructional supervision (INSTRSUP), professional development
(PROFDEV), mathematic grouping (MATGROUP), achievement lesson planning
(ACHLPLAN), student use of their experiences to learn higher order thinking skills in
response to teacher methods (TCHOTS), effectiveness of college courses (COLGPREP).
The results of the Pearson correlation analyses are shown in Table 9 (N = 37).
Table 9
Results on Pearson Correlation Analyses
Teacher perceptions about expectations for student performance, prediction on student
CRCT performance, and student motivation in mathematic classes in relation to
selected independent variables (N =37).
TCEXPEC GNSTCRCT STUMOTIV - -
TCEXPEC Pearson Correlation 1,000 .6 18 .565
Sig. (2-tailed) .OOO .OOO .OOO
GNSTCRCT Pearson Correlation .618 1 .OOO .690
Sig. (2-tailed) .OOO .OOO .OOO
STIJMOTIV Pearson Correlation .565 .690 1 .OOO
Sig. (2-tailed) .OOO .OOO .OOO
ACHLPLAN Pearson Correlation .583 .400 .414
Sig. (2-tailed) .OOO .014 .O 1 1
COLGPREP Pearson Correlation .333 .485 .429
Sig. (2-tailed) .044 .002 .008
INSTRSUP Pearson correlation .464 .377 .346
Sig. (2-tailed) .004 .02 1 .036
MATGROUP Pearson Correlation .561 .607 .544
Sig. (2-tailed) .OOO .OOO .001
64
Table 9 (continued)
TCEXPEC GNSTCRCT STUMOTIV
PROFDEV Pearson Correlation .398 .415 .276
Sig. (2-tailed) .O 15 .O 1 1 .099
TCHOTS Pearson Correlation .375 348 .223
Sig. (2-tailed) .022 .035 .I84
Legend
TCEXPEC: Teacher Expectations INSTRSUP Instructional Leadership
GNSTCRCT Gain Scores on CRCT MAGROUP Teacher Methodology
STUMOTIV Student Motivation PRODEV Professional Development
ACHLPLAN Achievement Lesson Planning TCHOTS Instructional Delivery
COLPREP Teacher Qualifications
Independent Variables that SigniJicantly Related to Teacher Expectations Gain Scores on
the CRCT, and Student Motivation
As Table 9 indicates, teachers' perceptions about teacher expectations, gain scores
on CRCT and student motivation are significantly interrelated in a chicken and egg
relationship. In addition, the independent variables: achievement lesson planning,
college effective preparation courses (teacher qualifications), instructional leadership,
mathematic grouping strategy (teacher methodology), professional development
activities, and students ability to utilize their experiences to respond to teacher methods
for teaching higher order thinking skills are significantly correlated at .05 level of
significance or less with teacher expectations for student performance and their
prediction about student performance on CRCT in mathematics. However, teacher
professional development courses and students responsiveness to teaching for higher
order thinking skills are not significantly related to student motivation on mathematic
tasks.
The conclusion might be that teacher perceptions about student performance
expectations, rating of student performance on CRCT and student motivation for math
tasks are significantly interrelated, and that at least teacher expectations and actual rating
for student performance on the CRCT in mathematics are significantly impacted by
achievement lesson planning, college effective preparation courses, instructional
leadership, teacher methodology, professional development activities, and students ability
to utilize their experiences to respond to teacher methods for teaching higher order
thinking skills. This has implications for the instructional leader.
It is not within the control of the instructional leader to influence the teaching of
college courses. However all the other variables are within the control of the
instructional leader? It is of worth to determine that if the instructional leader in this
specific case were to develop a strategy for improving teacher quality whether students'
actual performance on the CRCT in mathematics would improve as demonstrated in a
pre-posttest analysis.
Response to Data Questions
RQ1: Is there a significant relationship between teacher expectations and gain
scores on the CRCT mathematics teacher expectations and student
motivation?
66
The Pearson Correlation Coefficient was used to determine the significance of the
relationship between teacher expectations and gain scores on the CRCT. The correlation
for CRCT gain scores is .618 with a level of significance of .000. The Pearson
Correlation Coefficient was used to determine the significance of the relationship
between the teacher expectations and student motivation. The correlation for student
motivation is .565 with a level of significance of .000. Therefore, there is a significant
relationship between teacher expectations and gain scores on the CRCT in mathematics
and teacher expectations and student motivation.
RQ2: Is there a significant relationship between gain scores on the CRCT in
mathematics and student motivation?
The Pearson Correlation Coefficient was used to determine the significance of the
relationship between gain scores on the CRCT in mathematics and student motivation.
The correlation for student motivation is .690 with a level of significance of .000.
Therefore, there is a significant relationship between gain scores on the CRCT and
student motivation.
RQ3: Is there a significant relationship between achievement lesson planning
and teacher expectations; achievement lesson planning and gain scores on
the CRCT in mathematics and achievement lesson planning and student
motivation?
The Pearson Correlation Coefficient was used to determine the significance of the
relationship between achievement lesson planning and teacher expectations. The
correlation for teacher expectations is .583 with a level of significance of .000. The
67
Pearson Correlation Coefficient was used to determine the significance of the relationship
between the achievement lesson planning and gain scores on the CRCT in mathematics.
The correlation for gain scores on the CRCT in mathematics is .400 with a level of
significance of .014. The Pearson Correlation Coefficient was used to determine the
significance of the relationship between achievement lesson planning and student
motivation. The correlation for student motivation is .4 14 with a level of significance of
.011. Therefore, there is a significant relationship between achievement lesson planning
and teacher expectations, achievement lesson planning and gain scores on the CRCT in
mathematics and achievement lesson planning and student motivation.
RQ4: Is there a significant relationship between teacher qualifications in
mathematics and teacher expectations; teacher qualifications and gain
scores on the CRCT in mathematics and teacher qualifications in
mathematics and student motivation?
The Pearson Correlation Coefficient was used to determine the significance of the
relationship between teacher qualifications and teacher expectations. The correlation for
teacher expectations is .333 with a level of significance of .044. The Pearson Correlation
Coefficient was used to determine the significance of the relationship between the teacher
qualifications and gain scores on the CRCT in mathematics. The correlation for gain
scores on the CRCT in mathematics is .485 with a level of significance of .002. The
Pearson Correlation Coefficient was used to determine the significance of the relationship
between teacher qualifications and student motivation. The correlation for student
motivation is .429 with a level of significance of .008. Therefore, there is a significant
relationship between teacher qualifications and teacher expectations, teacher
qualifications in mathematics and gain scores on the CRCT in mathematics and teacher
methodology in mathematics and student motivation.
RQ5: Is there a significant relationship between instructional supervision and
teacher expectations; instructional supervision and gain scores on the
CRCT in mathematics and instructional supervision and student
motivation?
The Pearson Correlation Coefficient was used to determine the significance of the
relationship between perception of instructional supervision and teacher expectations.
The correlation for teacher expectations is .464 with a level of significance of .044. The
Pearson Correlation Coefficient was used to determine the significance of the relationship
between the instructional supervision and gain scores on the CRCT in mathematics. The
correlation for gain scores on the CRCT in mathematics is .377 with a level of
significance of .02 1. The Pearson Correlation Coefficient was used to determine the
significance of the relationship between instructional supervision and student motivation.
The correlation for student motivation is .346 with a level of significance of .036.
Therefore, there is a significant relationship between instructional supervision and
teacher expectations, instructional supervision and gain scores on the CRCT in
mathematics and instructional supervision and student motivation.
RQ 6: Is there a significant relationship between teacher methodology and
teacher expectations; teacher methodology and gain scores on the CRCT
in mathematics and teacher methodology and student motivation?
69
The Pearson Correlation Coefficient was used to determine the significance of the
relationship between teacher methodology and teacher expectations. The correlation for
teacher expectations is .561 with a level of significance of .000. The Pearson Correlation
Coefficient was used to determine the significance of the relationship between the teacher
methodology and gain scores on the CRCT in mathematics. The correlation for gain
scores on the CRCT in mathematics is .607 with a level of significance of .000. The
Pearson Correlation Coefficient was used to determine the significance of the relationship
between teacher methodology and student motivation. The correlation for teacher
methodology is .544 with a level of significance of .001. Therefore, there is a significant
relationship between teacher methodology and teacher expectations, teacher methodology
and gain scores on the CRCT in mathematics and teacher methodology and student
motivation.
RQ7: Is there a significant relationship between professional development and
teacher expectations; professional development and gain scores on the
CRCT in mathematics and professional development and student
motivation?
The Pearson Correlation Coefficient was used to determine the significance of the
relationship between professional development and teacher expectations. The correlation
for teacher expectations is .398 with a level of significance of .015. The Pearson
Correlation Coefficient was used to determine the significance of the relationship
between the professional development and gain scores on the CRCT in mathematics. The
correlation for gain scores on the CRCT in mathematics is .415 with a level of
significance of .Ol 1. The Pearson Correlation Coefficient was used to determine the
significance of the relationship between professional development and student
motivation. The correlation for student motivation is .276 with a level of significance of
.099. Therefore, there is a significant relationship between professional development and
teacher expectations and professional development and gain scores on the CRCT in
mathematics. There is not a significant relationship between professional development
and student motivation.
Results of Factor Analysis: Survey Instrument
Several independent variables were related to the dependent variable in the
correlation analyses. Hence, it was necessary to determine if some independent variables
had greater influence on the selected dependent variables than others. Factor analysis can
be defined as a statistical procedure for grouping the variables into factors, or
components, according to their highest inter-relationships. The variables loaded into a
factor are more highly related among themselves than with variables loaded into other
factors. In this way, the factors are independent of each other. According to Darren and
Mallery (2001), the Statistical Package for the Social Sciences (SPSS) calculates the
inter-correlations among all variables and develops a matrix of all correlations. Then the
variables are sorted from highest to lowest based upon their inter-relationships when the
sort command is used. The variables that are highly inter-related as indicated by their
factor coefficients are loaded into Factor I, or Component I. The next set of inter-related
variables is loaded into Component 11, followed by variables in Component 111, on and on
until all variables are loaded. A variable is loaded into a component if its factor
coefficient is highest in that component as compared with other components.
Table 9 showed that teacher expectations, gain scores on CRCT and student
motivation were used as the independent variables as well as the dependent variables.
A Factor analysis was conducted on all the selected variables and the results are shown in
Table 10. The placement of variables into two factors is as follows:
Factor I (Component 1) consists of teacher professional development, the leader
instructional supervision strategy, teacher rating the responsiveness of students to utilize
their experiences to learn higher order thinking skills, teacher utilizing mathematics
grouping strategy and teacher use of an achievement lesson planning system. These
variables are loaded in component 1 because the factor coefficient for each variable is
higher than that in Component 2.
Essentially, this means that when teachers perceive their professional
development activities as effective, they also perceive the instructional supervision,
teaching for higher order thinking skills, mathematics grouping strategy, and planning
lessons through the use of a causal and feedback analysis as effective. Therefore, it seems
to support the view that an administrator can enable teachers to be effective on these
dimensions by focusing staff development activities on the resolving problems of the
learners in actual classrooms.
Table 10
Rotated Factor Matrix in Two Components: Teacher Perceptions about the Listed
Variables
Component 1 Component 2
PROFDEV .858 .I68
INSTRSUP .771 .I86
TCHOTS .719 .I24
MATGROUP .662 .463
ACHLPLAN .605 .442
STUMOTIV .I67 .85 1
GNSTCRCT .299 .817
COLGPREP .lo0 ,693
TCEXPEC .452 .653
Variance Explained 50.987 13.103
Legend
TCEXPEC: Teacher Expectations INSTRSUP Instructional Leadership
GNSTCRCT Gain Scores on CRCT MAGROUP Teacher Methodology
STIJMOTTV Student Motivation PRODEV Professional Development
ACHLPLAN Achievement Lesson Planning TCHOTS Instructional Delivery
COLPREP Teacher Qualifications
Extraction Method: Principal Component Analysis.
Rotation Method: Varimax with Kaiser Normalization.
Factor I1 (Component 2) consists of teacher perceptions about: student
motivation to be on task in mathematics classes, predicting students' gain scores on the
CRCT in mathematics, effectiveness of college courses, and expectations for students to
perform at proficiency level. These variables are loaded in component 2 because the
factor coefficient for each variable is higher than that in component 1.
Essentially, only teacher perception about the effectiveness of their college
courses is associated with this teacher perception about students' outcome performance
on: task assignments and CRCT. It is not within the scope of the administrator to
influence the teaching of college courses, but the administrator could improve staff
develop and structure teachers in the teaching process so that they could become self-
generated learners on-the-job to counter deficiencies found. It would be of interest to
determine if a planned strategy by the administrators to enhance teacher capability could
improve actual student performance on the CRCT.
As evident in Table 10, when bounded together, professional development,
instructional supervision, teaching higher order thinking skills, teacher methodology and
achievement lesson planning will improve CRCT scores in mathematics. In component 2,
student motivation, college courses and teacher expectations will improve scores on the
CRCT in mathematics. Increasing college preparation supports Darling-Hammond
(2005) that if you increase quality of college preparation in building teacher's
expectations, schools will get higher test scores.
Three regression analyses were conducted on the following as dependent
variables. First, teacher perceptions of the gain scores that students were likely to make
74
on the CRCT in mathematics; second, teacher perceptions about students' capability as
demonstrated by their rating of students' perfomance in class which is the teacher
expectations; and third, teacher perceptions about the motivation of students to work on
math assignments. In each case all other selected variables were used as independent
variables. The purpose was to estimate the separate effect of each selected independent
variable on each dependent when controlling for the effects of the other independent
variabIes.
The data on the independent variable that explains gain scores on the CRCT are
shown in Table 1 1. In Table 1 1, student motivation in mathematics strictly speaking
barely misses the significant level of .05 (with .05 1). The number of teachers in the
sample was 37 although high for the school of 48 certified staff nearly covered the whole
sample. If the sample size was higher the results might have reach significant level. The
other variables made no significant contributions. It should be observed that all student
motivation and teacher expectations made significant contributions in models one and
two but as all three variables enter the equation
Simultaneously they took variances from each other and reduced their separate
contributions to insignificance. Therefore, the interpretation in the correlation and factor
analyses should hold that these variables tend to interact in concert.
75
Table 11
Results on Regression Analysis., Teacher Rating of Predicted Student Gain on the CRCT
(Dependent Variable. GNSTCRCT) in Mathematics by the Selected Independent
Variables
Standardized
Coefficients
Model Std. Error Beta t Sig.
3 (Constant)
STUMOTIV
TCEXPEC
INSTRSUP
PROFDEV
MATGROUP
ACHLPLAN
TCHOTS
COLGPREP -
Adjusted R Square: F Ratio = 6.142; S = .000
In Table 11 as a result of the regression analysis, in order to improve CRCT
scores, one would have to improve student motivation. Also, a recommendation would
be if a good college preparatory was not in place, professional development in higher
order thinking to improve motivation. Gain scores on the CRCT are explained by student
motivation.
76
Variables that Explain Student Motivation
The results when using student motivation as a dependent variable are shown in
Table 12. The results in this analysis indicate that teacher rating of gain score on the
CRCT misses the significant level of .05 (calculated beta coefficient equal .05 1). The
results confirm the relationships between these two variables.
This is a perfect chicken and egg relationship. As in Maslow's (1971) Hierarchy,
individuals can get opportunities for self-actualization. Therefore, the more the teacher
organizes the task for success, the more students will be motivated to do well.
Table 12
Results of Regression Analysis: Student Motivation as Dependent with Listed
Independent Variables
standardized
Coefficients
Model Std. Error Beta t Sig.
2 (Constant) 1.194 -.287 .777
GNSTCRCT .I98 289 2.040 .05 1
INSTRSUP .349 .I12 .622 .539
PROFDEV .229 -.3 19 -1.450 .I58
MATGROUP .253 .368 1.689 .lo2
ACHLPLAN .312 .035 .I85 355
TCEXPEC .I85 .I25 .683 .500
Table 12 (continued)
Standardized
Coefficients
Model Std. Error Beta t Sig.
2 TCHOTS
COLGPRE .I26 .180 1.1 16 .274
Adjusted R Square .453 FRatio=4.730:, S=.001
Variables that Explain Teacher Expectations
The results when using teacher expectations as dependent are shown in Table 13.
The results in this analysis indicate that teacher expectations are not influenced by any of
the listed variables. The implication is that teacher expectations are probably influenced
by several variables acting simultaneously as shown in the correlation analyses and factor
analysis. The closes one to being significant was achievement lesson planning and may
have been significant if it was not for such a small sample size of 37.
Table 13
Results of Regression Analysis: Teacher Expectations for Student Performance
(TCEXPEC) as Dependent with Listed Independent Variables (1V = 37)
Standardized
Coefficients
Model Std. Error Beta t Sig.
1 (Constant) .499 3.139 .003
GNSTCRCT .I36 .618 .4648 .OOO
78
Table 13 (continued)
Standardized
Coefficients
Model Std. Error Beta T Sig.
2 (Constant) 332 -.709 .483
GNSTCRCT .I34 .45 8 3.517 .001
ACHLPLAN .2 10 .400 3.076 .004
3 (Constant) 1.186 -1.010 .321
GNSTCRCT .206 303 1.512 .I42
ACHLPLAN .297 .341 1.846 .075
INSTRSUP .355 .049 .263 .794
PROFDEV .238 -.I23 -.530 .60 1
MATGROUP .265 .207 .900 .376
TCHOTS .I74 .081 .514 .6 1 1
STUMOTIV .I89 .I31 .683 SO0
COLGPREP .I30 -.068 -.406 .688
a. Dependent Variable TCEXPEC
Adjusted R Square = .453 F Ratio = 4.41; S = .002
Data Analysis on Treatment
There was treatment provided by the researcher as the principal and in
collaboration with the assistant principal. The third grade students and all teachers were
selected for treatment. The treatment consisted of training in lesson planning on the
Achievement Lesson Planning System (ALPS) and the Observation Based Instructional
Assessment (OBIA) system. A correlation design was used to determine the
effectiveness of the treatment by calculating the gain scores of each teacher on the OBIA
with respect to Higher Order Thinking Skills (HOTS) and correlating teacher and
students' demographic variables in order to explain any gain or loss in the pretest-posttest
scores. It was assumed that the treatment would counteract the effects of these
demographic variables rendering them less influential on the gain scores. Therefore, the
treatment was expected to be in this one group design if the demographic variables had
no significant effect on the gain scores on higher order thinking skills. This design
became necessary since there was no control group and/or random assignment of teachers
or students to an identified experimental and control group.
The treatment had three purposes. First, to determine the effectiveness of
delegating the management of students to grade achievement team (GAT) in which the
teachers of a grade level would serve as a team of equals, and one among them would
serve as a collaborative chair. The chair was trained in how to manage meetings by
balancing between human relation skills and planning the task area utilizing the
Empowerment Management of Meeting Model (EMOMM). It was expected that if the
80
chair were effective all teachers would collaborate in planning jointly the lessons to be
taught on a weekly basis.
Second, to determine if the grade achievement team were trained on how to
develop lesson plans following the Achievement Lesson Planning System (ALPS) the
team would not only plan lessons collaboratively but that each teacher would improve the
teaching of higher order thinking skills and that this would in turn impact student
performance on the CRCT. The reasons are that the ALPS facilitate teachers in
identifying the weak concept areas as performed by students on the CRCT, and to
determine the social characteristics of students. Next it requires teachers to select content
and methods to counteract the causal variables for low performance, and specifically
requires them to plan strategies to teach for higher order thinking skills through the use of
students' experiences and to evaluate outcomes for feedback and change. The
effectiveness of the lesson plans could be estimated by the teacher and students'
performance on higher order thinking skills during the observation of teaching.
Third, to train grade achievement team (GAT) in how to teach for higher order
thinking skills following the dimensions of the Observation Based Instructional
Assessment (OBIA) system, and to determine the extent to which each teacher would
improve in the teaching of higher order thinking skills. Again the expectations were that
the teaching of higher order thinking skills would translate into impacting student
performance on the CRCT. The reasons are that the OBIA allows an observer to rate
higher order thinking skills (as outcomes on a scale of 1-5) in terms of teacher and
students' explanations, questions and use of answers in the areas of: application, analysis,
8 1
synthesis and evaluation as defined on the Bloom's taxonomy. The teacher and students
are rated on such task areas as use of (a) students' experiences, (b) textbook knowledge,
(c) related concepts as previously taught, (d) related concepts in different subject areas,
(e) students' answers in developing and integrating concepts, and (f) positive
management of behavior problems. Knowledge in each of these six areas could be
transformed by explanations, questions and use and praising of students' answers into
cognitive dimensions such as: appiication, analysis, synthesis and evaluation as defined
by Bloom's taxonomy. The above was demonstrated on the OBIA during training.
Use of Data in Practical Demonstration, ANOK4, and Correlation Analyses
The data were utilized to demonstrate that the teachers improved in lesson
planning to meet the conditions of the Achievement Lesson Planning System (ALPS). A
posttest analysis of lesson planning is compared with the pre-test as rated on the
dimensions of the ALPS. Examples of re-test and posttest lesson plans are also utilized
to demonstrate the differences in the quality of the rating. It was expected that if teachers
prepared lessons based on the ALPS, they would engage their teacher in higher order
thinking skills (HOTS)
The gain scores on the OBIA were utilized to determine if there were differences
among the teachers on higher order thinking skills when the lessons were taught. The
results of ANOVA test the significant level at .05. It was expected that if teachers
showed gain in teaching higher order thinking skills as indicated in a pre-post
comparison, their students would show gains on the CRCT in mathematics.
The gain scores on the CRCT were utilized to demonstrate if there were
differences among the students of each teacher. The rating scale was Level 1 =1, Level
2 = 2, and Level 3 = 3. The results of ANOVA test the significant level at .05.
The lunch status of the students was utilized to demonstrate if there were
differences among the students of each student. The rating scale was 1 = pay, 2 =
reduced and 3 = free. Results of the ANOVA test were significant at level .05.
Correlation analyses were conducted to determine if the pretest CRCT scores
(PRECRCT), Pretest Higher Order Thinking Skills (PREHOTS) and other selected
demographic teacher and student variables as listed were related to the CRCTGAIN and
the HOTSGAIN scores
A factor analysis was conducted to reduce the number of relations into groups and
to determine if CRCT and HOTS gain scores would be placed in the same factor and
whether any of the demographic variables as selected would be included A Regression
analysis was conducted to determine what variables would explain HOTS GAIN scores.
The assumption was that if no demographic variable was included as a significant
contributor, then the gains could be explained by the treatment.
Improvement in Teaching for Higher Order Thinking Skills (HOTS) as Reflected on
teachers ' Mean Gain Scores
It was expected that teachers, when working as a Grade Achievement Team,
would respond to training to teach for higher order thinking skills (HOTS) and show an
increase in gain scores as compared with their-pretest scores.
83
The data with respect to the mean gain scores as calculated from the posttest
minus pretest mean scores are shown in Table 14. In the table, the mean gain scores are
demonstrated for the pretest, Posttest, and gain scores. The results of ANOVA indicated
significant differences among teachers in each condition (Table 15).
Table 14
Mean Score for Pretest, posttest, and Higher Order Thinking Skills (HOTS) by Teacher
Number of Pretest Posttest Gain
Teacher # Students HOTS Mean* HOTS Mean* HOTS Mean*
1 2 1 .3333 2.3492 2.0159
2 2 1 ,8333 2.9841 2.1508
3 17 .I667 1.8333 1.6667
4 16 .5000 2.5000 2.0000
5 20 3333 2.9833 2.1500
Total 95 .5474 2.5561 2.0088
"Significant differences at .05 probability level
Table 15
Results oJ14NOVA: Higher Order Thinking Skills (HOTSGAIN by Teachers
Sums of Mean Squares Square Sig.
Between Groups 2.814 4 .704 199.636 .OOO
Within Groups .317 90 3.524E-03
Total 3.132 94
It would appear that teachers differed significantly in the pretest but all made
gains in the posttest with some teachers making significant gains more than others. The
main observation is that Teacher #3 did not make as much gain as the others. Overall it
would appear, it is possible to train teachers to make improvement in teaching for higher
order thinking skills though all does not appear to respond in the same way.
The differences among the teachers in the posttest gain scores were significant at
less than .05 probability level as indicated in the ANOVA below. In the ANOVA, it
should be observed that between groups variance is reasonably high whereas the within
differences in scores is insignificantly small accounting for the high F ratio. This was to
be expected since the same score for each teacher was attached to each student.
Teachers' Improvement on CRCT in Math as Reflected on Their Students' Gain Scores
It was expected that when teachers made gains on the HOTS their students would
also show gains on the CRCT in math. The data on the CRCT in math are shown in
Table 16. In the table, the pretest CRCT, posttest, and gain scores are indicated. The
gains are insignificant. The results on the ANOV in Table 17 indicate no significant
difference.
Overall the results of CRCT in math indicated that while it was possible to
improve the teaching of higher order thinking skills by teachers, the same teachers were
unable to improve their students' CRCT scores.
Table 16
The CRCT Mean Scores-for Pretest, Posttest, and Gain in Math
Number of CRCT Math CRCT Math CRCT Math
Teacher Students Pretest Mean Posttest Mean Gain Mean
Table 17
Results of ANOVA for the CRCT Gain Scores in Math
Sums of Mean
Squares d f Square F Sig.
Between Groups .750 4 .I88 .512 .727
Within Groups 32.976 90 .366
Variables that Explain Variances in CRCT and Higher Order Thinking Skills in Math
The Pearson correlation analyses were conducted with the CRCT and HOTS for
the pretest, posttest, and gain scores. The correlation matrix in Table 18 provides the
data.
Table 18
Results on Pearson Correlations CRCT and Higher Order thinking Skills (HOTS) : Pre,
Post, and Gain Scores by Selected Variables (N = 95)
PRECRCT POSTCRCT CRCTGAIN HOTSPOST HOTSGAIN
PRECRCT
HOTSPRET
HOI'SGrnl
GENDER
MEALS
DAD JOB
TCHRATE
TCHGEND
TCHEXP
MATHGD
Pearson Correlation
Sig (2-tailed
Pearson Correlation
Sig (2-tailed
Pearson Correlation
Sig (2-tailed
Pear son Correlation
Sig. (2-tailed
Pearson Correlation
Sig (2-tailed
Pearson Correlation
Sig (2-tailed
Pear son Correlation
Sig (2-tailed
Pear son Correlation
Sig (2-tailed
Pearson Cor~elation
Sig (2-tailed
Pearson Correlation
Sig (2-tailed
87
In Table 18, PRECRCT is significantly related to POSTCRCT, DADJOB, and
teacher rating of students' ability in terms of higher order thinking skills (TCHRASTE)
positively and inversely with CRCT Gain scores, student gender, meals, and teacher
methodology as assigned by the teacher. There is no significant relationship with the
teaching of higher order thinking skills as observed. The teacher rating of students'
abilities in the area of higher order thinking skills and functioning in various areas of
teaching in the classroom is significant.
Post CRCT in math is significantly and positively correlated with PRECRCT and
father's job, but inversely and significantly with gender, meals and grade assigned in
mathematics. The gain scores on the CRCT (GAINCRCT) in math are significantly and
inversely correlated with PRECRCT only.
POSTHOTS is positively and significantly correlated with HOTSPRET and
inversely and significantly with teacher gender and grade assigned in mathematics.
HOTSGAIN is positively and significantly correlated with HOTSPRET and inversely
and significantly with teacher gender and grade assigned in mathematics.
Results of Factor Analysis: Treatment
A factor analysis was conducted to reduce the number of relationships according
to their significant groupings based on their factor coefficients. The SPSS VARIMAX
rotation was used to group the variables by their factor coefficient loadings. The
variables in a factor according to their highest factor coefficient loadings indicate that the
variables as loaded are highly related as a group independent of variables placed or
loaded in another factor (Table 19).
Table 19
Results on Rotated Component Matrix. All Selected Variables by Components as Loaded
Component 1 Component 2 Component 3 Component 4
HOTSPOST
HOTSGAIN
HOTSPRET
TCHGEND
PRECRCT
TCHRATE
GENDER
MATHGD
TCHEXP
MEALS
DADJOB
CRCTGAIN
POSTCRCT
Variance Explained
HOTSPOST HOTS post test MATHGD
HOTSGAIN HOTS gains TCHEXP
HOTSPRET HOTS pre test MEALS
TCHGEND Teacher gender DADJOB
GENDER Student gender CRCTGAIN
TCHRATE Teacher rating POSTCRCT
PRECRCT Level on CRCT in 2nd grade
Grade student received in math
Teacher Expectations
lunch status of students
Father's job
CRCT gain score
Level on CRCT in 3rd grade
89
The issue was to determine if the gain scores on the CRCT would be loaded
within the same factor as with other demographic variables. Since an experimental
design was not possible, it was necessary to determine whether the gain scores were due
to the training or the demographic variables.
Component I consists of all variables on higher order thinking skills PRETEST,
POSTTEST, and GAIN scores positively loaded among themselves and inversely with
teacher gender. Hence training though it had an impact on the gain scores shared
variances with teacher gender. Further, those teachers who had high rating at the
beginning made more gains than those who began low.
Component 2 consists of PRECRCT and TCHRATE positively loaded and
student gender and math grade inversely loaded.
Component 3 is loaded with teacher experience and meals positively loaded and
with father's job.
Component 4 is loaded with CRCTGAIN and CRCTPOST positively. Teacher
gender and pretest scores on HOTS were associated with gain scores on HOTS in the
factor analysis and with mathematics grade in the correlation therefore a regression
analysis was used to separate out these effects. Other demographic variables are also
included because they are associated with HOTSPRET and HOTSPOST and CRCT.
Table 20 presents the results of regression analysis.
90
Table 20
Results on Stepwise Regression Analysis. Higher Order Thinking Skills Gain Scores
(HOTSGAIN) with Selected Independent Variables
Standardized Beta Significant
Model 5 B Std. Error Coefficients T Value Level
(Constant)
TCHGEND
HOTSPRET
TCHRATE
GENDER
MEALS
MATHGD
DADJOB
PRECRCT --
Model 5 Adjusted R Square Change = 399
F Ratio = 93.491; Significant level = .000
In the table, teacher gender is the first significant but inverse contributor to
HOTSGAIN scores followed by HOTSPRET, TCHRATE of students' abilities on higher
order thinking skills and student gender as indicated by their positive beta weights.
Therefore while the training had some effects on improving HOTSGAIN, other variables
are associated with the impact.
9 1
Variables that Explain CRCT Gains
The next issue is to explain CRCT gain by the selected independent variables.
The results are shown in Table 2 1. In the table, PRECRCT and student gender are
inversely significant contributor while teacher rating of students on higher order thinking
skills abilities is a positive contributor.
Table 2 1
Results of Stepwise Regression Analysis (Model 3). CRCT Gain Scores as Dependent
with Selected Independent Variables
Standard Standardized Beta
Model 3 Error Coefficients t Sig.
(Constant)
PRECRCT
TCHRATE
GENDER
MEALS
DADJOB
TCHGEND
TCHEXP
MATHGD
HOTSGAIN
92
Variables that Explain TCHRA TE
The third issue is that teacher rating of student abilities on higher order thinking
skills is a significant contributor to both teacher gains on HOTS and on students gain on
CRCT, therefore it was necessary to determine the variables that explain TCHRATE.
TCHRATE was used as the dependent variables and the other variables were used in a
regression analysis as the independent. The results on regression analysis are shown in
Table 22. In the table, PRECRCT, and CRCT Gain are positive contributors, TCHGEND
and HOTSGAIN are positive and significant contributors while MATHGD is an inverse
significant contributor.
Table 22
Results on Stepwise Regression Analysis. TCHRATE as Dependent and Other Selected
Variables as Independent
Standard Standardized Beta
Model 6 Error Coefficients t Sig.
(Constant)
PRECRCT
MATHGD
CRCTGAIN
TCHGEND
HOTSGAIN
GENDER
MEALS
93
Table 22 (continued)
Standard Standardized Beta
Model 6 Error Coefficients t Sig.
DADJOB ..049 .092
HOTSPRET .477 -. 183 -- -
Adjusted R Square Change = .599
F Ration = 16.634and significant at .000
It would appear that teachers according to their gender form opinion about the
abilities of students on HOTTS based on PRECRCT scores (since the PRECRCT
S\scores were known to them). They nonetheless assigned higher grades in post teaching
to students who were low on CRCT (indicating they had high expectations for students'
performance). During teaching in post-training on HOTS those teachers who improved
on HOTS appear to rate students higher on TCHOTS.
Overall, it would appear that if training HOTS is to impact student achievement
on CRCT it would tend to do so by revising teacher rating of students abilities on higher
order thinking skills. Further teacher gender is an issue that must be overcome during
training.
CHAPTER VI
FINDINGS, CONCLUSIONS, IMPLICATIONS, AND RECOMMENDATIONS
The purpose of this study was to identify variation in students' mathematics
performance and to determine the variables that may significantly influence student
achievement in mathematics. Also, this study sought to map the field to identify if
teachers' effectiveness in mathematics as measured by student achievement depends on
having a nurturing instructional leader as a principal as seen in observations using the
Observation Based Instructional Assessment Instrument (OBIA), teacher questionnaire
and teacher related variables. The results of this study will be of interest to
superintendents, executive directors, human resources, educational researchers, and
educational leadership professors.
A review of relevant literature suggested that gain score in mathematics, student
motivation and teacher expectations were influenced by such variables as (a) instructional
leadership (Waters, Marzano, & McNultty, 2003; Lucas & Valentine 2002; Drago-
Steverson 2002; Acker-Hocevar & Touchton. 2001; Niedermeyer, 2003); (b)
professional development (Drago-Steverson 1997; Turchi, Johnson, Owens, &
Montgomery 2002; Elmore 2002; Lombardi 2008); (c) lesson planning and teacher
instructional delivery (Ediger 2004; Persaud & Turner, 2002; Candenas 1999; Todd
2006; Taylor, 2004; Iyer, 2006); (d) teacher qualifications (Ingersoll, 2002; Darling-
Hammond, 1999; Wilkes 2008; Weber, 2005; Rockoff, 2003; Williams & King, 2002).
94
95
The theoretical framework proposes the use of selected independent variables that
are measurable in the classrooms for the cohort of students selected from the school
environment. The state mandated curriculum in mathematics for second grade in 2006-
2007 school year represent the implementation year for the GPS alignment with the
GCRCT. This cohort of second graders will be provided instruction as third graders for
the 2007-2008 school year on the GPS for the third grade GCRCT. Hence, the selection
of independent variables such as: socioeconomic status of students, instructional
leadership, teacher professional development, teacher expectations, teacher lesson
planning, teacher methodology, teacher qualifications, and parent occupation. The
delivery system for the third grade treatment will include pretest analysis of second grade
independent variables on the second grade dependent variables. So, the professional
development from the results of teacher observation through the use of the OBIA
Instrument can be measured to determine its significance on student achievement of the
third grade year.
As viewed by the Getzel and Guba Model (1 957), the organization has to exist to
provide service through inputs and outputs. In this proposed study the input groups were
second grade students mandated to take the math CRCT based upon GPS 2006-2007.
Hence, their scores are dependent on a delivery system. This delivery process seeks to
obtain an outcome. This outcome should improve student achievement as measured by
meeting or exceeding performance targets on the CRCT mathematics test. The
influences on the dependent variables maybe measured through the use of school related
variables, teacher related variables and the process of treatment by the instructional
leader. The instructional leader will utilize selected professional development
opportunities in the areas of improved lesson planning, improved instructional strategies,
increased higher order thinking skills as measured by teacher performance on the OBIA
Instrument, (pre treatment results and post treatment results used to map the field of
professional development influence on student achievement).
The instructional leader may have the capacity to influence student achievement
through the motivation of teachers increased growth as deliveries of Achievement Lesson
Planning System (ALPS) (Persaud & Turner, 2002), lesson planning and improved
motivation towards the use of higher order thinking skills in the teaching and learning
delivery system.
The selected school system granted permission to the author of this study to
review the student achievement data within the district as the researcher is a school
principal. The school system's name was not mentioned to ensure anonymity of the
system, school and individual teachers. Benefits to the ieachers, school and school
system are expected in terms of identifying strategies that might positively impact student
achievement. The third grade teachers were informed that they could withdrawn from the
study at any time. Additional 37 teachers voluntarily responded to the teacher
questionnaire.
The study was conducted in a metropolitan inner city elementary school located in
the Metro Atlanta area. The school opened its doors in August 200 1. The school served
53 1 students where approximately 85% of the students qualify for free or reduced lunch
making it a Title I School. The school population consists of 86% African-American;
nine (9%) Hispanic; four (4%) Caucasian; and one (1%) Other. The School's
Comprehensive Reform Model was Modem Red Schoolhouse. The school has made
Adequate Yearly Progress every year it has been in existence.
Throughout the research, five third grade teachers were surveyed, videotaped, and
assessed via observed from this school. The teachers were from diverse backgrounds,
various states and universities. The students were mostly African-American with a
limited number of Caucasians, Hispanics, Asians, and African students. The researcher
found the average score for students in math from all the teachers. Students' math results
were the dependent variable while using the teacher experience and using higher order
thinking skills as defined by OBIA.
In order to control for selection as a bias in sampling, the observer selected a
lesson to observe that were based upon the lowest mathematics domain performed by
students from previous test scores (CRCT). Students were selected on the basis that they
represent the low achievement in mathematics. In this case all students in class
represented the actual variation that exists. Backgrounds of whether the teacher lesson
plans and teacher method of delivery were reviewed for alignment.
The school in this study was located in the inner city of metropolitan inner city in
Georgia. The school consists of grades pre-kindergarten through fifth. Grades
kindergarten through fifth are organized into Grade Achievement Teams (GAT). Each
grade achievement team has a chairperson, a recorder and three team members. The third
grade GAT was selected for this study. The third grade GAT follow a schedule for
collaborative planning each Friday for approximately two hours (8:30-10:40 AM). There
are five teachers on the third grade achievement team and ninety-six students. The
researcher selected third grade for this study because it was the first year that third
graders would take the math CRCT using the Georgia, Performance Standards. The third
grade students must meet state reading standards in order to be promoted to the fourth
grade and not mathematics. It was hoped that the results of this third grade treatment
would provide data for use on the Georgia Criterion Referenced Competency Tests
(CRCT) as the students will need to pass the GCRCT in mathematics in fifth grade in
order to be promoted to the sixth grade.
The framework for the treatment phrase involved the following: researcher
leading the professional development session on how to conduct grade level meetings;
videotape a mathematics lesson (Pre-OBIA) by each third grade teacher; review of
Bloom's Taxonomy with grade chair by researcher; OBIA training with grade level
chairs with Director of Field Services; grade level chair lead training on OBIA with grade
level; scoring of Grade level chair Video using OBIA with researcher; scoring of lesson
plans already in use by chairperson and researcher; professional development session
with researcher and grade level chair on Achievement Lesson Planning and constructing
of multiple choice questions; professional development by grade lesson chair and GAT
on ALPS and constructing multiple choice questions; videotaping of chair and researcher
co-teaching a mathematics lesson; scoring the researcher and grade chairperson lesson
videotape a mathematics lesson (Post-OBIA) by each third grade teacher; scoring of Post-
OBIA mathematics lesson and analysis of grade level performance on Post OBIA lead by
grade chairperson.
The teacher questionnaire was constructed to measure the dimensions of the
classroom teaching process as perceived by each teacher. The questionnaire was
administered to 37 teachers and the sample was utilized in a test of validity and reliability
utilizing the Cronbach alpha. The sample of teachers represented five third grade
teachers. The Cronbach alpha varies for 8 variables in a range of A270 to .9347
indicating high reliability. The instrument was considered valid and ready for further
analyses using SPSS programs on correlation, factor analysis and regression.
Data were collected from teachers via teacher surveys and observations.
Additionally, assessment data will be collected via Georgia Criterion Reference
Competency Test (GCRCT) data and student questionnaire filled out by their teachers.
Following the quantitative analysis of third grade data from Spring 2008
GCRCT, grade level teacher surveys and student data interview form was concluded and
summarized. Recommendations were made based upon research findings in the study.
The research questions asked about relationships were tested using the Cronbach Alpha
Reliability. Other research questions were tested using the Pearson Correlation, t-test for
differences and ANOVA. Surveys and observations of teachers will be tallied and
analyzed to triangulate teachers' effectiveness and student achievement relative to
nurturing or non-nurturing principals.
Findings
The findings for each research questioned have been summarized in relation to the
specific variables. A summary of the findings follows:
Research Question 1 can be answered in the positive. There is a statistical
significant relationship between teacher expectations and gain scores on the CRCT
mathematics teacher expectations and student motivation.
Research Question 2 can be answered in the positive. There is a statistical
significant relationship between gain scores on the CRCT in mathematics and student
motivation.
Research Question 3 can be answered in the positive. There is a statistical
significant relationship between achievement lesson planning and teacher expectations;
achievement lesson planning and gain scores on the CRCT in mathematics and
achievement lesson planning and student motivation.
Research Question 4 can be answered in the positive. There is a statistical
significant relationship between teacher qualifications in mathematics and teacher
expectations; teacher qualifications and gain scores on the CRCT in mathematics and
teacher qualifications in mathematics and student motivation.
Research Question 5 can be answered in the positive. There is a statistical
significant relationship between instructional supervision and teacher expectations;
instructional supervision and gain scores on the CRCT in mathematics and instructional
supervision and student motivation.
Research Question 6 can be answered in the positive. There is a statistical
significant relationship between teacher methodology and teacher expectations; teacher
methodology and gain scores on the CRCT in mathematics and teacher methodology and
student motivation.
Research Question 7 can be answered in the positive and negative. There is a
statistical significant relationship between professional development and teacher
expectations and professional development and gain scores on the CRCT in mathematics.
There is not a statistical significant relationship between professional development and
student motivation.
Research Question 8 can be answered in the positive and negative. There is a
statistical significant relationship between teacher instructional delivery and teacher
expectations and teacher instructional delivery and gain scores on CRCT. There is no
statistical relationship between teacher instructional delivery and student motivation.
Conclusions
In this study, the results indicate that all the independent variables are
significantly related to gain scores on CRCT and teacher expectations and all but two
were significantly related to student motivation. Teachers' perceptions about teacher
expectations, gain scores on CRCT and student motivation are significantly interrelated
in a chicken and egg relationship. In addition, the independent variables: achievement
lesson planning, college effective preparation courses (teacher qualifications),
instructional leadership, mathematic grouping strategy (teacher methodology),
professional development activities, and students ability to utilize their experiences to
respond to teacher methods for teaching higher order thinking skills are significantly
correlated at .05 level of significance or less with teacher expectations for student
performance and their prediction about student performance on CRCT in mathematics.
However, teacher professional development courses and students responsiveness to
102
teaching for higher order thinking skills are not significantly related to student motivation
on mathematic tasks.
The conclusion might be that teacher perceptions about student performance
expectations, rating of student performance on CRCT and student motivation for math
tasks are significantly interrelated. Teacher expectations and actual ratings for student
performance on the CRCT in mathematics are significantly impacted by achievement
lesson planning, college effective preparation courses, instructional leadership, teacher
methodology, professional development activities, and students' ability to utilize their
experiences to respond to teacher methods for teaching higher order thinking skills.
Implications
It is not within the control of the instructional leader to influence the teaching of
college courses. However all the other variables are within the control of the
instructional leader. It is of worth to determine that if the instructional leader in this
specific case were to develop a strategy for improving teacher quality whether students'
actual performance on the CRCT in mathematics would improve as demonstrated in a
pre-posttest analysis.
Recommendations
Recommendations are provided for classroom teachers, building administrators,
executive director, and the policy makers.
Recommendations for Classroom Teachers
Classroom teachers should work together as a grade level to teacher higher order
thinking skills (HOTS) in relations to the Georgia Performance Standards. The
103
classroom teacher should use the Achievement Lesson Planning System (ALPS) to write
lesson plans that address the students' social needs as well as academic needs. Teachers
should conduct peer observations to become empowered and in order to collegiality thus
provide each other with meaningful feedback and taking ownership of their professional
growth and student achievement. Teachers should also construct multiple-choice test
based on what they taught as an on-going process using the levels of Bloom's Taxonomy.
Recommendations for Building Level Administrators
The principal should provide professional development at the Grade Achievement
Team (GAT) level in the Management of Meeting (EMOM) model for conducting
Achievement Lesson Planning System (ALPS) and Observation Based Instructional
Assessment (OBIA) on the teaching of higher order thinking skills (HOTS). The
principal should also provide time for teachers to visit other classrooms and schools
where the data is showing students are performing well at high levels with similar
demographics. The principal should allocate funds for teachers to attend local, state and
national conferences. The principals should also make sure the GAT chairperson is
rotated every year in order to build accountability and leadership.
Other recommendations for principals include:
Lead CRCT data analysis at the beginning of the school year with leadership
teaddesign team in order to map the field of student performance in
mathematics and to identify professional development needed to prepare
faculty to address failed outcomes.
Leadership team/design team members lead similar data analysis with
respective Grade Achievement Team (GAT). The grade chairperson leads the
grade level in analyzing mathematics scores. The grade level will identify
professional development needs for counteracting failed student outcomes on
the CRCT.
Principal, assistant principal and instructional liaison specialist conduct daily
classroom visitations and weekly classroom observations to ensure that
teachers are implementing strategies as expected and to provide feedback..
Conduct on-goinglperiodic school-widelgrade level assessments in the CRCT
format to measure progress towards goals. The results should be used to
inform instruction.
Compare post CRCT with pre CRCT and analyze the results. List variables that
possibly contributed to outcomes.
Reward the successes and accomplishments of the teachers and staff.
Recommendations for Executive Directors
The executive directors should follow the recommendations and process as
outlined with the principal for all her schools which she supervises. The executive
director should provide human resources to support the school in their efforts to teach
higher order thinking skills and other strategies listed under the principal. Ongoing
feedback to the principals should be specifically related to mathematics achievement.
Recommendations for Policy Makers
Policy makers should monitor the schools using the Grade Achievement Team
(GAT) level in the Management of Meeting (EMOM) model for conducting
Achievement Lesson Planning System (ALPS) and Observation Based Instructional
Assessment (OBIA) on the teaching of higher order thinking skills (HOTS) to see if it is
being implemented with validity. The policy makers should allocate additional resources
to the schools using these strategies for professional development opportunities. Also,
the policy makers should tract the data to see if gains are made and at what rate compared
to schools not using these strategies.
Recommendations for Additional Research
1. Replications of the present study need to include additional variables possibly
affecting student achievement such as (e.g. class size, parental involvement).
2. Replication of the present study needs to involve a comparison response of
teachers from another school similar in demographics.
3. Replication of the present study needs to involve a comparison response of
teachers fi-om the same school.
4. Further research may wish to use other methods of measuring the independent
variables used in the study. (e.g. qualitative study).
5. Further research may wish to look at looping the teachers from second to third
grades.
Summary
The findings and conclusions from this study were outlined in this chapter.
Implications were discussed and recommendations based on findings were suggested. It
is hope that the recommendations from this study will assist district and school leaders
about a nurturing principal's leadership and other variables in a pre-post setting and how
it effects student achievement in mathematics.
APPENDIX A
Teacher Questionnaire
Dear Teachers:
You are asked to complete this questionnaire. I am conducting research for my dissertation at Clark Atlanta University. Therefore, I am interested in your honest opinion for a purely research basis. The study of human subjects requires that you provide your opinion anonymously. Please do not state your name. The results will be provided as group data and no person can be identified. Your participation is voluntary and you can withdraw at anytime. It is hoped that the results will provide recommendations for school improvement to benefit this school and the school system.
Danielle Sanders Battle
Questionnaire
Directions: Please circle the number that best represents your thinking about each of the following statements.
5 = Strongly Agree; 4 = Agree; 3 = Maybe, 2 = Disagree; 1 = Strongly Disagree
A. Supervision of Teachers involving collaboration around lesson planning for math in terms of cause for students; failure and strategies for improvement
-
To what extent do administrators:
I. Make the decisions and asks faculty to implement -.
2. Ask faculty to decide on how to solve problems
3. Discuss with faculty how to improve lesson planning so that weak students achieve to grade level or above
4. Utilize faculty opinions to develop lesson planning steps so that weak students could achieve to grade level or above
5
5
4
4
2
2
5 4 3 2 1
5 4 3 2 1
3
3
1
1
Appendix A (continued)
or on CRCT I
5. Ask teachers to identify weak students andlor those with low performance on CRCT
6. Ask teachers to identify causes for low performance in class 5
7. Ask teachers to develop instructional strategies to counteract causes
-
8. Discuss with teachers how to utilize differentiated instruction to improve students' performance
-
To what extent were professional development activities as provided at Workshops, seminars, etc..
5
5
9. Discuss with teachers how to teach weak students to master higher order thinking skills
-
10. Discuss with teachers how to develop tests to measure higher order thinking skills
11. Enabled weak students to exceed in performance in math I 5 / 4 1 3 1 2 1 1 I
4
- --
12. Showed teachers practically how to conduct
B. Professional development refers teachers' opinion about the effectiveness of workshops, seminars, and conferences that teachers attended as provided by the school system.
5
5 4 3 2 1
3
work in the classroom
4
instruction in math I
13. Showed teachers how to make classroom management work 5 in the classroom
-
14. Showed teachers how to make flexible grouping for math 5
C. Teacher feeling of efficacy to teach math refers to teachers' feelings about whether or not the available math strategies can work in the classroom
2
I In the area of math, the method($ available for: I
1
3
5 4 3 2 1
4
4
2
3
3
14. Grouping students based on pre-assessment data can work in real classrooms?
I
1
5
-- I -- 2
2
1
1
Appendix A (continued)
I D. In the area of lesson planning for math, the format includes the following: I
16. Organizing and managing several groups for math instruction can work in real classrooms.
17. Maintaining progress records of students performing at diverse academic levels can work in real classroom
18. Providing on-going assessment for students' performance at diverse academic levels can work in real classroom?
1 19. Identifying students who performed below grade level / 5 / 4 1 3 / 2 / 1 / -- -
20. Identifying the probable causes for students' failure
2 1. Explaining how the chosen methodology will counteract the causes so as to improve performance
--
22. Showing how differentiated instruction will be conducted to counteract the causes for low achievement
5
23. Assessing the performance of students to show improvement
24. Utilizing the results of evaluation to improve lesson planning
4
--
25. How much time do you spend each week grading papers?
26. How much time do you spend each week recording grades?
5 4 3 2 1
5 4 3 2 1
3
27. How much time do you spend each week preparing materials for math lessons?
E. Teacher expectation refers to teacher beliefs about the capability of students to learn higher order thinking skills
2 1
Generally,
28. Weak students in level I can move to level 2 or above
29. All students in level 1 can move to level 2
30. Weak students in level 2 can move to level 3?
2 1
2 1
2 1 5 4
5 4
5 4
3
3
3
Appendix A (continued)
t- i Generally, in the math classes, Weak or Level I students:
3 1. All students in level 3 can maintain their positions
32. All students can learn equally well
33. A student's CRCT pre-assessment score is a predictor of performance on the CRCT post-assessment?
I 34. Are responsive to innovative teaching strategies
F. Teacher effective instructional delivery in math refers to the extent to which teachers perceive that students are responsive to their teaching methods
5
36. Can relate math concepts to lessons in reading, social studies, and science
35. Tend to have personal experiences that are appropriate for teaching higher order thinking skills
37. Volunteer to ask higher order questions --
38. Utilize higher order thinking skills to provide answers to
4
the teacher's questions
39. Are motivated to be on task by praising them ---
5
G. Student motivation involves students staying on-task and seeking assistance when help is needed.
5 4 3 2 1
5 4 3 2 1
3
4
2
Generally, in math
40. Weak students are on task -.
41. Weak students can apply themselves on on-task if given attention I-- 42. Weak students know how to work collaboratively in groups
1
3
1 43. Weak students tend to become self-motivated if helped , I I , ,
5
2 1
4
5 4 3 2 1
3
5 4 3 2 1
5 4 3 2 1
2 1
Appendix A (continued)
of college course relevance refers to their views about course effectiveness for students with learning problems
46. College courses prepare teachers to teach different instructional levels in urban classrooms
Generally, I
44. College courses prepare teachers to teach math in urban 5 problem environments
45. College courses prepare teachers for classroom management of urban students
Generally, Weak students and/or Level I students on the CRCT Math
4
47. College courses prepare teachers to teach whole group instruction in urban classrooms
48. Have gained level I1 or average ability students as compared to beginning
49. Have made gains to level I11 or above average ability students as compared to the beginning
3
5 4 3 2 1
5
2
I 4 1 3
50. Have Gained in use of higher order thinking skills as 1 5 compared to the beginning
5 1. Made As and Bs on class assignments --
52. Made gains enough to reach or exceed performance on Level I1 CRCT Math
1
2
4
1
3
5 4 3 2 1
5 4 3 2 1
2 1
APPENDIX B
Treatment Plan
Number of Students: 95 School Year: 2007-2008 Grade Level Meeting: Friday, 830- 10:30
Obj ective(s)
Date Teachers will: Activities Resources/Follow-Up --
October 2007 Identi@ dependent and Third grade teachers will Student CRCT test data independent variables Use formative 2007 List possible causal CRCT mathematics factors results, rank order
class results Tell percent and Read .- Hess and Shipman actual number of article for next Monday we students in Level 1,2 will discuss their theory and 3 about language . Compare results of development in children girls versus boys at from low SES homes each level Show the lunch status of each student
October 2007 Summarize research Teachers will work in conducted by Hess and pairs to summarize Shipman the research article
Make Venn Diagram Discuss research findings to compare and implications for characteristics of classroom instruction population in the Hess
and Shipman article to their current student population. Teachers will discuss instructional implications based on Hess and Shipman
Researcher will prepare individual fact cards on the Hess and Shipman article which will answer the 5Ws and How. Third grade teachers will work in pairs to match the answer card with each question card.
Appendix B (continued)
Date Teachers will:
October 2007 Identify the interests of third grade boys and girls and discuss implications for instruction Demonstrate how to teach a reading lesson utilizing students' experiential background and everyday experiences
November 2007 Share the 10 multiple choice questions (MCQ) based on demonstrated lesson. Review Bloom's Taxonomy
November 2007 Compare and contrast the High Definition Lesson Planning document (Persaud, Turner, 2007) to the 26 Best Practices informal observation form
Select a third grade co- teacher for frst
Activities
Third grade teachers will generate a chart of'the things that interest boys and the things that interest girls and the things that they all like The researcher will use a short story or poem related to mathematics to demonstrate to the third grade teachers how to teach a reading lesson that incorporates the learners background with text,
Third grade teachers will share with the group sample questions The group will discuss any concerns or problems experienced in carrying out this task.
The researcher will summarize the components of the Achievement Lesson Planning form. The third grade teachers will identify where to fit each of the 26 Best Practices fit into the lesson
For next Monday's grade level meeting, teachers will prepare 10 multiple choice questions based mathematics demonstration lesson. Make six copies of your questions
Copies of each teacher's ten MCQs . Teacher's personal size flip chart of Bloom's Taxonomy.
Distribute copies of Achievement Lesson Planning document (Persaud and Turner, 2007). Teacher should compare this document to the 26 Best Practices informal observation instrument utilized by the district. Come prepared to discuss on Friday.
Achievement Lesson Planning document (Persaud and Turner, 2007)
Meet with third grade co- teacher to plan the demonstration mathematics lesson and to make arrangement for videotaping.
Appendix B (continued)
Date Teachers will:
demonstration lesson (grade chair)
November 2007 Discuss components of OBIA (Persaud & Turner, 2007) View third grade mathematics lesson as taught by researcher and a third grade teacher Critique mathematics lesson utilizing OBIA
November 2007 Continuation of objectives and activities from week of Nov. 19"
December 2007 Share MCQs with the grade level Discuss implications of writing MCQs To view and critique videotaping #2
December 2007 View and critique videotaped reading lessons as taught by third grade teachers
Activities Resources/Follow-Up -
document Distribute copies of OBIA (district requirement) (Persaud and Turner, 2007)
to be utilized at next grade level session.
The third grade team OBIA (Persaud & Turner, will review Bloom's 2007), flip chart of Bloom's Taxonomy as it Taxonomy and video of related to the OBIA. third grade mathematics Then, view the tape of lesson last week's co- teaching lesson. Continue this session for
next Friday, also.
Utilize critique from videotaping lesson #1 to plan and develop videotaping lesson #2 with the same third grade teacher. MCQs will be given to second grade students at the beginning and the end of the lesson..
Give the third grade teachers a different standard to write 12 MCQ- two for each level of Bloom's Taxonomy.
Third grade teachers Two of the remaining four will distribute MCQs. third grade teachers should Then, view and plan and prepare a critique lesson #2.. mathematics lesson utilizing They will offer the format and procedures recommendations, if as discussed and needed. demonstrated via
videotaping # 1 and #2.
The third grade team The remaining two third will view grade teachers will plan and mathematics lessons prepare a mathematics as taught by grade lesson utilizing the format level colleagues. and procedures as discussed
115 Appendix B (continued)
Objective(s)
Date Teachers will: Activities Resources/Follow-Up
They will use the OBIA(Persaud & Turner, 2007) to rate each lesson
December 2007 View and critique The third grade team videotaped mathematics will view lessons as taught by third mathematics lessons grade teachers as taught by grade
level colleagues They will use the OBIA (Persaud & Turner, 2007) to rate each lesson.
AprilMay 2008 Collect summative test All third grade data students will be
administered the Georgia CRCT mathematics test. Student performance will be compared based on gender and SES.
and demonstrated via videotaping 1-4
During the third semester of the school year 2007-2008, the third grade teachers will continue to implement instructional strategies developed over the past 8 weeks. They will also devote at least 25% of grade level meeting time for the discussion of student mathematics achievement. The researcher will conduct weekly visits to each third grade mathematics class and grade level meeting in order to monitor implementation.
APPENDIX C
Student Data
1 = Well Below Expectations 3 = Meets Expectations; 5 = Well Above Expectations
2 = Below Expectations 4 = Above Expectations
Rate this student to the extent that he/she is: 1 2 3 4 5
1. Able to utilize everyday experiences into learning textbook knowledge
2. Able to relate new concepts to previous concepts taught
3. Able to relate concepts in one subject area to other subject areas
4. Able to remember and recall basic facts as taught
5. Able to understand at a simple level
6. Able to apply knowledge to new situations
7. Able to see cause-effect relationships (or how ideas and concepts are inter-related)
8, Able to create new and worthy ideas
9. Able to selectljudge whether one idea is better than another idea
10. Able to accept responsibility (able to accept responsibility when wrong)
1 1. Able to cooperate and collaborate with others
Appendix C
Provide demographic data for student and teacher
12. Current grade in mathematics class: (1) A (2) B (3) C (4) F
13. CRCT Mathematics Pretest Scores: Level 1 (Does Not Meet); Level 2 (Meets); Level 3 (Exceeds)
14. CRCT Mathematics Posttest Scores: Level 1 (Does Not Meet); Level 2 (Meets); Level 3 (Exceeds)
15. Student gender: (1) Female; (2) Male
16. Race: (1) African American; (2) Caucasian; (3) Hispanic; (4) Asian; (5) Multi- racial; (6) Other
17. Meal Status: (1) Pay; (2) Reduced; (3) Free
18. Student lives with: (1) Both Parents; (2) Mom; (3) Dad; (4) Grandparent; (5) Grandparent and Mom; (6) Grandparent and Dad; (7) Other
19. Mother's job: (1) Unknown; (2) Unemployed; (3) Unskilled; (4) Semiskilled; (5) skilled; (6) Highly Skilled; (7) Lower Management; (8) Upper Management
20. Father's job: 1) Unknown; (2) Unemployed; (3) Unskilled; (4) Semiskilled; (5) Skilled; (6) Highly Skilled; (7) Lower Management; (8) Upper Management
21. Number of siblings: (1) 0; (2) 1; (3) 2; (4) 3; (5) 4 or more
22. Student job aspiration: (1) Unknown; (2) Unemployed; (3) Unskilled; (4) Semiskilled; (5) Skilled; (6) Highly Skilled; (7) Lower Management; (8) Upper Management
23. Teacher Gender: (1) female; (2) male
24. Years of teaching experience: (1) 0-5; (2) 6-1 0; (3) 1 1-1 5; (4) 16-20; (5) 21 -30
APPENDIX D
Observation Based Instructional Assessment (OBIA)
TEACHER Empowerment Evaluation Model:
Teacher ID: Grade Level:
Subject area: Date:
Teacher Initiating
Teacher Task Areas = A-G Means = 1-2-3: Explanation, Ask Questions,
Uses Answers
A Procedural Communication:
Explains, Asks questions,
uses answers
B Uses student social
experiences 1 Explains process 2 Asks question 3. Uses Answers, praises
C Uses textbook subject-
matter : 1 Explains content 2 Asks questions
3. Uses Answers, praises
D Relates knowledge to
previous lessons - in same
subject area 1 Explains 2 Asks questions
3. Uses answers, praises E Relates knowledge to
different subject areas 1 Explains 2 ~ s k s questions 3 Uses answers, praises
Activities
Computer. Code
1-4
5-8
9-12
1.3-16
17-20
Teacher
Knowledge
&
Comprehension
Q
1 2 3 4 5
Q
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
Q
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
Q
1 2 2 4 5 1 2 3 4 5 1 2 3 4 5
Q
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 I
Outcomes
Higher Order Thinking Skills
Q
1 2 3 4 5
Q 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
Q
1 2 2 4 5 1 2 3 4 5 1 2 3 4 5
0
1 2 2 4 5 1 2 3 4 5 1 2 3 4 5
Q
1 2 2 4 5 1 2 3 4 5 1 2 3 4 5
Student
Knowledge
&
Comprehension
- 0 1 2 3 4 5
Q 1 2 3 4 5 1 2 2 4 5 1 2 3 4 5
- 0 1 2 3 4 5 1 2 3 4 5 1 2 2 4 5
0
1 2 3 4 5 1 2 2 4 5 1 2 3 4 5
- 0
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
Outcomes -
Higher Order Thinking skills
Q 1 2 3 4 5
- 0 1 2 3 4 5 1 2 2 4 5 1 2 3 4 5
Q
1 2 2 4 5 1 2 3 4 5 1 2 3 4 5
0
- 1 2 3 4 5 1 2 2 4 5 1 2 3 4 5
- 0
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
119 Appendix D (continued)
Rating scale: Observations of'acts: 0 = None; 1 = 1-2; 2 = 3-4; 3 = 5-6; 4 = 7-8; 5 = 9 or more An act = a complete statement carrying a meaning: Yes and no are complete statements carrying meanings. Lower order thinking skills: Knowledge = Recall of facts, Comprehension = literal meanings, paraphrasing
Higher order thinking skills: Different application, analysis, synthesis (inferences) evaluation
29. Technology: Overhead, Power,-point, etc .: NO--- YES,-
G Behavlor Management
Uses cr~tic~sms to 1 2 2 4 5 1 2 2 4 5 control (0) Uses d~alogue,
Student Outcomes Teacher Initiating Activities
30. Role,-playing, groups: No- YES--
Teacher Outcomes
Knowledge
&
Comprehensron
- 0
1 2 2 4 5 1 2 3 4 5 1 2 3 4 5
Teacher Task Areas = A-G
Means = 1-2-3
Explanation, Ask Questions,
Uses Answers
F Demonstrates test concepts
1 Expla~ns
2 Asks questions
3 Uses answers, pra~ses
3 1. Class size: Below-,- 20-; 21 --23; 24--27; 28--3 1 ; 3 1+
Knowledge
&
Comprehension
0 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
Hlgher Order
Thlnklng skllls
0 1 2 3 4 5 1 2 2 4 5 1 2 2 4 5
Computer
Code
21-24
32. Subject area: (1) math-- (2) Science- (3) ReadingILanguage- (4) Social studies-
H~gher Order
Ihlnkrng Sk~lls
0 1 2 2 4 5 1 2 3 4 5 1 2 3 4 5
Other-
33. Cass ability: Low- Middle- High-
34. Free Lunch-Percent-
35. K-Grade Level:
TEEM & Observation-based instructional assessment system Ganga Persaud, copyright, 2005 revised fiom 1993
APPENDIX E
Reliability Analyses
R E L I A B I L I T Y A N A L Y S I S - S C A L E ( I N S T R S U P )
Reliability Coefficients
N of Cases = 37.0 N of Items = 10
Alpha = .a270
R E L I A B I L I T Y A N A L Y S I S - S C A L E ( P R O F D E V )
Reliability Coefficients
N of Cases =37.0 N of Items = 4
Alpha = ,9130
R E L I A B I L I T Y A N A L Y S I S - S C A L E ( M A T G R O U P )
Reliability Coefficients
N of Cases = 37.0 N of Items = 4
Alpha = .9156
R E L I A B I L I T Y A N A L Y S I S - S C A L E ( A C H L P L A N )
Reliability Coefficients
N of Cases = 37.0 N of Items = 6
Alpha = 3950
Appendix E (continued)
R E L I A B I L I T Y A N A L Y S I S - S C A L E ( T C E X P E C )
Reliability Coefficients
N of Cases = 37.0 N of Items = 6
Alpha = .8860
R E L I A B I L I T Y A N A L Y S I S - S C A L E ( T C H O T S )
Reliability Coefficients
N of Cases = 37.0 N of Items = 6
Alpha = 3958
R E L I A B I L I T Y A N A L Y S I S - S C A L E ( S T U M O T I V )
Reliability Coefficients
N of Cases = 37.0 N of Items = 4
Alpha = A969
R E L I A B I L I T Y A N A L Y S I S - S C A L E ( C O L G P R E P )
Reliability Coefficients
N of Cases = 37.0 N of Items = 4
Alpha = .9220
R E L I A B I L I T Y A N A L Y S I S - S C A L E ( G N S T C R C T )
Reliability Coefficients
N of Cases = 37.0 N of Items = 5
Alpha = .9347
APPENDIX F
Statistical Tables
Table F1
Results on Regression Analysis. Teacher Rating of Predicted Student Gain on the CRCT
(Dependent Variable: GNSTCRCT) in Mathematics by the Selected Independent
Variables
-- .-
Unstandardized Standardized
Coefficients Coefficients
Model B Std. Error Beta t Sig.
1 (Constant)
STUMOTIV
2 (Constant)
STUMOTIV
TCEXPEC
3 (Constant)
STUMOTIV
TCEXPEC
INSTRSUP
PROFDEV
MATGROUP
123 Appendix F (continued)
Table F 1 (continued)
Unstandardized Standardized
Coefficients Coefficients
Model B Std. Error Beta t Sig.
ACHLPLAN -.282 .273 -. 180 -1.034 .310
TCHOTS 8.507E-02 .153 .079 .555 .583
COLGPREP .I95 .lo9 .259 1.798 .083
F Ratio = 6.142 S = .OOO
Table F2
Results on Regression Analysis: Student Motivation as Dependent with Listed
Independent Variables
Unstandardized Standardized
Coefficients Coefficients
Model B Std. Error Beta t Sig.
1 (Constant) 1.084 .464 2.336 .025
GNSTCRCT .7 14 .127 .690 5.635 .OOO
2 (Constant) -.342 1.194 -.287 .777
GNSTCRCT .403 .I98 .389 2.040 .051
INSTRSUP .217 .349 .I12 ,622 .539
PROFDEV -.332 .229 -.319 -1.450 .I58
MATGROUP .427 .253 368 1.689 .lo2
Appendix F (continued)
Table F2 (continued)
Unstandardized Standardized
Coefficients Coefficients
Model B Std. Error Beta t Sig.
ACHLPLAN 5.757E-02 .312 .035 .I85 .855
TCEXPEC .I27 .I85 .I25 .683 SO0
TCHOTS -3.776E-02 .I73 -.034 -.219 .829
COLGPREP .I40 .I26 .I80 1.116 .274
Adjusted R Square = .453 F Ratio = 4.730 S = .001
Table F3
Results on Regression Analysis: Teacher Expectations for Student Performance
(TCEXPEC) as Dependent with Listed Independent Variables
- -- Unstandardized Standardized
Coefficients Coefficients
Model B Std. Error Beta t Sig. -
1 (Constant) 1.566 .499 3.139 .003
GNSTCRCT .634 .I26 .618 4.648 .OOO
2 (Constant) -.590 332 -.709 .483
GNSTCRCT .470 .I34 .458 3.517 .001
ACHLPLAN .645 .2 10 .400 3.076 .004
125 Appendix F (continued)
Table F3 (continued)
Unstandardized Standardized
Coefficients Coefficients
Model B Std. Error Beta t Sig.
3 (Constant)
GNSTCRCT
ACHLPLAN
INSTRSUP
PROFDEV
MATGROUP
TCHOTS
STUMOTIV
COLGPREP
a. Dependent Variable: TCEXPEC
Adjusted R Square = .43 1 F ratio = 4.41 S = .002
Appendix F (continued)
Table F4
HOTS Pretest Data
HOTSPRET N Mean
1 2 1 .3333
2 2 1 A333
3 17 .I667
4 16 .5000
5 20 3333
Total 95 .5474
ANOVA
Sum of Mean
Squares d f Square F Sig. -- --
Between Groups 6.815 4 1.704 3858341 .OOO
Within Groups 3.974E-3 1 90 4.41 6E-33
Total 6.815 94
Table F5
HOTS Posttest Data - -
HOTSPOST N Mean -
1' 2 1 2.3492
Total
127 Appendix F (continued)
Table F5 (continued)
ANOVA
Sum of Mean
Squares d f Square F Sig.
Between Groups 17.328 4 4.332 1229.13 .OOO
Within Groups .317 90 3.524E-03
Total 17.645 94
Table F6
HOTS Gain Data --
HOTSGAIN- N Mean
1 2 1 2.0159
2 2 1 2.1508
3 17 1.6667
4 16 2.0000
5 20 2.1500
Total 95 2.0088
ANOVA
Sum of Mean
Squares d f Square F Sig.
Between Groups 2.814 4 .704 199.636 .OOO
Within Groups .3 17 90 3.524E-03
Total 3.132 94
Appendix F (continued)
Table F7
PRECRCT Data
Std.
PRECRCT N Mean Deviation
1 2 1 1.90 -54
2 2 1 1.71 .56
3 17 1.88 .49
4 16 1.88 .62
5 20 1.05 .60
Total 9 5 1.88 .56 -- -
ANOVA
Sum of Mean
Squares d f Square F Sig.
Between Groups 1.166 4 .292 .919 .457
Within Groups 28.560 90 .317
Total 29.726 94
Table F8
POSTCRCT Data
-- Std. Std.
POSTCRCT N Mean Deviation Error
1 2 1 2.00 .77 .17
2 2 1 1.90 .62 .14
3 17 1.82 .81 .20
4 16 2.06 .77 .19
Appendix F (continued)
Table F8 (continued)
Std. Std.
POSTCRCT N Mean Deviation Error
5 20 2.20 .62 .14
Total 95 2.00 .71 7.33E-02
ANOVA
Sum of Mean
Squares d f Square F Sig.
Between Groups 1.582 4 .396 .767 .549
Within Groups 46.4 18 90 .5 16
Total 48.000 94
Table F9
CRCTGAIN Data
Std.
CRCTGAIN N Mean Deviation
1 2 1 9.524E-02 .6249
2 2 1 .I905 .60 16
3 17 -5.8824E-02 .7475
4 16 .I875 .655 1
5 20 .I500 2663
Total 95 .I158 .5990
ANOVA
Sum of Mean
Squares d f Square F Sig.
Between Groups .750 4 .I88 .512 .727
Within Groups 32.976 90 .366
Total 33.726 94
Appendix F (continued)
Fl0
Rotated Component Matrix
Component Component Component Component
1 2 3 4
HOTSPOST
HOTSGAIN
HOTSPRET
TCHGEND
PRECRCT
TCHRATE
GENDER
MATHGD
TCHEXP
MEALS
DADJOB
CRCTGAIN
POSTCRCT
Variance Explained 31.610 21.082 11.869 10.285
Appendix F (continued)
Table F 1 1
Factor Analysis
% of Cumulat~ve % of Cumulat~ve % of Cumulative
Component Total Valance % Total Vartance Ye Total Var~ance %
1 4 109 31 610 31 610 4 109 31 610 31 610 3 776 29 044 29 044
2 2 741 21 082 52 692 2 741 21 082 52 692 2 614 20 106 49 150
3 1 543 11 869 64 561 1543 11 869 64 561 1 768 13 599 62 749
4 1337 10 285 74 846 1 337 10 285 74 846 1573 12 098 74 846
5 914 7 030 81 877
6 798 6 136 88 013
7 648 4 981 92 993
8 498 1 8 3 1 96 825
9 305 2 345 99 170
10 5 889E-02 453 99 623
11 4 902E-02 377 100 000
12 3332E-16 256%-15 100 000
13 -2 45%-16 -1 891E-15 100 000
Extraction Method: Principal Component Analysis
Table F 1 2
Rotated Component Matrix
-
Component 1 Component 2 Component 3 Component 4
HOTSPOST
HOTSGAIN
HOTSPRET
TCHGEND
PRECRCT
TCHRATE
GENDER
MATHGD
Appendix F (continued)
Table F 12 (continued)
Component 1 Component 2 Component 3 Component 4
TCHEXP -6.780E-02 .I66 .881 1.4 16E-02
MEALS 4.4 18E-02 -.2 15 .626 - 1.749E-02
DADJOB -2.079E-02 .365 -.393 .I47
CRCTGAIN 8.541 E-02 -3.745E-02 1.228E-04 .992
POSTCRCT 5.277E-02 .645 -.I71 .673
Extraction Method: Principal Component analysis; Rotation Method: Varimax with Kaiser; Normalization. a. Rotation converged in 5 iterations.
Table F 13
Pearson Correlations (N = 95)
PRECRCT POSTCRCT CRCTGAIN HOTSPRET HOTSPOST HOTSGAIN
GENDER Pearson Correlation
Sig (2-tailed)
RACE Pearson Correlation
Sig (2-tailed)
MEALS Pearson Correlation
Sig (2-tailed)
PRECRCT Pearson Correlation
Sig (2-tailed)
POSTCRCT Pearson Correlation
Sig (2-tailed)
133 Appendix F (continued)
PRECRCT POSTCRCT CRCTGAIN HOTSPRET HOTSPOS 1 HOTSGAIN
MOMJOB Pearson 11 1 191 123 - 121 - 084 - 020 Correlation
Sig (2-tailed) 284 064 235 244 42 I 845
DAD JOB Pear son 286* 311* 103 Correlation
Sig (2-tailed) 005 002 321 99 1 868
LIVESWTH Pearson 02 7 131 132 - 097 - 123 - 147 Correlation
Sig (2-tailed) 796 204 204 348 237 154
MATHGD Pewson - 368* Correlation
Sig (2-tailed) 000 000 084 000 000
TCHRATE Peatson 592* 599 159 Correlation
Sig (2-tailed) 000 000 123 104 060
SIBLINGS Peatson - 146 - 177 - 075 - 012 - 019 - 027 Correlation
Sig (2-tailed) 161 087 4'7 5 907 857 799
CAREER Pear son 079 148 103 006 010 013 Correlation
Sig (2-tailed) 446 151 32 1 950 926 899
TCHGEND Pear son - 002 - 116 Correlation
Sig (2-tailed) 988 263 186 000 000
TCHEXP Pearson - 074 - 065 - 008 Correlation
Sig (2-tailed) 475 529 936 262 121
134 Appendix F (continued)
Table F 1 4
HOTSGAIN Model Summary
Adjusted Std. Error of
Model R R Square R Square the Estimate
a Predictors: (Constant), TCHGEND
b Predictors: (Constant), TCHGEND, HOTSPRET
c Predictors: (Constant), TCHGEND, HOTSPRET, TCHRATE
d Predictors: (Constant), TCHGEND, HOTSPRET, TCHRATE, GENDER
e. Predictors: (Constant), TCHGEND, HOTSPRET, TCHRATE, GENDER,
CRCTGAIN, MEALS, DADJOB, MATHGD, PRECRCT
Appendix F (continued)
Table F 1 5
ANOVA - Model Summary
Model
Sum of Mean
Squares d f Square F Sig.
1 Regression
Residual
Total
2 Regression
Residual
Total
3 Regression
Residual
Total
4 Regression
Residual
Total
5 Regression
Residual
Total
a Predictors: (Constant), TCHGEND
b Predictors: (Constant), TCHGEND, HOTSPRET
c Predictors: (Constant), TCHGEND, HOTSPRET, TCHRATE
d Predictors: (Constant), TCHGEND, HOTSPRET, TCHRATE, GENDER
e. Predictors: (Constant), TCHGEND, HOTSPRET, TCHRATE, GENDER,
CRCTGAIN, MEALS, DADJOB, MATHGD, PRECRCT
Appendix F (continued)
Table F 16
Dependent Variable: HOTSGAIN (Coef$cients)
Model
Unstandardized Standardized
Coefficients Std. Coefficients
B Error Beta t Sig.
1 (Constant)
TCHGEND
2 (Constant)
TCHGEND
HOTSPRET
3 (Constant)
TCHGEND
HOTSPRET
TCHRATE
4 (Constant)
TCHGEND
HOTSPRET
TCHRATE
GENDER
5 (Constant)
TCHGEND
HOTSPRET
TCHRATE
GENDER
Appendix F (continued)
Table F 1 6 (continued)
Model
Unstandardized Standardized
Coefficients Std. Coefficients
5 MEALS -8 438E-03 007 - 041 -1141 .257
MATHGD 2.700E-03 006 02 1 .437 .663
DADJOB -6.917E-03 .004 - 056 -1.549 .I25
PRECRCT -1 693E-02 .016 - 052 -1 077 .285
CRCTGAIN - 1.8298-02 012 -.060 -1.587 .I16
a Dependent Variable: HOTSGAIN
Table F 1 7
CRCTGAIN: Dependent Model Summary
Adjusted R Std. Error of
Model R R Square Square the Estimate
a Predictors: (Constant), PRECRCT
b Predictors: (Constant), PRECRCT. TCHRATE
c Predictors: (Constant), PRECRCT, TCHRATE, TCHGEND, MEALS, GENDER,
DADJOB, TCHEXP, MATHGD, HOTSGAIN
138 Appendix F (continued)
Table F 1 8
ANOVA. CRCTGAIN
Model
Sum of Mean
Squares d f Square F Sig.
1 Regression
Residual
Total
2 Regression
Residual
Total
3 Regression
Residual
Total
a Predictors: (Constant), PRECRCT
b Predictors: (Constant), PRECRCT, TCHRATE
c Predictors: (Constant), PRECRCT, TCHRATE, TCHGEND, MEALS, GENDER,
DADJOB, TCHEXP, MATHGD, HOTSGAIN
d. Dependent Variable: CRCTGAIN
Appendix F (continued)
Table F 19
Coefficients: CRCTGAIN
Model
Unstandardized Standardized
Coefficients Std Coefficients
B Err or. Beta t Sig.
1 (Constant)
PRECRCT
2 (Constant)
PRECRCT
TCHRATE
3 (Constant)
PRECRCT
TCHRATET
GENDER
MEALS
DADJOB
TCHGEND
TCHEXP
MATHGD
HOTSGAIN
a Dependent Variable: CRCTGAIN
140 Appendix F (continued)
Table F20
TCHMTE: Dependent Variable - Model Summary
Adjusted R Std. Error of
Model R R Square Square the Estimate
a Predictors: (Constant), PRECRCT
b Predictors: (Constant), PRECRCT, MATHGD
c Predictors: (Constant), PRECRCT, MATHGD, CRCTGAIN
d Predictors: (Constant), PRECRCT, MATHGD, CRCTGAIN, TCHGEND
e Predictors: (Constant), PRECRCT, MATHGD, CRCTGAIN, TCHGEND,
HOTSGAIN
f Predictors: (Constant), PRECRCT, MATHGD, CRCTGAIN, TCHGEND,
HOTSGAIN, MEALS, GENDER, DADJOB, HOTSPRET
Appendix F (continued)
Table 2 1
ANOVA: TCHRATE Dependent Variable
Model
Sum of
Squares
Mean
Square F Sig.
1 Regression
Residual
Total
2 Regression
Residual
Total
3 Regression
Residual
Total
4 Regression
Residual
Total
5 Regression
Residual
Total
6 Regression
Residual
Total
a Predictors: (Constant), PRECRCT
b Predictors: (Constant), PRECRCT, MATHGD
c Predictors: (Constant), PRECRCT, MATHGD, CRCTGAIN
d Predictors: (Constant), PRECRCT, MATHGD, CRCTGAIN, TCHGEND
e Predictors: (Constant), PRECRCT, MATHGD, CRCTGAIN, TCHGEND,
HOTSGAIN
f Predictors: (Constant), PRECRCT, MATHGD, CRCTGAIN, TCHGEND,
HOTSGAIN, MEALS, GENDER, DADJOB, HOTSPRET
g Dependent Variable: TCHRATE
Appendix F (continued)
Table F22
CoefJicients: TCHRATE: Dependent Variable
Model
Unstandardized Standardized
Coefficients Std. Coefficients
B Error Beta t Sig.
I (Constant)
PRECRCT
2 (Constant)
PRECRCT
MATHGD
3 (Constant)
PRECRCT
MATHGD
CRCTGAIN
4 (Constant)
PRECRCT
MATHGD
CRCTGAIN
TCHGEND
5 (Constant)
PRECRCT
MATHGD
CRCTGAIN
TCHGEND
HOTSGAIN
Appendix F (continued)
Table F22 (continued)
Model
Unstandardized Standardized
Coefficients Std. Coefficients
B Error Beta t Sig.
6 (Constant)
PRECRCT
MATHGD
CRCTGAIN
TCHGEND
HOTSGATN
GENDER
MEALS
DADJOB
HOTSPRET - -
a Dependent Variable: TCHRATE
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