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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)




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


Bloom's taxonomy in relation to experiences simulated in use of

technology

Table 5 (continued)



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


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)




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)




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


Bloom's taxonomy if experiential and/or f hands-on or group

work


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


STIJMOTIV Pearson Correlation .565 .690 1 .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



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?


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



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


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?


relationship between perception of instructional supervision and teacher expectations.

The correlation for teacher expectations is .464 with a level of significance of .044. The


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


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


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?


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


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


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


1 (Constant) .499 3.139 .003

GNSTCRCT .I36 .618 .4648 .OOO

78


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


Sig (2-tailed


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



(Constant)

PRECRCT

MATHGD

CRCTGAIN

TCHGEND

HOTSGAIN

GENDER

MEALS

93




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.


significant relationship between gain scores on the CRCT in mathematics and student

motivation.


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.


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.


significant relationship between instructional supervision and teacher expectations;

instructional supervision and gain scores on the CRCT in mathematics and instructional

supervision and student motivation.


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


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


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


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 )


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 )



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 )



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 )



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 )



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 )



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 )



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 )



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)




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




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)




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


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






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


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



ANOVA

Sum of Mean


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


Between Groups 2.814 4 .704 199.636 .OOO

Within Groups .3 17 90 3.524E-03

Total 3.132 94


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


Between Groups 1.166 4 .292 .919 .457


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



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


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


Between Groups .750 4 .I88 .512 .727


Total 33.726 94


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


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

-


HOTSPOST

HOTSGAIN

HOTSPRET

TCHGEND

PRECRCT

TCHRATE

GENDER

MATHGD


Table F 12 (continued)


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)


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


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


Table F 1 5

ANOVA - Model Summary

Model

Sum of Mean


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


Table F 16

Dependent Variable: HOTSGAIN (Coef$cients)

Model


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


Table F 1 6 (continued)

Model



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


Table F 1 8

ANOVA. CRCTGAIN

Model

Sum of Mean


1 Regression

Residual

Total

2 Regression

Residual

Total

3 Regression

Residual

Total


b Predictors: (Constant), PRECRCT, TCHRATE

c Predictors: (Constant), PRECRCT, TCHRATE, TCHGEND, MEALS, GENDER,

DADJOB, TCHEXP, MATHGD, HOTSGAIN

d. Dependent Variable: CRCTGAIN


Table F 19

Coefficients: CRCTGAIN

Model


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


Table F20

TCHMTE: Dependent Variable - Model Summary

Adjusted R Std. Error of

Model R R Square Square the Estimate


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


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


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


Table F22

CoefJicients: TCHRATE: Dependent Variable

Model



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



Model



B Error Beta t Sig.

6 (Constant)

PRECRCT

MATHGD

CRCTGAIN

TCHGEND

HOTSGATN

GENDER

MEALS

DADJOB

HOTSPRET - -

a Dependent Variable: TCHRATE

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