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1. Chapter 3
RESEARCH METHODOLOGY
This chapter presents and discusses the research
design, subject and respondents of the study, population,
sample size, sampling techniques, data gathering
instrument, validity and reliability of instruments, data
gathering procedures and data analyses.
Research Design
This study used a descriptive research design.
According to the Office of Human Research Protections
(OHRP, 1998), a descriptive study provide information about
the naturally occurring health status, behavior, attitudes
or other characteristics of a particular group. Likewise,
Shields, Patricia and Rangarjan (2013) stated that
descriptive research design is used to describe the
characteristics of a population or phenomenon being
studied.
Subject and Respondents of the Study
The subject of the study composed of two hundred fifty
three (253) Grade 6 pupils and the respondents were the
Grade 6 pupils and teachers in Mathematics from the eight

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(8) schools in the District of Valladolid, Division of
Negros Occidental.
Population and Sample Size
There were six hundred eighty six (686) Grade 6 pupils
population covered in the study. The overall sample size
were two hundred fifty three (253) Grade 6 pupils from the
eight (8) schools in the District of Valladolid, Division
of Negros Occidental. For the teacher respondents, all
Mathematics teachers were taken in the study.
Sampling Techniques
Of the total population, the sample size was
determined using the Slovin formula:
n = N / (1 + Ne2)
Where:
n = sample size
N = population size
e = margin of error
n = (1 + 686 X 0.05)2
/ 686
= (1 + 1.715) / 686
= 2.715 / 686
= 253
In determining the number of respondents from eight
(8) schools of District of Valladolid, Division of Negros
Occidental, the stratified random sampling technique was
used with the formula below:
ni = N1 ( n 1 )
Nt
Where;

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ni = sample size per section
N1 = population per section
nT = total sample size
Nt = total population
Table 1 below presents the distribution of respondents
per school.
Table 1. Population and Sample Size of Grade 6 Pupils by
Schools in the District of Valladolid, Division
of Negros Occidental
Schools in Valladolid
District
Population
(N)
Sample Size (n)
School A 75 28
School B 30 13
School C 20 10
School D 82 30
School E 38 17
School F 49 19
School G 223 77
School H 169 59
TOTAL 686 253
Table 2 below presents the distribution of teacher-
respondents from eight (8) schools in the District of
Valladolid, Division of Negros Occidental.
Table 2. Population and Sample Size of Grade 6 Teachers by
Schools in the District of Valladolid, Division
of Negros Occidental
Schools in Valladolid
District
Population (N)
Sample Size
(n)
School A
School B
School C
School D
School E
School F
School G
School H
1
1
1
1
1
1
4
1
1
1
1
1
1
1
4
1
TOTAL 11 11

4. 62
Data Gathering Instruments
The researcher utilized survey instrument for data
gathering. For the quantitative probe, a self-administered
survey questionnaire was employed.
Part 1: Questionnaire to determine pupil’s profile
To determine the pupils’ profile, a survey question
was used which include: gender, economic status, study
habit, attitude towards Mathematics and technological
gadgets;
Part 2: Questionnaire to determine teacher’s profile
To determine the teachers’ profile, a survey question
was used which include: gender, educational qualifications,
length of service, seminars and trainings attended, and
styles and strategies in teaching Mathematics.
Part 3: National Achievement Test (NAT) Results of Grade 6
Pupils in Mathematics
To determine the National Achievement Test (NAT)
results of Grade 6 pupils’ in Mathematics, the researcher
collected the results from eight (8) schools in the
District of Valladolid, Division of Negros Occidental from
school year 2011-2012 to 2013-2014.

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Validity and Reliability of the
Data Gathering Instrument
As emphasized by Maricon (1975), an instrument is
considered valid if it measures what it intends to measure
and has the ability to gather data suited to the specific
purpose of the study. On the other hand, it is reliable
when test is dependable, self-consistent and stable
Hence, the instruments used for the pupils and
teachers profile were valid and reliable for they were
evaluated, criticized and developed by the Division Program
Supervisor in Mathematics, School Heads and Mathematics
teachers.
Data Gathering Procedures
For the accomplishment of the study the following
procedures were used:
A Letter of permission to the Schools Division
Superintendent, to administer the questionnaires was
secured from the Division Office of Negros Occidental
(Appendix C).
A letter of permission to National Educational Testing
and Research Center (NETRC) was accomplished for the
utilization of National Achievement Test result of school
years 2011-2012 to 2013-2014.

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The researcher extracted the questionnaires for pupils
and teachers respondents and provides enough copies for the
distribution.
To ensure the appropriate and proper accomplishment of
the questionnaire, the researcher explained the purpose of
the study to the respondents.
The National Achievement Test (NAT) results in
Mathematics were collected from eight (8) schools in the
District of Valladolid, Division of Negros Occidental from
school year 2011-2012 to 2013-2014.
The data gathered were tabulated, classified and
analyzed to answer the specific statement of the problems.
Data Analysis
To analyze the collected data, the appropriate
statistical tests were used as follows:
To answer the statement of the problem no. 1 which
says, what is the profile of grade 6 pupils when grouped
according to gender, economic status, study habit, attitude
towards Mathematics and technological gadgets, the
frequency and percent distribution were used.
To answer the statement problem no. 2 which says, what
is the profile of grade 6 teachers when grouped according
to gender and styles and strategies in teaching

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Mathematics, the frequency and percent distribution were
used.
Frequency, according to Pagoso and Montana (1997), it
is a tool facilitates the tallying and counting of
frequencies falling under each category. In this study,
frequency was used to measure the respondents answer to
specific set of questions.
Percentage, stated by Triola (1997), it is the ratio
of the responses to the total, to find the trends in
opinion. This was used to determine the trends of the
subject of the study's profile as well as the significant
difference on the respondents' assessment.
Specifically, this is used to compare the frequency of
responses according to the number of sections.
% = F/N x 100
Where: F = Number of Respondents
N = Total no. of Respondents
% = Percentage
To answer the statement of the problem no. 3 which
says, what is the National Achievement Test performance of
Grade 6 pupils in the District of Valladolid, Division of
Negros Occidental for School Years 2011-2012, 2012-2013,
and 2013-2014, the weighted mean was used.
According to Triola (1997), mean is used when the
different scores weighted are assigned different test. This

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formula was used for the scale type of questions, to
measure the extent on how the respondents affected by
personal and environmental conditions.
It was computed using the following formula:
x = Σfx
N
Where:
Σ = Summation
f = Frequency
x = Class mark
N = Total frequency
In interpreting the Grade 6 pupils’ economic status,
study habit, attitude towards Mathematics, the Likert scale
was used, and it is considered as unidimensional scaling
method. It is categorized as; strongly agree which means
one is strongly favorable to the concept, agree refers
to somewhat favorable to the concept, undecided means
cannot decide for the concept, disagree refers to somewhat
unfavorable to the concept, and strongly disagree means
strongly unfavorable to the concept (William, 2008).
The Likert Scale used were as follows:
SCALE RANGE VERBAL
INTERPRETATION

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5 4.3 to 5.0 Strongly agree
4 3.5 to 4.2 Agree
3 2.7 to 3.4 Undecided
2 1.9 to 2.6 Disagree
1 1.0 to 1.8 Strongly disagree
To answer the statement of the problem no. 4 which
says, is there a significant relationship between the
profile of grade 6 pupils when grouped according to gender,
economic status, study habit, attitude towards Mathematics
and technological gadgets and the level National
Achievement Test performance in the District of Valladolid,
Division of Negros Occidental for School Year 2011-2012,
2012-2013, and 2013-2014 and to answer the statement of the
problem no. 5 which says, is there a significant
relationship between the profile of grade 6 teachers when
grouped according to gender, and styles and strategies in
teaching Mathematics and the level of National Achievement
Test performance in the District of Valladolid, Division of
Negros Occidental for School Year 2011-2012, 2012-2013, and
2013-2014, Chi-squared test was used.
The formula for chi-square is:
Formula: x² = (fo – fe)²
fe
Where: x² = chi-square value

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fo = (frequency according to the variables)
observed frequency
fe = (total frequency x number of
respondents) expected frequency
To answer the statement of the problem no. 6 which
says, Is there a significant difference between the
National Achievement Test performance among the eight
schools (8) in the District of Valladolid, Division of
Negros Occidental for School Year 2011-2012, 2012-2013, and
2013-2014, the F test was used. The F test formula is:
formula:
where: F = ration of variance of two observations
S² = sum of square between groups
S = degrees of freedom (groups – 1)
S² = sum of scores within groups
S² = degrees of freedom
(observation – group)
Likewise, Scheffe’s test was used to determine the
significant difference of NAT results between schools from
8 schools in the District of Valladolid.
It was computed using the following formula:
F’ = (X1 – X2)2
SW 2
(n1 + n2)

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n1 n2
Where: F’ = Scheffes test
X1 = mean of group 1
X1 = mean of group 2
n1 = number of sample in group 1
n2 = number of sample in group 2
SW 2
= within mean scores