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

(8) schools in the District of Valladolid, Division of

Negros Occidental.

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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 sizeN = population sizee = 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;

ni = sample size per sectionN1 = population per sectionnT = total sample size

Nt = total population

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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 28School B 30 13School C 20 10School D 82 30School E 38 17School F 49 19School G 223 77School H 169 59TOTAL 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

11111141

11111141

TOTAL 11 11

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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.

Validity and Reliability of the

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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.

The researcher extracted the questionnaires for pupils

and teachers respondents and provides enough copies for the

distribution.

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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 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

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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 RespondentsN = 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

formula was used for the scale type of questions, to measure

the extent on how the respondents affected by personal and

environmental conditions.

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It was computed using the following formula:

x = Σfx N

Where:Σ = Summationf = Frequencyx = Class markN = 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 VERBALINTERPRETATION

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

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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 valuefo = (frequency according to the variables)

observed frequencyfe = (total frequency x number of

respondents) expected frequency

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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 observationsS² = sum of square between groupsS = degrees of freedom (groups – 1)S² = sum of scores within groupsS² = 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) n1 n2

Where: F’ = Scheffes test

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X1 = mean of group 1X1 = mean of group 2n1 = number of sample in group 1n2 = number of sample in group 2

SW 2 = within mean scores