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INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 7, ISSUE 8, AUGUST 2018 ISSN 2277-8616

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Gradual Release Of Responsibility Instructional

Model: Its Effects On Students’ Mathematics

Performance And Self-Efficacy

Ian Paul B. Saligumba, Denis A. Tan

Abstract: The study assessed the mathematics performance and self-efficacy of Grade 9 students in a Gradual Release of Responsibility Instructional

Model (GRRIM) at Central Mindanao University Laboratory High School (CMULHS). It aimed to a) ascertain the performance level of students exposed

to GRRIM and those exposed to non-GRRIM in terms of pretest, posttest, and retention test; b) determine the self-efficacy level of the students exposed

to GRRIM and those exposed to non-GRRIM in terms of mastery experiences, vicarious experiences, verbal-social persuasion, and physiological and

emotional arousal; c) compare the performance of students exposed to GRRIM and those exposed to non-GRRIM in terms of posttest and retention test;

d) find the significant difference in the self-efficacy level of the students exposed to GRRIM and those exposed to non-GRRIM in terms of mastery

experiences, vicarious experiences, verbal-social persuasion, and physiological and emotional arousal. This study used the quasi-experimental research

design. The mathematics performance and self-efficacy level were gathered from the participants using validated instruments to answer the research

problems. The level of mathematics performance of the students in the pretest, posttest and retention test when exposed to GRRIM and those exposed

to non-GRRIM varies from very low to very high level. The self-efficacy level of Grade 9 students towards Mathematics when exposed to GRRIM and

non-GRRIM is moderately low. There was a highly significant difference in the posttest scores of those students exposed to GRRIM compared to those

exposed to non-GRRIM. On the contrary, there was no significant difference in the mathematics performance of the students when exposed to GRRIM

and non-GRRIM in terms of their retention test scores. There was no significant difference in the self-efficacy of students towards Mathematics in terms

of mastery experiences, vicarious experiences, verbal-social persuasions and physiological and emotional arousal when exposed to GRRIM and non-

GRRIM.

Index terms: Gradual Release of Responsibility Instructional Model (GRRIM), Mathematics Performance, Self-efficacy

————————————————————

1 INTRODUCTION

Our world today is continuously changing and with change

comes new challenges, problems and opportunities for

growth. With the advancement of science and technology

comes new jobs, changes in the way we communicate with

the advent of social media platforms, and the way we learn. In

our quest towards scientific and technological advancement,

we need nothing short of good performance in Mathematics at

all levels of education (NCTM, 2000). Unfortunately, the poor

performance of students in Mathematics remains to be a

widespread problem today. The results of the latest Trends in

Mathematics and Science Study (TIMSS) administered in

2003 revealed low achievement scores in Science and

Mathematics of selected Grade 4 and Grade 8 (Second Year

High School) students from sample schools (Gonzales, 2004).

The Philippines placed 23rd among 25 countries for both

Science and Mathematics for Grade 4 and 42nd in Science

and 41st in Mathematics among 45 countries for Grade 8

students.

Results of the survey also noted that the preparation of

Filipino students in TIMSS 2003 was similar to those in

TIMSS 1999. This study shows that students need to be

informed about different Mathematics study tips that they can

use to improve their academic performance in Mathematics.

The TIMSS result is in consonance with the 2014 – 2015

National Achievement Test for the 4th year which shows that

the Mean Percentage Score (MPS) of CMULHS in

Mathematics is 41.14 which is lower than the MPS of the

Division of Bukidnon which is 46.24 (DepEd, 2017). Thus,

there is a need to study the factors that affect the

mathematics performance of students. Several studies were

already conducted which helped increase the mathematics

performance of students by using innovative teaching

strategies, employing new assessment tools, interventions

and others. Aside from that, studies have shown that

psychological constructs such as self-efficacy, attitude, and

mathematics anxiety have a significant impact on the

mathematics performance of the students. Providing a quality

mathematics education has always been the dream of every

mathematics teacher in this country. Teachers are often faced

with problems not just professionally but also personally, and

this would somehow affect their work. With the advent of the

K to 12 Curriculum, teachers also need to adapt to the new

curriculum and think of ways on how to engage each learner

in every classroom activity to improve their performance in

Mathematics. Aside from that, teachers must also be aware of

the factors that would affect the performance in Mathematics.

Several studies were already employed by the researchers to

determine the performance of students in Mathematics and to

identify the factors that affect learning Mathematics. Asparin

(2013) conducted a study aimed to establish a causal model

on mathematics achievement of the second year high school

students of the Bukidnon National High School (BNHS) SY

2012-2013. In his study, Asparin found out that students’ level

of mathematics achievement is destitute and students’ levels

of understanding the problem, devising a plan, carrying out

__________________________________

Ian Paul B. Saligumba is a faculty of the College of

Education, Central Mindanao University (CMU),

Philippines. He is assigned to teach Mathematics

courses in the Laboratory High School. +639173081402,

ianpauls@cmu.edu.ph

Denis A. Tan is a faculty of the College of Education,

Central Mindanao University (CMU), Philippines. She is

currently the School Principal of the CMU Laboratory

High School and the Director of the Office of Admissions,

Scholarships and Placement in the same university.

+639177103100, teacher.tansined@gmail.com

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the plan, and looking back are very poor. Cordova and Tan

(2018) conducted a descriptive-correlational survey to six

private high schools in Valencia City with the Grade 9

students as respondents of the study and an Attitude towards

Mathematics Test, Mathematics Proficiency Test, and

Summative Test were used to gather data. The results of their

study show that mathematics proficiency and performance

level of Grade 9 students were described as beginning which

means that the students lack the basic mathematical skills

necessary for them to master Grade 9 Mathematics.

Moreover, they also found out a moderate positive correlation

between mathematics performance and parent’s (mother and

father) educational attainment. Their study also shows that

the mother’s educational attainment best predicts

mathematics performance. The study of Cordova supports the

study of Davis (2013) when he found out that occupation and

educational attainment of parents are the variables that best

predict the students’ mathematics achievement. Furthermore,

he also figured out that the students’ profile was more

favorable to the students to attain good performance in

Mathematics. Aside from that he also discovered that parental

support is another ingredient for the growth of learners not

only intellectually but also morally and spiritually. Lastly, his

study shows that the students’ socio-demographic profile is

significantly related to students’ mathematics achievement.

Researchers all around the world have been conducting

researches on how to improve the quality of mathematics

education. Various strategies have been tried by researchers

to improve the performance of students in Mathematics and

these strategies were found to be effective. Taylaran (2015)

studied the effects of Students Participation Dominated (SPD)

and Lecture Discussion Dominated (LDD) instructions on the

performance and anxiety level of the students in Mathematics

9 of Quezon National High School. The results of the study

showed that students’ performance in the Students

Participation Dominated (SPD) instruction were significantly

higher than those of the Lecture Discussion Dominated (LDD)

instruction regarding the pretest, posttest, and retention test

scores. The Gradual Release of Responsibility Instructional

Model in the ―I do it‖ phase is related to the Lecture

Discussion Dominated Instruction and the ―You do it together‖

phase is connected to the Students Participation Dominated

Instruction. The study of Villaver (2014) which aimed to

determine the effects of Experiential Learning Approach on

the Mathematics Performance and Attitude of the students

showed that the students’ level of performance in the pre- and

post-exposure of the experiential learning environment were

at the beginning level. The increase in scores is statistically

significantly higher compared to the pre-test. She also found

out that the conceptual retention is also at the beginning level,

but is not significantly different from the posttest scores.

Increase in the mathematics performance of students in the

study of Taylaran and Villaver supports the study of Miñao

(2013) on the effects of Multiple Intelligence-based Instruction

in the students’ performance and attitudes in Intermediate

Algebra. Performance of students exposed to Multiple

Intelligence-based Instruction (MIBI) was significantly higher

than those in the Non-Multiple Intelligence-based Instruction

group in terms of posttest scores. Calfoforo (2013) conducted

a research on the effects of the Multiple Representation-

Based Instruction to students’ performance and attitude in

Algebra. The researcher also made use of multiple

representations (listing, table, graph, function) in presenting

lessons about quadratic functions during the ―I do it‖ phase.

The study of Calfoforo supports the study of Miñao where she

found out that students’ performance in the Multiple

Representation-based Instruction group was significantly

higher than that in the Traditional Method of Instruction in

terms of the pretest, posttest, and retention test. Also, the

researcher considered the multiple intelligences of the

students in planning the lesson to cater to other forms of

intelligence. In addition, Ciubal and Tan (2018) studied about

the effects of using the Mathematics Communication

Strategies to students’ performance and attitude towards

Mathematics. The results showed that students exposed to

Mathematics Communication Strategies (MCS) had a

performance significantly higher than that in the Non-MCS

group regarding posttest and retention test. The positive

results in the study of Ciubal and Tan confirmed the study of

Paglinawan (2011) who conducted a study to examine the

effects of Interactive Computer-Assisted Instruction (CAI) on

the attitude and performance in High School Geometry of

sophomore students of Central Mindanao University

Laboratory High School. His study showed that students’

performance in the Computer-Assisted Instruction group were

significantly higher than those in the Non-Computer-Assisted

Instruction group in terms of posttest, retention test, and gain

scores. Environments that are rich in mathematical

opportunities for students are important if we want our

children to develop a deep understanding of Mathematics

(Sammons, 2010). Mathematics instruction can be enhanced

further through the use of technology such as Computer-

Assisted Instruction and tablet or smartphone which the

researcher used in explaining the graphs of quadratic

function. On the other hand, Ponsica (2011) administered a

study to find out the effect of UbD learning plan and an

NCTM-based lesson plan on the achievement and attitude

towards Mathematics of the first-year high school students of

Lake View Academy. The results of her study showed that

there was no significant difference in the pretest and posttest

scores between UbD-based learning plan and NCTM-based

lesson plan. It was also found out that the students under the

UbD-based learning plan and NCTM-based lesson plan

improved in their learning competencies. Another study by

Bermejo (2009) determined the effects of the Mathematics

Journal Writing on the learning skills and attitude of the senior

students of Bocboc National High School. Students exposed

to journal writing improved more in their learning

competencies than those who were not. The high achievers

and girls exposed to journal writing performed better than

those who were not exposed. It was also found out that

classroom instruction that incorporates journal writing gave a

positive relationship between attitude towards Mathematics

and learning competencies such as conceptual and

procedural understanding, problem-solving, and mathematical

communication. Ebuña (2008) administered a study to

determine the effects of vignette classroom technique on the

mathematics understanding of students, specifically on the

conceptual understanding and the computational skills of the

students. It was found out in her study that vignette classroom

technique which entails student discourse, and maximum

student involvement gave positive effects on the conceptual

understanding and computational skills of students on first-

degree equations and inequalities in one variable. Aside from

vignette classroom technique as used by Ebuña, Canarecio

(1998) made use of game-aided lessons and determine its

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effect on the students’ performance, retention ability, and

attitude towards Mathematics. His study showed that there

was a significant difference in the pretest scores between

Experimental and Control groups. Aside from that, there was

a significant difference in the pretest and posttest scores of

the Experimental group. However, there was no significant

difference in the retention test scores between Experimental

and Control groups. The study of Bersano (2016) supports the

study of Canarecio when she conducted a similar study on the

effects of Game-Aided Instruction to Grade 8 students’

mathematics performance and anxiety level. Her study

showed that there was an increase in the students’

mathematics performance as shown in their pretest, posttest

and retention test scores. Mathematics teachers and

researchers also have determined other factors that would

affect student’s performance in Mathematics. Velasquez and

Tan (2007) conducted a study to ascertain whether the

teachers’ teaching styles and students’ learning styles will

influence the academic performance of the students in

Mathematics, English and Science and Technology. Results

showed that teachers’ age, position and national seminars

attended were significantly correlated with the students’

academic performance. A highly significant relationship was

also established between the students’ academic

performance and learning styles. The majority of the students

got average grades except for students with avoidant learning

style, and only a few of them got high academic performance

in the rest of the learning styles. Correlation analysis also

revealed a significant relationship between the teachers’

teaching styles and the academic performance of the students

in Mathematics. In addition, Venkatesan and Karimi (2010)

found out in their study entitled ―Mathematics Anxiety,

Mathematics Performance and Overall Academic

Performance in High School Students‖ that Mathematics

anxiety significantly has a negative correlation with

Mathematics performances and overall academic

performance. Moreover, it was also found that there is a

significant gender difference in Mathematics anxiety. Aside

from that, there is no significant difference between boys and

girls in Mathematics performances and academic

performance. On the other hand, Andaya (2014) pointed out

other factors that would affect the achievements of students in

Mathematics such as individual, instructional, classroom

management and evaluation factors. Findings revealed that

the gains of students in Math Courses (Fundamental

Mathematics and Contemporary Mathematics) are poor and

students perform low in both subjects. Mathematics

achievements are highly correlated to individual and

instructional factors and moderately correlated with classroom

management and evaluation factors, and the instructional

factor is one of the factors that affects most the achievements

of students in Mathematics. What should the mathematics

teachers do as well as the school to improve the mathematics

performance of the Filipino students? It is in this perspective

that the researcher of this study was encouraged to explore

and use the Gradual Release of Responsibility Instructional

Model (GRRIM) to improve the performance of students in

Mathematics and increase their self-efficacy towards

Mathematics. GRRIM will allow the teachers to work with

small groups that are determined specifically by students’

achievement levels and needs which allow teachers to closely

observe student work, monitor student attention, provide

strong support for struggling learners, and provide extra

challenges for proficient learners.

1.1 Statement of the Problem

This study assessed the mathematics performance and self-

efficacy of Grade 9 students in a gradual release of

responsibility instructional model (GRRIM). Specifically, it

sought to answer the following questions:

1. What is the performance level of students exposed to

GRRIM and those exposed to non-GRRIM in terms of:

a. pretest;

b. posttest; and

c. retention test?

2. What is the self-efficacy level of the students exposed to

GRRIM and those exposed to non-GRRIM in terms of:

a. mastery experiences;

b. vicarious experiences;

c. verbal-social persuasion; and

d. physiological and emotional arousal?

3. Is there a significant difference in the performance of

students exposed to GRRIM and those exposed to non-

GRRIM in terms of:

a. posttest; and

b. retention test?

4. Is there a significant difference in the self-efficacy level of

the students exposed to GRRIM and those exposed to non-

GRRIM in terms of:

a. mastery experiences;

b. vicarious experiences;

c. verbal-social persuasion; and

d. physiological and emotional arousal?

2 METHODOLOGY

2.1 Research Design

This study utilized the quasi-experimental design with an

intact group of two sections. The dependent variables are the

students’ self-efficacy level and Mathematics performance in

terms of the pretest, posttest, and retention test. The two

groups of students were taught the same lessons. Gradual

Release of Responsibility Instructional Model was

implemented in teaching the experimental group during the

third grading period while the traditional method of teaching

was utilized in the control group. Pretest and Self-efficacy

tests were administered to the students before the start of the

experiment. The experiment was conducted during the entire

1st Grading Period as indicated in the course outline and

classes were held three hours per week. After the 1st Grading

Period, students took the same test which served as posttest

and the same self-efficacy test. These tests were employed to

determine the extent of learning of the students and whether

there was a change in the mathematics performance and self-

efficacy level. One week after the posttest, the same test was

also conducted to verify the retention of the students.

2.2 Locale of the Study

This study was conducted at Central Mindanao University

Laboratory High School, University Town, Musuan, Bukidnon.

CMULHS is under the regulation of the Commission on

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Higher Education which implements a Science High School

Curriculum and is a laboratory school of the College of

Education, Central Mindanao University. It is headed by a

dynamic principal supported by 35 competent faculty and staff

members. With the implementation of the K to 12 curriculum,

the school offers the Science, Technology, Engineering and

Math (STEM) strand to its junior high school completers.

During the conduct of the study, the school has 559 junior

high school students and 115 senior high school students with

a total of 674 students.

2.3 Classroom Instruction in GRRIM

Focus lesson (I Do It) is the first phase of the gradual release

of responsibility model. This is the when the teacher is

demonstrating, modeling and sharing his or her own thinking

with the students. Although this part may be brief (5-15

minutes), it is powerful. The three methods used most often in

the focus lesson phase are modeling, metacognitive

awareness, and think-aloud. Another phase of instruction

happens as teachers meet with needs-based groups. Guided

instruction (We Do It) is almost always done with small,

purposeful groups, which are composed based on students’

performance on the formative assessment. In this phase,

small group arrangements are evident and grouping changes

throughout the grading period. Dialogue is evident between

learners and the teacher as they begin to apply the skill or

strategy. The teacher also uses cues and prompts to support

understanding when a student commits an error and does not

directly tell the student the right answer. Collaborative

Instruction (You Do It Together) is the often neglected phase

of instruction. It is a special event and not just an established

instructional routine. When collaborative learning is done

right, it is during this phase that students combine their

thinking and understanding. Negotiating with peers,

deliberating ideas and information, or discussing with others

causes students to use what they have gained in focus

lessons and guided teaching. Collaborative learning is not just

the time to introduce novel information to students. Rather,

cooperative learning should be a venue for students to apply

information in new situations or to engage in a spiral

evaluation of prior knowledge. The last phase is the

Independent Learning (You Do It Alone). The ultimate goal of

this instruction is that students can independently apply

information, ideas, content, skills, and strategies in unique

situations. In this phase, students have received modeled,

guided, and cooperative learning experiences connected to

concepts needed to accomplish independent tasks.

Independent tasks cover beyond practice to application and

extension of novel knowledge. The teacher meets with

individual students for conferencing about the independent

learning tasks. Independent tasks will be given to the students

that would require the individual application of information

formerly taught. These tasks should provide students with

chances to use their knowledge to create new products.

2.4 Instrumentation

The researcher developed a 46-item mathematics

performance test (see Appendix K) on the covered topic

(quadratic equations, quadratic functions, graphs, and

properties). It was a test obtained from the 50-item first

periodic examination. The test obtained a KR21 reliability

coefficient of 0.867 using the item analysis software

developed by Bermundo, Bermundo and Ballester (2004).

The test’s table of specifications (TOS) was based on the

Department of Education’s Curriculum Guide for K to 12

Curriculum Grade 9 Mathematics (see Appendix F). Pretest,

posttest, and retention test were conducted before and after

the first grading period to measure the mathematics

performance of the students. The scale used to interpret the

score is as follows:

Range

Interpretation

90% - 100%

86 % - 89%

80% - 85%

75% - 79%

65% - 74%

Very High

High

Moderate

Low

Very Low

The Sources of Mathematics Self-Efficacy Scale is a 24-item

scale adapted from the work of Usher and Pajares (2009) and

an e-mail was sent by the author as permission to use their

instrument. The items were created to assess each of the four

sources of self-efficacy: mastery experience, vicarious

experience, social persuasions, and physiological and

affective state as described in the work of Bandura (1997)

entitled ―Self-Efficacy: The Exercise of Control.‖ Students’

responses were assessed using a 6-point Likert-type scale

modified for use with middle school students. Students were

asked to circle letters (T or F) in varying font sizes to indicate

how much each statement applied to them. It had gone

through two phases before it was finalized. Based on the

results, the author retained six items to represent each of the

four hypothesized sources with the alpha reliability

coefficients 0.88, 0.84, 0.88, and 0.87 for the final four

subscales respectively. This Sources of Mathematics Self-

Efficacy Scale was pilot tested to the Grade-9 students of

Valencia National High School (see Appendix N) which yields

a reliable instrument (see Appendix O). The scale used to

interpret the data gathered is as follows:

Descriptive Rating

Range

Interpretation

Definitely True

Mostly True

A little bit True

A little bit False

Mostly False

Definitely False

4.51-5.00

3.51-4.50

2.51-3.50

1.51-2.50

0.51-1.50

0.00-0.50

Very High

High

Moderately High

Moderately Low

Low

Very Low

2.5 Statistical Technique

Descriptive Statistics such as frequency counts, percentage,

mean and standard deviation were used to describe the

performance level of students in Mathematics and the self-

efficacy level of students in terms of (a) mastery experiences;

(b) vicarious experiences; (c) verbal-social persuasion; and

(d) physiological and emotional arousal. Analysis of

Covariance (ANCOVA) was used to determine if there is a

significant difference in the performance of students exposed

to GRRIM and those exposed to non-GRRIM in terms of (a)

posttest, and (b) retention test. ANCOVA was also used to

ascertain if there is a significant difference in the self-efficacy

level of the students exposed to GRRIM and those exposed to

non-GRRIM in terms of (a) mastery experiences; (b) vicarious

experiences; (c) verbal-social persuasion; and (d)

physiological and emotional arousal.

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3 RESULTS AND DISCUSSIONS

3.1 Mathematics Performance of Students

The Mathematics performance of the students exposed to

GRRIM and those exposed to non-GRRIM in terms of pretest

is presented in Table 1. As shown in Table 1, 2 students or

4.08% of the students in the GRRIM group had a low

performance and 47 students or 95.92% had a very low

performance in the pretest. On the other hand, 1 student or

2.04% of the students in the non-GRRIM group had a

moderate performance, 4 students or 8.16% had a low

performance and 45 students or 91.84% had a very low

performance in the pretest. The overall mean score of the

GRRIM group in the pretest is 11 which indicates a very low

performance while the non-GRRIM group has an overall

mean score of 12.69 which also indicates a very low

performance.

Table 1. Mathematics performance of students exposed to

GRRIM and those exposed to non-GRRIM in terms of

pretest.

Range

GRRIM

Non-GRRIM

f

%

Interpretation

f

%

Interpretation

90% -

100%

0

0

Very High

0

0

Very High

86 % -

89%

0

0

High

0

0

High

80% -

85%

0

0

Moderate

1

2.04

Moderate

75% -

79%

2

4.08

Low

4

8.16

Low

65% -

74%

47

95.92

Very Low

45

91.84

Very Low

(Very Low)

(Very Low)

The result of this study shows that both groups had a very low

level of performance in the pretest. It supports the study of

Bersano (2016) when she found out that the students’

performance in Mathematics in terms of pretest before

exposure to Game-Aided Instruction is very low. It also

supports the study of Villaver (2014) when she showed that

the level of mathematics performance of students before

exposure to experiential learning environment is in the

beginning level which indicates a very low performance.

Furthermore, this study also supports the study of Catli (2016)

when she found out that the mathematics performance of

students exposed to ICT-Integrated Instruction and those

exposed to non-ICT-Integrated Instruction showed a very low

performance. Table 2 shows the Mathematics performance of

the students exposed to GRRIM and those exposed to non-

GRRIM in terms of posttest. It can be seen in Table 2 that 6

students or 12.24% of the students in the GRRIM group had a

very high performance, 6 students or 12.24% had a high

performance, 14 students or 28.57% had a moderate

performance, 12 students or 24.49% had a low performance,

and 11 students or 22.45% had a very low performance in the

posttest. On the contrary, 8 students or 16.33% of the

students in the non-GRRIM group had a very high

performance, 3 students or 6.12% had a high performance,

10 students or 20.41% had a moderate performance, 12

students or 24.49% had a low performance, and 16 students

or 32.65% had a very low performance in the posttest. The

overall mean score of the GRRIM group in the posttest is

23.67 which indicates a moderate performance while the non-

GRRIM group has an overall mean score of 21.78 which

indicates a low performance.

Table 2. Mathematics performance of students exposed to

GRRIM and those exposed to non-GRRIM in terms of

posttest.

Range

GRRIM

Non-GRRIM

f

%

Interpretation

f

%

Interpretation

90% - 100%

6

12.24

Very High

8

16.33

Very High

86 % - 89%

6

12.24

High

3

6.12

High

80% - 85%

14

28.57

Moderate

10

20.41

Moderate

75% - 79%

12

24.49

Low

12

24.49

Low

65% - 74%

11

22.45

Very Low

16

32.65

Very Low

(Moderate)

(Low)

Table 2 shows that the GRRIM group had a moderate

performance level while the non-GRRIM group had a low

performance level. Villaver (2014) presented that the

mathematics performance of the students in the posttest after

exposure to experiential learning environment is still in the

beginning level which indicates a very low performance is not

in consonance to the result of this study. The result of this

study also disagree to the study of Bersano (2016) when

majority of the students’ mathematics performance after

exposure to Game-Aided Instruction is still in the very low

level. Moreover, it also contradicts to the study of Catli (2016)

when she found out that the level of mathematics competency

of students exposed to ICT-Integrated Instruction in terms of

posttest is moving towards mastery which indicates a high

performance. The Mathematics performance of the students

exposed to GRRIM and those exposed to non-GRRIM in

terms of retention test is presented in Table 3. It can be

gleaned in Table 3 that 3 students or 6.12% of the students in

the GRRIM group had a very high performance, 3 students or

6.12% had a high performance, 13 students or 26.53% had a

moderate performance, 16 students or 32.65% had a low

performance, and 14 students or 28.57% had a very low

performance in the retention test. On the other hand, 7

students or 14.28% of the students in the non-GRRIM group

had a very high performance, 4 students or 8.16% had a high

performance, 8 students or 16.33% had a moderate

performance, 10 students or 20.41% had a low performance,

and 20 students or 40.82% had a very low performance in the

retention test. The overall mean score of the GRRIM group in

the posttest is 21.78 which indicates a low performance while

the non-GRRIM group has an overall mean score of 21.10

which indicates a low performance.

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Table 3. Mathematics performance of students exposed to

GRRIM and those exposed to non-GRRIM in terms of

retention test.

Range

GRRIM

Non-GRRIM

f

%

Interpretation

f

%

Interpretation

90% -

100%

3

6.12

Very High

7

14.28

Very High

86 % -

89%

3

6.12

High

4

8.16

High

80% -

85%

13

26.53

Moderate

8

16.33

Moderate

75% -

79%

16

32.65

Low

10

20.41

Low

65% -

74%

14

28.57

Very Low

20

40.82

Very Low

(Low)

(Low)

The result of this study shows that the students’ mathematics

performance in the retention test is in the low level. Catli

(2016) found out in her study that the level of mathematical

competency of students in terms of retention test exposed to

non-ICT-Integrated Instruction is in the low level which is

supported by this study but the level of mathematical

competency of students in terms of retention test exposed to

ICT-Integrated Instruction is in the average level which is not

parallel to the result of this study. This does not support the

study of Bersano (2016) when majority of the students’

mathematics performance after exposure to Game-Aided

Instruction is in the very low level. In addition, this study does

not support the result of the study of Villaver (2014) that the

conceptual retention of students exposed to experiential

learning environment is still in the beginning level which

indicates a very low performance. Majority of the students

both in the GRRIM and non-GRRIM group had a low and very

low performance level before the intervention which implies

that majority of the students have poor performance in

Mathematics. Both groups improved their mean score after

the intervention. In the retention test, both groups show a

decline in the mean score but still the GRRIM group has a

higher mean than that of the non-GRRIM group. The results

of this study show that when a class is exposed to various

instructional models, the students’ performance increases and

the retention rate is higher as shown in their posttest and

retention test scores after the treatment. However, decline of

the mean score in the retention test of the students may be

caused by the delayed conduct of the retention test due to

school activities. These results conform to the study of De

Asis (2012) on the effects of cooperative and mastery learning

on grade six pupils’ performance in Mathematics, wherein the

level of pupils’ performance in the subject exposed to mastery

and cooperative learning increased. The cooperative learning

group had the greatest increase among the three groups and

this finding suggests that the ―You do it together‖ phase in the

Gradual Release of Responsibility Instructional Model may

possibly cause the increase in students’ performance in

Mathematics and must be used in every classroom. In

addition, the result is in consonance to the study of Silabay

(2002) about the use of Cooperative Computer Assisted

Instruction which shows higher result as compared to the

Individualized Computer Assisted Instruction. It also supports

the study of Asparin (2013) wherein he found out that the

students’ level of mathematics achievement is very poor. The

study of Cordova (2015) is parallel to the result of this study

wherein she found out that the mathematics proficiency and

performance level of Grade 9 students at private high schools

in Valencia City was described as beginning which means

that the students have a low performance in Mathematics.

3.2 Students’ Self-Efficacy

As shown in Table 4, two items with higher means in the

GRRIM group before the intervention are ―I do well on math

assignments‖ (2.88) and ―I got good grades in math on my

last report card‖ (2.31). However, two items with higher

means in the non-GRRIM group are ―I do well on math

assignments‖ (3.20) and ―Even when I study very hard, I do

poorly in math‖ (2.67). These results indicate that both groups

had moderately high self-efficacy on mastery experience in

terms of ―I do well in math assignments‖ before the

intervention. Also, the non-GRRIM group had moderately high

self-efficacy on mastery experience in terms of ―Even when I

study very hard, I do poorly in math‖, and ―I got good grades

in math on my last report card‖ before the intervention. Table

4 also shows that both the GRRIM and non-GRRIM group

have the same two items with lower means which are ―I do

well on even the most difficult math assignments‖ (1.90 and

1.80, respectively) and ―I have always been successful in

math‖ (2.00 and 1.96, respectively). Table 5 shows that both

the GRRIM and non-GRRIM group have the same two items

with higher means which are ―Seeing kids do better than me

in math pushes me to do better‖ (3.16 and 3.45, respectively)

and ―Seeing adults do well in math pushes me to do better‖

(3.06 and 3.41, respectively).

Table 4. Self-efficacy level of students towards Mathematics (mastery experiences) between GRRIM and non-GRRIM group

before intervention.

Self-efficacy Towards Mathematics

(Mastery Experiences)

GRRIM

Non-GRRIM

Mean

Interpretation

Mean

Interpretation

I make excellent grades on math tests.

2.27

Moderately Low

2.16

Moderately Low

I have always been successful with math.

2.00

Moderately Low

1.96

Moderately Low

Even when I study very hard, I do poorly in math.*

2.14

Moderately Low

2.67

Moderately High

I got good grades in math on my last report card.

2.31

Moderately Low

2.53

Moderately High

I do well on math assignments.

2.88

Moderately High

3.20

Moderately High

I do well on even the most difficult math assignments.

1.90

Moderately Low

1.80

Moderately Low

Overall Mean Interpretation

2.24

Moderately Low

2.40

Moderately Low

*negative indicators (scoring is reversed)

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Legend:

Range

Descriptive Rating

Qualitative Interpretation

4.51 – 5.00

Definitely True

Very High

3.51 – 4.50

Mostly True

High

2.51 – 3.50

A little bit True

Moderately High

1.51 – 2.50

A little bit False

Moderately Low

0.51 – 1.50

Mostly False

Low

0.00 – 0.50

Definitely False

Very Low

Table 5. Self-efficacy level of students towards Mathematics (vicarious experiences) between GRRIM and non-GRRIM group

before intervention.

Self-efficacy Towards Mathematics

(Vicarious Experiences)

GRRIM

Non-GRRIM

Mean

Interpretation

Mean

Interpretation

Seeing adults do well in math pushes me to do better.

3.06

Moderately High

3.41

Moderately High

When I see how my math teacher solves a problem, I can picture myself

solving the problem in the same way.

2.92

Moderately High

2.65

Moderately High

Seeing kids do better than me in math pushes me to do better.

3.16

Moderately High

3.45

Moderately High

When I see how another student solves a math problem, I can see myself

solving the problem in the same way.

2.63

Moderately High

2.73

Moderately High

I imagine myself working through challenging math problems successfully.

2.78

Moderately High

2.45

Moderately Low

I compete with myself in math.

2.70

Moderately High

2.40

Moderately Low

Overall Mean Interpretation

2.88

Moderately High

2.90

Moderately High

Legend:

Range

Descriptive Rating

Qualitative Interpretation

4.51 – 5.00

Definitely True

Very High

3.51 – 4.50

Mostly True

High

2.51 – 3.50

A little bit True

Moderately High

1.51 – 2.50

A little bit False

Moderately Low

0.51 – 1.50

Mostly False

Low

0.00 – 0.50

Definitely False

Very Low

The results show that both groups had moderately high self-

efficacy on vicarious experiences. It was also shown that the

GRRIM group had a moderately high self-efficacy on vicarious

experiences in all the indicators while the non-GRRIM group

had a moderately high self-efficacy on vicarious experiences

in terms of ―Seeing adults do well in math pushes me to do

better‖, ―When I see how my math teacher solves a problem, I

can picture myself solving the problem in the same way‖,

―Seeing kids do better than me in math pushes me to do

better‖ and ―When I see how another student solves a math

problem, I can see myself solving the problem in the same

way.‖ As shown in Table 5, two items with lower means in the

GRRIM group before the intervention are ―When I see how

another student solves a math problem, I can see myself

solving the problem in the same way‖ (2.63) and ―I compete

with myself in math‖ (2.70). On the other hand, two items with

lower means in the non-GRRIM group are ―I compete with

myself in math‖ (2.40) and ―I imagine myself working through

challenging math problems successfully‖ (2.45). The study

conducted by Zimmerman (1989) showed the superiority of

coping models which is related to vicarious experiences. In

his study where he compared an errorless model and a model

showing gradual elimination of errors, the coping model raised

children’s self-efficacy perceptions 86% from pretesting to

post-testing. It can be seen in Table 6 that the two items with

higher means in the GRRIM group before the intervention are

―My math teachers have told that I am good at learning math‖

(2.18) and ―Adults in the family have told me what a good

math student I am‖ (1.96). On the contrary, two items with

higher means in the non-GRRIM group are ―Adults in the

family have told me what a good math student I am‖ (1.69)

and ―Other students have told me that I’m good at learning

math‖ (1.61). Results show that the GRRIM group had a

moderately low self-efficacy on verbal-social persuasion in all

the indicators. The non-GRRIM group had a moderately low

self-efficacy on verbal-social persuasion in terms of ―Adults in

my family have told me what a good math student I am‖ and

―Other students have told me that I’m good at learning math‖

while the rest of the indicators had a low self-efficacy on

verbal-social persuasion. It was shown also in Table 6 that the

two items with the lower means in the GRRIM group are

―People have told me that I have a talent for math‖ (1.59) and

―Other students have told me that I’m good at learning math‖

(1.73). However, two items in the non-GRRIM group with a

lower mean score are ―People have told me that I have a

talent for math‖ (1.35) and ―I have been praised for my ability

in math‖ (1.35). The result of the study conducted by

Kampkuiper (2015) about the effect of positive and negative

feedback on self-efficacy, cognitive trust and affective trust

using coded video-based observations for feedback durations

and questionnaires for measuring self-efficacy, cognitive and

affective trust suggests that negative feedback is negatively

related to self-efficacy and cognitive trust. This supports the

result of this study wherein those exposed to GRRIM had a

higher self-efficacy level as compared to those exposed to

non-GRRIM.

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Table 6. Self-efficacy level of students towards Mathematics (verbal-social persuasion) between GRRIM and non-GRRIM group

before intervention.

Self-efficacy Towards Mathematics

(Verbal-Social Persuasion)

GRRIM

Non-GRRIM

Mean

Interpretation

Mean

Interpretation

My math teachers have told that I am good at learning math.

2.18

Moderately Low

1.37

Low

People have told me that I have a talent for math.

1.59

Moderately Low

1.35

Low

Adults in my family have told me what a good math student I am.

1.96

Moderately Low

1.69

Moderately Low

I have been praised for my ability in math.

1.78

Moderately Low

1.35

Low

Other students have told me that I’m good at learning math.

1.73

Moderately Low

1.61

Moderately Low

My classmates like to work with me in math because they think I’m good at

it.

1.90

Moderately Low

1.40

Low

Overall Mean Interpretation

1.86

Moderately Low

1.50

Low

Legend:

Range

Descriptive Rating

Qualitative Interpretation

4.51 – 5.00

Definitely True

Very High

3.51 – 4.50

Mostly True

High

2.51 – 3.50

A little bit True

Moderately High

1.51 – 2.50

A little bit False

Moderately Low

0.51 – 1.50

Mostly False

Low

0.00 – 0.50

Definitely False

Very Low

In Table 7, the two items with higher means in the GRRIM

group before the intervention are ―I get depressed when I

think about learning math‖ (2.53) and ―My whole body

becomes tense when I have to do math‖ (2.33). On the other

hand, two items with higher means in the non-GRRIM group

are ―I get depressed when I think about learning math‖ (3.18)

and ―My mind goes blank and I am unable to think clearly

when doing math work‖ (3.16). The result shows that in the

GRRIM group, the only indicator with a moderately high self-

efficacy is ―I get depressed when I think about learning math‖

and the rest are moderately low. Results also show that the

non-GRRIM group had a moderately high self-efficacy on

physiological and emotional arousal in all the indicators. As

shown in Table 7, the item with the lowest mean in the

GRRIM group before the intervention is ―I start to feel

stressed-out as soon as I begin my math work‖ (2.2).

However, two items in the non-GRRIM group with a lower

mean score are ―Just being in math class makes me feel

stressed and nervous‖ (2.65) and ―Doing math work takes all

of my energy‖ (2.67). The over-all mean score of the students

under CPAAG in Math anxiety is 2.86 (uncertain) and that of

students under non-CPAAG is 2.94 (uncertain). Both groups

disagreed on statement that they won’t worry in solving math

problems. It means that they feel worried in solving Math

problems. Thus, prior to the conduct of the study the anxiety

level of the students are neutral. It conforms to the study of

Bersano (2016) wherein her study found out that during the

pre-test the respondents have moderate level of anxiety or

neutral.

Table 7. Self-efficacy level of students towards Mathematics (physiological and emotional arousal) between GRRIM and non-

GRRIM group before intervention.

Self-efficacy Towards Mathematics

(Physiological and Emotional Arousal)

GRRIM

Non-GRRIM

Mean

Interpretation

Mean

Interpretation

Just being in math class makes me feel stressed and nervous.*

2.24

Moderately Low

2.65

Moderately High

Doing math work takes all of my energy.*

2.24

Moderately Low

2.67

Moderately High

I start to feel stressed-out as soon as I begin my math work.*

2.20

Moderately Low

2.90

Moderately High

My mind goes blank and I am unable to think clearly when doing math

work.*

2.31

Moderately Low

3.16

Moderately High

I get depressed when I think about learning math.*

2.53

Moderately High

3.18

Moderately High

My whole body becomes tense when I have to do math.*

2.33

Moderately Low

3.04

Moderately High

Overall Mean Interpretation

2.31

Moderately Low

2.94

Moderately High

*negative indicators (scoring is reversed)

Legend: (similar to Table 6)

Table 8 summarizes the comparison of students’ sources of

self-efficacy towards mathematics between GRRIM and non-

GRRIM before intervention in terms of mastery experiences,

vicarious experiences, verbal-social persuasion, and

physiological and emotional arousal. In the GRRIM group, the

source of self-efficacy with the highest mean is vicarious

experience (2.88) while the lowest is verbal-social persuasion

(1.86). In the non-GRRIM group, the source of self-efficacy

with the highest mean is physiological and emotional arousal

(2.94) while the lowest is verbal-social persuasion (1.50). As

reflected in Table 8, the overall mean of self-efficacy of the

GRRIM group before the intervention is 2.32 which indicates a

moderately low self-efficacy while the overall mean of self-

efficacy of the non-GRRIM group before the intervention is

2.41 which means that the group has a moderately low self-

efficacy. The GRRIM group builds their self-efficacy in

Mathematics through the vicarious experience of observing

others. They measure their performance in Mathematics by

comparing it with the performance of others. They are also

fond of comparing their performance to others like their

classmates and adults as they make judgment about their

own mathematical capabilities. On the other hand, the Non-

GRRIM group builds their self-efficacy in Mathematics by

avoiding stress and staying calm, setting their minds in a

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positive mood during math classes, and taking problems

slowly to avoid being tensed during math classes. The results

disagree with what Bandura (1986, 1997) hypothesized that

among the four sources of self-efficacy, the most powerful is

the mastery experience or the students’ interpreted result

from their previous accomplishments. In can be seen in Table

8 that in the GRRIM group, the source of self-efficacy with the

highest mean is vicarious experience (2.88), while in the non-

GRRIM group the source of self-efficacy with the highest

mean is physiological and emotional arousal (2.94). Table 9

on the next page sums up the comparison of students’

sources of self-efficacy towards mathematics between

GRRIM and non-GRRIM after intervention in terms of mastery

experiences, vicarious experiences, verbal-social persuasion,

and physiological and emotional arousal. In the GRRIM

group, the source of self-efficacy with the highest mean is

vicarious experiences (2.98) while the lowest is verbal-social

persuasion (1.83). In the non-GRRIM group, the source of

self-efficacy with the highest mean is physiological and

emotional arousal (2.84) and the lowest is verbal-social

persuasion (1.51).

Table 8. Summary of the Students Self-Efficacy Levels between GRRIM and Non- GRRIM group before intervention.

Self-efficacy Towards Mathematics

GRRIM

Non-GRRIM

Mean

Interpretation

Mean

Interpretation

Mastery Experiences

2.24

Moderately Low

2.40

Moderately Low

Vicarious Experiences

2.88

Moderately Low

2.90

Moderately High

Verbal-Social Persuasion

1.86

Moderately Low

1.50

Low

Physiological and Emotional Arousal

2.31

Moderately Low

2.94

Moderately High

Overall Mean Interpretation

2.32

Moderately Low

2.41

Moderately Low

Legend:

Range

Descriptive Rating

Qualitative Interpretation

4.51 – 5.00

Definitely True

Very High

3.51 – 4.50

Mostly True

High

2.51 – 3.50

A little bit True

Moderately High

1.51 – 2.50

A little bit False

Moderately Low

0.51 – 1.50

Mostly False

Low

0.00 – 0.50

Definitely False

Very Low

As presented in Table 9, the overall mean of self-efficacy of

the GRRIM group after the intervention is 2.41 which indicates

a moderately low self-efficacy while the overall mean of self-

efficacy of the non-GRRIM group after the intervention is 2.34

which also means that the group had moderately low self-

efficacy. However, it is noteworthy to mention that GRRIM

group had higher mean in all sources of self-efficacy

compared to the non-GRRIM group except for physiological

and emotional arousal. This shows that interventions must be

done to increase their self-efficacy especially in the

physiological and emotional arousal. It can also be observed

that the GRRIM group had a higher overall mean of self-

efficacy (2.41) as compared to the non-GRRIM group after the

intervention (2.34) although both group had moderately low

self-efficacy. This is in contrast to the results before

intervention wherein the non-GRRIM had a higher overall

mean of self-efficacy (2.41) as compared to the GRRIM group

(2.32) as presented in Table 9. The GRRIM group builds their

self-efficacy in Mathematics through the vicarious experience

of observing others. They measure their performance in

Mathematics by comparing it with the performance of others.

They are also fond of comparing their performance with

others like their classmates and adults as they make

judgment about their own mathematical capabilities. On the

other hand, the non-GRRIM group builds their self-efficacy in

Mathematics by avoiding stress and staying calm, setting their

minds in a positive mood during math classes, and taking

problems slowly to avoid being tense during math classes.

The results of this study after intervention did not conform to

what Bandura (1986, 1997) hypothesized that among the four

sources of self-efficacy, the most powerful is the mastery

experience or the students’ interpreted result from their

previous accomplishments. In can be seen in Table 13 that in

the GRRIM group, the source of self-efficacy with the highest

mean is vicarious experience (2.98), while in the non-GRRIM

group, the source of self-efficacy with the highest mean is

physiological and emotional arousal (2.84).

Table 9. Summary of the Students Self-Efficacy Levels between GRRIM and non-GRRIM group after intervention.

Self-efficacy Towards Mathematics

GRRIM

Non-GRRIM

Mean

Interpretation

Mean

Interpretation

Mastery Experiences

2.36

Moderately Low

2.28

Moderately Low

Vicarious Experiences

2.98

Moderately High

2.73

Moderately High

Verbal-Social Persuasion

1.83

Moderately Low

1.51

Moderately Low

Physiological and Emotional Arousal

2.46

Moderately Low

2.84

Moderately High

Overall Mean Interpretation

2.41

Moderately Low

2.34

Moderately Low

Legend:

Range

Descriptive Rating

Qualitative Interpretation

4.51 – 5.00

Definitely True

Very High

3.51 – 4.50

Mostly True

High

2.51 – 3.50

A little bit True

Moderately High

1.51 – 2.50

A little bit False

Moderately Low

0.51 – 1.50

Mostly False

Low

0.00 – 0.50

Definitely False

Very Low

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3.3 Analysis of Covariance of Posttest Results Between

GRRIM and non-GRRIM

Table 10 shows the analysis of covariance (ANCOVA) of

posttest results between treatments. As shown in the table,

the pretest was used as covariate to statistically equate

dissimilar prognostic variables which may have an effect on

the analysis. The F value between groups is 4.511 with a

probability value of 0.036 ( ) indicating a highly

significant difference, thus the null hypothesis that there is no

significant difference in students’ performance in terms of

posttest is rejected. This means that GRRIM group with mean

23.67 performed better than the non-GRRIM group with mean

21.78. Several studies were conducted which conform to the

result of this study that used varied teaching strategies to

improve the quality of mathematics instruction. The study of

Ciubal & Tan (2018) is supported by the result of this study

wherein there is a significant difference in the posttest scores

of the experimental group as compared to the control group

when exposed to Mathematics Communication Strategies

(MCS) which was also utilized by the researcher in the ―You

do it together‖ phase and ―You do it alone‖ phase of the

lesson. The result of the study also conforms to Calfoforo

(2013) wherein she found out that the students’ posttest

scores in the Multiple Representation-Based Instruction group

was significantly higher than in the Traditional Method of

Instruction. Also, it conforms with the findings of Miñao when

she found out that the students’ posttest scores in the Multiple

Intelligence-Based Instruction (MIBI) group was significantly

higher than in the non-MIBI group. However, it contradicts to

the result of the study of Ponsica (2011) wherein she found

out that there was no significant difference in the posttest

scores between the UbD-based learning plan group and

NCTM-based lesson plan group. It also contradicts to the

study of Catli (2016) when she showed that there was no

significant difference in the mathematical competency for the

students when exposed to ICT-Integrated Instruction and non

ICT-Integrated Instruction in terms of their posttest scores.

Table 10. Comparison of posttest results between GRRIM

and non-GRRIM group

Group

Mean

SD

N

GRRIM

23.67

7.163

49

Non-GRRIM

21.78

8.802

49

Total

22.72

8.040

98

Source

SS

df

MS

F-value

Sig.

Group

251.160

1

251.160

4.511

0.036*

Pretest

892.432

1

892.432

16.030

0.000

Error

5288.874

95

55.672

Total

56877.000

98

*Significant at 0.05 level

Table 11 shows the analysis of covariance (ANCOVA) of

retention test results between treatments. As presented in the

table, the F value is equal to 3.158 with a p-value of 0.079

( between groups which indicates a nonsignificant

difference, thus the null hypothesis that there is no significant

difference in students’ performance in terms of retention is

accepted. This finding means that students exposed to

GRRIM have more or less the same retention level compared

to the students exposed to non-GRRIM. Although the mean

score of GRRIM group in the retention test is nonsignificant

compared to the non-GRRIM group, the mean score of the

GRRIM group which is 21.78 is higher than the mean score of

non-GRRIM group which is 21.10.

Table 11. Comparison of retention test results between

GRRIM and non-GRRIM group

Group

Mean

SD

N

GRRIM

21.78

6.523

49

Non-GRRIM

21.10

8.898

49

Total

21.44

7.769

98

Source

SS

df

MS

F-value

Sig.

Group

143.658

1

143.658

3.158

0.079

Pretest

1521.032

1

1521.032

33.433

0.000

Error

4821.988

95

45.495

Total

50897.000

98

*Significant at 0.05 level

The result of this study contradicts to the result of the study of

Paglinawan (2011) wherein he found out that the students’

performance in the Computer Assisted Instruction (CAI) group

were significantly higher than that in the Non-CAI group in the

retention test. This study also contradicts to the study of

Taylaran (2015) when he found out that the students’

retention test scores in the Students Participation Dominated

(SPD) instruction was significantly higher than those of the

Lecture Discussion Dominated (LDD) instruction. The study of

Catli (2016) also contradicts to the result of this study when

she showed that there was a significant difference in the

mathematical competency for the students when exposed to

ICT-Integrated Instruction and non ICT-Integrated Instruction

in terms of their retention test scores. Although there is no

significant difference in the retention test between the two

groups, it is worthy to note that there was a significant

difference in the performance of the GRRIM group and non-

GRRIM group before the intervention as shown in Table 10

with a p-value of 0.000. The Gradual Release of

Responsibility Instructional Model was able to bridge the gap

between the performance of the experimental group and

control group considering the fact that the experimental group

is the third section while the control group is the second

section.

3.3 Analysis of Covariance of Students’ Self-Efficacy

when exposed to GRRIM and to non-GRRIM

It can be seen in Table 12 that the students’ self-efficacy

(mastery experiences) when exposed to GRRIM had a mean

score of 2.36 with a standard deviation of 0.77 while the non-

GRRIM group had a mean score of 2.28 with a standard

deviation of 0.89. Table 12 shows an F-value of 2.312 and a

p-value of 0.132 indicating a no significant difference in the

self-efficacy of two groups exposed to GRRIM and non-

GRRIM. Thus the null hypothesis, stating that there is no

significant difference in the self-efficacy of two groups

exposed to GRRIM and non-GRRIM in terms of mastery

experiences, is not rejected.

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Table 12. Comparison of Self-efficacy levels (Mastery

Experiences) between groups

Group

Mean

SD

N

GRRIM

2.36

0.77

49

Non-GRRIM

2.28

0.89

49

Total

2.32

0.83

98

Source

SS

df

MS

F-value

Sig.

Group

0.800

1

0.800

2.312

0.132

Pretest

33.933

1

33.933

98.114

0.000

Error

32.856

95

0.346

Total

594.278

98

*Significant at 0.05 level

However, it can be observed that even if the difference is not

significant, the mean score of the GRRIM group is higher

compared to the non-GRRIM group in terms of mastery

experiences. Even if there was no significant difference in the

self-efficacy of the students between groups in terms of

mastery experiences, it was observed that there was a

significant difference in their self-efficacy before the

intervention as shown in Table 12 with a p-value of 0.000. The

self-efficacy of the GRRIM group in terms of mastery

experiences increased after the intervention from 2.24 to 2.36

while the self-efficacy of the non-GRRIM group in terms of

mastery experiences decreased from 2.40 to 2.28. The

Gradual Release of Responsibility Instructional Model was

able to bridge the gap in the self-efficacy of the two groups in

terms of mastery experience which led to the increase of self-

efficacy among GRRIM group. Each person creates their self-

efficacy through the four sources but the most influential

source is mastery experience according to Bandura (1977).

However, in this study, the source of self-efficacy with the

highest mean is the vicarious experiences. Mastery

experiences refers to the tasks and activities that each person

experiences. Self-efficacy increases if outcomes are

successful but those failures lower the self-efficacy. As shown

in Table 12, the Grade 9 students have low self-efficacy

towards Mathematics in terms of mastery experiences

because majority of them don’t make excellent grades on

math tests as shown in the pretest, posttest and retention test

scores. Their low performance in Mathematics tests in the

past lowered their belief in themselves that they will succeed

in any Mathematics courses which led to the decrease in their

performance. Even if some students achieve success in their

Mathematics tests through persistent efforts, others continue

to doubt their self-efficacy that they could mount the same

effort. The study of Sewell and St. George (2000) supports

the result of this study when they found out that the use of

Creative Problem Solving (CPS) can have positive effects on

self-efficacy for learning as shown in the increase of the self-

efficacy level. Table 13 shows that the students’ self-efficacy

(vicarious experiences) when exposed to GRRIM had a mean

score of 2.98 with a standard deviation of 0.79 while the non-

GRRIM group had a mean score of 2.73 with a standard

deviation of 0.92. As shown in Table 18, the F-value is 2.890

and the p-value is 0.092 indicating a no significant difference

in the self-efficacy of two groups exposed to GRRIM and non-

GRRIM. Thus the null hypothesis, stating that there is no

significant difference in the self-efficacy of two groups

exposed to GRRIM and non-GRRIM in terms of vicarious

experiences, is not rejected.

Table 13. Comparison of Self-efficacy levels (Vicarious

Experiences) between groups

Group

Mean

SD

N

GRRIM

2.98

0.79

49

Non-GRRIM

2.73

0.92

49

Total

2.86

0.86

98

Source

SS

df

MS

F-value

Sig.

Group

1.305

1

1.305

2.890

0.092

Pretest

27.216

1

27.216

60.242

0.000

Error

42.920

95

0.452

Total

870.694

98

*Significant at 0.05 level

On the other hand, it can also be observed that although there

is no significant difference in the self-efficacy between the two

groups, the mean score of the GRRIM group is higher

compared to the non-GRRIM group in terms of vicarious

experiences. Even if there was no significant difference in the

self-efficacy of the students between groups in terms of

vicarious experiences, it was observed that there was a

significant difference in their self-efficacy before the

intervention as shown in Table 13 with a p-value of 0.000. The

self-efficacy of the GRRIM group in terms of vicarious

experiences increased after the intervention from 2.88 to 2.98

while the self-efficacy of the non-GRRIM group in terms of

vicarious experiences decreased from 2.90 to 2.73. The

Gradual Release of Responsibility Instructional Model was

able to bridge the gap in the self-efficacy of the two groups in

terms of vicarious experiences which led to the increase of

self-efficacy among GRRIM group. Vicarious experience is

the source of self-efficacy which comes from observing others

perform a certain task. In this study, vicarious experiences is

the source of self-efficacy with the highest mean which

indicates that they believe in their capacity to do Mathematics

if they see others (classmates, peers, parents, teachers) do

Mathematics. Moreover, their self-efficacy increases if they

see adults do well in Mathematics pushes them to do better

and if they see kids do better than them in Mathematics

pushes them to do better. In this context, the effects of

modeling are very relevant and timely since their self-efficacy

will increase even higher if best models teach them better

ways of doing things. Sewell & St. George (2000) stated that

one of the major sources of self-efficacy information comes

from models, and this is utilized within the framework of CPS

technique. CPS employed teacher modeling strategies and

peer modeling as steps of the CPS process and the result

yields an increase in the self-efficacy of the students which

supports the result of this study. Result of the study of

Zimmerman (1989) showed the superiority of coping models

where he compared an errorless model and a model showing

gradual elimination of errors, the coping model raised

children’s self-efficacy perceptions 86% from pretesting to

post-testing. This results support the result of the study

wherein there was an increase in the self-efficacy level of the

students after implementing the GRRIM. As shown in Table

14, students’ self-efficacy (verbal-social persuasion) when

exposed to GRRIM had a mean score of 1.83 with a standard

deviation of 0.86 while the non-GRRIM group had a mean

score of 1.51 with a standard deviation of 1.01. It can be seen

also in the table that the F-value is 0.056 and a p-value of

0.813 indicating a no significant difference in the self-efficacy

of two groups exposed to GRRIM and non-GRRIM. Thus the

null hypothesis, stating that there is no significant difference in

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the self-efficacy of two groups exposed to GRRIM and non-

GRRIM in terms of verbal-social persuasion, is not rejected.

Table 14. Comparison of Self-efficacy levels (Verbal-Social

Persuasion) between groups

Group

Mean

SD

N

GRRIM

1.83

0.86

49

Non-GRRIM

1.51

1.01

49

Total

1.67

0.95

98

Source

SS

df

MS

F-value

Sig.

Group

0.022

1

0.022

0.056

0.813

Pretest

47.801

1

47.801

123.944

0.000

Error

36.638

95

0.386

Total

360.278

98

*Significant at 0.05 level

However, it can be seen that even if the difference is not

significant, the mean score of the GRRIM group is higher

compared to the non-GRRIM group. Even if there was no

significant difference in the self-efficacy of the students

between groups in terms of verbal-social persuasion, it was

observed that there was a significant difference in their self-

efficacy before the intervention as shown in Table 14 with a p-

value of 0.000. The self-efficacy of the GRRIM group in terms

of verbal-social persuasion decreased slightly after the

intervention from 1.86 to 1.83 while the self-efficacy of the

non-GRRIM group in terms of verbal-social persuasion

increased slightly from 1.50 to 1.51. Verbal-social persuasion

is the only source of self-efficacy towards Mathematics that

decreased after the intervention. Verbal-social persuasions

has the lowest mean score among the four sources of self-

efficacy. This indicates that they create their self-efficacy less

from what others say about their performance. Although

verbal-social persuasions is a weak source of self-efficacy,

what others say regarding their performance greatly affects

their self-efficacy. Teachers, parents and peers play an

important role in the development of a person’s self-efficacy.

Teachers must cultivate student’s beliefs in their mathematical

abilities while at the same time assure them that success is

achievable. In fact, it is much easier to weaken the self-

efficacy of a student through negative remarks than to

strengthen such beliefs through positive appraisals. Sewell

and St. George (2000) also made use of verbal persuasion in

increasing the self-efficacy of students as part of the CPS

technique. This supports the result of the study wherein the

experimental group had a higher self-efficacy in terms of

verbal-social persuasion as compared to the control group

after using the GRRIM. Along the CPS process,

encouragement was supported by the provision of specific,

differentiated feedback. Clear feedback about specific skill

development, especially when combined with specific,

proximal goals, can be an important influence on self-efficacy

(Alderman, 1999; Brophy, 1998) which is also part of the

Gradual Release of Responsibility Instructional Model

(GRRIM). The result of the study conducted by Kampkuiper

(2015) about the effect of positive and negative feedback on

self-efficacy, cognitive trust and affective trust using coded

video-based observations for feedback durations and

questionnaires for measuring self-efficacy, cognitive and

affective trust suggests that negative feedback is negatively

related to self-efficacy and cognitive trust. This supports the

result of this study wherein those exposed to Gradual Release

of Responsibility Instructional Model (GRRIM) had a higher

self-efficacy level as compared to those exposed to non-

GRRIM. Kampkuiper also emphasized that such results

demonstrate the importance of examining the complex

cognitive mechanisms relating to feedback which might affect

the self-efficacy of the learners. Another study conducted by

Hattie and Timperley (2007) pointed out that feedback is one

of the most powerful influences on learning and achievement

but it could either be positive or negative. Verbal-social

persuasions could be in a form of feedback and GRRIM also

made use of feedback to enhance its effectiveness in

classrooms. The study of Hattie and Timperley shows that

although feedback is among the major influences, the type of

feedback and the way it is given can be differentially effective.

Table 15 shows that the students’ self-efficacy (physiological

and emotional arousal) when exposed to GRRIM had a mean

score of 2.46 with a standard deviation of 0.99 while the non-

GRRIM group had a mean score of 2.84 with a standard

deviation of 1.14. As presented in Table 15, the F-value is

0.308 and a p-value of 0.580 implying a no significant

difference in the self-efficacy of two groups exposed to

GRRIM and non-GRRIM. Thus the null hypothesis, stating

that there is no significant difference in the self-efficacy of two

groups exposed to GRRIM and non-GRRIM in terms of

physiological and emotional arousal, is not rejected.

Table 15. Comparison of Self-efficacy levels (Physiological

and Emotional Arousal) between groups

Group

Mean

SD

N

GRRIM

2.46

0.99

49

Non-GRRIM

2.84

1.14

49

Total

2.65

1.08

98

Source

SS

df

MS

F-value

Sig.

Group

0.172

1

0.172

0.308

0.580

Pretest

56.016

1

56.016

99.919

0.000

Error

53.258

95

0.561

Total

801.806

98

*Significant at 0.05 level

Even if there was no significant difference in the self-efficacy

of the students between groups in terms of physiological and

emotional arousal, it was observed that there was a significant

difference in their self-efficacy before the intervention as

shown in Table 15 with a p-value of 0.000. The self-efficacy of

the GRRIM group in terms of physiological and emotional

arousal increased after the intervention from 2.31 to 2.46

while the self-efficacy of the non-GRRIM group in terms of

physiological and emotional arousal decreased from 2.94 to

2.84. The Gradual Release of Responsibility Instructional

Model was able to help increase the self-efficacy of the

students in terms of physiological and emotional arousal

through the support of the teachers and their peers.

Physiological and emotional arousal is the only source of self-

efficacy wherein the mean score of the GRRIM group is lower

than the mean score of the non-GRRIM group. The GRRIM

group has a moderately low self-efficacy in terms of

physiological and emotional arousal as compared to the non-

GRRIM group which has a moderately high self-efficacy.

Psychological constructs such as anxiety, stress, and others

also provide data about the self-efficacy of a person. A person

can already gauge their self-efficacy by the emotional state

that they experience as they reflect in their own actions. When

a certain student experience failures or negative thoughts

regarding their performance in Mathematics, those emotional

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states can lower their self-efficacy and would trigger additional

stress that would lead to poor performance. Students who are

in a depressed mode would decrease their self-efficacy about

learning Mathematics. To improve their self-efficacy, the

teachers must improve the physical and emotional well-being

of a student and reduce negative emotional states. As what

Bandura (1997) has observed, we live in a psychic

environment that are products of our own thinking. Maloney,

Schaeffer and Beilock (2013) pointed out some ways how

affective factors such as mathematics anxiety and stereotype

threat can have a negative impact on the mathematics

performance of the learners that may lead to avoidance of

Mathematics. Furthermore, they suggested a number of

interventions aimed at reducing the negative consequences of

anxiety and stereotype threat on mathematics performance.

Instructional approaches such as GRRIM may help reduce

math anxiety and stereotype threat by supporting the learners

with an environment conducive for mathematics learning.

Table 16 presents the comparison of all the sources of self-

efficacy of students between those exposed to GRRIM and

those exposed to non-GRRIM. The mean score of the GRRIM

group is 2.41 with a standard deviation of 0.62 while the non-

GRRIM group has a mean score of 2.34 with a standard

deviation of 0.77.

Table 16. Comparison of the Students’ Self-efficacy levels

between groups

Group

Mean

SD

N

GRRIM

2.41

0.62

49

Non-GRRIM

2.34

0.77

49

Total

2.37

0.70

98

Source

SS

df

MS

F-value

Sig.

Group

0.464

1

0.464

2.586

0.111

Pretest

30.084

1

30.084

167.531

0.000

Error

17.060

95

0.180

Total

599.632

98

*Significant at 0.05 level

As seen in Table 16, the F-value is 2.586 and the p-value is

0.111 implying a no significant difference in the self-efficacy of

two groups exposed to GRRIM and non-GRRIM. Thus the null

hypothesis, stating that there is no significant difference in the

self-efficacy of two groups exposed to GRRIM and non-

GRRIM, is not rejected. On the contrary, even if the difference

is not significant, the overall mean score of the GRRIM

group’s self-efficacy is higher compared to that of the non-

GRRIM group. Even if there was no significant difference in

the self-efficacy of the students between groups from all

sources of self-efficacy towards Mathematics, it was observed

that there was a significant difference in their self-efficacy

before the intervention as shown in Table 16 with a p-value of

0.000. The overall self-efficacy of the GRRIM group towards

Mathematics increased after the intervention from 2.32 to 2.41

while the self-efficacy of the non-GRRIM group towards

Mathematics decreased from 2.41 to 2.34. The Gradual

Release of Responsibility Instructional Model was able to help

increase the self-efficacy of the students towards

Mathematics through the various phases of the model and by

utilizing varied teaching methods and strategies. The result of

this study contradicts to the result of the study of Jose (2015)

wherein he found out that there is a significant difference in

the self-efficacy of students exposed to ICT-GDLE as

compared to those exposed to Non-ICT GDLE. The findings

also suggest that efforts are needed to promote mathematics

self-efficacy for the students because self-efficacy in

Mathematics was positively associated with mathematics

performance. This was shown in the study of Liu & Koirala

(2009) when the results of the correlation analysis indicated

that mathematics achievement and mathematics self-efficacy

were positively related. Research results have shown that

self-efficacy could be increased by using the right instructional

strategies (Schunk, 1991 as cited by Liu & Koirala, 2009) and

the use of the Gradual Release of Responsibility Instructional

Model can help increase the mathematics self-efficacy as

shown in the pretest and posttest results.

4 CONCLUSIONS AND RECOMMENDATIONS

4.1 Conclusions

Based on the findings of the study, the following conclusions

were drawn: The level of mathematics performance of the

Grade 9 students in their pretest both for the GRRIM group

and non-GRRIM group is very low. After the intervention, the

GRRIM group had a moderate performance while the non-

GRRIM group had a low performance which shows an

increase from very low level in the pretest. On the retention

test, both groups had a low retention test scores. The self-

efficacy of Grade 9 students towards Mathematics when

exposed to GRRIM and non-GRRIM is moderately low.

Specifically, the self-efficacy of GRRIM group and the non-

GRRIM group in terms of mastery experiences is moderately

low. Both groups have moderately high self-efficacy in terms

of vicarious experiences. Also, both groups have moderately

low self-efficacy in terms of verbal-social persuasions. Lastly,

the self-efficacy of the GRRIM group in terms of physiological

and emotional arousal is moderately low while the self-

efficacy of the non-GRRIM group in terms of physiological and

emotional arousal is moderately high. Those students

exposed to GRRIM have a significantly higher posttest scores

as compared to those exposed to non-GRRIM. However,

there is no significant difference in the mathematics

performance of the Grade 9 students when exposed to

GRRIM and non-GRRIM in terms of their retention score. The

Grade 9 students of Central Mindanao University Laboratory

High School have a high posttest score when the Gradual

Release of Responsibility Instructional Model (GRRIM) is

integrated in the instruction which resulted to a highly

significant difference as compared to those exposed to non-

GRRIM. There is no significant difference in the self-efficacy

of students exposed to GRRIM and non-GRRIM. Specifically,

there is no significant difference in the self-efficacy of students

exposed to GRRIM and non-GRRIM in terms of mastery

experiences, vicarious experiences, verbal-social persuasion,

and physiological and emotional arousal.

4.2 Recommendations

The results and findings of the study led to the following

recommendations for further research and actions:

Mathematics teachers may use varied teaching models such

as the Gradual Release of Responsibility Instructional Model

(GRRIM) to improve the mathematics performance of the

learners since it is noted in this study that there is an increase

in the performance of the students before and after the

intervention. As part of the Gradual Release of Responsibility

Instructional Model, teachers should provide an avenue for

their students to discuss their answers with their peers

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through cooperative learning since it would help improve their

performance. The GRRIM helps increase the self-efficacy of

the students. Teachers are encouraged to use the GRRIM to

increase the self-efficacy of the students by using different

teaching strategies in every phase of the instructional model,

the use of games and performance tasks relevant to the topic.

Teachers can conduct pretest and posttest of the lessons to

determine if students have prior knowledge of the topic and if

they have learned something from the lesson along with the

use of GRRIM in their classes. Follow up activities such as

retention test and remedial classes are also recommended to

correct the misconceptions of students about the topic.

Teachers, parents and peers need to be very careful when

making judgments about the mathematics performance of

students because among the four sources of self-efficacy,

both groups scored the lowest in verbal-social persuasion.

Teachers may give feedbacks and constructive criticisms to

avoid discouragements on the part of the learner and should

also believe that all students are capable of learning all the

topics.

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