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INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 7, ISSUE 8, AUGUST 2018 ISSN 2277-8616
276
IJSTR©2018
www.ijstr.org
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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