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1 INTRODUCTION
For more than two millenniums, mathematics has
been a part of the human search for understanding.
Mathematical discoveries and breakthroughs attempt
to reveal the natural world and arrive to the truth
using careful reasoning (Lewis, 2008).
Development of a Supplemental Learning Material in
Mathematics for Seamanship (Trim and Stability)
C.K.S. Gabasa
& T.S. Melliza
John B. Lacson
Foundation Maritime University, Arevalo, Iloilo City, Philippines
ABSTRACT: This developmental research aimed to produce a supplemental learning material in Mathematics
for Seamanship (Trim and Stability) using the ADDIE model. Mathematics concepts were determined through
content analysis by examining the Seamanship Instructor’s Guide and class handouts and validated by two
maritime teachers of JBLFMU-Arevalo. An outline of the lessons was drafted from the results of the content
analysis. The supplemental learning material was then developed using the 4E Instructional model – Engage,
Explore, Explain, and Evaluate. Furthermore, simple random sampling was used to select the 30 BSMT 2
students taking up Seamanship during the second semester of school year 2018-
2019 as respondents.
Meanwhile, a purposive sampling was used to determine 18 experts – 12 in Maritime Education and 6 in
Mathematics. A researcher-made questionnaire that underwent validation and reliability testing was utilized to
gather data. The statistical tools used were frequency, mean, and standard deviation. The results of the study
showed that the mathematics concepts embedded in Seamanship lessons were: (1) Integers, (2) Fractions, (3)
Decimals, (4) Percent, (5) Algebra, and (6) Trigonometry. I
t was also found that students have a “Very High”
satisfaction towards the supplemental material when taken as a whole and in terms of physical aspects,
objectives, learning activities, evaluation procedure, and usefulness. On the other hand, experts believed the
supplemental learning material has a “Very High” acceptability when taken as a whole and in terms of physical
aspects, objectives, and usefulness. However, experts found that it only has a “High” acceptability in terms of
learning activities, and evaluation procedure. Thus, the supplemental learning material in Seamanship is
appropriate, relevant, and useful in general and in terms physical aspects, objectives, learning activities, and
evaluation procedure. It has also met the expectations and standards of chosen experts as reflected on their
evaluation rating. Furthermore, the supplemental learning material may be subjected to the scrutiny of experts
in the production of instructional materials and may be edited, if the expert suggests to do so. The university
may use this supplemental learning material in improving students’ mastery of important mathematics lessons
needed in Seamanship. Similarly, future researchers may conduct an experimental study to determine if the use
of this supplemental learning material may improve students’ academic performance in Seamanship or another
developmental research to produce similar supplemental learning materials for other maritime and general
education subjects.
http://www.transnav.eu
the
International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 18
Number 3
September 2024
DOI: 10.12716/1001.18.03.1
8
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Mathematics serves as an instrument in the
development of other sciences and has been applied
to various aspects of the human world [1, 2, 3]. It is
utilized in technology, art, educational assessment,
and even in navigation. In the 17th and 18th centuries,
the leading scientific question, perhaps, was how to
find out exactly where you are at sea [4].
Mathematics is important in navigation [5].
Mathematics, an exact science, has advanced for
thousands of years throughout history. Maritime
activities, which are almost as old, transport
passengers and goods from one location to another
conveniently and economically. Though the link
between the two is not reciprocal, it is undeniable that
without the application of mathematical models,
maritime affairs, as we know them today, would not
exist [6].
One of the most important things that one should
know in navigation is about a ship’s trim and
stability. One must have a basic understanding of
trigonometry and the functions of right triangles to
comprehend the principles of ship stability fully.
There are also certain principles of physics needed in
order to have sufficient understanding of stability.
One should be familiar with terms such as volume,
density, weight, center of gravity, force, and
moments. [7].
Seamanship (SEAM) 2B, a professional subject in
the BSMT Program is mostly centered on Trim and
Stability. It covers the advanced competencies for
monitoring the loading, stowage, securing, and care
during voyage and the unloading of cargoes. In
addition, students are also taught how to maintain the
seaworthiness of the ship and the control of trim,
stability, and stress of the ship [8].
Meanwhile, Mathematics is considered a difficult
subject by most of the students. However, it is a
fundamental part of school curriculum [1]. In this
case, it is an essential tool in the subject, SEAM 2B. It
is therefore, a must for students to master certain
mathematical concepts and skills. Thus, this research
study is conducted.
This developmental research aimed to produce a
supplemental learning material for SEAM 2B.
2 MATERIALS AND METHODS
2.1 Research Design
This study employed a developmental research
design specifically, instructional material (IM) design.
Richey and Klein [9] labeled it as an approach where
new procedures, techniques, and tools are created
based upon a systematic analysis of specific cases.
This study particularly fell under the Type 1
developmental research since it focused on the
production of an instructional material.
To develop the supplemental learning material,
this study followed the ADDIE Model. It stands for
Analysis, Design, Development, Implementation, and
Evaluation.
2.2 Respondents
The respondents of this study were 30 BSMT students
taking SEAM 2B (Trim and Stability) that were
selected through simple random sampling. They were
asked to determine their satisfaction towards the
supplemental learning material.
Meanwhile, six experts in the field of Mathematics,
and 12 experts in the field of maritime education were
chosen through purposive sampling. They
determined the acceptability of the supplemental
learning material.
Table 1 shows the distribution of the respondents.
Table 1. Distribution of Respondents (N=48)
________________________________________________
Category f %
________________________________________________
Students 30 100
Experts 18 100
Mathematics 6 33
Maritime Education 12 67
________________________________________________
2.3 Instrument
The instruments used in the study were the matrix for
content analysis, students’ satisfaction survey form,
and experts’ evaluation form. These were validated by
three teachers who have an expertise in research and
grammar. Furthermore, the students’ satisfaction
survey form and experts’ evaluation form were
reliability-tested using Cronbach alpha. The reliability
test showed that the instrument is 0.98 or 98% reliable.
2.4 Data Collection
Based on the ADDIE Model [10], the data gathering
procedure can be best illustrated in Figure 1.
Figure 1.
In the Analysis phase, the researchers looked
through the instructional guide and instructional
materials for SEAM 2B (Trim and Stability) using
content analysis to determine mathematics concepts
645
embedded in the lessons. These topics were included
in the supplemental learning material.
In the Design phase, the researchers consulted
maritime teachers to review the outline/list of
mathematics concepts for the supplemental learning
material. This was done through an informal
interview. They suggested other mathematics topics
that the researcher has not included.
In the Development phase, exercises and problems
were written. These were validated by both a
mathematics and a professional teacher. The material
was patterned with the 4E Instructional model. 4E
stands for Engage, Explore, Explain, and Evaluate
[11]. In the Engage stage, the student’s interest was
involved and the topic was connected on a personal
level. This phase of the learning cycle helps students
answer questions such as: Why is this topic important
to me? In the Explore stage, students reinforce their
understanding of concepts, apply the concepts, and
practice the process through learning activities. In this
learning phase, students begin to construct for
themselves the meaning from the exploration
activities. In the Explain stage, students read the text
chapter, which develops a context for important
concepts. This strengthens the students’ personal
understanding of key concepts they have generated in
the Engage and Explore phases. The Explain phase is
supported by step-by-step computation examples
which contain discussions so that students can study
independently. It also contains practice items for
formative assessment. In Evaluation stage, students
find self-assessment which has been based on the
Engage, Explore, and Explain phases. These quizzes
may contain computation and problem-solving items
depending on the objectives of the lesson.
In the Implementation phase, the supplemental
learning material was given to students for their
perusal. A copy of the supplemental learning material
was provided to each student so that they can fully go
through the material.
In the Evaluation phase, the supplemental learning
material was evaluated by both the students and the
experts. In addition, their satisfaction and
acceptability level were determined at this phase.
2.5 Data Analysis
Both qualitative and quantitative techniques were
used in the conduct of this study.
The qualitative analysis technique employed the
content analysis. It was used to determine the
mathematics concepts embedded in the SEAM 2B
lessons.
Meanwhile, frequency, mean, and standard
deviation were the statistical tools utilized.
Frequency was used to determine the number of
respondents in the study.
Mean was used to determine the acceptability of
the developed supplemental learning material in
SEAM 2B (Trim and Stability) through the students’
satisfaction and experts’ evaluation rating.
The mean scale, description, and indicators for
satisfaction and acceptability in the supplemental
learning material in Mathematics for SEAM 2B (Trim
and Stability) are found in Table 2.
Table 2 Levels of Satisfaction and Acceptability in the
Supplemental Learning Material
________________________________________________
Mean Description Indicators
Scale Satisfaction Acceptability
________________________________________________
3.51-
4.00 Very High Students find the Experts think that the
overall appearance overall aspects of the
and content of the supplemental learning
supplemental material are excellent and
learning material have minimal revisions.
excellent. They find
it very useful in the
subject.
2.51- High Students find most Experts think that the
3.50 parts and content of overall aspects of the
the supplemental supplemental learning
learning material material are very good
sufficient. They find but still have several
it somehow useful in revisions.
the subject.
1.51- Low Students find most Experts think that the
2.50 parts and content of overall aspects of the
the supplemental supplemental learning
learning material material are good but
insufficient. need a lot of revisions.
1.00- Very Students find the Experts think that the
1.50 Low overall appearance overall aspects of the
and content of the supplemental learning
supplemental material should all be
learning material revised or scratched.
not usable.
________________________________________________
Standard deviation was used to determine the
spread of the responses that were obtained in the
students’ satisfaction and experts’ evaluation.
3 RESULTS AND DISCUSSION
To create the supplemental learning material, various
Mathematics topics were determined based on the
SEAM 2B (Trim and Stability) lessons. Table 3
presents the Mathematics lessons found in SEAM 2B
(Trim and Stability) lessons. These are: (1) Integers, (2)
Fractions, (3) Decimals, (4) Percent, (5) Algebra, and
(6) Trigonometry.
These concepts support the claim of Gafoor and
Kurukkan [1] that mathematics is a fundamental part
of school curriculum and an essential tool in the
subject. Moreover, the results are also aligned to the
claim of Stanivuk et al. [6] that there is a link between
mathematics and maritime affairs.
Furthermore, specific competencies in the
mathematics lessons were identified. These
competencies are found in the Mathematics
Framework for Philippine Basic Education [12]. These
can be best illustrated in Figure 2.
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Table 3 Mathematics Concepts Embedded in Seamanship 2B (Trim
and Stability) Lessons
________________________________________________
Seamanship Lessons Mathematics Lessons
________________________________________________
1. Stability Integers, Decimals, Fractions,
Algebra, Trigonometry
2. Cargo Calculations and Cargo Integers, Decimals, Fractions,
Plans Algebra
3. Stress tables and stress Algebra (Graphs)
calculating equipment
4. Draught, Trim, and Stability Integers, Decimals, Algebra
5. Approximate Calculations of Integers, Decimals, Algebra
Areas and Volume
6. Effects of Density Integers, Decimals, Algebra
7. Stability at Moderate and Large Integers, Decimals, Algebra,
Angles of Heel Trigonometry
8. Dynamical Stability Integers, Decimals, Percent,
Algebra
9. Approximate GM by Means of Integers, Decimals, Algebra,
Rolling Period Test Trigonometry
10. Intact Stability Requirements Integers, Decimals, Algebra
for Carriage of Grain
11. Effect on trim and stability of Integers, Decimals, Percent,
a ship in the event of damage Algebra
to and consequent flooding of
a compartment and
countermeasure to be taken
12. Calculation of Vessel Integers, Decimals, Percent,
Condition after Flooding Fractions, Algebra
13. Effect of Flooding on Trim Integers, Decimals, Algebra
________________________________________________
Figure 2.
Meanwhile, Table 4 shows the mean satisfaction of
students towards the developed supplemental
learning in SEAM 2B in general and in terms of
physical aspects, objectives, learning activities,
evaluation procedure, and usefulness.
Table 4. Students’ Satisfaction Towards the Supplemental
Material in Seamanship 2B (Trim and Stability)
________________________________________________
Category n Mean Description SD
________________________________________________
Overall 30 3.66 Very High 0.62
Physical Aspect 30 3.71 Very High 0.63
Objectives 30 3.64 Very High 0.62
Learning Activities 30 3.62 Very High 0.68
Evaluation Procedure 30 3.66 Very High 0.64
Usefulness 30 3.67 Very High 0.63
________________________________________________
Note. 3.51-4.00=Very High Satisfaction; 2.51-3.50=High
Satisfaction; 1.51-2.50=Low Satisfaction; and 1.00-1.50=Very
Low Satisfaction.
The results show that in general, students have a
“Very High” satisfaction (M=3.66, SD=0.62) towards
the supplemental learning material. In addition, they
also have a “Very High” satisfaction in terms of
physical aspects (M=3.71, SD=0.63), objectives
(M=3.64, SD=0.62), learning activities (M=3.62,
SD=0.68), evaluation procedure (M=3.66, SD=0.64),
and usefulness (M=3.67, SD=0.63).
The findings of this study support the notion that
learning satisfaction is the effect of the processes
which have taken place during the students’ learning
process. Additionally, satisfaction can also be
regarded as relative outcomes between expectation
and perceived service either with pleasure or with
displeasure [13]. In addition, the quality of learning
materials affects the satisfaction of the learners. The
more confidence and trust the learners have in the
quality of materials used for their learning, the more
satisfied they are [14]. Therefore, one can say that
students’ expectations of the supplemental learning
material have been met, thus resulting to a “Very
High” satisfaction. Meanwhile, Table 5 presents the
experts’ acceptability of the supplemental learning
material in SEAM 2B in general and in terms of
physical aspects, objectives, learning activities,
evaluation procedure, and usefulness. Data were
based on the responses of experts in maritime
education and in mathematics.
Table 5 Acceptability of the Supplemental Learning Material
in SEAM 2B (Trim and Stability) According to Experts
________________________________________________
Category n Mean Description SD
________________________________________________
Overall 18 3.52 Very High 0.52
Physical Aspect 18 3.51 Very High 0.43
Objectives 18 3.55 Very High 0.54
Learning Activities 18 3.50 High 0.51
Evaluation Procedure 18 3.45 High 0.59
Usefulness 18 3.57 Very High 0.66
________________________________________________
Note. 3.51-4.00=Very High Acceptability; 2.51-3.50=High
Acceptability; 1.51-2.50=Low Acceptability; and 1.00-
1.50=Very Low Acceptability.
The results show that in general, experts deem that
the supplemental learning material has a “Very High”
acceptability (M=3.52, SD=0.52). Moreover, it also has
a “Very High” acceptability in terms of physical
aspects (M=3.51, SD=0.43), objectives (M=3.55,
SD=0.54), and usefulness (M=3.57, SD=0.66). On the
other hand, it has a “High” acceptability in terms of
learning activities (M=3.50, SD=0.51) and evaluation
procedure (M=3.45, SD=0.59).
The findings show that the supplemental learning
material has exceeded the standards of the chosen
experts in terms of the physical aspects, objectives,
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and usefulness and has met their expectations in
terms of learning activities and evaluation procedure.
The findings of this study is similar to that of Gayagay
[15] and Menor and Limjap [16].
4 CONCLUSIONS
Based on the findings, it is clear that various
mathematics lessons were imbedded in the SEAM 2B
(Trim and Stability) lessons. One way to strengthen
learning in Seamanship 2B may be done by helping
students master these mathematics lessons. Secondly,
the supplemental learning material in SEAM 2B is
appropriate, relevant, and useful in general and in
terms physical aspects, objectives, learning activities,
and evaluation procedure as shown by the students’
satisfaction rating and has met the expectations and
standards of chosen experts as reflected on their
evaluation rating.
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