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Development and Effectiveness of a Textbook on Advanced
Mathematics for Engineering Programs
Harold Jan R. Terano
College of Engineering, Camarines Sur Polytechnic Colleges, Philippines
E-mail: haroldterano@cspc.edu.ph
KEYWORDS ADDIE Model. Book. Engineering Education. Instruction. Instructional Material
ABSTRACT Advanced Engineering Mathematics is a course that introduces higher concepts of mathematics and
its applications to engineering. A textbook was developed to supplement the teaching-learning processes. The
study had utilized the ADDIE (Analysis, Design, Develop, Implement, and Evaluate) model in developing the
instructional material. The acceptability of the contents, structure and format and assessment in the IM was
determined using a validated evaluation instrument. The instrument together with the IM was distributed to 22
engineering professors from various academic institutions and 80 engineering students using expert-based method
of obtaining evaluation. Thirty civil engineering students were the participants to test the effectiveness of the
material. Results showed that the IM is highly acceptable, and is effective and found that there is a significant
improvement in the students’ performance in the pretest-posttest. The study is important in providing an
effective IM for engineering students to improve their proficiency in advanced engineering mathematics.
INTRODUCTION
Education is an important aspect for every-
one in succeeding life and future. It helps a lot in
combating life challenges and difficulties.
Knowledge, skills and values gained through-
out the education period enables every individ-
ual to be confident in their respective lives.
Learning in the sense of cognitive improve-
ment is a multi-faceted construct related to mul-
tiple educational and individual factors (Drigas
and Karyotaki 2014). It has been an actively fo-
cused on the process of acquiring new objec-
tive knowledge in the subject (Sousa-Vieira et al.
2015). The concept of a learner-centered and not
teacher-centered is the new vision of the whole
educational system (Maceiras et al. 2013). One
of these factors include teaching and learning
materials of various forms. Instructional materi-
als refer to the human and non-human materials
and facilities, which can be used to ease, en-
courage, improved and promote teaching and
learning activities.
Instructional materials are very vital in the
teaching-learning processes. This is in a form of
textbooks, reference text, the chalk and black-
board, computer aided presentations and other
materials that are important and useful in the dis-
cussion and teaching. Instructional material is a
prominent factor toward academic excellence. It
is remarkable for the teacher to develop instruc-
tional material to guide the student in their aca-
demic performance (Quisumbing et al. 2017).
Textbooks are materials containing all the top-
ics that should be discussed in a particular
course. These instructional materials should be
curriculum based and substantial for the pur-
pose of teaching and the learning of the stu-
dents. To concretize and substantiate learning,
it is important to provide adequate, appropriate
and varied instructional materials (Tominez et
al. 2013).
Instructional design models are useful in
developing course materials for effective teach-
ing-learning processes. Instructional designers
use learning theories as a source for verifying
strategies and as a foundation for intelligent
selection of strategies (Ertmer and Newby 2013).
According to Branch and Kopcha (2014), de-
veloping instructional materials require a sys-
tematic approach and a more defined model.
There are variety of instructional development
models. ADDIE model is an acronym for ana-
lyze, design, develop, implement, and evaluate
(Aldoobie 2015). The phases of ADDIE repre-
sent the fundamental concepts of instructional
development process ensuring that the design
has to be student-centered, goal-oriented with
meaningful performance and outcomes that can
be validly measured (Reiser and Dempsey 2012).
Advanced Engineering Mathematics is a
higher course in engineering mathematics. The
course description for advanced engineering
mathematics for civil and mechanical engineer-
Int J Edu Sci, 23(1-3): 7-13 (2018)
DOI: 10.31901/24566322.2018/23.1-3.1069
© Kamla-Raj 2018
PRINT: ISSN 0975-1122 ONLINE: ISSN 2456-6322
8HAROLD JAN R. TERANO
ing is stated in CMO 29, s. 2007 and CMO 9, s.
2008.
One of the significant challenges in teach-
ing advanced engineering mathematics is on
how to deliver to the students the concepts of
the subject since majority of the topics focused
on higher topics in mathematics that needs prior
knowledge of the basic engineering mathemat-
ics. Also, there is a need to revisit the arrange-
ment of the topics taking into considerations
the pre-requisite topics. Several developments
and evaluation study of instructional materials
were conducted (Terano 2015; Tabal 2015; Dio
2017; Magulod 2017). Such studies are useful
for other professors who intended to design
their instructional materials related to their fields
of specializations.
Objectives
This study focused on the development and
effectiveness of a textbook in advanced engi-
neering mathematics. Specifically, this study
sought to address the following objectives,
namely, 1) to design a textbook in terms of con-
tents, structure and format, and assessments; 2)
to determine the acceptability of the material in
terms of contents, structure and format, and as-
sessments; and 3) to test the effectiveness of
the proposed textbook.
METHODOLOGY
This research employed a descriptive-devel-
opment research design in the whole processes
of the research. The study considered two ma-
jor phases, namely, the development and evalu-
ation phases. The development phase included
several stages such as planning, designing and
development of the proposed textbook. The eval-
uation phase included the validation of the con-
tents, structure and format, and assessment, and
evaluation on the effectiveness of the material.
Development Phase
The planning phase of this study included
preliminary activities in which the researcher
considered the analysis of the present require-
ments for the course based on the course de-
scription and outlines of the Philippine Commis-
sion on Higher Education (CHED). The design
of the material considered the contents and struc-
ture and format. Along the contents, the research-
er considered the minimum requirements for the
course in accordance with the CHED. Table 1
shows the outline for the course as prescribed
in the CHED CMOs.
Along the structure and format, the research-
er devised his own style on how he can make
the material based on the needs of the students
and on how this material can capture the inter-
ests of the students. This is to take note that
according to Quisumbing et al. (2017), it is im-
portant for a teacher to develop instructional
material to guide the student in their academic
performance.
Evaluation Phase
After the completion of the textbook, twen-
ty-two (22) engineering professors from the var-
Table 1: Course requirements
Course title: Advanced Engineering
Mathematics for CE
Course description: A study of selected topics in
mathematics and their applications in advanced
courses in engineering and other allied sciences. It
covers the study of Complex numbers, Laplace and
Inverse Laplace Transforms, Power Series, Matrices
and Determinants, Vector Analysis and Numerical
Methods.
Course Outline:
1. Complex Numbers
2. Laplace and Inverse Laplace Transforms
3. Power Series
4. Fourier Series
5. Vector Analysis
6. Numerical Methods
Course title: Advanced Engineering
Mathematics for ME
Course description:A study of selected topics in
mathematics and their applications in advanced
courses in engineering and other allied sciences. It
covers the study of Complex Numbers, Laplace and
Inverse Laplace Transforms, Power series, Fourier
series, Matrices and Determinants, Vector Analysis
and Numerical Methods.
Course Outline:
1. Complex Numbers
2. Laplace and Inverse Laplace Transforms
3. Power Series
4. Fourier Series
5. Vector Analysis
6. Numerical Methods
DEVELOPMENT AND EFFECTIVENESS OF A TEXTBOOK 9
ious universities and colleges in the Bicol re-
gion evaluated the material as expert evaluators.
They were five (5) professors from the Cama-
rines Sur Polytechnic Colleges (CSPC), three (3)
professors from the Bicol University College of
Engineering (BUCENG, Legazpi City), three (3)
professors from the Bicol University Polangui
Campus (BUPC), three (3) professors from the
University of Northeastern Philippines (UNEP),
two (2) professors from the University of Saint
Anthony (USANT), three (3) professors from
the Sorsogon State College (SSC) and three (3)
professors from the Camarines Norte State Col-
lege (CNSC). Data were collected in January 2017.
Each of them received a sample copy and
were asked to evaluate the acceptability of the
contents, structure and format and assessment
of the material. Also, another group of evalua-
tors on the acceptability of the material were the
80 engineering students in 2 universities, name-
ly, Camarines Sur Polytechnic Colleges and Uni-
versity of Northeasthern Philippines who had
used the material. Since they had used the mate-
rial, they were able to answers evaluation forms
given to them to evaluate the acceptability of
the contents, structure and format and assess-
ment of the material. Weighted mean was used
in order to consolidate the results that was ob-
tained based on the response of the evaluators.
The computed mean ratings were evaluated ac-
cording to the scale as shown in Table 2.
To test the effectiveness of the material, the
researcher seek permission from the Dean of the
College of Engineering of the Camarines Sur
Polytechnic Colleges to allow the researcher to
conduct experimental study to 30 engineering
students as his participants in the study. The
researcher conducted one-group pretest-post-
test experimental research design in testing the
effectiveness of the material as part of the vali-
dation process. t-test was used to determine if
there is a difference between the results of the
pretest and posttest.
RESULTS AND DISCUSSION
The development and evaluation of the text-
book in advanced engineering mathematics were
conducted to satisfy the objectives of this re-
search, namely, the design, acceptability and the
effectiveness of the textbook in advanced engi-
neering mathematics.
The Design of the Material
The textbook in advanced engineering math-
ematics is composed of nine (9) chapters together
with its discussions, sample problems and exer-
cises. Table 3 shows the contents of the book
against the content topics in accordance with
the minimum requirements of the Commission
on Higher Education (CHED) in the Philippines.
Identifying the contents of instructional materi-
als can be aided with sample syllabi or course
website (Peterson 2003).
The design of the material was carefully
made to enhance the interests of the students in
the course. Each chapter has the format and se-
quence using English as the language. The or-
der of presentation is as follows: (1) Chapter
Number and Title which provides the order and
name of the chapter respectively; (2) Chapter
Table 2: Likert scale
Scale Verbal interpretation
4.50 – 5.00 Highly acceptable
3.50 – 4.49 Very acceptable
2.50 – 3.49 Acceptable
1.50 – 2.49 Fairly acceptable
1.00 – 1.49 Not acceptable
Table 3: Contents of the book
CHED requirements The proposed textbook
I. Complex Numbers Chapter 1: Complex Numbers and Complex Variables
II. Laplace Transforms Chapter 2: Laplace Transforms
III. Power Series Chapter 3: Infinite Series
IV. Fourier Series Chapter 4: Power Series
V. Matrices and Determinants Chapter 5: Fourier Series
VI. Vector Analysis Chapter 6: Matrices and Determinants
VIII. Numerical Methods Chapter 7: Vector Analysis
Chapter 8: Numerical Methods
Chapter 9: Introduction to Partial Differential Equations
10 HAROLD JAN R. TERANO
Overview which provides an introduction and
overview of the topics that were included in each
chapter; (3) Chapter Outline which indicates the
list of the topics that was covered by the chap-
ter; (4) Learning Objectives which indicates the
objectives or learning outcomes of the study
after the completion of each chapter; (5) Lesson
Number and Topic which indicates the order and
the name of the topic in every chapter, respec-
tively; (6) Discussions which is the presenta-
tion of the basic concepts, formulas, theories
and insights of the lesson; (7) Sample Problems
and Solutions which are carefully solved prob-
lems in every lesson/topic; and (8) Exercises
which are the activities that will be done by the
students after taking the lesson. According to
Hartley (2013), the format and sequence of in-
formation have practical significance to clarify
the structure of the text and help the readers
gain access to the information.
Acceptability of the Material
The acceptability of the textbook was done
by tabulating the data gathered on the evalua-
tion of the textbook by a total of twenty-two
professors and eighty engineering students.
Table 4 shows that the acceptability of the text-
book in terms of the contents are highly accept-
able. Taking into considerations the indicators
evaluated, the results confirmed that the gener-
al contents of the IM which include the topics,
problems and exercises are aligned with the ob-
jectives of the lesson. The results imply that the
contents could provide students the instruction-
al strategies that would enhance their cognitive,
psychomotor and affective domains of learning
since the objectives developed are based on
Bloom’s Taxonomy (Adams 2015). The contents
are highly acceptable considering that during
the designing of the IM, the CHED course out-
lines were used as a guide to ensure that the
required standards and competencies are met.
The results also imply that the contents are suit-
able to the learner’s ability and needs. This re-
sult was supported by Reiser and Dempsey
(2012), that suitability is attained when the con-
tents are student-centered and goal oriented
coupled with relevant activities.
Table 5 shows that the acceptability of the
textbook in terms of the structure and format are
highly acceptable. The results imply that the
structure, format and presentation of the dis-
cussions are suitable to the level of student un-
derstanding. The findings also suggest that
there is clarity in the discussions of the topic
and presentation of concepts and theories. It is
further assumed from the results that the sample
problems and solutions that were developed are
based on the objectives and are clearly illustrat-
ed for easy understanding of the topic. Accord-
ing to Hartley (2013), students have different
needs and preferences in the learning preferences
and the clarity of the discussion could help ad-
dress such variation. Clarity in the text is man-
datory and regarded as the most effective crite-
rion for an effective instructional material (IM)
(Gerson 2000).
Table 6 shows that the acceptability of the
textbook in terms of the assessment are highly
acceptable. The results confirmed that the exer-
cises given are sufficient for the students to learn
the concepts and theories in every topic in each
chapter. According to Paas and Sweller (2014),
Table 4: Acceptability of the contents
Indicators Students Professors Total
WM SD WM SD WM VI
1. Support of the objectives to the topics, 4.83 0.380 4.73 0.538 4.78 HA
problems and exercises
2. Relevance of the problems and exercises on 4.86 0.344 4.59 0.577 4.73 HA
the topics
3. Relevance of the problems and exercises 4.93 0.263 4.91 0.287 4.92 HA
on the objectives
4. Suitability of the topics to the learning ability 4.90 0.300 4.77 0.419 4.84 HA
of the students
5. Suitability of the discussions on the interests 4.88 0.331 4.82 0.386 4.85 HA
and needs of the students
Total 4.88 0.038 4.76 0.118 4.82 HA
Legend: WM-Weighted Mean; SD-Standard Deviation; VI-Verbal Interpretation; HA-Highly Acceptable
DEVELOPMENT AND EFFECTIVENESS OF A TEXTBOOK 11
sufficient exercises avoids overloading the learn-
er’s cognitive capacity. The results also showed
that the problems are clearly stated, and exercis-
es are suitable for the level of the learner. As-
sessment must be parallel to and able to mea-
sure the learners’ ability to perform what is de-
scribed in the objectives (Dick et al. 2014). Prob-
lem sets will enhance the critical thinking of stu-
dents. Terano (2015) stressed that, the focus on
tertiary curriculum should not only be on the
theoretical aspects but also on the skills which
involve activities that will enhance the critical
thinking of students.
Table 7 shows the summary of the perceived
acceptability of the textbook along its contents,
structure and format and assessment. As shown
in the table, the various indicators as perceived
by the professors and students, it is found that
there is no significant difference on their per-
ceptions on the acceptability of the textbook in
terms of the contents, structure and format, and
assessment.
Generally, the developed material is highly
acceptable in terms of its contents, structure and
format and assessment. This only implies that
the developed material is suitable for use in engi-
neering programs. Results of the study support
the claims of Dio (2017), Tabal (2015) and Terano
(2015), that developed instructional materials were
appropriate to be used in the classroom.
The developed material was highly accept-
able based on the evaluations as discussed in
the previous section. Some of the suggestions
and recommendations of the evaluators were;
(1) include an overview of each chapter, (2) pro-
vide separate page (one whole page) for the start
of every chapter, and (3) include in every chap-
ter page the list of topics/chapter outline. Based
on these suggestions, the researcher had revised
the material.
Table 5: Acceptability of the structure and format
Indicators Students Professors Total
WM SD WM SD WM VI
1. Simplicity of the structure 4.93 0.263 4.91 0.287 4.92 HA
2. Organized format 4.96 0.190 4.86 0.457 4.91 HA
3. Clear presentation of the discussions 4.90 0.300 4.77 0.419 4.84 HA
Total 4.93 0.030 4.85 0.071 4.89 HA
Legend: WM-Weighted Mean; SD-Standard Deviation; VI-Verbal Interpretation; HA-Highly Acceptable
Table 6: Acceptability of the assessment
Indicators Students Professors Total
WM SD WM SD WM VI
1. Sufficiency of the Exercise given 4.88 0.331 4.55 0.498 4.72 HA
2. Clearly stated problems 4.91 0.283 4.68 0.466 4.80 HA
3. Suitability of the exercises to the level of the learner4.85 0.357 4.82 0.386 4.84 HA
Total 4.88 0.030 4.68 0.135 4.79 HA
Legend: WM-Weighted Mean; SD-Standard Deviation; VI-Verbal Interpretation; HA-Highly Acceptable
Table 7: Over-all results of the acceptability of the textbook in advanced engineering mathematics
Indicators Weighted means F-value p-value
Students Professors
Content 4.88 4.76 4.36 0.070*
Structure and Format 4.93 4.85 3.51 0.134*
Assessment 4.88 4.68 6.06 0.069*
Total 4.90 4.76 6.61 0.062*
Legend: *not significant at 0.05 level of significance
12 HAROLD JAN R. TERANO
Effectiveness of the Textbook in
Advanced Mathematics for Engineering
The effectiveness of the textbook was test-
ed using the one-group pretest-posttest experi-
mental design among the group of third-year
civil engineering students in one state college
in the Bicol region. This was conducted to de-
termine the effectiveness of the developed text-
book. Pretest was conducted before the actual
utilization of every chapter of the material. Post-
test was conducted after the utilization and ex-
posure to the developed material to determine
whether there is a significant difference in the
pretest percentage scores and the posttest per-
centage scores of the students. Table 8 shows
the mean performance of the civil engineering
students during the pretest and posttest includ-
ing the corresponding t-value for each topic.
As observed in Table 8, the students signif-
icantly improved during the posttests as com-
pared to the pretests. The pretest results of the
topics Complex Numbers and Complex Variables,
Laplace Transforms and Matrices and Determi-
nants showed that some of the students had al-
ready prior knowledge about these topics while
the remaining topics showed that the students
had no background at all. Generally, there is a
significant improvement in their performance in
the posttest as compared to their pretest results.
CONCLUSION
The design of the Textbook in Advanced
Engineering Mathematics follows the minimum
requirements for the course in accordance with
the CHED CMOs of the Philippines. The design
of the material was carefully made to enhance
teaching-learning processes in the course. Each
chapter has the format and sequence using En-
glish as the language. The material is highly ac-
ceptable based on the evaluations of professors
and students in terms of the contents, structure
and format, and assessment. The material is ef-
fective based on the results of the pretests and
posttests of the students. The material is suit-
able for use in engineering programs. The con-
tent of the material was revised based on the
suggestions and recommendations of the eval-
uators.
RECOMMENDATIONS
The proposed material can be used in the
various institutions of higher learning offering
courses in advanced engineering mathematics.
Further evaluation can be done to improve the
content, structure and format and assessment
of the material. Item analysis can be conducted
to further improve the acceptability of the mate-
rial in terms of the assessment. The professors
and students in advanced engineering mathe-
matics can use the material for an effective teach-
ing and learning processes. Revisions on the
content can be done in accordance with chang-
es and updates in curriculum. This material can
serve as input to other researchers in conduct-
ing similar studies.
ACKNOWLEDGEMENTS
The author would like to acknowledge the
participation of the professors and students from
various institutions of higher learning in the Bi-
Table 8: Effectiveness of the textbook in improving the performance of the students
Indicators Mean performance (%) t-value
Pretest Posttest
Complex Numbers and Complex Variables 55.83 88.33 10.50*
Laplace Transforms 12.67 83.83 52.74*
Infinite Series 0.83 86.00 74.92*
Power Series 0.00 84.33 70.73*
Fourier Series 0.00 83.83 71.86*
Matrices and Determinants 63.00 90.17 8.57*
Vector Analysis 1.33 88.83 63.78*
Numerical Methods 0.00 89.33 68.34*
Introduction to Partial Differential Equations 0.00 88.67 75.60*
Total 14.85 87.04 89.20*
*Significant at 0.05, tcri = 2.045
DEVELOPMENT AND EFFECTIVENESS OF A TEXTBOOK 13
col region, Philippines. Also, he would like to
extend warmest thanks to the Camarines Sur
Polytechnic Colleges, Philippines for the sup-
port in the conduct of the study.
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Paper received for publication on December 2018
Paper accepted for publication on December 2018
