Development and Acceptability of the Simplified Text in Differential Calculus for Engineering

Abstract

Differential Calculus is a course that introduces the concepts and theories of higher mathematics and their applications to engineering. A large majority of engineering students fail to attain proficiency in mathematics as the foundation course of engineering programs. One way to help students obtain skills and competency is to develop an effective instructional material (IM). In an attempt to provide the engineering students IM that can supplement their learning process, this study aimed to develop a Simplified Text in Differential Calculus for engineering and determine its acceptability. The study utilized the ADDIE (Analysis, Design, Develop, Implement, and Evaluate) model in developing the IM. The acceptability of the objectives, contents, presentation and style, and exercises in the IM was determined using a validated evaluation instrument. The instrument together with the IM was distributed to 22 engineering professors from the different academic institutions in the Bicol Region using the expert-based method of obtaining the evaluation. The weighted mean was the statistical tool used. Results showed that all text features are highly acceptable. The study is important in providing an effective IM for engineering students to improve their proficiency in higher mathematics.

Full text

Journal of Multidisciplinary Studies Vol. 4 No. 2, pp. 106-126, December 2015
ISSN 2350-7020 (Print)
ISSN 2362-9436 (Online)
doi: http://dx.doi.org/10.7828/jmds.v4i1.851
106
Development and Acceptability of the Simplified Text
in Differential Calculus for Engineering
Harold Jan R. Terano
College of Engineering, Camarines
Sur Polytechnic Colleges, Nabua,
Camarines Sur, Philippines
Corresponding author: Harold Jan R. Terano, email: haroldjan1010@gmail.com
Abstract
Differential Calculus is a course that introduces the concepts and theories of
higher mathematics and their applications to engineering. A large majority of
engineering students fail to attain proficiency in mathematics as the foundation
course of engineering programs. One way to help students obtain skills and
competency is to develop an effective instructional material (IM). In an attempt
to provide the engineering students IM that can supplement their learning
process, this study aimed to develop a Simplified Text in Differential Calculus
for engineering and determine its acceptability. The study utilized the
ADDIE (Analysis, Design, Develop, Implement, and Evaluate) model in
developing the IM. The acceptability of the objectives, contents, presentation
and style, and exercises in the IM was determined using a validated
evaluation instrument.
The instrument together with the IM was distributed to
22 engineering professors from the different academic institutions in the Bicol
Region using the expert-
based method of obtaining the evaluation.
The weighted mean was the statistical tool used. Results showed that all text
features are highly acceptable. The study is important in providing an effective
IM for engineering students to improve their proficiency in higher
mathematics.
Keywords: design, evaluation, learning, mathematics, model
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Journal of Multidisciplinary Studies Vol. 4, No. 2, pp. 106-126, December 2015Journal of Multidisciplinary Studies Vol. 4, No. 2, pp. 106-126, December 2015
ISSN 2350-7020 (Print)
ISSN 2362-9436 (Online)
doi: http://dx.doi.org/10.7828/jmds.v4i1.851

Journal of Multidisciplinary Studies Vol. 4 No. 2, pp. 106-126, December 2015
107
Introduction
It is a great challenge in every educational institution on how to
enhance the quality and standards of the engineering program.
There have been issues that drive the advancement of engineering
education in the United States in particular. These include a
declining interest of students in engineering (Melsa, 2007), a decrease in
national achievement in mathematics and sciences at pre-college
levels (Tran & Nathan, 2010), and a lack of technological literacy
(Pearson & Young, 2002). Hence, focusing on the education of pre-
college population becomes an alternative to improve situations facing
science, technology, engineering, and mathematics (STEMs) education
(Honey, 2014).
In the Philippines, engineering education also has such
concerns on how to improve the knowledge and skills of students.
In K-12 program implementation, the present quality of education is
reflected in the inadequate preparation of high school graduates for
higher education because they lack the core competencies or emotional
maturity (DepEd, 2010).
With the prevailing issues, Terano (2015) stressed that the
educational curriculum at the tertiary level should focus both on theories
and skills which involve activities that enhance the critical thinking.
Differential Calculus is a higher engineering mathematics course that is
taken mostly during the first semester of the second year. The course
introduces the concepts and theories of higher mathematics and their
applications to engineering. However, a large majority of engineering
students fail to attain proficiency in higher mathematics subjects that
serve as foundation courses of engineering programs (Terano, 2015).
One way to help students develop skills and competency is to
design a course material for effective instruction (Morrison et al., 2010;
McClure, 2006). Instructional materials are a prime concern in teaching
(Terano, 2015). They are in the form of textbooks, reference text, the
chalk and blackboard, computer-aided presentations and other materials
necessary and useful in the learning process.
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Learning theories and instructional design (ID) models
are helpful in developing course materials for effective instruction.
For instance, instructional designers may use the learning theories as a
source for verifying strategies and as a foundation for intelligent
selection of strategies (Ertmer & Newby, 2013). Behaviorism,
cognitivism, and constructivism are three primary learning theories that
provide the andragogical basis for understanding how students learn
(Keesee, 2012).
Behaviorism only focuses on objectively observable behaviors
and discounts mental activities of the mind while cognitivism focuses on
the “brain” as it emphasizes intelligence as a special endowment for an
individual to develop intellectually (Keesee, 2012). Constructivism, on
the other hand, focuses on how learners construct the meaning from new
and prior knowledge.
In addition to the primary learning theories, the adult learning
theory, cognitive load theory, and multimedia theory are important
theories that also affect the approach in designing instruction to
accommodate the learners’ characteristics and experience. Applying the
adult learning theory when designing instruction, one should capitalize
on the learner’s experience (Merriam et al., 2012). The application of the
cognitive load theory in ID lies on the limitation of the learner’s working
memory (Sweller et al., 1998). The multimedia theory has a similar goal
with the cognitive load theory which is the use of evidence-based
principles for ID that avoids overloading the learner's cognitive
capacity (Paas & Sweller, 2014).
Developing instructional materials requires a systematic
approach and a more defined model according to Branch and Kopcha
(2014). There are a variety of ID models developed earlier (Gustafson &
Branch, 1997) and all of these contain the core elements of ADDIE
which is an acronym for analyze, design, develop, implement, and
evaluate (Aldoobie, 2015). The phases of ADDIE represent the
fundamental concepts of the ID process ensuring that the design has to
be student-centered, goal-oriented with meaningful performance and
outcomes that can be validly measured (Reiser & Dempsey, 2012).
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The phases of the ADDIE model are related to and interact with
each other (Aldoobie, 2015). In the analysis phase, the instructional
designer analyzes the existing knowledge, skills, experience, and
attitudes of the target learner and determines instructional goals as well
as the learning environment. Beishuizen and Stoutjesdijk (1999) stated
that the quality of learning material is enhanced if the students’ learning
styles are taken into account.
In the design phase, the designer identifies the learning
objectives to outline contents and instructional strategies. The Bloom’s
Taxonomy is helpful in writing the learning objectives and classifying
them based on complexity and specificity using the cognitive,
psychomotor, and affective learning domains (Adams, 2015).
The learners must be able to access and engage with the learning
materials which match or accommodate their learning preferences
(Jonassen & Wang, 1993). Hence, the designer would think of how the
instruction can be effective in ways that able the learners to interact with
the materials (Aldoobie, 2015).
In the development phase, the designer creates the instructional
contents, a prototype, and assessment tools while the implementation
phase is the actual delivery of IM in the settings for which it was
designed (Aldoobie, 2015). The evaluation phase includes formative and
summative evaluation (Dick et al., 2014).
Evaluation studies of the quality of IM to improve the instruction
are few (Weiten et al., 1999; De Jong & Lentz, 1996; Hamilton, 1985;
Weston et al., 1997; Baktash & Talebinejad, 2015). The book
of
Hartley (2013) offers guidelines for writing instructional text and
explains the methods of evaluating its quality. Evaluation studies of the
quality of Engineering textbooks, in particular, are carried out in other
Asian countries like Japan, China, and Korean and are more focused on
language barrier (Yan & Jie, 2014; Arimitsu et al., 2014). The recent
development and evaluation study of IM for engineering was conducted
by Terano (2015). Such study is useful for other instructors who intend
to design their IM related to their field of specialization.
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In an attempt to provide the engineering students quality
instructional material (IM) that can supplement their learning process,
this study aimed to develop a Simplified Text in Differential Calculus
for engineering and determine its acceptability. The study is important in
providing an effective IM for engineering students to improve their
proficiency in higher mathematics.
Materials and Methods
This study is a descriptive developmental research. The ADDIE
framework described by Aldoobie (2015) was used to design and
develop the Simplified Text in Differential Calculus for Engineering.
The acceptability of the objectives, contents, presentation and style, and
exercises in the IM was determined using a validated evaluation
instrument.
The development of the IM started with the planning and
conceptualization of what to do to generate material for Differential
Calculus useful for engineering programs. A review of related studies
and literature served as the guide on what to develop based on student
needs and the curriculum in the engineering education. The information
was analyzed and used for designing the IM.
During the designing process, the objectives were formulated,
and other references were examined to outline the contents. The other
features in the IM designed were the presentation and style, and
exercises. The topics included in the material followed the CHED
(Commission on Higher Education) minimum requirements for
Differential Calculus for engineering programs based on CHED
Memorandum Order (CMO) No. 12, series of 2008 (CHED, 2008) as
shown here.
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CHED Course Outline for Differential Calculus
1. Functions
2. Continuity
3. Limits
4. The Derivative
5. The Slope
6. Rate of Change
7. The Chain Rule and General Power Rule
8. Implicit Differentiation
9. Higher-Order Derivatives
10. Polynomial Curves
11. Applications of the Derivatives: Optimization Problems
12. Applications of the Derivatives: Related Rates
13. The Differential
14. Derivatives of Trigonometric Functions
15. Derivatives of Inverse Trigonometric Functions
16. Derivatives of Logarithmic Functions
17. Derivatives of Hyperbolic Functions
18. Solution of Equations
19. Transcendental Curve Tracing
20. Parametric Equations
21. Partial Differentiation
During the development of the IM, a careful analysis of the
contents based on the course outline was undertaken. The discussions
were in the correct sequence with the outline and kept simple to suit the
level of the learner's understanding. Encoding the contents of the
material took a lot of time since it is necessary not to make any error
especially in the equations. Grammar editing and checking of the right
terms were done.
After developing the material, an evaluation instrument was
formulated and validated to determine the acceptability of the material.
The instrument was composed of four parts, namely: objectives,
contents, presentations and style, and exercises. The instrument has a
total of 14 indicators of acceptability. Three indicators were evaluated to
determine if the objectives were acceptable and these are:
1) The cognitive, psychomotor and affective statements of the
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objectives, 2) Simplicity and attainability, and 3) Suitability to the
particular topic. Five indicators were evaluated to determine if the
contents were acceptable. These indicators include 1) Support of
the objectives to the topics, problems and exercises, 2) The relevance of
the problems and exercises on the topics, 3) The relevance of the
problems and exercises on the objectives, 4) Suitability of the topics to
the learning ability of the students, and 5) Suitability of the discussions
on the interests and needs of the students. Three indicators were assessed
to determine if the presentation and style were acceptable and these are:
1) Terms used, 2) Language used, and 3) Clear presentation of the
discussions. Three indicators were also evaluated to determine if the
exercises were acceptable and these are: 1) Sufficiency of the exercises
given, 2) Clearly stated problems, and 3) Suitability of the exercises to
the level of the learner.
The evaluation instrument together with the IM was distributed
to 22 engineering professors from the target academic institutions in the
Bicol Region using the expert-based method of Schriver (1989, 1990,
1997) in determining the acceptability of the IM. The evaluators were
composed of 10 professors from Camarines Sur Polytechnic Colleges
(CSPC) in Nabua, Camarines Sur; four (4) professors from the Bicol
University Polangui Campus (BUPC) in Polangui, Albay; five (5)
professors from the University of Northeastern Philippines (UNEP), and
three (3) professors from the University of Saint Anthony (USANT),
both institutions are situated in Iriga City.
The five-point Likert scale was used to evaluate the level of
acceptability of the material. The weighted mean was the descriptive
statistics used to determine the acceptability. The following continuum
was used to generate the interpretation of the evaluation:
4.20–5.00 (Highly acceptable); 3.40–
4.19 (Somewhat acceptable);
2.60–3.39 (Moderately acceptable); 1.80–2.59 (Fairly acceptable);
1.00–1.79 (Not acceptable). The standard deviation (SD) was
determined to calculate the coefficient of variation (CV) which was
interpreted as the
percentage of variability of the responses.
The standard value is at most 10% which assures that the responses are
comparable.
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Results and Discussion
Eleven chapters compose the Simplified Text in Differential
Calculus for Engineering. These chapters are presented as follows: (1)
Functions, Limits and Continuity, (2) Derivatives, (3) Algebraic
Functions, (4) Applications of Derivatives, (5) Trigonometric and
Inverse Trigonometric Functions, (6) Exponential and Logarithmic
Functions, (7) Hyperbolic and Inverse Hyperbolic Functions,
(8) Parametric Equations, (9) Curvature, (10) Indeterminate Forms,
and (11) Partial Differentiation. The CHED minimum requirement for
Differential Calculus for engineering serves as the guide in outlining the
contents of each chapter. The instructional outline provided by the
CHED is an essential reference to analyze in developing the contents of
the material. Peterson (2003) emphasized that identifying the contents of
the material can be aided with sample syllabi or course website.
Accordingly, instructors or designers when developing an IM have to
examine standards and competencies to establish a foundation when
determining what topics that student would need. Updated Policies,
Standards and Guidelines (PSG) for the engineering program are
accessible online in CHED website and can provide a workable template
when preparing the contents of the material.
Each chapter follows the same format and sequence using
English as the language. The order of presentation is as follows:
(1) Chapter Number and Title which state the order and name of the
chapter, respectively; (2) Learning Objectives which serve as the guide
for the students on what to learn in a particular chapter; (3) Lesson
Number and Topic which indicate the order and the name of the topics
in every chapter, respectively; (4) Discussion which is the presentation
of the basic concepts, formulas, theories and insights of the lesson;
(5) Sample Problems and Solutions which are carefully and
systematically solved problems in every lesson; and (6) Exercises,
which are problems for every topic or subtopics in every chapter.
The format and sequence of information have practical
significance to clarify the structure of the text and help the readers gain
access to the information (Hartley, 2013). Readers tend to skim, search,
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and re-read the text instead of only reading the material from beginning
to end (Hartley, 2004). The devices that aid students navigate the text
include titles, outlines, headings and subheadings, and numbering
system. Moreover, these devices can help students recall what the text is
all about. Concrete titles for example rather than those that are abstract
may improve the recall, comprehension, and interest of undergraduate
students (Sadoski et al., 2000).
In this simplified text, the learning objectives are designed to
articulate the knowledge and skills that the students acquire by the end
of the course. They are simple, attainable, and suitable to the topic.
The learning objectives of the material were constructed using the
Bloom’s Taxonomy of the cognitive, affective, and psychomotor
learning domains as emphasized by Adams (2015). The learning
objectives are important in examining the quality of an IM. With the
expert-based method of evaluating the quality of the instructional text,
the concern lies on whether the material could meet the objectives as to
the depth of the contents. Teacher, for example, may want to decide
whether the IM is suitable for their students and the learning objectives
can aid them in their judgment (Hartley, 2013). The effectiveness of IM
depends on the manner and the degree to which they meet the needs of
teachers and students (Idowu, 2010). From the reader-based perspective
of determining the quality of an IM, a study showed that the learning
objectives are among the text features that different groups of students
rated useful (Marek et al., 1999). An earlier study also showed
that the learning objectives are cues that direct the reader’s attention
(Schallert et al., 1988).
Lesson number is another feature in this simplified text used to
clarify the structure of the IM and to organize topics in the text as
Hartley (2013) also stressed. Chapter subheading is also a cue to signal
content and organization (Schallert et al., 1988). The topics included in
the text followed the CHED minimum requirements for Differential
Calculus for engineering programs based on CMO No. 12, series of
2008 to ensure relevance of contents. Books and reference texts are
valuable IMs that encompass all the topics to tackle in a particular
course and need to be curriculum-based and substantial (Terano, 2015).
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The topics were identified based on the objectives defined for every
lesson with relevant problems and exercises that are specific to the topic.
Experts usually examine the relevance of contents when evaluating the
quality of school textbooks (Hartley, 2004). The suitability of the topic to
the learner’s ability was also considered in this text. The contents were
developed in such a way that they are student-centered and goal-oriented
with relevant activities (Reiser & Dempsey, 2012).
The clarity of the discussion in the text is mandatory and
regarded as the most effective criterion for an effective IM
(Gerson, 2000). In this simplified text, the presentation of concepts and
theories is made simple, concise, and accurate for engineering students
with sample problems and solutions that are developed based on the
lesson objectives and illustrated clearly for easy understanding of the
topic as Hartley (2013) and Gerson (2000) emphasized. Also, presenting
the greater detail of the examples may have made the discussions clearer
(Atkinson et al., 2000).
The exercises are presented at the end of every topic or subtopic
in the simplified text with problems clearly stated. They were
constructed based on the objectives defined for every lesson to ensure
their relevance to the topic. They were sufficient for a given period
allowing the students to learn more while they have to answer the
questions. Paas and Sweller (2014) noted that it is important to provide
sufficient exercises so as not to overload the learner’s cognitive
capacity. The suitability of the exercises to the level of the learner is
therefore necessary. The study of Weiten et al. (1999) also showed that
review exercises are useful and it is helpful to place them close to where
they are referred to in the text. Students claim that the primary uses of
the text are to help them answer the exercises or questions and to
provide the supplementary reading (Hartley, 2013).
The acceptability of the text features is shown in
Tables 1-4 and the responses of the evaluators are comparable.
The objectives are highly acceptable as shown in Table 1. The results
confirmed that the objectives presented include the cognitive,
psychomotor and affective aspects of learning guided by the Bloom’s
Taxonomy. These findings are similar to that of Terrano (2015).
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Several taxonomies were developed for higher education, but Finelli
et al. (2015) claimed that Bloom’s Taxonomy is still very widely used.
Riazi and Mossalanejad (2010) for example used Bloom’s as the
framework of their evaluation study of course books. Razmjoo and
Kazempourfard (2012) evaluated the learning objectives of course books
but this time using the Bloom's Taxonomy Revised. Baktash and
Talebinejad (2015) evaluated the acceptability of the developed Iranian
series books also using Bloom’s Taxonomy Revised to improve the
quality of instruction.
Table 1. Acceptability of objectives.
Indicators
Weighted
mean
Verbal
interpretation
1.
The cognitive, psychomotor and
affective statements of the objectives.
4.86
Highly acceptable
2. Simplicity and attainability.
4.73
Highly acceptable
3. Suitability to the particular topic.
4.77
Highly acceptable
Overall Weighted Mean
4.79
Highly acceptable
SD
0.0666
CV
1.39%
Wilson (2014) discussed the revisions to Bloom’s classic
cognitive taxonomy by Anderson and Krathwohl published in 2001.
The major differences lie in the comprehensive additions of how the
taxonomy intersects and acts upon factual, conceptual, procedural and
metacognitive different types and levels of knowledge. Nevertheless,
it is important to note that the learning objectives in this simplified text
can be classified into levels of complexity and specificity using the
cognitive, psychomotor, and affective learning domains (Adams, 2015).
Table 2 shows that the contents of the simplified text are highly
acceptable. Taking into account the indicators evaluated, the results
confirmed that the general contents which include the topics, problems
and exercises are aligned with the objectives of the lesson ensuring their
relevance. The results also imply that the contents could provide learners
the instructional strategies that would be effective for cognitive,
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psychomotor, and affective learning since the objectives are developed
using the Bloom’s Taxonomy (Adams, 2015). The contents are highly
acceptable considering that during the design phase of the study the
CHED course outline was used as the guide to ensure that the required
standards and competencies are met. The results further imply that the
contents are suitable to the learner’s ability and needs. Suitability is
attained when the contents are student-centered and goal-oriented
coupled with relevant activities (Reiser & Dempsey, 2012).
Table 2. Acceptability of the contents.
Indicators
Weighted
mean
Verbal
interpretation
1.
Support of the objectives to the topics,
problems and exercises.
4.86
Highly acceptable
2. The relevance of the problems and exercises
on the topics.
4.77
Highly acceptable
3. The relevance of the problems and exercises
on the objectives.
4.90
Highly acceptable
4. Suitability of the topics to the learning ability
of the students.
4.90
Highly acceptable
5. Suitability of the discussions on the interests
and needs of the students.
4.77
Highly acceptable
Overall Weighted Mean
4.84
Highly acceptable
SD
0.0660
CV
1.36%
The presentation and style of the simplified text as shown in
Table 3 are highly acceptable. The results imply that the terms and the
language used in the text are suitable to the level of student
understanding. The findings also suggest that there is clarity in the
discussions of the topic and the presentation of concepts and theories is
simple, concise, and accurate. It can be further deduced from the results
that the sample problems and solutions that are developed based on the
objectives are clearly illustrated for easy understanding of the topic.
Hartley (2013) emphasized that students have different needs and
preferences in the learning process and the clarity of the discussion
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could help address such variation. Clarity in the text is mandatory and
regarded as the most effective criterion for an effective IM
(Gerson, 2000).
Instructional material plays a significant role in leaping
intentions and plans to classroom activities by organizing contents and
making them available, and by setting out learning tasks in a form
designed to be appealing to students (Schmidt et al., 1997). Based on the
three primary learning theories, the instructional strategies devised in the
IM should aim for students to develop their cognitive potentials
and be able to construct their meaning from new and prior knowledge
(Keesee, 2012).
Table 3. Acceptability of presentation and style.
Indicators
Weighted
mean
Verbal
interpretation
1. Terms used
4.86
Highly acceptable
2. Language used
4.86
Highly acceptable
3. Clear presentation of the discussions
4.90
Highly acceptable
Overall Weighted Mean
4.87
Highly acceptable
SD
0.0231
CV
0.47%
Table 4 shows that the exercises in the simplified text are highly
acceptable. The results confirmed that the exercises given are sufficient
for the students to learn the concepts and theories of every topic in a
chapter for a specified period. Providing sufficient exercises avoids
overloading the learner’s cognitive capacity (Paas & Sweller, 2014). The
results also showed that the problems are clearly stated, and the
exercises are suitable for the level of the learner. Dick et al. (2014)
emphasized that the assessment must be parallel to and able to measure
the learners’ ability to perform what is described in the objectives.
Problem sets will enhance the critical thinking of students.
Terano (2015) stressed that in the tertiary curriculum, the focus should
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not only be on the theoretical aspects but also on the skills which
involve activities that will enhance the critical thinking of students.
Table 4. Acceptability of exercises.
Indicators
Weighted
mean
Verbal
interpretation
1. Sufficiency of the exercises given
4.90
Highly acceptable
2. Clearly stated problems
4.77
Highly acceptable
3. Suitability of the exercises to the level of the learner
4.86
Highly acceptable
Overall Weighted Mean
4.84
Highly acceptable
SD
0.0666
CV
1.38%
The overall results of the acceptability of the IM based on the
features evaluated are shown in Table 5. All text features are highly
acceptable which imply that the simplified text could be an effective
instructional material for engineering students.
Table 5.
Overall results of acceptability of the simplified text in
Differential Calculus for engineering.
Indicators
Weighted
mean
Verbal
interpretation
1. Objectives
4.79
Highly acceptable
2. Contents
4.84
Highly acceptable
3. Presentation and style
4.
Exercises
4.87
4.84
Highly acceptable
Highly acceptable
Overall Weighted Mean
4.84
Highly acceptable
SD
0.0332
CV
0.69%
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Conclusion and Recommendations
The simplified text in Differential Calculus for Engineering
follows the CHED minimum requirement for engineering programs.
Objectives, contents, presentations and style, and the exercises are text
features evaluated by engineering professors as highly acceptable which
imply that the simplified text could be an effective instructional material
for engineering students.
Further evaluation can improve the design of the material.
Periodic revision of the simplified text can accommodate changes or
updates in the CMOs. Item analysis may be carried out to improve the
acceptability. The format of the material could be used as the matrix for
the development of other instructional materials in related fields.
Acknowledgment
The researcher would like to thank the Camarines Sur Polytechnic Colleges,
Nabua, Camarines Sur with its President Dr. Dulce F. Atian, the Dean of the
College of Engineering Engr. Francia H. Tomenio, to his colleagues from the
College of Engineering, to his students, family and most of all to Almighty
God for the continuous support for the completion of this study.
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