Proceedings of the 3rd International Conference of Teaching and Learning (ICTL 2011)
INTI International University, Malaysia
EFFECTIVENESS OF THE MODULAR INSTRUCTIONAL
MATERIAL IN THE BASIC INTEGRATION
FORMULAS IN INTEGRAL CALCULUS
Rolando J. Aquino1, Luisito C. Hagos2, Yolanda Evangelista3,
Ulyses V. Lim4 and Florencio V. Reyes5
2
1,3,4
Rizal Technological University, Philippines (4ulvlim_519@yahoo.com)
Rizal Technological University; Philippine College of Health and Sciences, Philippines
(dochagosneu@yahoo.com)
5
University of Batangas, Philippines
ABSTRACT
This study aimed to determine the effectiveness of the modular instructional materials for college students
enrolled in Integral Calculus by promoting understanding and mastery of the application of the different
integration formulas in evaluating and simplifying integrals. Findings reveals that modular instruction was
found to be as effective as the traditional method based on the improved performance of the students in
respective subjects. The programmed instruction such as in module form is an important educational innovation
and a teaching technique offers a solution to the problems of teaching instruction for a more efficient mass
education and more effective individual instruction. Furthermore, the developed modular instructional material
in Integral Calculus helped students develop logical and correct thinking and have better understanding of the
different standard integration formulas.
KEYWORDS
Modular instruction, Module, Integral calculus, Integration, Integration formulas, Effectiveness of modular
instruction
INTRODUCTION
Mathematics is a difficult subject, both to learn and to teach (Abalajon, 1993). Being an exact
science and the foundation of science and technology, the curricula at all levels of the
educational system feature mathematics among the major subjects. However, because of its
abstract nature, mathematics is usually a subject to be wrestled with or at best endured rather
than enjoyed by most young learners who are not mathematically inclined (Acelajado, 2006).
Over the years, schools have always been concerned with the development of effective
learning experience for the learners. It is generally accepted that the quality of education
students get largely dependent upon the quality of instruction they are given. There is then a
necessity to use better teaching strategies in all levels of learning especially in mathematics.
A mathematics teacher must be very creative in his methods and approaches in teaching. He
is expected to possess a thorough knowledge of the criteria of good teaching and the subject
matter to be taught, a broad knowledge of various methods and strategies of teaching
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Proceedings of the 3rd International Conference of Teaching and Learning (ICTL 2011)
INTI International University, Malaysia
different kinds of students with the aid of the appropriate visual aids and techniques (Aquino,
1998).
It should be borne in mind that the act of teaching is so complex that it is nearly impossible to
claim that a specific way of teaching is superior to other ways. Certain procedures, teaching
styles and techniques that are generally not recommended seem to work well for a specific
teacher. There are however many good ways to teach (Cachero, 1994).
One way of maintaining the interest of the learners is to provide them with activities which
they can perform individually, after being given the proper guidance, direction, instruction
and encouragement by the teacher. This is the use of programmed instruction as a teaching
tool. These programmed materials claim to make learning interesting (Cudia, 1985).
Programmed instruction in module form is an important educational innovation and a
teaching technique. It also offers a solution to the problems of teaching instruction. Modular
instruction promises a more efficient mass education by offering more effective individual
instruction at a time when teacher is faced with a problem of producing learning in a large
group all at the same time. It is a technique of self-instruction that involves the presentation
of instructional materials to demonstrate their skills and comprehension (Goldschmid, 2005).
An example of individualized instruction is the use of modules or modular instruction. It
accommodates individual differences and provides a variety of learning strategies and a
systematized way of developing and implementing subject matters (Jimenez, 1987). The
student has the responsibility of learning by himself. He will be involved in responding to the
instructional material as well as interacting with his classmates and also the teacher itself.
Background of the Study
A considerably low achievement in mathematics and a relatively low self-efficacy among
students who are impatient in solving mathematical problems pose real great challenge to
present day mathematics educators. This challenge may be addressed by introducing new
programs of instructions, new instructional materials, and new teaching methods and
approaches. In the light of the preceding arguments, this study attempted to use the modular
teaching approach in Integral Calculus and investigate its effects on the students’
achievement.
It is a fact that no two individuals are alike in their physical, mental, and emotional
development: one may grow faster, another can easily recognize concepts, and still others
tend to be more mature as compared to others of the same age. Luna (1978) emphasized that
a student may be recognized as an individual by giving him tasks specifically geared to his
needs and interests, and by providing him with instructional materials that will allow him to
progress at an optimal rate on his own pace.
The researcher thought of pursuing this study because he believes that this method of
presenting a subject matter to the learners is important and it focuses the teacher’s role as a
guide and a helper rather than a dominant figure who does everything while students just
listen. The researcher also believes that this will be of help in improving mathematics
instruction on the different standard integration formula in Integral Calculus.
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Proceedings of the 3rd International Conference of Teaching and Learning (ICTL 2011)
INTI International University, Malaysia
This study aimed to determine the effectiveness of the module instructional material for
college students enrolled in Integral Calculus by promoting understanding and mastery of the
application of the different integration formulas in evaluating and simplifying integrals.
The module was developed following the standard syllabus in Integral Calculus as mandated
by the Commission on Higher Education and approved by the Mathematics Department of
Rizal Technological University. The first seven topics that cover the mid-term period were
included in the manual focusing on the basic integration formulas – power formula,
logarithmic formula, exponential formula, trigonometric formula, inverse trigonometric
formula, and integration by parts.
This study was limited to the evaluation of the appropriateness of the module, its validity and
effectiveness in the presentation of the lessons in Integral Calculus to students.
The study was conducted at Rizal Technological University, Boni. Avenue, Mandaluyong
City, to a group of second year B.S. Statistics and Mechanical Engineering Technology
students for the first semester of school year 2010-2011.
THEORETICAL FRAMEWORK
This study is anchored with the intensive researches on the psychological theories of learning
such as the Theory of Concept Formation (Nocon, 1992) which is a powerful framework
within which to explore how an individual constructs a new mathematical concept. In
particular, this theory is able to bridge the gap between an individual’s mathematical
knowledge and the body of socially sanctioned mathematical knowledge. It can also be used
to explain how idiosyncratic usages of mathematical signs by students (particularly when just
introduced to a new mathematical object) get transformed into mathematically acceptable
usages and it can be used to elucidate the link between usages of mathematical signs and the
attainment of meaningful mathematical concepts by an individual.
Another theory that could best fit this study is the Theory of Reinforcement (Nocon, 1992)
which states that any stimulus that, when contingent on a response, serves to increase the rate
of responding. The main idea that reinforces can control behavior. The definition has two
main components: Contingency, where the occurrence of the reinforcer depends on the
occurrence of the learner's response, and Rate of Responding, where the reinforcer serves to
increase the learner's rate of responding
(http://wik.ed.uiuc.edu/index.php/Reinforcement_theory).
Research Design
The original intention of using experimental design in this study was not possible due to
insufficient number of class sizes during the time the study was conducted. Descriptive
method was then used. Descriptive method was utilized because it determines the prevailing
conditions. According to Young (1991) “descriptive method of research is a fact-finding
study with adequate and accurate interpretation of the findings. It describes with emphasis
what actually exist such as current conditions, practices, situations, or any phenomena”.
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Proceedings of the 3rd International Conference of Teaching and Learning (ICTL 2011)
INTI International University, Malaysia
The research and development cycle (R and D) by Borg (2005) as shown in Figure 1 was
used in making and preparing a modular instruction in the basic integration formulas in
Integral Calculus.
List the need for developing a modular instruction
Decide on the topics to be included in the module
Determine the importance of each topic included in the module
Select the contents/topics
Select appropriate module model to be used
Prepare the first graft of the module
Evaluation the modular instruction
Analyze the evaluation for possible improvement
Revised the module
Figure 1. Research and Development Cycle
Respondents of the Study
The subjects were grouped into two groups – the experimental group and the control group
composed of 31 students each. The experimental group was subjected to the use of the
module while the control group was exposed to the conventional method of teaching
mathematics. The groups were carefully matched as to I.Q. and final grade in their common
math subjects in College Algebra, Trigonometry, Analytic and Solid Geometry, and
Differential Calculus.
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Proceedings of the 3rd International Conference of Teaching and Learning (ICTL 2011)
INTI International University, Malaysia
Two sections of Integral Calculus for Mechanical Engineering Technology and BS Statistics
students of Rizal Technological University in Boni. Avenue, Mandaluyong City were offered
in that semester school year 2010-2011. So they were utilized as the respondents of the study.
Instruments Used
The research instruments utilized were questionnaire, unstructured interview and observation.
The researchers used the following statistical tool to get answer for specific problems and for
understanding, interpretation and obtaining accurate results of data percentage, weighted
mean and z-test was used.
Respondents Assessment on the Extent of Validity of the tasks presented in the Module
The respondents assessed the module excellent since it offers more effective individual
instruction for more efficient mass education (wm = 4.67) but their assessment made was that
the module was satisfactory as it helps arouse the interest of the learners as reflected from the
mean score of 3.29.
Performance in the Pre-test and in the Post-test of the Experimental Group and Control
Groups
The following data summarizes the performance of the respondents in the pre-test and posttest of the experimental group and control groups on power formula, logarithmic formula,
exponential formula, trigonometric formula, inverse trigonometric formula and integration by
parts.
Power Formula. The pre-test scores reveal that there are 12 or 40 percent of the respondents
who belong to the control group earned a fair grade ranging from 75 – 80. On the other hand,
there are 12 or 39% of the respondents who are in the experimental group got a satisfactory
grade of 81 – 86. Based on the result of the posttest, there are 19 or 61% from the control
group who earned a fair grade ranging from 75 – 80 and 6 or 19% who earned a poor grade of
70 – 74.
Logarithmic Formula. The pre-test scores reveal that there are 16 or 52% of the respondents
from the control group who were rated poor with grades of 70 – 74 followed immediately by
9 or 29% who earned a fair grade of 75 – 80. Based on the data, nobody earned an excellent
and very satisfactory grade. On the other hand, 13 or 42% of respondents from the
experimental group earned a grade 70 – 74 with 8 or 26% of the respondents who earned a
satisfactory grade of 81 – 86. Results of the post-test scores reveal that there are 12 or 39
percent of the respondents from the control group who earned a poor grade ranging from 70 74 with 1 or 3% of the respondent who earned a very satisfactory grade of 87 – 92. On the
other hand, 9 or 29% from the experimental group got a poor grade ranging from 70 – 74
with 7 or 23% of the respondents who earned a fair grade of 75 – 80.
Exponential Formula. The pre-test score from the control group reveals that there are 14 or
45 of the respondents who are rated fair with grades ranging from 75 – 80 with 1 or 3% who
earned a very satisfactory grade of 87 – 92. The experimental group has 13 or 42% who
earned a fair rating of 75 – 80 with nobody who scored a very satisfactory or excellent grade.
The post-test results, 12 or 39% from the control group earned a fair grade of 75 – 80 with 11
or 36% of the respondents from the experimental group earned a satisfactory grade ranging
from 81 – 86.
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Proceedings of the 3rd International Conference of Teaching and Learning (ICTL 2011)
INTI International University, Malaysia
Trigonometric Formula. There are 13 or 42% of the respondents from the control group
earned both a fair and poor grade 75 – 80 and 70 – 74. There are 12 or 39% of the
respondents who are rated poor with grades ranging from 70 – 74 with 1 or 3% earned a very
satisfactory grade of 87 – 92. With regards to the result of the post-test, there are 12 or 39 %
of the respondents from the control group who are rated fair with grades ranging from 75 –
80. On the other hand, there are 11 or 35% from the experimental group got a satisfactory
grade of 81 – 86.
Inverse Trigonometric Formula. Data from the post-test results shows that there are 16 or
52% and experiment group earned a poor grade of 70 – 74, respectively. On the other hand,
results of the post-test show that there are 11 or 35% from the control group who earned a
satisfactory grade of 81 – 86.
Integration by Parts. There are 16 or 52% from the control group earned a poor grade of 70 –
74 with nobody earned both a very satisfactory or excellent grade. The post-test results reveal
that there are 16 or 52% of the respondents who earned a satisfactory grade of 81 – 86.
Significant Difference in the Post-test Result between the Experimental group and the
Control Group
The following data summarizes the significant difference in the post-test result between the
experimental group and control groups on power formula, logarithmic formula, exponential
formula, trigonometric formula, inverse trigonometric formula and integration by parts.
Power Formula. Since the computed z-value of 7.21 is greater than the tabular value of 1.96
it led to the rejection of the hypothesis and concluded that there is significant difference in the
performance in the post-test between the experimental group and control group on power
formula.
Logarithmic Formula. Since the computed z-value of 2.01 is greater than the tabular value of
1.96 led to the rejection of the hypothesis and concluded that there is significant difference in
the performance in the post-test between the experimental group and control group on
logarithmic formula.
Exponential Formula. There is significant difference in the performance in the post-test
between the experimental group and control group on logarithmic formula since the
computed z-value of 2.49 is greater than the tabular value of 1.96.
Trigonometric Formula. Results of the z test reveals that there is significant difference in the
performance in the post-test between the experimental group and control group on
trigonometric formula since the computed z-value of 2.20 is greater than the tabular value of
1.96.
Inverse Trigonometric Formula. The hypothesis that there is no significant difference in the
performance in the post-test between the experimental group and control group on
trigonometric formula was accepted since the computed z-value of -1.40 is less than the
tabular value of 1.96.
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Proceedings of the 3rd International Conference of Teaching and Learning (ICTL 2011)
INTI International University, Malaysia
Integration by Parts. Since the computed z-value of 0.26 is less than the tabular value of
1.96, the hypothesis was accepted and concluded that there is no significant difference in the
performance in the post-test between the experimental group and control group on integration
by parts.
CONCLUSION
Based on the findings from this study, the following conclusions are drawn:
1.
Programmed instruction such as module form is an important educational innovation and
a teaching technique that offers a solution to the problems of teaching instruction for a
more efficient mass education and more effective individual instruction.
2.
The developed modular instructional material in Integral Calculus helped students
develop logical and correct thinking and have better understanding of the different
standard integration formulas.
3.
There is significant difference in the post-test result between the experimental group and
control groups on power formula, logarithmic formula, exponential formula and
trigonometric formula but there is no significant difference on inverse trigonometric
formula and integration by parts.
4.
Modular instruction was found to be as effective as, if not more effective than, the
traditional method based on the improved performance of the students in respective
subjects.
RECOMMENDATION
Based on the significant findings and conclusion on this study, the researcher proposes the
following recommendations:
1.
Develop a proposed module in Integral Calculus not only on the basic integration
formulas but also in higher integration techniques.
2.
Encourage teachers to develop modular instructional materials not only in Integral
Calculus but also in other mathematics topics to enable students to perform better
because the material strictly follows the principles underlying modular instruction.
3.
Enhance the modular instructional materials developed in integral calculus to improve
the students’ performance in inverse trigonometric formula and integration by parts.
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Proceedings of the 3rd International Conference of Teaching and Learning (ICTL 2011)
INTI International University, Malaysia
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