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EZTRIGO MNEMONIC DIAGRAM: A COMPARISON STUDY OF STUDENTS’ PERFORMANCE IN PRE AND POST RESULT FOR BASIC DIFFERENTIATION AND INTEGRATION OF TRIGONOMETRIC FUNCTIONS TEST

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International Journal of Civil Engineering and Technology (IJCIET)
Volume 10, Issue 03, March 2019, pp. 807–813, Article ID: IJCIET_10_03_078
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJCIET&VType=10&IType=3
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication
Scopus Indexed
EZTRIGO MNEMONIC DIAGRAM: A
COMPARISON STUDY OF STUDENTS’
PERFORMANCE IN PRE AND POST RESULT
FOR BASIC DIFFERENTIATION AND
INTEGRATION OF TRIGONOMETRIC
FUNCTIONS TEST
Rusliza Ahmad*, Nur Azila Yahya, Ini Imaina Abdullah, Nadzri Mohamad,
Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA,
Perak Branch, Tapah Campus, 35400 Tapah Road, Perak, Malaysia
Khairunnisa Mohd Daud
Academy of Language Studies, Universiti Teknologi MARA,
40450 Shah Alam, Selangor, Malaysia
ABSTRACT
The objective of this study is to compare the performance of Applied Sciences
students’ in a Pre and Post Basic Differentiation and Integration Test during their
second year of study at the Faculty of Applied Sciences, Universiti Teknologi MARA,
Perak Branch, Tapah Campus. This paper focuses on the students’ understanding in
basic differentiation and integration for trigonometric functions. A total of 95
Semester 3 students of session 2 2017/2018 from the Department of Applied Sciences
are chosen to answer the test. The pre-test was held in week 10, while the post-test
was conducted in week 13 of the semester. In pre-test, the students need to answer the
questions based on traditional method while in post-test, the EzTrigo Mnemonic
Diagram is introduced and the students applied the technique in order to answer the
questions. The results showed that the students’ performance in post-test was better
compared to that pre-test.
Key words: Calculus, Differentiation, Integration, Mnemonic, Trigonometric
Functions.
Cite this Article: Rusliza Ahmad, Nur Azila Yahya, Ini Imaina Abdullah,
Nadzri Mohamad, Khairunnisa Mohd Daud, Eztrigo Mnemonic Diagram: A
Comparison Study of Students’ Performance in Pre and Post Result for Basic
Differentiation and Integration of Trigonometric Functions Test, International Journal
of Civil Engineering and Technology 10(3), 2019, pp. 807–813.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=10&IType=3
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Rusliza Ahmad, Nur Azila Yahya, Ini Imaina Abdullah, Nadzri Mohamad, Khairunnisa Mohd Daud
1. INTRODUCTION
Mathematics is one of the core subjects in science and any engineering fields. However,
students in higher education institutions, especially in both fields were found to have
insufficient basic mathematics skills and knowledge [1]. Universiti Teknologi MARA
(UiTM), Perak Branch, Tapah Campus is one of the UiTM’s branches which offer Science based programs that is Applied Sciences program. One of the important subjects that support
and relates to Applied Sciences program is Calculus I. Calculus I subject focuses on limits,
differentiation, integration and applications of differentiation and integration. In the topic of
differentiation and integration for trigonometric functions, most of the students meet
difficulties to memorize the formulas given in textbook. Calculus I is one of the courses that
has been identified as high failure rate course. High failure rate course is a course with
passing rate below 70% [2]. Suresh in [3] mentioned that, Calculus is one of the high failure
rate courses other than Physics and Statistics for engineering students.
Many researchers have implemented various strategies to improve students’ performance
in Mathematics. Ponte in [4] reported that the use of specific teaching unit facilitates the
students’ understanding in mathematics through investigation and exploration task in the
classroom. A group of researchers from Nanyang Technological University, Singapore has
suggested that by refining the curriculum and teaching strategies, the practice of technology
devices, instilling thinking and creativity and establishment of training will expand Calculus
and Mathematic education [5]. According to Awang Salleh and Zakaria in [1], it is found that
students failed to perform in certain topics of mathematic especially integration as the practice
of traditional method of teaching was not helping the students to comprehend the topic better.
The authors have suggested that an innovative way of teaching and learning mathematics
should be initiated to establish the quality of future engineers and scientists.
A visual representation, such as a diagram, can be an effective strategy for mathematical
problems solving [6, 7].Visual mnemonic is one of the techniques that use diagram or
illustration to present information. By using mnemonic in learning mathematics can be one of
the instructional strategies to enhance remembrance such as providing a visual or verbal
prompt for students who encounter difficulty to memorize important information.
DeLashmutt in [8] introduced three methods of teaching mnemonics that are keyword,
pegword and letter strategies. The author used keyword mnemonic to place numerator and
denominator for fraction number while pegword mnemonic for improper fraction. Wood and
Frank in [9] also used a pegword method where students were taught a rhyming sentence to
match a math fact. Liataud and Rodriguez in [10] introduced Times Tables the Fun Way
(TTFW) that used pictures and stories as mnemonic devices for recalling basic multiplication
facts. In 2017, Yahya et al in [11] developed two innovative techniques of basic
differentiation and integration for trigonometric functions by using mnemonic diagram. These
techniques emphasize square and triangle shape to be used for original and chain rule.
This study is a continuity from the work done by [11] by comparing the performance of
Applied Sciences students in a pre and post differentiation and integration test. In pre - test,
the students need to answer all the questions by memorizing the formulas while in post - test,
students need to apply mnemonic diagram proposed by Yahya et al in [11] as in Figure 1 and
Figure 2 in order to answer the questions. This diagram is called as EzTrigo Mnemonic.
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Eztrigo Mnemonic Diagram: A Comparison Study of Students’ Performance in Pre and Post
Result for Basic Differentiation and Integration of Trigonometric Functions Test
Figure 1 Mnemonic of basic differentiation and integration for trigonometric functions (original rule)
Figure 2 Mnemonic of basic differentiation and integration for trigonometric functions (chain rule)
From Figure 1 and Figure 2, the differentiation formulas can be get by clockwise direction
and integration formulas by counterclockwise direction.
2. METHODOLOGY
This study was conducted to compare the performance of Applied Sciences students’ in basic
differentiation and integration of trigonometric functions during their second year of study at
the Faculty of Applied Sciences, Universiti Teknologi MARA, Perak Branch, Tapah Campus.
The pre-test for basic differentiation and integration of trigonometric functions test was held
in week 10, while the post-test was conducted in week 13 of the semester. The basic
differentiation and integration test consisted of 20 questions; 10 questions in Section A
focused on basic differentiation of trigonometric functions, while 10 questions in Section B
focused on basic integration of trigonometric functions. In pre-test, the students need to
answer the questions based on traditional method where students need to memorize the given
formulas in textbook. In post-test, the mnemonic diagram is introduced and the students
applied the technique in order to answer the questions. Students are given 10 minutes before
the test to draw the diagram that have been explained by lecturer. The time given to answer all
the question is 30 minutes. Table 1 exhibits the contents descriptions in the basic
differentiation and integration test.
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Rusliza Ahmad, Nur Azila Yahya, Ini Imaina Abdullah, Nadzri Mohamad, Khairunnisa Mohd Daud
The target population of this study was Diploma students from semester 3, Faculty of
Applied Sciences and implemented in session 2 2017/2018. The sample of the study consisted
of 95 students, from six different classes. A summary of total number of students for each
classes is shown in Table 2.
Table 1 Description of content in basic differential and integration test
Section
A
B
Content
Differentiation
Integration
No. of Questions
10
10
Weightage
100
100
Table 2 Total of semester 3 students in Department of Applied Sciences by classes
Class
A
B
C
D
E
F
TOTAL
Number of Students
13
10
15
17
15
25
95
3. RESULTS AND DISCUSSION
3.1. Overall Results
Figure 3 shows a comparison of students’ performance in the pre and post test of Semester 3
by classes in Applied Sciences Program. Result shows that there was a significant increase
between the pre and post test result where more than 50% of students could understand the
mnemonic diagram and answer the questions correctly while the others made a mistake on
positive and negative sign when differentiate and integrate the function and failed to
differentiate functions when the radian measure of trigonometric functions is not x .
Figure 3 Students’ performance in pre and post test by classes in Applied Sciences Program
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Eztrigo Mnemonic Diagram: A Comparison Study of Students’ Performance in Pre and Post
Result for Basic Differentiation and Integration of Trigonometric Functions Test
Figure 4 shows the percentage of students’ performance in pre and post test by content of
the questions. Section A consists of differentiation of trigonometric functions questions while
Section B integration of trigonometric functions questions. The graph shows changes in the
percentage of students’ obtaining correct answers between the pre and post test. From the
graph, 71.16 % of trigonometric questions while 73.47% answered correctly the integration of
trigonometric functions questions. Based on this graph, it can be seen that students have equal
understanding on mnemonic diagram to solve differentiation and integration of trigonometric
functions.
Figure 4 Percentage of students’ performance in pre and post test by content of questions
3.2. Hypothesis Testing
The purpose of this section was to test the significant difference in students’ performance
after taking the pre and post test. This study is carried out with the following two hypotheses:
H0: There is no significant difference between pre and post test.
H1: There is significant difference between pre and post test.
From Table 5, the paired sample t-test was employed to test the mean difference between
scores using traditional method and mnemonics diagram. The sample of this study was 95
students and all the assumptions for paired sample t-test was checked and satisfied. Based on
the result, there was statistically significant difference between score using traditional method
and mnemonics diagram since the p-value was 0.000 which is less than 0.05. Thus the null
hypothesis (H0) is rejected, which also implies that there was significant difference between
pre and post test. In addition, it is found that the mean score of post-test was higher compared
to mean score of pre- test which are 14.46 and 6.41 respectively (Table 3). Furthermore, we
are 95% confident that the mean difference of the score between pre-test and post-test is
between 6.703 and 9.402.
Table 3 Paired samples statistics
Pre Test
Post Test
Mean
6.41
14.46
Number of Samples
95
95
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Standard Deviation
5.631
5.416
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Rusliza Ahmad, Nur Azila Yahya, Ini Imaina Abdullah, Nadzri Mohamad, Khairunnisa Mohd Daud
Table 4 Paired samples correlation
Correlation (r)
0.281
Pre Test & Post Test
Sig. Value
0.006
Table 5 Paired samples test
Pre Test – Post
Test
Mean
Difference
-8.053
Confidence
Interval
-9.402 , -6.703
t-statistics
p-value
-11.846
0.000
4. CONCLUSION AND RECOMMENDATION
This study focuses on relative relationship in students’ achievement in pre and post basic
differentiation and integration test for trigonometric functions. There were two section of
questions in the test, which were section A is questions on differentiation and section B is
questions on integration. The trigonometric functions questions for both sections involved
original rule where the radian of the function measure is x , for example f ( x)  sin( x) and
chain rule where the radian measure (argument) is not x but defined as u where u is a
differentiable function of x , for example f (u )  sin(u ) . The result shows there was
significant difference between pre and post test. The percentage of students getting the right
answers in post test was quite high.
In Section A that covers the questions of differentiation of trigonometric functions,
knowledge on differentiation of basic functions such as Algebraic, Logarithmic and Exponent
are really important to solve the given questions. Based on the findings, students failed to
differentiate functions when the radian measure of trigonometric functions is not x . Students
mostly repeated the same error in pre and post test probably because they had lack of
understanding and knowledge in the basic topic of differentiation. Part B component involved
integration of trigonometric functions. In this topic, students also need knowledge in
differentiation of basic functions as in Section A. Most of the students failed to give the
correct answers because the solution of integration need to be divided with the derivative of
the argument (radian measure) but they were unable to differentiate the argument.
This study indicates that the mnemonics diagram of basic differentiation and integration
for trigonometric functions could be useful for university and matriculation students who take
Calculus course. These new innovative techniques are easy and simple to use. In order to have
a good performance in solving differentiation and integration, the students themselves need to
have strong knowledge in basic differentiation technique.
Suggestion for further research is to get students feedback regarding the new techniques
proposed in order to see whether these techniques are useful and effective for students in
learning Calculus.
REFERENCES
[1]
Awang Salleh, T. S. and Zakaria, E. Integrating computer algebra system (CAS) into
integral calculus teaching and learning at the university. International Journal of
Academic Research, 3(3), 2011, pp. 397 – 401.
[2]
Eng, T. H., Li, V. L. and Julaihi, N. H. The Impact of ‘High-Failure Rate’ Mathematics
Courses on UiTM Sarawak full-time diploma students’ academic performance. Research
Management Institute, Universiti Teknologi MARA, Malaysia, 2008.
http://www.iaeme.com/IJCIET/index.asp
812
[email protected]
Eztrigo Mnemonic Diagram: A Comparison Study of Students’ Performance in Pre and Post
Result for Basic Differentiation and Integration of Trigonometric Functions Test
[3]
Sureh, R. Persistence and attrition in Engineering: Understanding the nature of students’
experience with barrier courses. Ph.D Dissertation, University of New York, 2002.
[4]
Ponte, J. P. Investigations and explorations in the mathematics classroom. ZDM
Mathematics Education, 39, 2007, pp. 419-430.
[5]
Ahuja, O. P., Lim-Teo, Suat, K., and Lee, P. Y. Mathematics teachers’ perspective of their
students’ learning in traditional calculus and its teaching strategies. Journal of the Korea
Society of Mathematical Education Series D, 2(2), 1998, pp. 89-108.
[6]
Hambree, R. Experiments and relational studies in problem solving meta-analysis. Journal
for Research in Mathematics Education, 23, 1992, pp. 242 – 273.
[7]
Uesaka, Y., Manalo, E. and Ichikawa, S. What kinds of perceptions and daily learning
behaviors promote students’ use of diagrams in mathematics problem solving?. Journal of
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[8]
DeLashmutt, K. A study of the role of Mnemonics in Learning Mathematics. Summative
projects for MA Degree, 2007.
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Wood, D. K and Frank, A. R. Using memory-enhancing strategies to learn multiplication
facts. Teaching Exceptional Children, 32, 2000, pp. 78 – 82.
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Liataud, J. and Rodriguez, D. Times Table the Fun Way: Book for Kids: A Picture
Method of Learning the Multiplication Facts, 3rd Edition. Key Publishing, Sandy, UT,
1999.
[11]
Yahya, N. A., Ahmad, R., Abdullah, I. I., Mohamad, N. and Mohd Daud, K. Mnemonics
of Basic Differentiation and Integration for Trigonometric Functions. International
Journal of Academic Research in Business and Social Sciences, 7(11), 2017, pp. 1332 –
1344.
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813
[email protected]
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