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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 http://www.iaeme.com/IJCIET/index.asp 807 [email protected] 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. http://www.iaeme.com/IJCIET/index.asp 808 [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 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. http://www.iaeme.com/IJCIET/index.asp 809 [email protected] 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 http://www.iaeme.com/IJCIET/index.asp 810 [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 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 http://www.iaeme.com/IJCIET/index.asp 811 Standard Deviation 5.631 5.416 [email protected] 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 Learning and Instruction, 17, 2007, pp. 322 – 335. [8] DeLashmutt, K. A study of the role of Mnemonics in Learning Mathematics. Summative projects for MA Degree, 2007. http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1006&context=mathmidsumm ative [9] Wood, D. K and Frank, A. R. Using memory-enhancing strategies to learn multiplication facts. Teaching Exceptional Children, 32, 2000, pp. 78 – 82. [10] 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. http://www.iaeme.com/IJCIET/index.asp 813 [email protected]