Penyelesaian masalah trigonometri dalam kalangan pelajar matrikulasi: Satu kajian kes

Competency in the subject of Trigonometry is crucial for the learning of Mathematics at higher levels. Trigonometric Functions are related to algebra, graph reasoning and calculus. Unfortunately, for some students, the initial stages of learning about Basic Trigonometric Functions are fraught with d...

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Main Author:	Sharimah, Ibrahim
Format:	Thesis
Language:	eng eng
Published:	2014
Subjects:	LB2300 Higher Education QA Mathematics
Online Access:	https://etd.uum.edu.my/4471/1/s807530.pdf https://etd.uum.edu.my/4471/2/s807530_abstract.pdf
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id	my-uum-etd.4471
record_format	uketd_dc
institution	Universiti Utara Malaysia
collection	UUM ETD
language	eng eng
advisor	Md Ali, Ruzlan
topic	LB2300 Higher Education QA Mathematics
spellingShingle	LB2300 Higher Education QA Mathematics Sharimah, Ibrahim Penyelesaian masalah trigonometri dalam kalangan pelajar matrikulasi: Satu kajian kes
description	Competency in the subject of Trigonometry is crucial for the learning of Mathematics at higher levels. Trigonometric Functions are related to algebra, graph reasoning and calculus. Unfortunately, for some students, the initial stages of learning about Basic Trigonometric Functions are fraught with difficulties. As a concequence, students often made errors when solving questions in Trigonometry. Students who have a weak understanding of basic concepts in Trigonometry may faced difficulty in understanding Sine and Cosine functions. The purpose of this study was to explore the understanding of Basic Trigonometry and Trigonometric Functions of Sine and Cosine among students in a Matriculation College. The study also explored the process and common errors students made when solving Trigonometric questions. This qualitative multi-case study was carried out on 60 One-Year Program (PST) students enrolled in three Modules. The data for the study was obtained via a written test, the Trigonometry Understanding Test (UPT), which consisted of six items. The identification of types of understanding was based on Skemp‟s (1982) notion of relational and instrumental understanding, Hiebert and Lefevre‟s (1986) view of conceptual and procedural understanding, and also Gray and Tall‟s (1995) ideas of proceptual knowledge. Four subjects were selected for the clinical interviews and were selected based on their achievement in the UPT. The results of the study showed that the research subjects‟ understanding of Basic Trigonometry was limited to instrumental and procedural understandings. The subjects did not indicate understanding of Basic Trigonometric Functions as procept. Their solutions for the Basic Trigonometry questions were mainly establishing procedures for getting the right answers. The common errors made included carelessness and calculation errors, failure to perform basic multiplication of fractions, and the inability to understand symbolism in Basic Trigonometry, which explained their inability to use the formulas correctly when solving trigonometric questions. Integration of conceptual, procedural and proceptual understanding could contribute to the construction of meaningful understanding of the Trigonometric Functions. This study contributes to the research findings in mathematics education and the formation of policy related to the development of mathematics education curriculum for matriculation students.
format	Thesis
qualification_name	masters
qualification_level	Master's degree
author	Sharimah, Ibrahim
author_facet	Sharimah, Ibrahim
author_sort	Sharimah, Ibrahim
title	Penyelesaian masalah trigonometri dalam kalangan pelajar matrikulasi: Satu kajian kes
title_short	Penyelesaian masalah trigonometri dalam kalangan pelajar matrikulasi: Satu kajian kes
title_full	Penyelesaian masalah trigonometri dalam kalangan pelajar matrikulasi: Satu kajian kes
title_fullStr	Penyelesaian masalah trigonometri dalam kalangan pelajar matrikulasi: Satu kajian kes
title_full_unstemmed	Penyelesaian masalah trigonometri dalam kalangan pelajar matrikulasi: Satu kajian kes
title_sort	penyelesaian masalah trigonometri dalam kalangan pelajar matrikulasi: satu kajian kes
granting_institution	Universiti Utara Malaysia
granting_department	Awang Had Salleh Graduate School of Arts & Sciences
publishDate	2014
url	https://etd.uum.edu.my/4471/1/s807530.pdf https://etd.uum.edu.my/4471/2/s807530_abstract.pdf
_version_	1747827742552883200
spelling	my-uum-etd.44712016-04-25T01:07:04Z Penyelesaian masalah trigonometri dalam kalangan pelajar matrikulasi: Satu kajian kes 2014 Sharimah, Ibrahim Md Ali, Ruzlan Awang Had Salleh Graduate School of Arts & Sciences Awang Had Salleh Graduate School of Arts and Sciences LB2300 Higher Education QA Mathematics Competency in the subject of Trigonometry is crucial for the learning of Mathematics at higher levels. Trigonometric Functions are related to algebra, graph reasoning and calculus. Unfortunately, for some students, the initial stages of learning about Basic Trigonometric Functions are fraught with difficulties. As a concequence, students often made errors when solving questions in Trigonometry. Students who have a weak understanding of basic concepts in Trigonometry may faced difficulty in understanding Sine and Cosine functions. The purpose of this study was to explore the understanding of Basic Trigonometry and Trigonometric Functions of Sine and Cosine among students in a Matriculation College. The study also explored the process and common errors students made when solving Trigonometric questions. This qualitative multi-case study was carried out on 60 One-Year Program (PST) students enrolled in three Modules. The data for the study was obtained via a written test, the Trigonometry Understanding Test (UPT), which consisted of six items. The identification of types of understanding was based on Skemp‟s (1982) notion of relational and instrumental understanding, Hiebert and Lefevre‟s (1986) view of conceptual and procedural understanding, and also Gray and Tall‟s (1995) ideas of proceptual knowledge. Four subjects were selected for the clinical interviews and were selected based on their achievement in the UPT. The results of the study showed that the research subjects‟ understanding of Basic Trigonometry was limited to instrumental and procedural understandings. The subjects did not indicate understanding of Basic Trigonometric Functions as procept. Their solutions for the Basic Trigonometry questions were mainly establishing procedures for getting the right answers. The common errors made included carelessness and calculation errors, failure to perform basic multiplication of fractions, and the inability to understand symbolism in Basic Trigonometry, which explained their inability to use the formulas correctly when solving trigonometric questions. Integration of conceptual, procedural and proceptual understanding could contribute to the construction of meaningful understanding of the Trigonometric Functions. This study contributes to the research findings in mathematics education and the formation of policy related to the development of mathematics education curriculum for matriculation students. 2014 Thesis https://etd.uum.edu.my/4471/ https://etd.uum.edu.my/4471/1/s807530.pdf text eng validuser https://etd.uum.edu.my/4471/2/s807530_abstract.pdf text eng public masters masters Universiti Utara Malaysia Ahmad Sarji. (2003). Wawasan 2020Malaysia: Memahami konsep, implikasi dan cabaran. Kuala Lumpur: Utusan Publications Dan Distributor Sdn Bhd. Arias, C.C., Schorr, R.Y., & Warner, L. B. (2010). Video Analysis as a Method for Developing Preservice Teachers’ Beliefs about Teaching and their understanding of children, Pedagogy and Assessment. AERA Annual Meeting, Denver, CO. Ausubel, D. (1963). The psychology of meaningful verbal learning. New York: Grune & Startton Inc. Ausubel, D. (1968). Educational psychology: A cognitive view. New York: Holt, Rinehart & Winston. Baykul, Y. (1999). Primary mathematics education(pp. 35-45). Ankara, Turkey: Ani Printing Press. Benito, R. P. (n.d). Analysis of the performance in trigonometry of the first year college students of Divine Word college of Vigan(Tesis sarjana yang tidak diterbitkan). University of ... Diakses dari http://www.eisrjc .com/journals/journal_1/dwcv-08-09-7.pdf. Blackett, N., & Tall, D. (1991). Gender and the versatile learning of Trigonometry using computer software. Proceedings International Group for The Psychology of Mathematics Education XV, Assisi, Italy, (1991), 1,144-151. Bransford, Brown, J. D., Ann, L.,& Cocking, Rodney, R. (1999). How people learn: Brain, mind, experience and school. Washington: D.C National Academy Press. Breidenback, D., Dubinsky, E., Hawks, J., & Nichols, D. (1992). Development of the process conception of function. Educational Studies in Mathematics, 23, 247-285. Brown, S.A. (2005).The Trigonometric connection: Students' understanding of sine and cosine (Tesis doktor falsafah). Pro Quest Dessertations and Theses.UMI Number 3233908. Chabi, M., & Hijazi, S. A. (2009). Errors student make in Mathematics courses. Proceedings of the 5th Asia Mathematical Conference, Malaysia 2009. Challenger, M. (2009). From triangle to a concept: a phenomenographic study of A-Level students’ development of the concept of Trigonometry (Tesis doktor falsafah yang tidak di terbitkan). University of Warwick, United Kindom. Chin, E. T.,& Tall, D. (2002). Proof as a Formal Procept in Advanced Mathematical Thinking, International Conference on Mathematics: Understanding Proving and Proving to Understand,National Taiwan Normal University, Taipei, Taiwan, 212-221. Chua, Y. P. (2006). Kaedah dan statistik penyelidikan kaedah penyelidikan. Malaysia: Mc Graw Hill Sdn Bhd. Confrey, J. (1980). Clinical interviewing: Its potential to reveal insights in mathematics education. Proceedings of the 4th International Conference for PME (pp. 400-408). Berkeley, CA: U niversity of California Press. Creswell, J. W. (2012). Educational research planning, conducting and evaluating quantitative and qualitative research (4rd ed.). New Jersey: Pearson Merrill Prentice Hall. Davis, R. B. (1992). Understanding “understanding”. Journal of Mathematical Behavior, 11, 225–241. Denzin, N. K., & Lincoln, Y.S (2000). Handbook of qualitative research. Thousand Oaks, CA: Sage Publications, Inc. Dienes, Z. (1973). Building up Mathematics: Psychological foundations. Ohio U.S.A : Charles A Jones Pub. Co. Dreyfus, T. & Eisenberg, T. (1983).. The function concept in college students: Linearity, Focus on Learning Problems in Mathematics, 5(3&4), 119-132.. Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. O. Tall (Ed.), Advanced Mathematical thinking (pp. 95- 126). Dordrecht: Kluwer. Fuson, K. C. (1990). Conceptual structures for multiunit numbers: Implication for learning and teaching multidigit addition, substraction, and place value. Cognition and Instruction,7,343-404. Gay, L. R., & Airasian, P. (2006). Educational research: Competencies for analysis and application (8th ed.). New Jersey, NJ: Prentice Hall. Gagne, R. M. (1970). The learning of concepts. The School Review, 75, 187-196. Gardner, H.,& Boix-Mansilla, V. (1999). Teaching for understanding in the disciplines and beyond. San Francisco: Jossey Bass. Ginsburg, H. P. (1997). Entering the child’s mind: The clinical interview in Psychological research and practice. UK: Cambridge University Press. Groff, P. (1994). "The future of fractions". International Journal Math. Educ. Sci. Technology.25(4), 549-561. Gray, E., Pinto, M., Pitta, D.,& Tall, D. (1999). Knowledge construction and diverging thinking in elementary and advanced mathematics. Educational Studies in Mathematics, 38, 111-133. Gray, E., & Tall, D. O. (1992). Success and failure in Mathematics: The flexible meaning of symbols as process and concept. Mathematics Teaching, 142, 6-10. Gray, E. M. & Tall, D. O. (1994). Duality, ambiguity and flexibility: a proceptual view of simple arithmetic. Journal for Research in Mathematics Education, 26(2), 115-141. Grouws, Dougias, A., & Cebulla, Kristin, J. (2000). Improving student achievement in Matematics. Geneva, Switzerland: International Academy of Education. Gur, H. (2009). Trigonometry learning. New Horizons in Education, 57(1), 67-80. Hazrul Abdul Hamid., Azimah Othman.,& Norazilah Zainon. (2006). Perbandingan Keberkesanan Penggunaan Kalkulator Grafik Dalam Proses Pengajaran dan Pembelajaran Kamiran.Prosidingseminar penyelidikan pendidikan Program Matrikulasi Kementerian Pendidikan Malaysia tahun 2006. Hlm. 393-406. Hestenes, M.D., & Hill, R.D.(1986). Algebra and Trigonometry with Calculators. New Jersey: Prentice-Hall. Hiebert, J.,& Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research on Mathematics teaching and learning (pp. 65-97). New York: McMillan. Hiebert, J.,& Lefevre, P. (1986). Procedural and conceptual knowledge. In J.Hiebert (Ed.), Conceptual and procedural knowledge: The case of Mathematics (pp. 1-27). Hillsdale, NJ: Erlbaum. Hoyles, C., Newman, K.,& Noss, R. (2001). Changing patterns of Transition from school to University Mathematics. International Journal of Mathematical Education in Science and Technology, 32, 829-845. Hunting, R.P., & Doig, B. A. (1997). Clinical assessment in mathematics: Learning the Craft. Focus on Learning Problems in Mathematics, 19(3),29-48. Isleyen, T., & Isik. (2003). A conceptual and procedural learning in Mathematics. Journal of the Korea Society of Mathematical Education Series D: Research in Mathematical Education. 7( 2), 91-99. Khor Seng Chye., Heong Seok Tin., Tey Kim Soon., & Poh Ah Hai. (2003). STPM MathematicsT-Paper 2. Kuala Lumpur : Penerbitan Pelangi Sdn Bhd. Kendal, M., & Stacey, K. (1997). Teaching Trigonometry. Vinculum, 34(1), 4-8. Kementerian Pendidikan Malaysia, (2006a). Kurikulum Bersepadu Sekolah Menengah, Huraian Sukatan Pelajaran Matematik Tingkatan 4. Kuala Lumpur : Pusat Perkembangan Kurikulum. Kementerian Pendidikan Malaysia, (2006b). Kurikulum Bersepadu Sekolah Menengah, Huraian Sukatan Pelajaran Matematik Tambahan Tingkatan 5. Kuala Lumpur: Pusat Perkembangan Kurikulum. Lia Agustina. (2009). Identifikasi kesalahan siswa dalam menyelesaikan soal-soal Trigonometri. Jurnal FKIP, Pustaka Ilmiah Universitas Lampung. Lial, M.L., Miller, C.D., & Schneider, D.I. (1994). Algebra and Trigonometry (6th ed.). New York: HarperCollins College Publishers. Lutfiyya, L. A. (1998). Mathematical thinking of high school student in Nebraska. International Journal of Mathematics Education and Science Technology. 29(1), 55-64. MacDonald, B., & Walker, R. (1977). Case study and the social philosophy of educational research. In D. Hamilton, D. Jenkins, C. King, & M. Parlett (Eds.), Beyond the number games. London: Macmillan Education Co. Marcus, R., Fukawa- Connelly, T., Conklin, M., & Fey, J. T. (2007). New thinking about college mathematics: Implication for high school teaching. Mathematics Teacher, 101, 354-358. Maznah Banu Bt Mohamed Habiboo Raman. (2008). A Study on Factors involved in University Student Learning of Calculus. Kertas kerja dibentangkan di Seminar Kebangsaan Sains dan Matematik. Anjuran Bersama: Persatuan Pendidikan Sains dan Matematik Johor, Fakulti Pendidikan, Universiti Teknologi Malaysia & Jabatan Pendidikan Negeri Johor, 11-12 Okt 2008. Merriam, S. B. (1988). Case study research in education: A qualitative approach. San Francisco, CA: Jossey-Bass. Miles, M.B.,& Huberman, A.M. (1994). Qualitative data analysis. Thousand Oaks, CA: SAGE Publications, Inc. Minichiello, V., Aroni, R., Timewell, E., & Alexander, L. (1990). In-depth Interviewing:Researching people. Melbourne: Longman Cheshire Pty Limited. Ministry of Education Malaysia. (2006). Mathematics QS026 Syllabus Specification. Matriculation Division. Mohd Azmi Saleh., Ezrinda Mohd Zahidee., & Zuhaidi Mukrim. (2006). Salah Faham pelajar dalam Pembezaan: Satu kajian Kes Di Kolej Matrikulasi Perak.ProsidingSeminar Penyelidikan Pendidikan Program Matrikulasi Kementerian Pendidikan Malaysia Tahun 2006.Hlm. 439-453. Moore, K.C. (2009). An investigation intoprecalculus students' conceptions of angle measure. Kertas kerja yang dibentangkandi Twelfth Annual Special Interest Group of theMathematical Association of America on Research in Undergraduate MathematicsEducation (SIGMAA on RUME) Conference, Raleigh, NC: North Carolina State University. Moore, K.C. (2010). The role of quantitative reasoning in precalculus student learning central concepts of Trigonometry(Tesis doktor falsafah). ProQuest Dessertations and Theses. UMI Number 3425753. Muhammad Firdaus Seman, (2011). Masalah Pembelajaran Matematik dalam tajuk Trigonometri II di kalangan Pelajar Tingkatan Empat, Ijazah sarjana Muda UTM.(Tesis sarjana muda). Universiti Teknologi Malaysia Di akses dari www.fp.utm.my_ePusatSumber_pdffail_ ptkghdfwp_FIRDAUSAP070061D2011TTP.pdf. Nabilah Abdullah., Rohaya Abdul Wahab., Ghaziah Mohd Ghazali., Shireena Basree Abdul Rahman., & Norshidah Nordin. (2010).Ciri-ciri dalam penyelidikan kualitatif. Dalam Noraini Idris, (Ed.), Penyelidikan dalam pendidikan. Hlm. 276-304. Kuala Lumpur: McGraw-Hill Sdn Bhd. National Council of Teachers of Mathematics. [NCTM] (2000). Principles and standards for school mathematics. Reston, VA: NCTM. Nik Aziz Nik Pa. (1996). Penghayatan matematik KBSR-KBSM: Perkembangan professional. Kuala Lumpur: Dewan Bahasa dan Pustaka. Nik Aziz Nik Pa. (1999). Pendekatan Konstruktivisme Radikal dalam Pendidikan Matematik. Kuala Lumpur: Penerbit Universiti Malaya. Noor Shah Saad. (2002).Teori & Perkaedahan Pendidikan Matematik Siri I, (2nd ed). Malaysia: Prentice Hall. Noriah Mohd Ishak., Siti Fatimah Mohd Yassin., Mohd Izham Mohd Hamzah., & Siti Rahayah Ariffin. (2010). Kajian Kes. Dalam Noraini Idris, (Ed.), Penyelidikan dalam pendidikan.(hlm.). Kuala Lumpur: McGraw-Hill Sdn Bhd. Orhun, N. (2000). Student‟s mistakes and misconceptions on teaching of Trigonometry, Jurnal of Curriculum Studies, 32. Parish, C. R., & Ludwig, H. J. (1994). Language, intellectual structures, and c Common mathematical errors: A call for research. School Science and Mathematics, 94(5), 235–239. Peck, D. M., & S. M. Jencks. (1981). Conceptual issues in the teaching and learning of fractions. Journal for Research in Mathematics Education 12(5):339-348. Piaget, J. (1950).The psychology of Intelligence. San Diego, California: Harcourt Brace Jovanovich. Raja Sulaiman Raja Hassan. (2002). Memaujudkan konsep Matematik.Prosiding Persidangan Kebangsaan Pendidik Matematik 2002, Anjuran Kementerian Pendidikan Malaysia dan UPSI. (Hlm 255-262). Rashidi Razali., & Tall, D. (1993). Diagnosing students‟ difficulties in learning Mathematics.International Journal of Math Ed, Sci & Techn., 24(2), 209–202. Robson, C. (2002). Real world research: A resource for social scientists and practitioner-researchers (2nd ed.). Oxford: Blackwell. Rohani Aziz., Mohamad Johari Yaakob., & Affandi Zakaria. (2007). Pemahaman konseptual dan prosedural dalam Matematik. Dalam Effandi Zakaria, Norazah Mohd Nordin & Sabri Ahmad. Trend pengajaran dan pembelajaran Matematik. Kuala Lumpur:Utusan Publications & Distributors Sdn Bhd. Ruhaizam Mohammad Yasin., & Maizam Alias. (2010). Latar belakang penyelidikan. Dalam Noraini Idris (Ed), Penyelidikan dalam pendidikan Hlm. 1-14. Kuala Lumpur: Mc Graw Hill Sdn Bhd. Schoenfield, A. H. (1985). Mathematical problem solving. New York: Academic Press. Sierpinska, A. (1994). Understanding in Mathematics.Great Britain: Burgess Science Press. Skemp, R. R. (1982). The psychology of learning Mathematics. Harmondsworth, UK: Penguin. Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematic Teaching, 77, 22-26. Sharida Hashim.,& Nik Azis Nik Pa. (2002). Mental image and representation of ogive by student of Diploma in Accountancy in a Mara Institute of Higher Education. International Conference on Mathematic Education Research (2010). Son, T. S., & Low, A. (2007). The front-runner Matriculation Mathematics for Science semester 2. Selangor, Malaysia: Arah Pendidikan Sdn Bhd. Steckroth, J. J. (2007). Technology-enhanced mathematics instruction: Effects of visualization on student understanding of Trigonometry (Tesis doktor falsafah). ProQuest Dessertations and Theses. UMI Number 3282501. Sudirman, (2005). Upaya meningkatkat pemahaman konsep Trigonometri pada siswa kelas 3 SMP Muhammadiyah Margasari tahun pelajaran 2004/2005 dengan menggunakan teknik hapalan dan alat peraga klinometer. (Thesis Sarjana Pendidikan yang tidak diterbitkan). Universitasi Negeri Semarang, Indonesia. Suhaidah Tahir, (2006). Pemahaman Konsep Pecahan Dalam Kalangan Tiga Kelompok Pelajar Secara Keratan Lintang. (Tesis doktor falsafah). Universiti Teknologi Malaysia. Suzieleez Syrena Abdul Rahim., & Tajularipin Sulaiman. (2006). Gambaran mental dan perwakilan pelajar lepasan Sijil Pelajaran Malaysia tentang konsep Fungsi. Jurnal Teknologi, 44(E), 45-60. Tall, D. (1979). Qualitative thought process in clinical interviews. Proceedings of the Third International Conference for the Psychology of Mathematics Education, Warwick, 206-207. Talley, J. R. (2009). Calculus instructors’ responses to prior knowledge errors.(Thesis doktor falsafah). University of Oklahoma. Tall, D., & Vinner S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12, 151-169. Tengku Zawawi Tengku Zainal., Ramlee Mustapha., & Abdul Razak Habib. (2009). Pengetahuan pedagogi isi kandungan guru Matematik bagi tajuk Pecahan: Kajian kes di sekolah Rendah. Jurnal Pendidikan Malaysia 34(1), 131–153. Weber, K. (2005). Students‟ understanding of Trigonometric Functions. Matematics Education Research Journal 2005: 17(3), 91-112. Yin, R.K. (2009). Case study research design and methods (4th ed).United States of America: SAGE Publications, Inc. Yudariah Mohammad Yusof., & Tall, D. (1996). Conceptual, procedural approches to problem solving. Proceeding of PME 20, Valencia 1996, 4, 3-10. Zazkis, R., & Hazzan, O. (1999). Interviewing in Mathematics education research: Choosing the questions. Journal of Mathematical Behavior, 17(4), 429-439

Penyelesaian masalah trigonometri dalam kalangan pelajar matrikulasi: Satu kajian kes

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