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Determination of Water Viscosity By Tracking The Brownian Motion of A Single Particle Using Video MicroscopyPenentuan Kelikatan Air dengan Menjejaki Gerakan Brownian Satu Zarah menggunakan Mikroskopi VideoSugeng Riyanto, Shahrul Kadri Ayop, Agus Purwanto & Wan Nor Suhaila Wan Aziz

Tahap Pencapaian Kemahiran Proses Sains Bersepadu Dalam Mata Pelajaran Sains Dalam Kalangan Pelajar Tingkatan LimaThe Level of Achievement on the Integrated Science Process Skills in Science Subject among Form Five StudentsWun Thiam Yew & Sunita Binti Tajuddin

The potential of Ferrocenium as a Sensing Reagent for Determination of 2,4,6-Trichlorophenol In Water SamplesPotensi Ferosenium sebagai Reagen Penderia bagi Penentuan 2,4,6-Triklorofenol dan Sampel AirNorlaili Abu Bakar, Norhayati Hashim, Wan Rusmawati Wan Mahamod, Saripah Salbiah Syed Abd Azziz, Yusnita Juahir, Rozita Yahaya, Wong Chee Fah, Ramli Ibrahim, Muhammad Farid Aziz& Nor Azira Mahmad Basir

A Narrative Review of Two-Arm and Three-Arm Non-Inferiority Clinical TrialsTinjauan Naratif Ujian Klinikal Tidak Inferior bagi 2-Kumpulan dan 3-Kumpulan RawatanZurina Mohd Yusof & Nor Afzalina Azmee

Hubungan antara Kemahiran Membuat Keputusan dalam Fizik dengan Kemahiran Membuat Keputusan dalam Kehidupan Seharian dalam Kalangan Pelajar FizikRelationship between the Decision-Making Skills in Physics with Decision-Making Skills in Daily Life among Physics StudentsYeoh Sik Mei1 & Razak Abd. Samad bin Yahya

The Central Subgroup of the Nonabelian Tensor Square of the Second Bieberbach Group with Dihedral Point GroupSubkumpulan Pusat bagi Tensor Kuasa Dua Tak Abelan untuk Kumpulan Bieberbach Kedua dengan Kumpulan Titik DwihedronWan Nor Farhana Wan Mohd Fauzi, Nor’ashiqin Mohd Idrus, Rohaidah Masri, Tan Yee Ting& Nor Haniza Sarmin

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J. Sci. Math. Lett. UPSI

J. Sci. Math. Lett., Volume 3 (2015) 1 - 6ISSN 2462-2052

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Determination of Water Viscosity by Tracking The Brownian Motion of a Single Particle using Video Microscopy

Penentuan Kelikatan Air dengan Menjejaki Gerakan Brownian Satu Zarah menggunakan Mikroskopi Video

Sugeng Riyanto1,2, Shahrul Kadri Ayop1*, Agus Purwanto3 & Wan Nor Suhaila Wan Aziz1,3

1Department of Physics, Faculty Science and Mathematics,Universiti Pendidikan Sultan Idris, Malaysia2Universitas Negeri Yogyakarta, Indonesia

3Physics Unit, Department of Nuclear Medicine, Kuala Lumpur Hospital, 50586, Jalan Pahang,Kuala Lumpur, Malaysia

*[email protected]

Abstract

Micron sized particle exhibits Brownian Motion (BM) in fluidic material. The BM of the particle characterizes the vicinity material due to the existance of thermal force. This paper describes an experiment to determine the water viscosity via BM observation using video microscopy technique. Video microscopy technique using open source Tracker software were employed to track the temporal displacement of the microparticle as a probe. Our viscosity measurement results (906 µPa s at 25.9 oC, 839 µPa s at 26.0 oC and 867 µPa s at 30.1 oC) are within the range resulted by measurement using rheometer. One of the merit of using particle tracking technique is the requirement of only microliter sample.

Keywords Brownian motion (BM), water viscosity, video microscopy technique

Abstrak

Zarah bersaiz mikro mempamerkan Gerakan Brownian (GM) dalam bahan bendalir. GM zarah tersebut mencirikan bahan persekitarannya kesan daripada kewujudan daya terma. Makalah ini menjelaskan uji kaji untuk mendapatkan kelikatan air melalui pencerapan GM menggunakan teknik mikroskopi video. Teknik mikroskopi video dan perisian sumber terbuka Tracker digunakan untuk menjejaki sesaran dalam fungsi masa bagi zarah mikro yang bertindak sebagai prob. Hasil pengukuran kelikatan (906 µPa s pada 25.9 oC, 839 µPa s pada 26.0 oC dan 867 µPa s at 30.1 oC) setanding dengan nilai pengukuran menggunakan rheometer. Salah satu kelebihan menggunakan teknik penjejakan zarah ialah pengukuran hanya memerlukan beberapa mikroliter isipadu sampel.

Kata kunci gerakan Brownian (GM) , kelikatan air, teknik mikroskopi video

INTRODUCTION

The Brownian Motion (BM) is one of the phenomenon describing random motion. Besides, it also provide local rheological characteristics of a fluidic material. The undeterministic pattern follows the Gaussian or Normal statistics (Gillespie, 1996). It means that the system


2

has unique response and free from the external perturbation, such as electric, magnetic or nuclear field. Every parameter inside the system gives same weighting contribution, such as mass distribution, displacement, velocity and acceleration. The local information in the material represents the thermal contribution (Toyabe & Sano, 2008). The exploration of the thermal related factors from the BM give advantages in studies of microrheological properties for fluidic materials (Mason, 2000).

Researchers utilize these benefits to explore and to find pattern of the system and other physical information. The motion of the probe can be explored using the mathematical tools such as analysis and synthesis of algorithms or transformation process. As an example, the previous study of the BM was done to determine viscoelastic moduli of polyethylene oxide solutions (Dasgupta, Tee, Crocker, Frisken, & Weitz, 2002). There are relationships and dependencies between angular frequencies and concentrations of that solutions. These relationships make an impression to the values of viscoelastic moduli. Then, from the viscoelastic moduli, researchers described certain model and energy distribution of the solutions (Popescu, Dogariu, & Rajagopalan, 2002).

There were many ways to study the BM in passive microrheology (Squires & Mason, 2009). One of the study is the application of Generalized Stokes-Einstein Relation (GSER). For the GSER, Mean-Squared Displacements (MSD) can be used directly in order to calculate the Complex Shear Modulus (CSM). The linearity degree of the MSD discriminates between Newtonian or non-Newtonian type of viscoelastic material. The MSD describes the relation between inter-positions and the response toward thermal force using Autocorrelation Function (ACF). The ACF is widely applied in stationary and non-stationary signals (Meirovitch, 2001). The ACF is for the special case, used when the random motion depends on time factor but independent of spatial/space factor.

Although the analysis of BM which lead to the viscosity calculation is widely discussed theoretically, but still rarely proven by experimental work or technique (Grimm, Jeney, & Franosch, 2011; Metzler & Klafter, 2000; Savin & Doyle, 2005). Currently, the viscosity of a fluid is measured by using rheometer which requires several milimeters of sample. However for delicate sample in microliter order, viscosity measurement using rheometer is imposible. Therefore, another techniques such as the one suggested in this study by using a video microscopy is explored.

This paper describes the use of BM to determine the viscosity of water under room temperatures condition. This technique also can be performed to characterize viscoelastic material such as polymer, surfactant solutions and biological materials (Fischer & Berg-Sorensen, 2007; Popescu et al., 2002).

Viscoelastic and Brownion Motion

The motion of a probe in one degree of freedom system is represented by the particle displacement, x, which is subjected to stochastic force, Fs, on the probe due to the thermal fluctuation as described by the following relation:

mx + βx = Fs (t) (1)

where m is the mass of the probe [kg] and β is the drag coefficient [kg/s].


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In time domain, the motion of the microparticle in water is determined according to GSER. GSER is applied in Diffusing-Wave Spectroscopy (DWS) by Mason and Weitz and in microrheology studies by Schnurr and Gittes et al. (Yanagishima, Frenkel, Kotar, & Eiser, 2011). This equation also known as Diffusion Equation which is related to the mean MSD of the probe and the diffusion constant, D is given by Equation 2,

2 2

1

1( ) ( ) 2N n

i n ii

x t x x D tN n

−

+=

∆ ∆ = − = ∆− ∑

(2)

where i = data position index =1, 2,..., N; N is the recorded number of frames; n=increment of dt =1, 2,..., N˗1 and t∆ is lag time (Michalet, 2010). It was found that the diffusion constant, D depends on the probe geometry, vicinity temperature and viscosity as Equation 3.

D = kBT6πηR (3)

where kB is Boltzmann constant [J/K], η is the viscosity [Pa.s], R is radius of probe particle [m] and T is the absolute temperature [K] (Jia, Hamilton, Zaman, & Goonewardene, 2007).

By combining Equation 2 and Equation 3, we get the viscosity of the fluid by observing the temporal displacement in one dimension of the probe at known temperature as expressed in Equation 4.

Δx2 (Δt) = 2 kBT6πηR

⎛⎝⎜

⎞⎠⎟Δt (1 dimension) (4)

METHODOLOGY

Samples were prepared using a microparticle as a probe. The microparticle is polybead® polystyrene (2.95±3%) μm. This bead exhibits no chemical reaction with water and available in standard diameter size. The microparticle solution was diluted with deionzed water at the ratio of 1:1,000.

The probe trajectory was observed under Inverted Microscope (Olympus GX51, Oil Immersion, 100×) and the video of probe motion were recorded using digital camera (Motic® Video 3.0 MP). We use Tracker freeware (https://www.cabrillo.edu/~dbrown/tracker/) to get the position of particle probe as function of time by frame rate (fps) which is more than 21 frames/s. We use (Equation 4) to analyze the BM by implementing the equations in algorithms using Matlab® program.

RESULT AND DISCUSSION

The temporal displacement in one dimension of the probe from one of our measurement is shown in Figure 1. The random nature of the motion is clearly visible. Within 15 s, the


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motion range is in the order of several micrometers.The MSD give information about the amount of thermal energy in order to change

the displacements of particle toward the stability condition. Equation 2 is used to convert signal in Figure 1 into mean square displacement as a function of lag time. Figure 2 shows the result after the conversion is performed.

0 5 10 15-0.5

0

0.5

1

1.5

2

2.5x 10

-11

Lagtime ∆t(s)

∆x2 (

∆t)

(m2 )

∆x2(∆t) = 6.5e-013*∆t- 1.8e-012

MSD linearBest Fitting

MSD of Deionized water at 25.9oC

Figure 2 The graph was illustrated shows the MSD and linear fit for data set 24.9oC

The gradient of the graph in Figure 2 includes the diffusion constant, which contains information about the surrounding viscosity. By performing linear fitting, we can determine the value of viscosity of deonized water. The obtained values of viscosity are summarized in Table 1 from 3 set of measurements.

0 5 10 150

1

2

3

4

5

6x 10

-6

Time (s)

x(m

)

Figure 1 Temporal displacement of a particle shows the Brownian motion


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Table 1 Viscosity of deionzed water at different temperatures.

Data set Temperature [oC] η experiment[µPa.s]

η reference [µPa.s]

Discrepancy(%)

1 30.1 867 800 7.72 26.0 839 876 4.43 25.9 906 878 3.4

The viscosity values of deionzed water at different temperatures were found to be comparable to the standard values. The measurement is very sensitive to temperature variation at micron scale. Therefore, it is highly advisable to control the environment temperature at constant value during measurement.

CONCLUSION

The viscosity of deonized water was determined by observing the BM of a microparticle using video microscopy with Tracker freeware. The measured viscocity values of deionzed water (906 µPa s at 25.9 oC, 839 µPa s at 26.0 oC and 867 µPa s at 30.1 oC) are found within the range of values using rheometer.

ACKNOWLEDGEMENTS

This work is supported by Research Acculturation Grant Scheme (RAGS) of Malaysian Ministry of Education under UPSI code 2013-0003-102-72.

REFERENCES

Dasgupta, B. R., Tee, S.-Y., Crocker, J. C., Frisken, B. J., & Weitz, D. A. (2002). Microrheology of polyethylene oxide using diffusing wave spectroscopy and single scattering. Physical Review E, 65(5), 051505.

Fischer, M., & Berg-Sorensen, K. (2007). Calibration of trapping force and response function of optical tweezers in viscoelastic media. Journal of Optics A: Pure and Applied Optics, 9(8), S239.

Gillespie, D. T. (1996). The mathematics of Brownian motion and Johnson noise. American Journal of Physics, 64(3), 225-239[page 233].

Grimm, M., Jeney, S., & Franosch, T. (2011). Brownian motion in a Maxwell fluid. Soft Matter, 7(5), 2076-2084.

Jia, D., Hamilton, J., Zaman, L. M., & Goonewardene, A. (2007). The time, size, viscosity, and temperature dependence of the Brownian motion of polystyrene microspheres. American Journal of Physics, 75(2), 111-115.

Mason, T. G. (2000). Estimating the viscoelastic moduli of complex fluids using the generalized Stokes-Einstein equation. Rheologica Acta, 39(4), 371-378.

Meirovitch, L. (2001). Fundamentals of vibrations (International ed.). Singapore: Mc Graw Hill.Metzler, R., & Klafter, J. (2000). The random walk’s guide to anomalous diffusion: a fractional

dynamics approach. Physics reports, 339(1), 1-77.Michalet, X. (2010). Mean Square Displacement Analysis of Single-Particle Trajectories with


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Localization Error: Brownian Motion in an Isotropic Medium. Physical Review E, 82(4), 041914.

Popescu, G., Dogariu, A., & Rajagopalan, R. (2002). Spatially resolved microrheology using localized coherence volumes. Physical Review E, 65(4), 041504.

Savin, T., & Doyle, P. S. (2005). Static and dynamic errors in particle tracking microrheology. Biophysical journal, 88(1), 623-638.

Squires, T. M., & Mason, T. G. (2009). Fluid mechanics of microrheology. Annual Review of Fluid Mechanics, 42(1), 413.

Toyabe, S., & Sano, M. (2008). Energy dissipation of a Brownian particle in a viscoelastic fluid. Physical Review E, 77(4), 041403.

Viswanath, D. S. (2007). Viscosity of liquids: theory, estimation, experiment, and data. Netherlands: Springer Science & Business Media.

Yanagishima, T., Frenkel, D., Kotar, J., & Eiser, E. (2011). Real-time monitoring of complex moduli from micro-rheology. Journal of Physics: Condensed Matter, 23(19), 194118.


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Tahap Pencapaian Kemahiran Proses Sains Bersepadu Dalam Mata Pelajaran Sains Dalam Kalangan Pelajar Tingkatan LimaThe Level of Achievement on the Integrated Science Process Skills in Science Subject

among Form Five Students

1Wun Thiam Yew & 2Sunita Binti Tajuddin1Pusat Pengajian Ilmu Pendidikan, Universiti Sains Malaysia, Pulau Pinang.

2Sekolah Menengah Kebangsaan Selinsing, Simpang Empat, [email protected]

Abstrak

Kajian ini bertujuan untuk menentukan tahap pencapaian kemahiran proses sains bersepadu (KPSB) bagi mata pelajaran sains dalam kalangan pelajar tingkatan lima. Kajian ini menggunakan pendekatan kuantitatif dengan reka bentuk kajian tinjauan. Sampel kajian ini terdiri daripada 150 orang pelajar tingkatan lima yang dipilih secara rawak berkelompok daripada empat buah sekolah dalam Daerah Kerian, Perak. Dalam kajian ini, penyelidik menggunakan satu instrumen kajian, iaitu Ujian Kemahiran Proses Sains Bersepadu (UKPSB), untuk menentukan tahap pencapaian KPSB bagi mata pelajaran sains dalam kalangan pelajar tingkatan lima. Dapatan kajian ini menunjukkan tahap pencapaian KPSB pelajar secara keseluruhannya adalah sederhana. Dapatan kajian ini juga menunjukkan bahawa tidak terdapat perbezaan min skor pencapaian pelajar yang signifikan dalam KPSB mengikut jantina.

Kata kunci tahap pencapaian, kemahiran proses sains bersepadu, sains, pelajar tingkatan lima

Abstract

The purpose of this study was to determine the level of achievement on the integrated science process skills in science subject among form five students. This study employed quantitative approach with survey research design. Sample of this study consisted of 150 form five students selected using stratified random sampling from four schools in Kerian District, Perak. In this study, the researchers employed one research instrument, namely Integrated Science Process Skills Test (ISPST), to determine the level of achievement on the integrated science process skills in science subject among form five students. The finding of this study showed that the level of students achievement on the overall integrated science process skills was moderate. The finding also showed that there was no significant difference in the mean score of integrated science process skills by gender.

Keywords level of achievement, integrated science process skills, science, form five students


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PenDAhuLuAn

Kurikulum Sains memberi penekanan kepada kemahiran saintifik (KS) yang terbahagi kepada kemahiran proses sains (KPS) dan juga kemahiran manipulatif (KM). KPS merupakan satu proses mental yang menggalakkan pemikiran secara kritis, analitik dan sistematik. Di samping itu, KPS merupakan kemahiran yang membolehkan pelajar mempersoalkan sesuatu masalah yang ada dan mencari jawapan secara bersistem daripada kemahiran mudah kepada kompleks (Bahagian Pembangunan Kurikulum, 2010).

KPS terdiri daripada dua komponen iaitu kemahiran proses sains asas (KPSA) dan kemahiran proses sains bersepadu (KPSB) (Padilla, Cronin, & Twiest, 1985). KPSB merangkumi kemahiran-kemahiran mentafsir data, mendefinisi secara operasi, mengawal pemboleh ubah, membuat hipothesis dan menjalankan eksperimen (Zurida, 1998).

Beberapa kajian telah dijalankan mengenai tahap pencapaian KPS dalam kalangan pelajar di Malaysia (Chan, 1984; Tan & Chin, 1992; Zurida, 1998). Dapatan-dapatan daripada kajian ini menunjukkan bahawa penguasaan KPS oleh pelajar di Malaysia adalah tidak memuaskan. Pelajar didapati masih lemah dalam KPSA dan KPSB.

Antara alasan bagi kelemahan dalam penguasaan KPSB daripada kajian-kajian yang telah dijalan (Chan, 1984; Tan & Chin, 1992; Zurida, 1998) ialah pelajar jarang mempraktikkan kemahiran saintifik, corak pengajaran kurang menekankan kemahiran berfikir seperti yang dicadangkan dalam kurikulum sains, pelajar kurang didedahkan kepada kemahiran proses sains, guru sendiri tidak faham tentang KPS mengakibatkan kesukaran dalam merancang pengajaran, guru sendiri kurang yakin sebab tidak tahu ciri-ciri setiap KPS dan tidak tahu menyatukan kedua-dua pengetahuan dan kemahiran dalam pengajaran dan sebagainya. Kajian-kajian di atas menunjukkan bahawa masih terdapat kelemahan dalam penguasaan KPS dalam kalangan pelajar dan guru.

OBjeKTif KAjiAn

Kajian ini bertujuan untuk menentukan tahap pencapaian kemahiran proses sains bersepadu (KPSB) dalam mata pelajaran sains dalam kalangan pelajar tingkatan lima. Secara khusus, objektif kajian ini adalah untuk:1. Menentukan tahap pencapaian KPSB dalam mata pelajaran sains dalam kalangan

pelajar tingkatan lima.2. Menentukan tahap pencapaian pelajar tingkatan lima dalam kemahiran mengawal

pemboleh ubah, membuat hipotesis, mendefinisi secara operasi, mentafsir maklumat dan menjalankan eksperimen.

3. Menentukan sama ada terdapat perbezaan min skor pencapaian pelajar yang signifikan dalam KPSB mengikut jantina.

hiPOTeSiS KAjiAn

Terdapat satu hipotesis nol dalam kajian ini iaitu:Tidak terdapat perbezaan min skor pencapaian yang signifikan dalam KPSB di antara pelajar lelaki dan pelajar perempuan.


9

MeTODOLOGi

Reka Bentuk Kajian

Kajian ini menggunakan pendekatan kuantitatif dengan reka bentuk kajian tinjauan. Kajian tinjauan melibatkan pengumpulan data untuk menguji hipotesis atau menjawab soalan tentang pandangan seseorang terhadap sesuatu topik atau isu (Gay, Mills, & Airasian, 2014). Kajian ini meninjau tahap pencapaian KPSB dalam mata pelajaran sains dalam kalangan pelajar tingkatan lima.

Kajian ini juga menguji hipotesis sama ada terdapat perbezaan min skor pencapaian pelajar yang signifikan dalam KPSB mengikut jantina. Dalam kajian ini, pemboleh ubah bersandar ialah tahap pencapaian KPSB dan pemboleh ubah bebas ialah jantina pelajar iaitu pelajar lelaki dan pelajar perempuan.

Kaedah Persampelan

Terdapat empat buah zon dalam Daerah Kerian, Perak. Penyelidik memilih secara rawak empat buah sekolah menengah di Daerah Kerian, Perak. Jumlah sekolah menengah di Daerah Kerian adalah sebanyak 22 buah. Seramai 150 orang pelajar tingkatan lima dari empat buah sekolah tersebut yang dipilih secara rawak berkelompok telah dijadikan sebagai sampel kajian ini.

instrumen Kajian

Dalam kajian ini, penyelidik menggunakan satu instrumen kajian iaitu Ujian Kemahiran Proses Sains Bersepadu (UKPSB) yang juga dikenali sebagai TIPS II (Test of Integrated Science Process Skills). Kajian ini menggunakan instrumen TIPS II yang telah diterjemah ke Bahasa Melayu oleh Zurida (1998). Ujian TIPS II terdiri daripada lima KPSB iaitu kemahiran mengawal pemboleh ubah, kemahiran membuat hipotesis, kemahiran mendefinisi secara operasi, kemahiran mengeksperimen dan kemahiran mentafsir data.

UKPSB ini merupakan ujian kertas dan pensel yang mengandungi 36 item aneka pilihan yang setiap item disediakan dengan empat pilihan jawapan. Setiap item ini juga diskorkan sama ada betul atau salah iaitu 1 atau 0. Justeru itu, markah minimum ialah 0 dan markah maksimum ialah 36.

Item 5, 9, 11, 25, 28 dan 34 mengukur kemahiran mentafsir maklumat. Item 2, 7, 22, 23, 26 dan 33 mengukur kemahiran mendefinisi secara operasi. Item 1, 3, 13, 14, 15, 18, 19, 20, 30, 31, 32 dan 36 mengukur kemahiran mengawal pembolehubah. Item 4, 6, 8, 12, 16, 17, 27, 29 dan 35 mengukur kemahiran membuat hipotesis dan item 10, 21 dan 24 mengukur kemahiran mengeksperimen.

Penganalisisan Data

Kajian ini menggunakan perisian SPSS versi 16.0 untuk menganalisis data yang diperoleh daripada UKPSB. Penganalisisan data secara kuantitatif dilakukan dengan menggunakan statistik deskriptif dan inferential. Statistik deskritif digunakan untuk menentukan nilai


10

maksimum, jumlah jawapan yang betul (skor), min, peratus min dan sisihan piawai terhadap tahap pencapaian kelima-lima KPSB mengikut subskala.

Data yang terkumpul dianalisis dengan mengira skor setiap KPSB dan diolah ke dalam bentuk peratusan. Oleh kerana skor maksimum untuk setiap KPSB adalah berbeza, peratusan min dikira untuk memudahkan perbandingan skor min. Peratusan skor min dikira dengan jumlah jawapan betul mengikut subskala dibahagi dengan jumlah sebenar soalan sub skala seperti dalam Jadual 5. Tahap pencapaian KPSB responden ditentukan berdasarkan markah min peratusan yang digunakan dengan meluas dalam sistem penilaian di sekolah sebagaimana dalam Jadual 1.

jadual 1 Skor bagi penentuan tahap pencapaian KPSBSkor item Betul Skor (Peratus) Tahap Pencapaian29 -36 80 - 100 Cemerlang22- 28 60 - 79 Baik15 – 21 40 – 59 Sederhana8 -14 20 – 39 Lemah0 – 7 0 - 19 Sangat Lemah

Statistik inferential, iaitu ujian t-sampel bebas (independent sample t-test) digunakan untuk menentukan sama ada terdapat perbezaan min pencapaian KPSB yang signifikan dalam mata pelajaran sains merentas jantina.

DAPATAn KAjiAn

Statistik Diskriptif Sampel Kajian

Sampel kajian ini terdiri daripada 150 orang pelajar tingkatan lima yang mengambil mata pelajaran sains dalam Daerah Kerian, Perak. Jadual 2 menunjukkan sampel kajian mengikut jantina di mana bilangan pelajar lelaki ialah seramai 56 orang (37.7%) manakala pelajar perempuan seramai 94 orang (62.7%).

jadual 2 Sampel kajian mengikut jantinajantina n %LelakiPerempuanJumlah

5694150

37.362.7100

Tahap Pencapaian KPSB Secara Keseluruhan

Tahap pencapaian KPSB secara keseluruhan dalam kalangan pelajar tingkatan lima di Daerah Kerian yang mengambil mata pelajaran sains diukur berdasarkan skor keseluruhan diperoleh oleh sampel kajian dalam UKPSB. Nilai minimum, maksimun, julat, min dan sisihan piawai bagi skor keseluruhan ditunjukkan dalam Jadual 3.


11

jadual 3 Statistik deskriptif bagi pencapaian KPSB secara keseluruhanStatistik Deskriptif Skor Peratus SkorMinimumMaksimumJulatMinSisihan piawai

63226

19.535.30

16.6788.8972.2254.26

Jadual 3 menunjukkan bahawa skor min yang diperoleh oleh sampel kajian dalam ujian KPSB ialah 19.53 dengan sisihan piawai 5.30 dan peratus min ialah 54.26%. Skor minimum ialah 6 (16.67%) manakala skor maksimum ialah 32 (88.89%). Ini menghasilkan julat skor 26 (72.22%). Taburan skor pencapaian keseluruhan pelajar dalam UKPSB ditunjukkan dalam Jadual 4.

jadual 4 Taburan skor pencapaian keseluruhan pelajar dalam UKPSBSkor Pencapaian Keseluruhan

Skor (peratus) Kekerapan Peratus Kekerapan Tahap Pencapaian KPSB

0 – 78 – 1415 – 2122 – 2829 – 36

0 – 19 20 – 3940 – 59 60 – 79

80 – 100

13058547

0.720.038.736.04.6

Sangat lemahLemah

SederhanaBaik

Cemerlang

Dapatan kajian ini menunjukkan bahawa majoriti responden kajian, iaitu 58 orang (38.7%) mendapat skor pencapaian keseluruhan dalam lingkungan15–21 dengan skor peratusnya 40–59, berada pada tahap pencapaian sederhana. Seramai 54 responden (40.6%) mendapat skor pencapaian dalam lingkungan 22–28 dengan skor peratusnya 60–79 berada pada tahap baik. Dapatan kajian ini menunjukkan hanya 7 responden (4.6%) mendapat skor dalam lingkungan 80-100 berada pada tahap cemerlang. Seramai 30 responden (20.0%) berada pada tahap pencapaian lemah dan seorang responden (0.7%) dikenal pasti berada pada tahap pencapaian sangat lemah.

Dapatan kajian ini menunjukkan bahawa tahap pencapaian KPSB dalam kalangan pelajar tingkatan lima yang mengambil mata pelajaran sains yang dikaji adalah pada keseluruhannya pada tahap sederhana (lihat Jadual 5).

Tahap Pencapaian KPSB Mengikut Subskala

Jadual 5 menunjukkan tahap pencapaian KPSB pelajar secara keseluruhan dan mengikut subskala. Berdasarkan Jadual 5, didapati bahawa kemahiran mentafsir data mendapat skor min 4.03 dengan peratus min yang paling tinggi, iaitu 67.11% dan berada pada tahap pencapaian baik manakala kemahiran mengeksperimen adalah kemahiran yang paling rendah dikuasai oleh para pelajar pada tahap pencapaian sederhana dengan skor min 1.39 dan peratus min yang paling rendah, iaitu 46.44%.

Peratusan min bagi subskala dalam susunan menaik ialah mengeksperimen (46.44%), mendefinisi secara operasi (48.22%), mengawal pemboleh ubah (52.72%), membuat


12

hipotesis (54.37%) dan mentafsir data (67.11%). Dapatan kajian ini menunjukkan bahawa pelajar tingkatan lima dalam kajian ini dapat menguasai kemahiran mentafsir data pada tahap baik tetapi hanya dapat menguasai KPSB yang lain pada tahap sederhana (lihat Jadual 5).

Tahap Pencapaian KPSB Merentas jantina

jadual 6 Analisis tahap pencapaian KPSB merentas jantina

Jantina N Min Sisihan piawai Nilai t df Signifikan

LelakiPerempuan

5694

19.1419.81

.66

.56 -.75 148 .14*signifikan pada aras p < 0.05

Keputusan ujian t sampel bebas dalam Jadual 6 menunjukkan bahawa tidak terdapat perbezaan min skor pencapaian pelajar yang signifikan dalam KPSB mengikut jantina, t (148) =-.75, p > .05. Hipotesis kajian ini gagal ditolak. Ini bermakna min skor pencapaian pelajar lelaki dalam KPSB (M = 19.14, SD = .66) tidak berbeza secara signifikan dengan min skor pencapaian pelajar perempuan dalam KPSB (M = 19.81, SD = .56).

PeRBinCAnGAn DAPATAn KAjiAn

Tahap Pencapaian KPSB Secara Keseluruhan

Dapatan kajian ini menunjukkan tahap pencapaian KPSB pelajar secara keseluruhannya adalah sederhana. Dapatan ini konsisten dengan dapatan kajian Yew (2000) yang mendapati bahawa tahap kemahiran proses sains pelajar secara keseluruhannya adalah sederhana (44.18%) berdasarkan kajiannya yang mengambil pelajar-pelajar tingkatan empat sebagai responden.

Tahap Pencapaian KPSB Mengikut Subskala

Dapatan kajian ini menunjukkan pencapaian pelajar bagi kemahiran mentafsir data berada pada tahap baik dengan peratus min sebanyak 67.11%. Dapatan ini selaras dengan dapatan

jadual 5 Tahap pencapaian KPSB secara keseluruhan dan mengikut subskala

KPSB Skor Maks

Jumlah Betul Min Peratus Min Sisihan

PiawaiTahap

PencapaianMentafsir data 6 604 4.03 604/900×100 = 67.11 1.56 BaikMembuat hipotesis 9 734 4.89 734/1350×100 = 54.37 1.66 SederhanaMengawal pembolehubah

12 949 6.33 949/1800×100 = 52.72 2.58 Sederhana

Mendefinisi secara operasi

6 434 2.89 434/900×100 = 48.22 1.20 Sederhana

Mengeksperimen 3 209 1.39 209/450×100 = 46.44 0.78 SederhanaKeseluruhan 36 2933 19.53 2933/5400 x 100=54.26 5.30 Sederhana


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kajian Yew (2000) yang menunjukkan bahawa pencapaian pelajar bagi kemahiran mentafsir data berada pada tahap yang baik dengan peratus min sebanyak 79.9%.

Dapatan kajian ini menunjukkan pencapaian pelajar bagi kemahiran membuat hipotesis berada pada tahap sederhana dengan peratus min sebanyak 54.37%. Dapatan ini konsisten dengan dapatan kajian Nor Hasniza (2010) yang menunjukkan bahawa pencapaian pelajar bagi kemahiran membina hipotesis berada pada tahap sederhana dengan peratus min sebanyak 55%.

Dapatan kajian ini menunjukkan pencapaian pelajar bagi kemahiran mengawal pemboleh ubah berada pada tahap sederhana dengan peratus min sebanyak 52.72%. Dapatan ini sama dengan dapatan kajian Zurida (1998), iaitu pencapaian pelajar bagi kemahiran mengawal pemboleh ubah berada pada tahap sederhana.

Dapatan kajian ini menunjukkan pencapaian pelajar bagi kemahiran mendefinisi secara operasi berada pada tahap sederhana dengan peratus min sebanyak 48.22%. Dapatan ini selari dengan dapatan kajian Nor Hasniza (2010) di mana pencapaian pelajar bagi kemahiran mendefinisi secara operasi berada pada tahap sederhana dengan peratus min sebanyak 55.67%. Dapatan ini juga sama dengan dapatan kajian Burns, Okey dan Wise (1985) di mana pencapaian pelajar bagi kemahiran mendefinisi secara operasi berada pada tahap sederhana dengan peratus min sebanyak 55.00%.

Dapatan kajian ini menunjukkan pencapaian pelajar bagi kemahiran menjalankan eksperimen berada pada tahap sederhana dengan peratus min sebanyak 46.44%. Dapatan ini berbeza dengan dapatan kajian Nor Hasniza (2010) di mana pencapaian pelajar bagi kemahiran mengeksperimen berada pada tahap rendah.

Tahap Pencapaian KPSB Merentas jantina

Dapatan kajian ini menunjukkan bahawa tidak terdapat perbezaan min skor pencapaian pelajar yang signifikan dalam KPSB mengikut jantina. Dapatan ini adalah selaras dengan dapatan kajian Chan (1984) dan Ezan Haizurah (2010) yang turut mendapati bahawa tidak terdapat perbezaan min skor pencapaian pelajar yang signifikan dalam KPSB di antara pelajar lelaki dan pelajar perempuan.

KeSiMPuLAn

Sebagai kesimpulan, tahap pencapaian KPSB pelajar secara keseluruhannya adalah sederhana. Dari segi subskala KPSB, pelajar tingkatan lima dalam kajian ini dapat menguasai kemahiran mentafsir data pada tahap baik tetapi hanya dapat menguasai KPSB yang lain pada tahap sederhana. Oleh itu, perhatian dan penekanan yang lebih harus diberikan supaya dapat meningkatkan lagi tahap pencapaian pelajar dalam KPSB.

RujuKAn

Bahagian Pembangunan Kurikulum, Kementerian Pelajaran Malaysia (2010). Kurikulum Bersepadu Sekolah Menengah: Spesifikasi Kurikulum Sains Tingkatan 5. Putrajaya: Bahagian Pembangunan Kurikulum.

Burns, J. C., Okey, J. R., & Wise, K. C. (1985). Development of an integrated process skill test: TIPS II. Journal of Research in Science Teaching, 22, 169-177.


14

Chan, S. G. (1984). Acquisition of science process skills among form 4 students in Kota Bahru. Unpublished Master of Education dissertation, University of Malaya, Kuala Lumpur.

Ezan Haizurah Ahmad (2010). Tahap pencapaian kemahiran proses sains dalam mata pelajaran fizik di kalangan pelajar sekolah menengah Daerah Kluang. Latihan ilmiah Ijazah Sarjana Muda yang tidak diterbitkan, Universiti Teknologi Malaysia, Skudai, Johor.

Gay, L. R., Mills, G. E., & Airasian, P. (2014). Eductional research: Competencies for analysis and application (10th ed.). London: Pearson Education.

Nor Hasniza Ibrahim (2010). Tahap penguasaan kemahiran membuat hipotesis dan mendefinisi secara operasi di kalangan pelajar kimia Fakulti Pendidikan. Latihan ilmiah Ijazah Sarjana Muda yang tidak diterbitkan, Universiti Teknologi Malaysia, Skudai, Johor.

Padilla, M. J., Cronin, L., & Twiest, M. (1985). The development and validation of a test of basic proces skills. Annual Meeting of the National Association for Research in Science and Teaching. French Link, Indiana.

Tan, M. T., & Chin, T. P. (1992). Satu kajian awal konsepsi kemahiran proses sains di kalangan guru sains PKPG 14 minggu di Maktab Perguruan Batu Lintang. Sarawak: Unit Sains, Maktab Perguruan Batu Lintang.

Yew, K. S. (2000).Tahap kefahaman kemahiran membuat inferens dan menganalisis kajian di kalangan pelajar-pelajar tingkatan empat. Latihan ilmiah Ijazah Sarjana Muda yang tidak diterbitkan, Universiti Teknologi Malaysia, Skudai, Johor.

Zurida Ismail (1998). Penguasaan kemahiran proses sains di kalangan pelajar sekolah rendah dan menengah. Jurnal Kurikulum, 1 (1), 109-120.


15

The Potential of Ferrocenium as a Sensing Reagent for Determination of 2,4,6-Trichlorophenol in Water Samples

Potensi Ferosenium sebagai Reagen Penderia bagi Penentuan 2,4,6-Triklorofenol dan Sampel Air

1*Norlaili Abu Bakar, 1Norhayati Hashim, 1Wan Rusmawati Wan Mahamod, 1Saripah Salbiah Syed Abd Azziz , 1Yusnita Juahir, 1Rozita Yahaya, 2Wong Chee Fah, 1Ramli Ibrahim,

1Muhammad Farid Aziz & 1Nor Azira Mahmad Basir1Department of Chemistry, Faculty of Science and Mathematics,

Universiti Pendidikan Sultan Idris (UPSI), 35900 Tanjong Malim, Perak.2Department of Biology, Faculty of Science and Mathematics,

Universiti Pendidikan Sultan Idris (UPSI), 35900 Tanjong Malim, Perake-mail: *[email protected]

Abstract

A ferrocenium namely bisferrocenium bis(tetrachloroantimonate) trichloroantimony ((Fe(C2H5)2)[SbCl4]2[SbCl3]) was proposed as a sensing reagent to detect the presence of 2,4,6-trichlorophenol (2,4,6-TCP) in domestic tap water and river water by using a UV-Visible spectrophotometric. The absorbance intensity of ferrocenium was found to decrease at wavelength 617 nm and cause the reagent solution to change its colour from blue to yellowish green which indicates the conversion of ferrocenium to ferrocene. This sensing reagent (2000 mg/L) showed optimum respon in acidic medium (pH 5) within 3 minutes. A good linear concentration was obtained in the range of 20 to 190 mg/L with limit of detection to be 1.56 mg/L. The proposed reagent was recommended as a potential reagent for 2,4,6-TCP detection in aqueous solution.

Keywords ferrocenium, optical sensor, pesticides, phenolic compound, 2,4,6-trichlorophenol

Abstrak

Sebatian ferosenium iaitu bisferosenium bis(tetrakloroantimonat) trikloroantimoni ((Fe(C2H5)2)[SbCl4]2[SbCl3]) telah dicadangkan sebagai reagen penderia untuk mengesan kehadiran 2,4,6-Triklorofenol (2,4,6-TCP) di dalam air paip domestik dan air sungai dengan menggunakan spektrofotometri UV-nampak. Keamatan keserapan ferosium didapati menurun pada panjang gelombang 617 nm dan warna larutan reagen bertukar dari biru ke hijau kekuningan yang menunjukkan penukaran ferosenium kepada ferosena. Reagen penderia ini (2000 mg/L) menunjukkan tindak balas optimum dalam medium berasid (pH 5) dalam jangka masa 3 minit. Kepekatan linear yang baik telah diperolehi dalam julat 20-190 mg/L dengan had pengesanan 1.56 mg/L. Reagen penderia yang dicadangkan ini berpotensi digunakan sebagai reagen penderia untuk pengesanan 2,4,6-TCP dalam larutan akueus.

Kata kunci ferosenium, penderia optik, racun perosak, sebatian fenolik, 2,4,6-triklorofenol


16

InTRoDucTIon

Pesticides are a powerful tool to reduce the agricultural problems in order to control the number of pests and continuous application of pesticides can cause severe environmental problems and food contaminations (Pinto et al., 2010). As a result of their wide usage, pasticides find their way to rivers water, groundwater, wastewater, sediments and soils (Fakhr Eldin et al., 2006) which were finally become sources of contamination in drinking water (van Leeuwen, 2000). Due to the demand of drinking water supplies by human being, therefore it is necessary to ensure that treated water is safe and free from harmful substance. Phenolic compounds is one of the harmful substances release into our natural water resources which give bad impact to aquatic life and human being if the water is not treated in a right way. Some phenolic compound, mainly chlorophenols and nitrophenols have been clarified as priority pollutant by US Environmental Protection Agency (EPA) and European Union (EU) (Galve et al., 2002; Santana et al., 2009). Since the early 1930s, chlorophenol namely 2,4,6-trichlorophenol (2,4,6-TCP) has been applied as formulation in insecticides, bactericides and antiseptic as well as becoming an intermediate in the production of chlorophenoxy acid herbicides and other important organic substance. Concentration of phenol which is higher than 2 mg L-1 with four days exposure is considered toxic to the fish while concentrations between 10 mg L-1 and 100 mg L-1 are lethal to most aquatic life (Andrade et al., 2006). Prolonged oral exposure leads to damages to the lungs, liver, kidneys and genitor-urinary tract. Therefore, US Environmental Protection Agency (EPA) recommends a maximum of 1.0 mg L-1 of total phenolic compounds in domestic water and 5 mg L-1 of other water resources (El-Kosasy et al., 2001).

Over the past decades, many researchers preferred to use high performance liquid chromatography (HPLC) for the separation and determination of chlorophenols. Various detectors that are frequently use are ultraviolet-visible (UV), fluorescence, electrochemical and mass spectroscopy (Jin-Feng et al., 2006). El Kosasy et al. (2001) has succesfully determine phenolic pollutants in waste water by using poly (vinyl chloride) matrix membrane electrodes sensor. Their suggested sensor exhibit fast response time (1 minute), low detection limit, good stability and reasonable selectivity to phenolic compounds in the presence of other water pollutants. This sensor was successfully used for direct potentiometric determination of traces of these phenolic compounds in waste water sample. Ribeiro et al., (2002) developed and validated a new methodology regarding solid-phase microextraction (SPME) with gas chromatography and mass spectrometry (GC-MS). Throughout this study, they proved that SPME was a suitable methodology to extract 13 chlorophenols and phenol from leachate sample. Even though this SPE method use small amounts of organic solvents but it can be expensive as the cartridge used need to be dispose after one to four extraction.

Analysis of chlorophenols in environmental samples has been proposed by various methods but the prior method is based on chromatographic separation. In most cases, this method often required a previous pre-concentration or cleaning step. Unfortunately, even with the use of pre-concentration step, some of the methods exhibit relatively high limits of detection (LODs) and therefore only restricted to a very contaminated samples (de Morais et al., 2011). Therefore a usage of reagent for determination of phenolic compound will overcome the problems such as time consumed, expensive and lots of solvent usage.


17

A new proposed reagent namely ferrocenium can be synthesized by oxidation of ferrocene by using organic or inorganic solvents. This oxidation will yield a blue and relatively stable ferrocenium ion (Manzi-Nshutti & Wilkie, 2007). It has been found that ferrocene yields highly reversible heterogenous redox processes in most organic solvents, including ionic liquids. As a result, its heterogenous electron transfer kinetics has been widely studied and redox potential has been established in many different solvents. Due to its electron-transferring abilities, ferrocene act as “redox mediator” in amperometric biosensors and has been introduced for the first time to detect glucose (Sanchis et al., 2008). Based on redox mediator properties of ferrocenium, it was believed that this reagent has a potential to become a sensing reagent for the determination of 2,4,6-TCP in aqueous solution.

Regarding to the dangerous effects of phenolic componud especially of 2,4,6-TCP to the community, time consumed and expensive cost of method to detect phenolic compound, it is vital to develop an accurate and simple detection method to give early warning to the public and continuous contamination monitoring by enforcement officers. Therefore, a new reagent bisferrocenium bis(tetrachloroantimonate) trichloroantimony ((Fe(C2H5)2)[SbCl4]2[SbCl3]) is proposed to ensure the detection of phenolic compound (2,4,6-TCP) in our environment especially in water sample to be more efficient, fast result and aplicable to on-site detection.

ExPERImEnTAl

materials and reagents

Antimony (III) trichloride was purchased from Sigma-Aldrich. Ferrocene and 2,4,6-TCP was supplied by Across Organic. Hexane, acetic acid glacial and sodium acetate was obtained from R & M Chemicals. All chemicals were used without any further purification.

The preparation of sensing reagent ferrocenium was carried out based on method by Razak et al. (2000). About 1.86 g of ferrocene and 2.28 g of antimony trichloride was dissolved in acetonitrile separately. Both solutions were mixed and stirred for 2 hours. The mixture was allowed to dry for 4 to 5 days in a fume hood. The mixture turned slowly to blue green solution and finally formed dark blue precipitate. The precipitate was filtered and washed with hexane until the filtrate formed clear solution. Finally, the ferrocenium yielded was allowed to dry and kept in desiccators for further experiment.

Stock solution of ferrocenium (5000 mg/L) was prepared by dissolving dark blue solid ferrocenium in 50 mL of acetonitrile. The stock solution of ferrocenium was freshly prepared before used in a further experiment. All 2,4,6-TCP solution were daily fresh prepared in deionized water before used.

pH studies, optimize reagent and steady state response time

The pH study was carried out by varying the pH of reaction solution with buffer. A ferrocenium solution (2000 mg/L) was mix with 1 mL of 100 mg/L 2,4,6-TCP in 25 mL volumetric flask. Then the buffer solution was added in the flask and the pH value was measured with pH meter and recorded. This procedure was repeated by using different buffer


18

solution to obtain different pH. The absorbance spectrum of ferrocenium before and after react with 2,4,6-TCP in different pH was recorded using UV-Visible specthrophotemeter. The relative absorbance was calculated at wavelength 617 nm for each pH effect using Equation (1).

Relative Absorbance = IF – Ii (1)

where,IF =Absorbance intensity of ferrocenium after react with 2,4,6-TCPIi =Absorbance intensity before react with 2,4,6-TCP

Optimum concentration of ferrocenium reagent was studied by using various concentration of ferrocenium solution (1000 – 5000 mg/L). 1 mL of stock solution of 2,4,6-TCP, buffer solution pH 5 was added into ferrocenium solution. The absorbance spectrum of ferrocenium was recorded as same as in pH effect.

Steady state response time was studied by adding 100 mg/L of 2,4,6-TCP, buffer solution pH 5 into ferrocenium solution. The absorbance intensity of ferrocenium at 617 nm was recorded in different time interval (0.5 – 3 minutes) using UV-Visible spectrophotometer.

Effect of 2,4,6-TcP concentration

The effect of 2,4,6-TCP concentration on the relative absorbance of ferrocenium was done with optimum concentration of 2000 mg/L, buffer solution pH 5 and steady-state response time of 2 minutes. The analyte concentration was varied in the range of 20 – 190 mg/L. A ferrocenium was added with different concentration of 2,4,6-TCP separately. The absorption spectrum of ferrocenium solution was recorded with Agilent Cary 60 UV-Visible spectrophotometer. The relative absorbance of ferrocenium response to the presence of 2,4,6-TCP which was calculated using Equation (1).

RESulTS AnD DIScuSSIon

pH studies, optimize reagent and seady state reponse time

Figure 1 showed the absorbance spectrum of ferrocenium before and after react with 2,4,6-TCP. The absorbance intensity of ferrocenium at 617 nm decrease in the presence of 2,4,6-TCP. The decreased in absorbance intensity showed colour change from blue colour ferrocenium solution to yellowish green. The colour changes were considered to the conversion of ferrocenium ion to ferrocene (Hurvois & Moinet 2005). This occurrence was believed due to a redox reaction between ferrocenium and 2,4,6-TCP. The ferrocenium ion, [FeCp2

+], is a mild one-electron oxidant, usually regarded as an outer-sphere reagent. The stability of the couple ferrocenium ion/ferrocene, [FeCp2

+]/[FeCp2] suggest the ferrocenium ion act as a potential redox catalyst (Conelly & Geiger 1996). Ferrocenium which act as oxidizing agent will oxidized 2,4,6-TCP to 2,4,6-trichlorocyclohexanone (Figure 2). The oxidation will disrupt the aromatic ring (Smith 2002) leading to the formation of 2,4,6-trichlorocyclohexanone.


19

Figure 1 The absorbance spectrum of ferrocenium (a) before and (b) after react with 2,4,6-TCP in aqueous solution

Blue colour

Yellowish green colour

Figure 2 The reaction equation of Ferrocenium and 2,4,6-TCP in aqueous solution.

The effect of solution pH against the reaction of ferrocenium and 2,4,6 – TCP was conducted in range of pH 2 – 8. The absorbance intensity of ferrocenium increased from pH 2 to pH 5 and start decreasing sharply when approaching pH 7 (Figure 3). This situation occurred due to the instability of phenolic compound at neutral pH (Sirajuddin et al., 2007). The optimum absorbance intensity was obtained at pH 5. Consequently, this pH was selected as working pH.

(a)

(b)


20

Figure 3 Effect of solution pH against the reaction of Ferrocenium and 2,4,6-TCP in aqueous solution

The optimum concentration of ferrocenium concentration react with 2,4,6-TCP was 2000 mg/L (Figure 4). An increase in ferrocenium concentration will give more reaction to 2,4,6-TCP. After 2000 mg/L, the absorbance intensity decreased due to limiting 2,4,6-TCP presence in solution. After all the limiting reactant was reacted, therefore the absorbance intensity will decrease (Robinson & Schwartz 1956).

Figure 4 Optimum concentration of ferrocenium against 2,4,6-TCP in aqueous solution.

The absorbance intensity increase with time and reach steady state within 2 minutes (Figure 5). This is an optimum time for the formation of stable colour which may be assigned as the stability of ferrocenium solution to detect the presence of 2,4,6-TCP in aqueous solution.


21

Figure 5 The steady state response time of ferrocenium against 2,4,6-TCP in aqueous solution

Effect of analytes concentration to the absorbance of ferrocenium

The effect of 2,4,6-TCP concentration against ferrocenium has been studied in the range of 20 to 190 mg/L (Figure 6). The absorbance intensity of ferrocenium increases with the 2,4,6-TCP concentration and this was expected due to more reaction occurred when more 2,4,6-TCP available in the solution. An increase in absorbance intensity due to the added analyte will exhibit a linear relationship (Robinson et al., 2005).

The plot of relative absorbance against concentration of 2,4,6-TCP which was arranged in logarithme form give linear correlation in the range of 20 to 190 mg/L (Figure 5). The limit of detection was calculated and found to be 1.56 mg/L which apparently indicates that ferrocenium can detect the presence of 2,4,6-TCP in low concentration as compared to the

Figure 4 Effect of 2,4,6-TCP concentration against Ferrocenium


22

conventional method using HPLC which can only detect the presence of 2,4,6-TCP in 2.85 mg/L (Opeolu et al., 2010).

concluSIon

The ferrocenium showed a good sensitivity against 2,4,6-TCP, fast steady state response time with lower detection limit (1.56 mg/L). This proposed reagent was recommend as a potential reagent for determination of 2,4,6-TCP in aqueous solution.

AcKnoWlEDgEmEnT

The authors would like to thanks Universiti Pendidikan Sultan Idris (UPSI), Malaysia for the research fund under university grant code, GPU: 2011-0057-102-01.

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Smith, M. B. 2002. Organic Synthesis.(Second Edition). New York :Mc-Graw Hill Education.US Environmental Protection Agency. Phenolics (Spectrophotometric, Manual 4-AAP with Distillation), EPA Method 420.1: US, 1978.


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A Narrative Review of Two-Arm and Three-Arm Non-Inferiority Clinical Trials

Tinjauan Naratif Ujian Klinikal Tidak Inferior bagi 2-Kumpulan dan 3-Kumpulan Rawatan

Zurina Mohd Yusof1 & Nor Afzalina Azmee2

Department of Mathematics, Universiti Pendidikan Sultan Idris, 35900 Tanjung Malim, [email protected] & [email protected]

Abstract

Clinical trial is a research conducted to test the effectiveness and safety of the experimental drugs or treatments or diagnostic tools before approval using consenting human subjects as sample size. Non-inferiority test in clinical trial is performed to demonstrate that the experimental treatment is not worse than the reference treatment by more than a pre-defined margin. This type of design has accumulated much attention from the researchers as it is viewed as an alternative to the existing superiority trials. However, issues in the design and analysis of non-inferiority trials are still at large and highly debatable. Thus, the object of this paper is to address the gap in the literature, by providing a concise, narrrative review of some selected papers related to non-inferiority trials. The review of 162 published papers indicates potential studies related to two-arm and three-arm non-inferiority trials, focusing on the implementation of Bayesian design and analysis.

Keywords non-inferiority trial, two-arm, three-arm, Bayesian analysis

Abstrak

Ujian klinikal merupakan satu penyelidikan yang dijalankan bagi menguji keberkesanan dan keselamatan ubat atau rawatan atau alat diagnostik, sebelum ia diluluskan dengan menggunakan subjek manusia sebagai saiz sampel. Ujian klinikal tidak inferior bertujuan untuk membuktikan yang rawatan percubaan tidak kurang baik berbanding dengan rawatan piawai. Dengan pengurangan keberkesanan haruslah tidak melebihi had tertentu yang ditetapkan. Reka bentuk ujian ini telah mendapat perhatian ramai penyelidik dan ia dianggap sebagai alternatif kepada ujian klinikal yang bertujuan untuk membuktikan bahawa rawatan percubaan lebih unggul daripada rawatan piawai. Walau bagaimanapun, isu-isu yang berkaitan dengan reka bentuk dan analisis ujian tidak inferior masih banyak diperbahaskan. Justeru, objektif kertas ini adalah untuk menangani jurang literatur dengan menyediakan ulasan naratif yang ringkas dan padat berkenaan ujian tidak inferior. Tinjauan sebanyak 162 kertas penyelidikan ini menunjukkan yang kajian lanjut diperlukan dalam pelaksanaan reka bentuk dan analisis Bayesian bagi ujian tidak inferior untuk 2-kumpulan dan 3-kumpulan rawatan.

Keywords ujian tidak inferior, 2-kumpulan, 3-kumpulan, analisis Bayesian


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INTRoduCTIoN

Clinical trial is a scientific experiment that is bounded by ethical regulations in order to protect the patients’ interest. For example, patients can only be recruited in a trial after they have given their informed written consent and these patients must have been clearly informed about the risks or the side effects they might experience when taking the medications. These scientific experiments are governed by well-recognized, regulatory bodies such as the International Conference of Harmonisation, the Commitee for Medical Products for Human Use, the U.S. Food and Drugs Administration and the Agency for Healthcare Research and Quality (see details in ICH, 1998; CHMP, 2005; FDA, 2010; AHRQ, 2012).

Any type of clinical trial can possibly have the objective of showing either superiority, equivalence or non-inferiority of the experimental treatment with respect to the current, reference treatment. In the late 1990s, non-inferiority trials started to garner interest among the researchers in either statistical or medical background. This type of trial is often sought after by the researchers to demonstrate that although the experimental treatment is non-inferior to reference with respect to efficacy, it possesses other advantages such as being cheaper, easier to be administered or has fewer side effects as opposed to reference (see discussion by Pigeot et al., 2003; Koch & Rohmel, 2004; Tang & Tang, 2004). It is important to note that non-inferiority trials can only be conducted if a good reference treatment exists.

In general, the non-inferiority trials can be commonly categorized as the two-arm trial and three-arm trial. A simple two-arm non-inferiority trial involves experimental and refererence arms, whereas a three-arm non-inferiority trial includes an extra placebo arm. More than 30 years has past since the idea of non-inferiority trial was first introduced and it is high time to revisit the issues surrounding the conduct of non-inferiority trials. The narrative review of these selected papers is hoped to impart an adequate background study to novice researchers and to identify potential areas for further studies.

MeThod

The aim of of this paper is to provide an overview of two-arm and three-arm non-inferiority trials, hence termed as a narrative review. In this case, explicit or systematic literature search protocol was not implemented in selecting and appraising evidence. Selected articles were extracted from clinical and non-clinical non-inferiority trials published between 1982 and early 2014. Those articles were obtained via a literature search, using the following keywords; non-inferiority, sample size determination, assurance. The following criteria such as general information related to authors, publication year, journal name, main theme discussed, type of non-inferiority clinical trials conducted, the sample size methods and the statistical analyses considered were noted. Some of the articles were not accessible and for such a problem, the review was based on just the abstract.

The Narrative Review of Non-Inferiority Trials

One of the earliest problem in conducting non-inferiority trials is the perplexity of analyzing such trials. The trials are often, wrongly analyzed by using the conventional hypothesis testing for superiority trials, where non-rejection of the null hypothesis is implied as successfully


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showing that an experimental treatment is non-inferior to reference. Blackwelder (1982) offered a solution to this problem, proposing that the null hypothesis should be stated in terms of a specified difference, δ. Although the fundamental idea of testing non-inferiority was given much earlier in Blackwelder (1982), it was not immediately picked up until early 2000s (see Figure 1).

During that period of 1980s – 1990s, non-inferiority trials were at the early stage of development and lack of understanding was common among practitioners. The issues commonly raised include how the non-inferiority margin should be chosen or how assay sensitivity can be assessed. Defining a non-inferiority margin is an important part of the methodology in the two-arm non-inferiority trials. This margin represents the reduction in efficacy in the experimental treatment that is thought to be tolerable. Because subjective and divergent opinions may arise with respect to either statistical or medical reasons, determining a margin becomes a debatable and controversial issue (see Hwang & Morikawa, 1999; D’Agostino et al., 2003). On the other hand, assay sensitivity is defined as the ability of a trial to differentiate between effective and ineffective treatments. This problem is inherited in two-arm non-inferiority trials and leads to a challenge of assuring that the experimental treatment is at least as good as the standard treatment (Hwang & Morikawa, 1999; Laster & Johnson, 2003). A solution to this problem is proposed by Blackwelder (2004), stressing the importance of maintaining a high degree of adherence protocol in the equivalence and non-inferiority trials and demonstrating a strong interim evidence which may be an indicator that an experimental treatment is superior to reference.

Figure 1 Classification of 162 overall published papers across the years

Across the years, the debates regarding the pros, the cons, the barriers and the challenges of conducting non-inferiority trials continously appeared in academic journals (see Snappin, 2000; Pocock, 2001; Hung et al., 2001; D’Agostino et al., 2003; Wangge et al., 2012). Some other studies were devoted to designing the protocol and reporting the non-inferiority trials (Weins, 2002; Brittain & Lin, 2005; Le Henanff et al., 2006; Piaggio et al., 2006). In particular, Piaggio et al. (2006) recommended some examples


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on how to write an effective report on non-inferiority trials to avoid unethical issues and misunderstanding in the trials. Ethical issues have also been raised in Garratini & Bertele’ (2007) and Hung et al. (2007). For example, the non-inferiority trials have been viewed by some as a platform to justifiably enter patients into a trial that will not provide them any advantage. The non-inferiority trials are also seen as means to merely cut down the cost and shorten the time. Others argued that non-inferiority is still needed in some clinical trials such as in the treatment of diseases for tuberculosis, leukimia and treatment involving antibiotics (see Temple & Ellenberg, 2000; Nunn et al., 2008; Chuang-Stein, 2008).

As given in Figure 2, the design of three-arm non-inferiority trial started to receive considerable attention from the year 2003 onwards, due to the unresolved problems found in the design of two-arm non-inferiority trials, which includes assuring assay sensitivity and defining a proper margin. The inclusion of a placebo arm allows for direct proof of efficacy of the new experimental treatment, with respect to placebo. In situations where delaying the current reference treatment is not going to cause irreversible morbidity, three-arm non-inferiority trial is seen as an appealing choice (Pigeot et al., 2003; CHMP, 2005; Britton, 2007; Munk et al., 2007; Dette et al., 2008; Ghosh et al., 2011; Hida & Tango, 2011). In particular, Koch & Rohmel (2004) summarized clear-cut situations where the inclusion of a placebo arm may well be supported; such as when the reference treatment is traditional, weak or volatile or that the trial is conducted to cure a disease that is not fully understood yet. The hot topics being discussed in the context of three-arm non-inferiority trials include methods of data analysis and sample size determination.

Figure 2 Comparison of published papers specifically related to two-arm and three-arm non-inferiority trials.

In three-arm non-inferiority trials, multiple comparisons arise due to the interest of comparing both the experimental and the reference with respect to placebo and then assessing the relative efficacy between the two active treatments. To have a meaningful interpretation of non-inferiority, it is important to establish superiority of both active treatments with respect to placebo. To conduct several multiple tests simultaneously will


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lead to a problem of multiplicity and this is discussed in Pigeot et al. (2003) and Koch & Rohmel (2004). The papers reviewed also indicates the tendency of investigators to adopt the Bayesian approach in data analysis (for example Britton, 2007; Ghosh et al., 2011). A Bayesian approach was implemented in Britton (2007) to examine the deviance information criterion used in camparing various models. The evaluation took into account twelve different prior distributions to produce posterior distribution, in order to assess the best fit model. On the other hand, Ghosh et al. (2011), considered a Bayesian analysis, which incorporated parametric as well as semi-parametric models. The benefit of the proposed Bayesian method was assessed via simulation, allowing for the conditions presumed in the study protocol.

Sample size determination is another important element in the design stage of clinical trial. Sample size that is either too small or too large may be judged unethical and may lead to serious consequences. As an example, a trial that has a small sample size may have little chance of showing the difference between the mean populations of two treatment groups, should the difference truly exists. On the other hand, a study that has a too large sample size could have met the objectives of the trial before the end of the study. In a latter case, some patients may have unnecessarily entered the trial and results in waste of resources. Papers advocating the frequentist method for sample size calculation for two-arm and three-arm include Pigeot et al. (2003), Julious (2004) and Friede & Kieser (2008). In particular, Pigeot et al. (2003) proposed an optimal sample size allocation across the three distinct groups, assuming the case of normally distributed variables with homogeneity of variances. Other studies who proposed a Bayesian approach had one unified theme, that is Bayesian approach allows the uncertainty of estimation be represented by using proper prior distributions. The constructions of these priors have to be based on evidence and sound judgement and subjectively vary from trial to trial. Among the earliest paper found is in Joseph et al. (1997), who gave a note on Bayesian methods in sample size calculation based on length and coverage criteria. An application of variation of that methods, such as the average length criteria (ALC) or the average coverage criteria (ACC) in non-inferiority trials is given in Wang & Stamey (2010). Assurance is another method that falls under Bayesian category. It is an interesting concept because it is close to the idea of power, that is by setting assurance at a certain level, one should find the sample size that fulfills the desired assurance. The application of assurance method was first introduced by O’Hagan & Steven (2001) in the study of cost-effective comparison between competing interventions, but the application in non-inferiority trials is seen later in O’Hagan et al. (2005). The study related to application in one sided superiority, two sided superiority, equivalence and non-inferiority trials with examples of simple problems of normal, binary and gamma distributed. Recently, a study in Azmee et al. (2013) demonstrated the application of Bayesian Clinical Trial Simulation in finding the required sample size via assurance for the case of three-arm non-inferiority trials, with normally distributed variables and homogeneity of variances.

CoNClusIoN

Non-inferiority trials are considered to be a new area in medical statistics and some of the issues in the design and analysis are still debatable and being researched. These certainly illustrate the needs and motivations to continue exploring those areas in non-inferiority


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trials. The review of literature indicates that the frequentist approach has been the dominant approach in both design and analysis of data. However, there is a considerable trend of switching from the conventional approach to Bayesian approach, a substantial gap that can be addressed in the near future. Example of potential studies include the implementation of Bayesian analysis, allowing for covariates or the implementation of Bayesian approach in sample size determination in three-arm non-inferiority trials, assuming normally distributed variables with heterogeneity of variances.

ReFeReNCes

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Azmee, N.A., Zulkifley, M. & Ahmad, A. (2013) Determination of the required sample size with assurance for three-arm non-inferiority trials. Jurnal Teknologi. 63: 89-93.

Blackwelder, W.C. (1982). Proving The Null Hypothesis in clinical trials. Controlled Clinical Trials. 3:345-353.

Blackwelder, W.C. (2004). Current Issues in Clinical Equivalence Trial. Journal of Dental Research. 83:113-115.

Brittain, E & Lin, D. (2005) A comparison of intent-to-treat and per-protocol results in antibiotic non-inferiority trials. Stat Medicine. 24:1-10.

Britton, M.C. (2007). Bayesian Approach to Three-arm Non-Inferiority Trials. Unpublished Mathematics Thesis, Georgia State University. [Online]. Available from: http://scholarworks.gsu.edu/cgi/viewcontent.cgi?article=1026&context=math_theses [Accessed 25th September 2014].

Chuang-Stein, C. (2008). Assay Sensitivity. Wiley Online Library.CHMP – Committee for Medicinal Products for Human Use (2005). Guideline on the choice of

non-inferiority margin. [Online]. Available from: http://www.ema.europa.eu/docs/en_GB/document_library/Scientific_guideline/2009/09/WC500003636.pdf [Accessed 25th September 2014].

D’Agostino, R.B Sr., Massaro, J.M. & Sullivan L.M. (2003). Non-inferiority trials: design concepts and issues - the encounters of academic consultants in statistics. Stat Med. 22:169-186.

Dette, H., Trampisch, M. & Hothorn, L.A. (2008). Robust Design in Non-Inferiority Three-arm Clinical Trials with Presence of Heteroscedasticity. [Online]. Available from: http://www.ruhrunibochum.de/imperia/md/content/mathematik3/publications/revision_unblinded_final__3_.pdf [Accessed 25th September 2014].

FDA (2010). Guidance for Industry: Non-Inferiority Clinical Trials [Online]. Availabe from: http://www.fda.gov/downloads/Drugs/Guidances/UCM202140.pdf [Accessed 25th September 2014].

Friede, T. & Kieser, M. (2008) Sample Size Reestimation in Non-Inferiority Trials. [Online]. Available from: http://www.efspi.org/PDF/activities/international/non_inf_2008/7_re-estimation_TF.pdf [Accessed 25th September 2014].

Garattini, S. & Bertele’, V. (2007). Non-inferiority trials are unethical because they disregard patients’ interests. Lancet. 270:1875-1877.

Ghosh P.. Nathoo, F. Gonen, M. & Tiwari, R.C. (2011). Assessing non-inferiority in a three-arm trials using the Bayesian Approach. Stat Med. 30: 1795-1808.

Hida, E. & Tango, T. (2011). On the three-arm non-inferiority trial including a placebo with a prespecified margin. Stat Med. 30:224-231.

Hung, H.M.J., Wang S.J., Tsong Y, Lawrence J & O’Neil RT. (2001). Some Fundamental Issues with Non-Inferiority Testing In Active Controlled Trial. Stat Med. 22:213-225.


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Hung, H.M.J., Wang, S.J. & O’Neill, R. (2007). A regulatory perspective on choice of margin and statistical inference issue in non-inferiority trials. Biometrical Journal, 47 :28-36, 2007.

Hung, H.M.J.,. Wang, S.J. & O’Neill, R (2007). Issues with statistical risks for testing methods in noninferiority trial without a placebo arm. Journal of Biopharmaceutical Statistics, 1:213.

Hwang, I.K. & Morikawa, T. (1999). Design Issues in Non-Inferiority/Equivalence Trials. Drug Information Journal. 33:1205-1218.

ICH – International Conference on Harmonization (1998) Note for guidance on statistical principles for clinical trials. [Online]. Available from: http://www.ema.europa.eu/docs/en_GB/document_library/Scientific_guideline/2009/09/WC500002928.pdf [Accessed 25th September 2014].

Joseph, L., du Berger, R. & Belisle, P. (1997). Bayesian and Mixed Bayesian/Likelihood criteria for Sample Size determination. Statistics In Medicine. 16:769-781.

Julious, S.A. (2004). Tutorial in Biostastics:Sample sizes for clinical trials with Normal data. Statistics in Medicine. 23:1921-1986.

Koch, A. & Rohmel, J. (2004) Hypothesis testing in the “gold standard” design for proving the efficacy of an experimental treatment relative to placebo and a reference. Journal of Biopharmaceutical Statistics. 14: 315-325.

Laster, L.L. & Johnson, M.F. (2003). Non-inferiority trials: the ‘at least as good as’ criterion. Statistics In Medicine. 22: 187-200.

Le Henanff, A., Giraudeau, B., Baron, G. & Ravaud, P. (2006) Quality of reporting of noninferiority and equivalence randomized trials. Journal of American Medical Association. 295:1147-1151.

Munk, A., Meilke, M., Skipka, G. & Freitag, G. (2007). Testing Non-Inferiority in Three-Armed Clinical Trials Based on The likelihood Ratio Statistics. The Canadian Journal of Statistics. 35:413-431.

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O’ Hagan, A., Stevens, J.W. & Campbell, M.J. (2005). Assurance in Clinical Trial Design. Pharmaceutical Statistics. 4:187-201

Piaggio, G., Elbourne D.R., Altman, D.G., Pocock, S.J., Evans, S.J. & Group, C. (2006). Reporting of Noninferiority and Equivalence Randomized Trials An Extension of the CONSORT Statement. Journal of American Medical Association. 295:1152-1160.

Pigeot, I., Schafer, J., Rohmel, J. & Hauschke, D. (2003). Assessing Non-Inferiority of a New Treatment in a Three-arm Trial Including Placebo. Statistics in Medicine. 22:833-889.

Pocock, S.J. (2001). The pros and cons of noninferiority trials. Blackwell Publishing. Fundamental & Clinical Pharmacology. 17:483-490.

Snappin, S.M. (2000). Non-Inferiority trials. Current Controlled Trials. Cardiovasc. Med. 1:19-21.Tang, M.L. & Tang, N.S. (2004) Test of noninferiority via rate difference for three-arm clinical

trials with placebo. Journal of Biopharmaceutical Statistics. 14: 337-347. Temple, R. & Ellenberg, S.S. (2000). Placebo-Controlled Trials and Active-Control Trials in

the Evaluation of New Treatment. Part 1: Ethical and Scientific Issues. Annals of Internal Medicine.133:455-463.

Wang, J. & Stamey, J.D. (2010). A Bayesian algorithm for sample size determination for equivalence and non-inferiority test. Journal of Applied Statistics. 37: 1749-1759.

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Hubungan antara Kemahiran Membuat Keputusan dalam Fizik dengan Kemahiran Membuat Keputusan dalam Kehidupan

Seharian dalam Kalangan Pelajar FizikRelationship between the Decision-Making Skills in Physics with Decision-Making Skills

in Daily Life among Physics Students

Yeoh Sik Mei1 & Razak Abd. Samad Yahya2

1Sekolah Menengah Jenis Kebangsaan Phor Tay, Pulau Pinang, Malaysia.2Fakulti Sains dan Teknologi, Universiti Pendidikan Sultan Idris, 35900 Tanjung Malim, Perak Malaysia.

[email protected] & [email protected]

Abstrak

Kajian ini dilaksanakan untuk menentukan hubungan antara kemahiran membuat keputusan dalam fizik dengan kemahiran membuat keputusan dalam kehidupan seharian dalam kalangan pelajar fizik. Kajian ini juga untuk menentukan kesan jantina terhadap kemahiran membuat keputusan. Sampel kajian terdiri daripada 215 orang pelajar tingkatan empat di Pulau Pinang. Instrumen kajian yang digunakan adalah Ujian Kemahiran Membuat Keputusan Fizik (UKMKF) dan Ujian Kemahiran Membuat Keputusan Kehidupan Seharian (UKMKKS). Item dalam UKMKF adalah soalan tahun lepas SPM manakala item dalam UKMKKS adalah soalan daripada dua sumber berwibawa. Ujian-t untuk sampel-sampel bebas dan korelasi Pearson digunakan untuk menganalisis data. Dapatan kajian menunjukkan hubungan yang sangat lemah antara kedua-dua kemahiran membuat keputusan dalam fizik dengan kemahiran membuat keputusan dalam kehidupan seharian (r = .18, p < .05). Dapatan kajian juga menunjukkan jantina tidak mempengaruhi kemahiran membuat keputusan fizik. Hubungan lemah antara kemahiran membuat keputusan dalam fizik dengan kemahiran keputusan dalam kehidupan harian menunjukkan tidak berlaku pemindahan kemahiran membuat keputusan dari pembelajaran formal kepada kehidupan seharian pelajar. Gender pula tidak memberi kesan kepada keupayaan pelajar menguasai kemahiran membuat keputusan.

Kata kunci kemahiran fizik, pemindahan kemahiran, kemahiran kehidupan seharian

Abstract

This study was conducted to determine the relationship between the decision-making skills in physics with the decision-making skills in daily life among physics students. The sample consisted of 215 form four physics students from Penang. The instruments used were the Decision Making Skills in Physics Test (UKMKF) and the Decision Making Skills in Daily Life Test (UKMKKS). The items for UKMKF were SPM past-years questions, while the items for UKMKKS were questions from two valid sources. The independent sample t-test and the Pearson correlation were used to analyze the data. The results showed a very weak relationship between the decision-making skills in physics and the decision-making skills in daily life (r = .18, p <.05). The results also showed that the decision-making skills in physics amongst students were not influenced by gender. The weak relationship between


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the decision-making skills in physics and the decision-making skills in daily life suggests that there were no conclusive transfer of decision-making skills in formal classroom to the student’s daily life. Gender has no effect to one’s ability to master decision-making skills.

Keywords skills in physics, transfer of skills, skills in everyday life

PengenAlAn

Kajian terhadap kemahiran membuat keputusan adalah satu usaha yang penting kerana sebarang keputusan yang dibuat oleh individu boleh mempengaruhi kehidupan mereka dan kehidupan masyarakat di sekeliling mereka (Miller, 2000). Apabila kita dapat menguasai kemahiran ini maka kita akan dapat membuat keputusan yang berkesan pada masa kini supaya kita dapat mengawal masa depan kita (Brezina, 2008). Campbell, Lofstrom dan Jerome (1997) menyatakan akan kepentingan kemahiran membuat keputusan ini didedahkan kepada generasi muda. Oleh kerana penguasaan kemahiran membuat keputusan ini penting maka pada tahun 1991, ianya diperkenalkan dalam sukatan pelajaran Fizik Kurikulum Bersepadu Sekolah Menengah (KBSM). Selaras dengan ini, bakal guru fizik dan guru fizik dalam perkhidmatan dilatih supaya dapat menerapkan kemahiran ini semasa pengajaran dan pembelajaran fizik di sekolah (BPK, 2012). Mengikut KBSM, kemahiran membuat keputusan adalah satu aktiviti yang mana pelajar memilih alternatif penyelesaian yang terbaik dari beberapa alternatif berdasarkan kriteria tertentu bagi mencapai matlamat yang ditetapkan (BPK, 2012). Sesuai dengan perkembangan ini, soalan-soalan SPM turut diubahsuai supaya tahap penguasaan kemahiran membuat keputusan dalam kalangan pelajar fizik dapat dinilai. Setiap tahun komponen kemahiran membuat keputusan yang dinilai dalam kertas soalan SPM Fizik Kertas 2 adalah lebih kurang 17% (LPM, 2002). Menurut Abd. Rahim Abd. Rashid (1999), proses membuat keputusan penting kepada penilaian kerana ia adalah satu dimensi utama dalam kurikulum. Kemahiran membuat keputusan juga penting dalam penilaian kerana proses penilaian akan mencabar daya pemikiran pelajar semasa membuat keputusan.

Mann, Harmoni dan Power (1989) menegaskan bahawa kemahiran membuat keputusan seharusnya diajar secara rutin di peringkat menengah rendah lagi kerana pada peringkat ini proses pemilihan mula diperkenalkan kepada pelajar. Kemahiran membuat keputusan adalah satu kemahiran yang boleh dipelajari secara formal dalam bilik darjah. Baron dan Brown (1991a) berpandangan bahawa kemahiran membuat keputusan sepatutnya turut diterapkan dalam mata pelajaran lain seperti sejarah, sastera, matematik dan sains. Kurikulum sekolah hendaklah digubal untuk memberi peluang kepada remaja mempelajari dan menguasai kemahiran membuat keputusan dengan berkesan (Mincemoyer & Perkins, 2003).

Salah satu matlamat pendidikan Malaysia adalah untuk menghasilkan insan menyeluruh dari segi jasmani, emosi, rohani dan intelek agar mereka dapat menyumbang kepada kemajuan dan kesejahteraan rakyat dan negara. Inilah juga harapan setiap guru atau pendidik agar setiap pelajar dapat menguasai ilmu yang disampaikan atau kemahiran yang diterapkan dalam kelas formal. Setelah pelajar berjaya menguasai ilmu atau kemahiran maka peringkat seterusnya adalah untuk memindahkan kemahiran berkenaan kepada situasi baharu dalam kehidupan seharian mereka. Secara ringkas, pemindahan ilmu atau pemindahan kemahiran


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merujuk kepada keupayaan yang perolehi oleh pelajar untuk mengembangkan apa yang telah dipelajari dalam satu keadaan ke keadaan baharu (Marton, 2006). Menurut Sasson dan Dori (2012), proses pemindahan ilmu atau kemahiran melibatkan kemahiran berfikir aras tinggi (KBAT) yang menggambarkan keupayaan pelajar menggunakan kemahiran dan pengetahuan untuk topik atau disiplin yang nampaknya tidak berkaitan. Guru sentiasa berharap agar pelajar dapat menunjukkan bukti berlaku pemindahan ilmu atau kemahiran dari satu masalah ke satu masalah lain dalam kursus yang sama atau dari pada satu kursus ke kursus yang lain (Bransford & Schwartz, 2001). Pemindahan kemahiran menjadi semakin penting dalam sistem pendidikan kita kerana ia adalah indikator kepada kejayaan proses penyampaian dalam bilik darjah.

Faktor jantina dalam pendidikan sangat relevan terutama di Malaysia memandangkan jumlah pelajar perempuan yang berada di pusat pengajian tinggi lebih ramai berbanding lelaki. Menurut buku Indikator Pengajian Tinggi Malaysia (IPTM, 2010), terdapat 103,483 (37.7%) pelajar lelaki dan 171,207 (62.3%) pelajar perempuan yang mengikuti Program Sarjana Muda di Universiti Awam (UA) pada tahun 2010. Ini secara umum mengambarkan pencapaian pelajar perempuan lebih baik berbanding pelajar lelaki. Pada masa yang sama, jantina juga mungkin merupakan satu faktor yang mempengaruhi kemahiran membuat keputusan (Severian & ten Dam, 1997). Mereka menyatakan pengaruh jantina mungkin berbeza-beza mengikut konteks tugas yang diberikan. Terdapat penyelidikan yang memberi tumpuan kepada perbezaan jantina dalam membuat keputusan (Barnett & Karson, 1989) tetapi amat sedikit kajian yang mengkaji perbezaan antara jantina bagi kemahiran membuat keputusan dalam kalangan pelajar fizik.

PernyAtAAn MASAlAH

Kemahiran membuat keputusan adalah salah satu daripada tiga strategi berfikir dalam KBSM. Dua lagi strategi berfikir adalah menyelesaikan masalah dan mengkonsepsikan. Salah satu matlamat pendidikan sains di Malaysia adalah memberikan kesedaran kepada pelajar tentang betapa pentingnya saling hubungan antara hidupan dan pengurusan alam semula jadi untuk keberterusan hidup manusia sejagat (BPK, 2012). Demi memastikan matlamat ini tercapai melalui pendidikan maka pelajar didedahkan kepada kemahiran membuat keputusan supaya akhirnya mereka dapat menggunakan kemahiran tersebut dalam kehidupan seharian. Oleh itu, hubungan antara kemahiran membuat keputusan dalam fizik dengan kemahiran membuat keputusan dalam kehidupan seharian dalam kalangan pelajar fizik penting diketahui supaya dapat ditentukan sekiranya telah berlaku proses pemindahan kemahiran. Walau bagaimanapun, isu ini jarang diberi perhatian oleh pendidik sendiri kerana tidak ada maklumat yang jelas tentang aspek ini di sekolah. Oleh itu, kajian ini dijalankan untuk menentukan hubungan antara kemahiran membuat keputusan dalam fizik dengan kemahiran membuat keputusan dalam kehidupan seharian dalam kalangan pelajar fizik. Isu ini sangat relevan dikaji. Menurut Kortland (2001), pengubal kurikulum fizik perlu mengubah penumpuan daripada kandungan, kemahiran dan proses pengajaran dan pembelajaran kepada kandungan sains dalam konteks kehidupan seharian dan kemahiran membuat keputusan untuk menghasilkan kandungan yang lebih produktif.


34

SoAlAn KAjiAn

Penyelidikan ini ditumpukan kepada dua soalan kajian seperti berikut:1. Adakah terdapat hubungan yang signifikan antara kemahiran membuat keputusan

dalam fizik dengan kemahiran membuat keputusan dalam kehidupan seharian dalam kalangan pelajar fizik?

2. Adakah terdapat perbezaan yang signifikan pada tahap kemahiran membuat keputusan dalam fizik dalam kalangan pelajar fizik mengikut jantina?

inStruMen KAjiAn

Instrumen kajian yang digunakan adalah Ujian Kemahiran Membuat Keputusan Fizik (UKMKF) dan Ujian Kemahiran Membuat Keputusan Kehidupan Seharian (UKMKKS). Item dalam UKMKF terdiri daripada soalan-soalan lepas SPM Fizik Kertas 2 (Bahagian C) manakala item dalam UKMKKS terdiri daripada soalan-soalan yang dipetik dari sumber berwibawa (Switzer, 2009; Laskey & Campbell, 1991). Semua item kedua-dua instrumen adalah soalan berbentuk esei.

KAjiAn rintiS

Instrumen UKMKF dan UKMKKS telah disemak oleh dua pensyarah kanan fizik untuk menentukan kesahan dalamannya. Untuk menentukan kebolehpercayaan pula, UKMKKS telah ditadbir kepada 75 orang pelajar fizik tingkatan empat. Pelajar diberi masa 30 minit untuk menjawab UKMKKS dan pelajar berjaya menamatkan sesi tanpa masalah. Kebolehpercayaan dalaman UKMKKS ditentukan dengan kaedah test-retest. Analisis menunjukkan kebolehpercayaan yang tinggi (r = .832, p < .01) dan boleh diterima (Best & Kahn, 2006). Walau bagaimanapun, kajian rintis tidak dilakukan ke atas UKMKF. Soalan-soalan UKMKF adalah sah dan boleh percaya sesuai dengan tarafnya sebagai soalan SPM yang dibina oleh Lembaga Peperiksaan Malaysia (LPM).

Metodologi KAjiAn dAn AnAliSiS dAtA

Instrumen UKMKF dan UKMKKS dalam kajian kuantitatif ini ditadbir ke atas pelajar setelah mendapat kebenaran sekolah. UKMKF ditadbir dahulu dan UKMKKS seminggu kemudian. Skrip jawapan UKMKF dan UKMKKS disemak oleh penyelidik dan disemak juga oleh pemeriksa kedua, seorang guru fizik yang berpengalaman. Menurut Gay, Mills dan Airasian (2009), sebarang jawapan ujian berbentuk ayat dan mempunyai lebih daripada satu perkataan boleh menimbulkan isu tentang kebolehpercayaan. Kajian rintis menunjukkan bahawa skor kedua-dua pemeriksa adalah setara. Ini bermakna proses penyemakan kertas adalah boleh percaya.

Data yang dikumpul daripada penyelidikan kemudiannya dianalisis sewajarnya dengan menggunakan korelasi Pearson dan Ujian-t untuk sampel-sampel bebas. Untuk persoalan pertama, hubungan antara skor UMKKF dan skor UKMKKS ditentukan dengan korelasi Pearson dan untuk persoalan kajian kedua, ujian-t (sampel-sampel bebas) dilakukan ke atas skor UKMKKS mengikut gender.


35

dAPAtAn KAjiAn

A. Hubungan antara kemahiran membuat keputusan fizik dengan kemahiran membuat keputusan kehidupan seharian

Jadual 1 menunjukkan hubungan antara kemahiran membuat keputusan dalam fizik dengan kemahiran membuat keputusan dalam kehidupan seharian ( r = .18, p < .05). Pekali korelasi Pearson yang rendah ini menunjukan wujud perhubungan yang sangat lemah sehingga hampir boleh diabaikan (Best & Kahn, 2006).

jadual 1 Keputusan korelasi Pearson antara kemahiran membuat keputusan dalam fizik dengan kemahiran membuat keputusan dalam kehidupan seharian

Fizik Kehidupan seharian

FizikKorelasi Pearson 1 .175*

Sig. (2-hujung) .010N 215 215

Kehidupan seharianKorelasi Pearson .175* 1Sig. (2-hujung) .010

N 215 215* Korelasi signifikan pada paras 0.05 (2-hujung).

b. Kesan jantina terhadap tahap kemahiran membuat keputusan dalam fizik dalam kalangan pelajar fizik

Keputusan Ujian-t untuk sampel-sampel bebas dalam Jadual 2 menunjukkan bahawa skor min pelajar lelaki adalah 58.40 (S.P.=20.99) manakala skor min pelajar perempuan adalah 61.11 (S.P.=23.11). Keputusan kajian ini menunjukkan kedua-dua jantina mempunyai kemahiran membuat keputusan yang sederhana. Seterusnya, Jadual 2 juga menunjukkan tidak terdapat perbezaan yang signifikan pada tahap kemahiran membuat keputusan dalam fizik dalam kalangan pelajar fizik mengikut jantina (p = .372).

jadual 2 Keputusan Ujian-t untuk sampel-sampel bebas bagi tahap kemahiran membuat keputusan fizik dalam kalangan pelajar fizik mengikut jantina

Pembolehubah Min (M) S.P. Nilai t Sig* (2-hujung)

Lelaki 58.40 20.99 -.895 .372

Perempuan 61.11 23.11* Signifikan p<0.05

PerbincAngAn

a. Hubungan antara kemahiran membuat keputusan fizik dengan kemahiran membuat keputusan kehidupan seharian

Hubungan yang lemah antara kemahiran membuat keputusan fizik dengan kemahiran membuat keputusan kehidupan seharian dalam kalangan pelajar fizik menunjukkan bahawa


36

kemahiran membuat keputusan dalam fizik tidak dapat dipindahkan ke dalam konteks kehidupan seharian mengikut kajian ini. Dapatan kajian selaras dengan kajian Yang (2004) di mana responden gagal menggunakan penaakulan saintifik semasa memberi pandangan dan hujah untuk menyokong pilihan mereka dalam isu sosio-saintifik. Menurut Yang (2004) lagi, pelajar sememangnya boleh menguasai kemahiran berfikir seperti kemahiran membuat keputusan tetapi, mereka mungkin mempunyai peluang yang sedikit untuk mengamalkan kemahiran tersebut dalam konteks kehidupan seharian. Kesimpulannya, kemahiran berfikir saintifik seperti kemahiran membuat keputusan dalam fizik tidak boleh dipindahkan ke keadaan lain yang kurang saintifik. Pelajar mungkin mempunyai kesukaran untuk memindahkan kemahiran membuat keputusan ini dari konteks fizik ke konteks kehidupan seharian.

Isu kritikal dalam kemahiran membuat keputusan bagi pelajar ialah pemindahan kemahiran dari bilik darjah ke keadaan sebenar atau pengalaman hidup sebenar. Menurut Barnett dan Ceci (2002), pembelajaran mengenai pemikiran saintifik dan penaakulan jarang dapat dipindahkan di luar kandungan mata pelajaran tertentu yang telah diajar oleh guru. Ratcliffe (1996) pula menyatakan bahawa orang dewasa akan menunjukkan kebolehan penaakulan saintifik yang lemah apabila kebolehan itu diletakkan dalam konteks kehidupan seharian.

Di Malaysia, kemahiran berfikir telah lama diperkenalkan dalam pengajaran dan pembelajaran sejak tahun 1991. Pada tahun 2002, sukatan pelajaran (semakan semula) telah memperkenalkan komponen kemahiran berfikir yang lebih dikenali sebagai kemahiran berfikir kritis dan kreatif (KBKK) yang ditekankan untuk diintergrasikan dalam pengajaran dan pembelajaran. Daripada dapatan kajian, hubungan yang sangat lemah antara kedua-dua kemahiran membuat keputusan dalam fizik dan dalam kehidupan seharian menunjukkan bahawa pengaplikasian dan pemindahan kemahiran membuat keputusan dalam kalangan pelajar fizik masih tidak mencukupi. Menurut Baron dan Brown (1991c), kebanyakan guru tidak pernah mengkaji perkara ini. Ini selaras dengan pendapat Zheng (2007) yang menyatakan bahawa sesetengah guru fizik yang berpengalaman masih mempercayai bahawa aktiviti bilik darjah perlu penuh dengan praktikal, ujian dan ceramah, penyampaian kandungan dan konsep fizik dengan cara abstrak.

Guru juga mengalami dilema semasa melaksanakan pengajaran dan pembelajaran untuk memperkenalkan atau menerapkan kemahiran ini. Menurut White, Russell dan Gunstone (2002), guru terperangkap di antara keinginan untuk berubah dengan usaha untuk memperbaiki amalan dan corak yang lama wujud di bilik darjah dan pembelajaran pelajar. Wildy dan Wallace (1995) mendapati walaupun ada sokongan professional dan usaha guru yang terbaik tetapi naluri pelajar cenderung menentang percubaan guru untuk menggunakan kaedah berpusatkan pelajar. Pelajar memilih penyelesaian yang siap sedia dan bukannya membuat keputusan mereka sendiri kerana mereka telah dibiasakan oleh sistem persekolahan dan jenis pengetahuan sains yang diajar (White, Russell & Gunstone, 2002). Ini menyebabkan guru cepat kembali kepada cara lama pengajaran mereka. Baron dan Brown (1991b) juga menyatakan bahawa sesetengah pelajar akan melihat arahan atau langkah membuat keputusan sebagai suatu gangguan dalam pembelajaran.


37

b. Kesan jantina terhadap tahap kemahiran membuat keputusan dalam fizik dalam kalangan pelajar fizik

Keputusan kajian ini menunjukkan bahawa pelajar perempuan dan lelaki mempunyai prestasi yang lebih kurang sama dalam kemahiran membuat keputusan dalam fizik. Keputusan kajian ini disokong oleh Hazel, Logan dan Gallagher (1997) yang menyatakan bahawa pelajar perempuan dan lelaki mempunyai prestasi yang sama dalam peperiksaan berbentuk soalan pendek dalam fizik. Häussler dan Hoffmann (2002), mendapati bahawa pelajar perempuan dan lelaki yang belajar di sekolah satu jantina (monoeducation) mencapai keputusan yang sama baik dalam mata pelajaran fizik.

c. implikasi kajian

Kajian ini menunjukkan bahawa terdapat hubungan yang sangat lemah antara kemahiran membuat keputusan dalam fizik dan kemahiran membuat keputusan dalam kehidupan seharian. Apabila KBSM diperkenalkan, kemahiran membuat keputusan telah diterapkan dalam kurikulum fizik Malaysia. Hubungan yang sangat lemah mencadangkan bahawa kemahiran membuat keputusan sangat sukar atau sangat kurang diterapkan dalam pengajaran dan pembelajaran fizik di negara kita. Semasa mengajar, guru fizik cenderung memberi tumpuan kepada kandungan dan keputusan dan bukannya pada apa yang mereka inginkan pelajar pelajari (Tuminaro & Redish, 2007). Gaya pengajaran tradisional di sekolah memberi penekanan yang terlalu banyak pada penggunaan persamaan fizik dan berorientasikan hasil. Jenis gaya pengajaran ini menghantar mesej yang tidak diingini kepada pelajar iaitu apa yang paling diutamakan adalah persamaan dan hasil fizik (Sim, 2010).

Apabila kemahiran membuat keputusan tidak diterapkan dengan sempurna maka ia membawa erti kemahiran ini tidak boleh dipindahkan dari satu konteks ke konteks yang lain dengan mudah (Barnett & Ceci, 2002; Yang, 2004). Oleh yang demikian, kurikulum fizik KBSM perlu disemak sekali lagi supaya kemahiran yang diajar dalam kelas dapat digunakan dalam kehidupan seharian supaya pelajar sentiasa dapat membuat keputusan yang betul dan tepat. Oleh itu, peningkatan keupayaan berfikir secara saintifik perlu diambil berat oleh guru. Guru juga perlu menekankan pembelajaran dalam suasana yang sahih supaya pelajar dapat melihat di mana, bila dan bagaimana kemahiran yang berkaitan sesuai digunakan. Selain itu, guru dan penggubal kurikulum harus sedar bahawa penerapan kemahiran membuat keputusan bukan sahaja memerlukan masa yang panjang tetapi memerlukan juga guru yang mempunyai banyak pengalaman.

Kajian ini juga menunjukkan bahawa jantina tidak memberi sebarang kesan kepada tahap kemahiran membuat keputusan dalam fizik dalam kalangan pelajar fizik. Banyak kajian lepas yang mendapati bahawa pelajar perempuan sering dianggap sebagai kumpulan yang lemah dalam mata pelajaran sains terutamanya fizik dan matematik (Murphy, 2000).

KeSiMPulAn

Kemahiran membuat keputusan adalah satu kemahiran yang penting dalam kehidupan. Dalam kajian ini, hubungan antara kemahiran membuat keputusn fizik dan kemahiran


38

membuat keputusan dalam kehidupan seharian adalah sangat lemah. Keputusan ini menunjukkan tidak berlaku permindahan kemahiran membuat keputusan dari pembelajaran formal kepada kehidupan seharian pelajar. Kajian juga mendapati jantina tidak mempengaruhi kemahiran membuat keputusan fizik. Maka ini menunjukkan bahawa jantina tidak memberi kesan kepada keupayaan pelajar untuk menguasai kemahiran membuat keputusan.

PengHArgAAn

Ucapan terima kasih kepada Kementerian Pelajaran Malaysia yang menaja pengajian Yeoh Sik Mei. Penyelidik juga mengucapkan berbanyak terima kasih kepada pengetua dan pelajar di sekitar Pulau Pinang yang telah sudi bekerjasama menjayakan kajian ini.

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Barnett, S.M. & Ceci, S.J. (2002). When and where do we apply what we learn? A taxonomy for far transfer. Psychological Bulletin, 128, 612–637.

Baron, J. & Brown, R.V. (1991a). Introduction. In Baron, J. & Brown, R.V.. (Eds.), Teaching decision making to adolescents (pp. 1 – 18), Hillsdale, New Jersey: Lawrence Erlbaum Associates, Inc.

Baron, J. & Brown, R.V. (1991b). Toward improved instructional in decision making to adolescents: A conceptual framework and pilot program. In Baron, J. & Brown, R.V.. (Eds.), Teaching decision making to adolescents (pp. 95 – 122), Hillsdale, New Jersey: Lawrence Erlbaum Associates, Inc.

Baron, J. & Brown, R.V. (1991c). Prologue: Why Americans can’t think straight. In Baron, J. & Brown, R.V.. (Eds.), Teaching decision making to adolescents (pp. 1 – 6), Hillsdale, New Jersey: Lawrence Erlbaum Associates, Inc.

Best, J.W. & Kahn, J.V. (2006). Research in education(10thed.). Boston, USA: Pearson Education Inc.

BPK. (2012). Spesifikasi Kurikulum Fizik Tingkatan 4. Putrajaya: Terbitan Bahagian Pembangunan Kurikulum, Kementerian Pelajaran Malaysia.

Bransford, J.D. & Schwartz, D.L. (2001). Rethinking transfer: A simple proposal with multiple implications. In A. Iran-Nejad & P. D. Pearson (Eds.), Review of research in education: Vol. 24, pp. 61 – 100. Washington, DC: American Educational Research Association (AERA).

Brezina, C. (2008). Great decision-making skills. New York: The Rosen Publishing Group, Inc.Campbell, V., Lofstrom, J. & Jerome, B. (1997). Decisions based on science. United State of

America: National Science Teachers Association. Gay, L.R., Mills, G.E. & Airasian, P. (2009). Educational research: competencies for analysis and

applications 9th edition. New Jersey: Pearson Education, Inc.Häussler, P. & Hoffmann, L. (2002).An interview study to enhance girls’ interest, self-concept, and

achievement in physics classes.Journal of Research in Science Teaching, 39(9), 870–888.Hazel, E., Logan, P. & Gallagher, P. (1997). Equitable assessment of students in physics: importance

of gender and language background. International Journal of Science Education, 19(4), 381–392, doi: 10.1080/0950069970190 402


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IPTM. (2010). Indikator Pengajian Tinggi Malaysia. Kementerian Pelajaran Malaysia Kortland, J. (2001). A problem-posing approach to teaching decision making about the waste issue

(Doctoral dissertation). Retrieved from http:// www.cdbeta.uu.nlLaskey, K.B. & Campbell, V.N.. (1991). Evaluation of an intermediate level decision analysis

course. In Baron, J. & Brown, R.V.. (Eds.), Teaching decision making to adolescents (pp. 123 – 146), Hillsdale, New Jersey: Lawrence Erlbaum Associates, Inc.

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Mincemoyer, C. C. & Perkins, D. F. (2003). Assessing decision-making skills of youth. The Forum for Family and Consumer Issues 8 (1). Retrieved from http://ncsu.edu/ffci/publications/2003/v8-n1-2003-january/ar-1-accessing.php

Murphy, P. (2000). Are gender differences in achievement avoidable? In Sears, J. & Sorensen, P. (Eds.), Issues in science teaching (pp.165–174). London: Routledge Falmer.

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40 J. Sci. Math. Lett., Volume 3 (2015) 40 - 49ISSN 2462-2052

The Central Subgroup of the Nonabelian Tensor Square of the Second Bieberbach Group with Dihedral Point Group

Subkumpulan Pusat bagi Tensor Kuasa Dua Tak Abelan untuk Kumpulan Bieberbach Kedua dengan Kumpulan Titik Dwihedron

Wan Nor Farhana Wan Mohd Fauzi1, Nor’ashiqin Mohd Idrus2, Rohaidah Masri3, Tan Yee Ting4 & Nor Haniza Sarmin5

1,2,3,4Department of Mathematics, Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, 35900 Tanjung Malim, Perak, Malaysia.

5Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia.

[email protected]

Abstract

The properties of a group can be explored by computing the homological functors of the group. One of the homological functors of a group is the nabla, which is the central subgroup of the nonabelian tensor square. In this study, the nabla of the second Bieberbach group of dimension five with dihedral point group of order eight is computed. The abelianization of the group is first determined in order to compute its nabla.

Keywords homological functors, nabla, abelianization, Bieberbach group

Abstrak

Ciri-ciri suatu kumpulan boleh diterokai dengan mengira fungtor homologi kumpulan tersebut. Salah satu fungtor homologi bagi suatu kumpulan ialah nabla, iaitu subkumpulan pusat bagi tensor kuasa dua tak abelan. Dalam kajian ini, nabla bagi kumpulan Bieberbach kedua berdimensi lima dengan kumpulan titik dwihedron berdarjah lapan telah dikira. Abelanisasi bagi kumpulan tersebut telah ditentukan terlebih dahulu untuk mengira nablanya.

Kata kunci fungtor homologi, nabla, abelanisasi, kumpulan Bieberbach

INTroDuCTIoN

A Bieberbach group is defined as a torsion free crystallographic group which is given by a short exact sequence 11 →→→→ PGL such that G /ϕL != P Here, L is called a lattice group and P is a finite point group. Since Bieberbach groups are crystallographic groups, any findings regarding these groups will give benefit to the chemists and physicists who are interested in the field of crystallography and spectroscopy. A Bieberbach group with dihedral point group has become an interest in this research where the group is explored by computing its homological functors such as the central subgroup of the nonabelian tensor square, denoted as ( ).G∇ The nonabelian tensor square G G⊗ is a group generated by

41J. Sci. Math. Lett., Volume 3 (2015) 40 - 49ISSN 2462-2052

the symbols ,g h⊗ for all , ,g h G∈ subject to relations gh⊗ k = (gh ⊗ kh )(h⊗ k) and g⊗ hk = (g⊗ k)(gk ⊗ hk ) for all , ,g h k G∈ where 1hg h gh−= (Brown & Loday, 1987). The ( )G∇ is a normal subgroup generated by the element g g⊗ , for all g G∈ (Ellis, 1998). In order to compute ( ),G∇ the abelianization of the group is first determined since it plays an important role in the computation of the homological functor. The abelianization of the group, denoted as abG is a factor group of / 'G G , where 'G is a derived subgroup.

Some research related to the computation of ( )G∇ and abG of some Bieberbach groups have been done since 2009 starting with Rohaidah (2009) where she determined

( )G∇ and abG of the Bieberbach groups with cyclic point group of order two. Nor’ashiqin & Nor Haniza (2010) also constructed the abG of the Bieberbach group of dimension four with dihedral point group of order eight. The result was used to compute ( )G∇ of the group. Wan Nor Farhana et al. (2014) did the same work as Nor’ashiqin (2011) but with the first Bieberbach group of dimension five with dihedral point group of order eight. Besides that, Hazzirah Izzati et al. (2014) determined abG for all Bieberbach groups with cyclic point group of order three. Recently, Tan et al. (2014) have determined abG for all Bieberbach groups of dimension four with symmetric point group of order six. In this paper, the computation of ( )G∇ and abG for the second Bieberbach group of dimension five with dihedral point group of order eight, denoted as 2 (5)B , is presented.

PrelImINArIeS

This section provides some basic and structural results that been used in the computation of ( )G∇ and abG . Definition 1 and 2 give the definition of polycyclic presentation and consistent polycyclic presentation, respectively.

Definition 1 (Eick & Nickel, 2008)

Let nF be a free group on generators 1,..., ng g and R be a set of relations of group G. The relations of a polycyclic presentation /nF R have the form:

, ,1 ...i i ie x i i x n

i i ng g g++= for ,i I≤

, , 1 , ,11 ...i iy j j y j n

j i j j ng g g g g+−+= for ,j i≤, , 1 , ,11 ...i iz j j z j n

j i j j ng g g g g+−+= for j i≤ and j I∉

for some {1,..., }, iI n e⊆ ∈Ν have i I∈ and , , , , , ,i j i j k i j kx y z ∈Ζ for all i, j and k.

Definition 2 (Eick & Nickel, 2008)Let G be a group generated by ngg ,...,1 . The consistency of the relation in G can be determined using the following consistency relations:

( ) ( )k j i k j ig g g g g g= for ,k j i> >


1

( ) ( )j je ei i j j ig g g g g

−

= for , ,j i j I> ∈1

( ) ( )i ie ej i j i ig g g g g

−

= for , ,j i i I> ∈

( ) ( )i ie ei i i ig g g g= for i I∉

1( )j j i ig g g g−= for , .j i i I> ∉

Theorem 1 shows some structural results of the nonabelian tensor square of group, provided by Blyth et al. (2010).

Theorem 1 (Blyth et al., 2010)

Let G be any group. Theni. The nonabelian tensor square of any group G satisfies:

( ) / ( / ') ( ),G G K G G G G⊗ ≅ ∇ × ∧

where K is the kernel of the epimorphism ( ) ( / ').G G G∇ →∇ii. If '/ GG has no element of order 2 then,

)'/()( GGG ∇≅∇ and )'/()( GGG ∇≅Γ .

iii. If H is any finitely generated abelian group with independent generating set { }a a a, ,..., n1 2 then ( ) ( ) ( )H H H H H⊗ =∇ × ∧

, where the independent generators is

)(H∇ are the image of )( ii aa ⊗ for ni ,...,1= and of ( )( )i j j ia a a a⊗ ⊗ for all nji ≤<≤1 and the independent generators of HH ∧ are the image of )( ji aa ⊗

for all nji ≤<≤1 .

The group v G( ) has been introduced by Rocco (1991) and its definition is given as follows:

Definition 3 (Rocco, 1991)

Let G be a group with presentation and let Gϕ be an isomorphic copy of G via the mapping ϕ :G→Gϕ for all .g G∈ The group v G( )is defined to be

Theorem 2 shows that the commutator subgroup of v G( )is isomorphic to the nonabelian tensor square of group G. Therefore, the computation of can be done by using the commutator subgroup.

φ φ φ φ φφ


Theorem 2 (Ellis & Leonard, 1995)

Let G be a group. The map σ →G G G G v G: , ( )defined by σ (g⊗ h) = g,hϕ⎡⎣ ⎤⎦

for all ,g h in G is an isomorphism.

Theorem 3 (Magidin & Morse, 2010)

Let G be any group. Then the natural homomorphism µ :G→G /G ' induces the epimorphism

)'/()'/(],[: GGGGGGf ⊗→ϕ

with x, yϕ⎡⎣ ⎤⎦! µ(x)⊗ µ(y) for all x and y in G.

Lemma 1 (Rohaidah, 2009)

Let G be a group. If c G∈ is a commutator of the form [ , ]x y then a,cϕ⎡⎣ ⎤⎦ = c,aϕ⎡⎣ ⎤⎦−1

in v G( ) for , ,a x y G∈ .

Theorem 4 (Blyth et al., 2010)

Let G be any group whose abelianization is finitely generated by the independent set ', 1,..., .ix G i n= Let K be the kernel of the epimorphism ( ) ( / ')G G G∇ →∇ and let E(G)

be the subgroup of v G( ) defined by E(G) = xi , x jϕ⎡⎣ ⎤⎦ 1≤ i < j ≤ n G / (G ')ϕ⎡⎣ ⎤⎦ . Then

i. ( )G∇ is generated by the elements of the set xi , xi

ϕ⎡⎣ ⎤⎦, xi , x jϕ⎡⎣ ⎤⎦ xi , xi

ϕ⎡⎣ ⎤⎦ 1≤ i < j ≤ s{ } ;

ii. ( ) ( )G E G K∇ ∩ = and ∇(G)E(G) = G,Gϕ⎡⎣ ⎤⎦ .

Theorem 5 (Zomorodian, 2005)

Let A, B and C be any abelian group. Consider the ordinary tensor product of two abelian groups. Then,

i. 0 ,C A A⊗ ≅

ii. 0 0 0 ,C C C⊗ ≅

iii. gcd( , )n m n mC C C⊗ ≅ for , ,n m∈Ζ andiv. A⊗ (B⊗C) = (A⊗ B)× (A⊗C) .


main results

A consistent polycyclic presentation of the group B2(5), which is determined based on Definition 1 and 2, is given as follows:

2 1 2 1 2 14 2 1

1 1 1 14 4 1 2 3

11 2 2 1 3 3 4 4 5 5

2 1 2 3, 4 5 1 1 1 11 1 2 2 3 3 4 4 5 5

1 1 11 1 2 2 3 3 4 4 5

, , ,

, , ,

, , , , ,(5) , , , , , ,

, , , , ,

, , , ,

a a b

a a a a a

b b b b b

c c c c c

a l b l c lb cl c bl c cl l ll l l l l l l l l l

B a b c l l l l ll l l l l l l l l ll l l l l l l l l

− − −

− − − −

−

− − − −

− − −

= = =

= = =

= = = = ==

= = = = =

= = = =1

1 1

15 ,

, , for ,1 , 5.l lj j j j

l

l l l l j i i j−

−=

= = > ≤ ≤

The determination of the abelianization of 2 (5)B as in Lemma 2 and the computation of the nonabelian tensor square of the abelianization of 2 (5)B as in Lemma 3 are presented. The computation of 2( (5))B∇ are then shown.

Lemma 2

The abelianization of 2 (5)B is generated by the cosets '2 (5)aB and '

2 (5)cB of order 4 and '

5 2 (5)l B of order 2. In particular, we write ' 22 2 2 4 2(5) (5) / (5) .abB B B C C= ≅ ×

Proof: From the relation of 2 (5)B ,

1 1 1 11 1 1 1 1 2 1[ , ] ( ) ,aa l a l al l l l l− − − −= = =

1 1 1 12 2 2 2 2 1 2[ , ] ( ) ,aa l a l al l l l l− − − −= = =

1 1 1 23 3 3 3 3 3[ , ] ( ) ,aa l a l al l l l− − −= = =

1 1 1 14 4 4 4 4 4 4[ , ] ( ) ,aa l a l al l l l l e− − − −= = = =

1 1 1 15 5 5 5 5 5 5[ , ] ( ) ,aa l a l al l l l l e− − − −= = = =

1 1 1 21 1 1 1 1 1[ , ] ( ) ,bb l b l bl l l l− − −= = =

1 1 1 12 2 2 2 2 2 2[ , ] ( ) ,bb l b l bl l l l l e− − − −= = = =

1 1 1 23 3 3 3 3 3[ , ] ( ) ,bb l b l bl l l l− − −= = =

1 1 1 24 4 3 4 4 4[ , ] ( ) ,bb l b l bl l l l− − −= = =

1 1 1 25 5 5 5 5 5[ , ] ( ) ,bb l b l bl l l l− − −= = =

1 1 1 11 1 1 1 1 1 1[ , ] ( ) ,cc l c l cl l l l l e− − − −= = = =


1 1 1 22 2 2 2 2 2[ , ] ( ) ,cc l c l cl l l l− − −= = =

1 1 1 23 3 3 3 3 3[ , ] ( ) ,cc l c l cl l l l− − −= = =

1 1 1 24 4 4 4 4 4[ , ] ( ) ,cc l c l cl l l l− − −= = =

1 1 1 25 5 5 5 5 5[ , ] ( ) ,cc l c l cl l l l− − −= = =

1 1 1 14[ , ] ( ) ,aa b a b ab b b l c b− − − −= = =

1 1 1 14[ , ] ( )aa c a c ac c c l b c− − − −= = = and

1 1 1 13 2 1[ , ] ( ) .bb c b c bc c c l l l− − − −= = =

Then, 1 1 2 2 2 2 22 2 1 1 2 3 1 2 3 4 5(5) ' , , , , , , , , .B bc l l l l l l l l l l− −=

The abelianization 2 2(5) / (5) 'B B of 2 (5)B is generated by the cosets ' '

2 2(5) , (5) ,aB bB ' '2 1 2(5) , (5) ,cB l B ' ' ' '

2 2 3 2 4 2 5 2(5) , (5) , (5) and (5) .l B l B l B l B However, since by relation of 2 (5)B , we have 2 1 2 1 2 1

4 2 1, , ,a l b l c l− − −= = = hence we have ' 2 ' ' 2 '

1 2 2 2 2 2(5) (5) , (5) (5)l B c B l B b B− −= = and '4 2 (5)l B 2 '

2 (5) .a B−= Moreover, since we have 1

4 ,ac bl−= hence ,b aca= so ' '2 2(5) ( ) (5) .bB aca B= Since we also

have 1 11 2 3 ,bc cl l l− −= hence 1 1 1 2

3l b c bc b− − −= 1 1 1 1 1 2 2 2.a c a c acac a c a− − − − −= Thus ' 1 1 1 1 1 2 2 2 '

3 2 2(5) ( ) (5) .l B a c a c acac a c a B− − − − −=Since we have 2 1

4 ,a l−= then 4 24a l−= . Furthermore, since 2 '

4 2 (5)l B∈ hence 2 '

4 2 (5)l B− ∈ . Similarly, we have 2 11 ,c l−= then 4 2

1 .c l−= Since 2 '1 2 (5)l B∈ so we

have 2 '1 2 (5)l B− ∈ . It follows that both ' '

2 2(5) and (5)aB cB have order 4. Besides that, 2 '5 2 (5)l B∈ . So, '

5 2 (5) 2.l B = Then, with all of the above, we have

' ' ' ' 22 2 2 2 2 5 2 4 4 2 4 2(5) (5) / (5) (5) (5) (5) .abB B B aB cB l B C C C C C= ≅ × × ≅ × × ≅ ×

Next, the nonabelian tensor square of the abelianization of 2 (5),B namely 2 2(5) (5)ab abB B⊗ is determined as in Lemma 3.

Lemma 3

The nonabelian tensor square of abelianization of 2 (5)B is given as

4 52 2 4 2(5) (5) .ab abB B C C⊗ ≅ ×

Proof: Let 2 2 5 5 2(5) ' , (5) ' and (5) '.a aB c cB l l B= = =

Hence by Theorem 1(iii), 2 2(5) (5)ab abB B⊗ is generated by

5 5 5 5 5 5, , , ( )( ), ( )( ), ( )( ), ,a a c c l l a c c a a l l a c l l c a c⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ and

5 5, .a l c l⊗ ⊗ Hence, by Theorem 4 and Lemma 2,


2 2 4 4 2 4 2 2 4 2 24 54 2

(5) (5)

.

ab abB B C C C C C C C C CC C

⊗ ≅ × × × × × × × ×

≅ ×

Next, we want to show the computation of 2( (5))B∇ .

Theorem 6

Let 2 (5)B be a Bieberbach group of dimension five with dihedral point group of order eight. Then,

2 5 5 5 5 5 5

2 2 28 4 2

( (5)) [ , ],[ , ],[ , ],[ , ][ , ],[ , ][ , ],[ , ][ , ]

.

B a a c c l l a c c a a l l a c l l c

C C C

ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ∇ =

≅ × ×

Proof : By Lemma 2, 2 (5)abB is generated by ' ' '2 2 5 2(5) , (5) and (5)aB cB l B . Then by

Theorem 4(i),

2 5 5 5 5 5 5( (5)) [ , ],[ , ],[ , ],[ , ][ , ],[ , ][ , ],[ , ][ , ] .B a a c c l l a c c a a l l a c l l cϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ∇ =

Next, we need to show the order of [ , ]a aϕ and [ , ]c cϕ are 8, 5 5[ , ]l l ϕ and [ , ][ , ]a c c aϕ ϕ are of order 4 and 5 5[ , ][ , ]a l l aϕ ϕ and 5 5[ , ][ , ]c l l cϕ ϕ are of order 2. By relation of 2 (5)B ,

16 4 4

2 24 42 24 4

[ , ] [ , ][ , ]

[ , ]1

a a a al ll l

ϕ ϕ

ϕ

ϕ

− −

=

=

== and

16 4 4

2 21 12 2

1 1

[ , ] [ , ][ , ]

[ , ]1.

c c c cl ll l

ϕ ϕ

ϕ

ϕ

− −

=

=

==

These mean that the order of [ , ]a aϕ and [ , ]c cϕ divide 16. Hence, the order of [ , ]a aϕ and [ , ]c cϕ maybe 2, 4, 8 or 16. By the epimorphism f as stated in Theorem 3,

([ , ]) ( ) ( )f a a a a a aϕ µ µ= ⊗ = ⊗ and ([ , ]) ( ) ( )f c c c c c cϕ µ µ= ⊗ = ⊗ and both have order 4 by Lemma 3. Hence ],[ ϕaa and ],[ ϕcc are of order a multiple of 4. So they are not of order 2.

The order of ],[ ϕaa and ],[ ϕcc cannot be 4 since:

4 2 2

14 4

4 4

[ , ] [ , ][ , ]

[ , ]1

a a a al ll l

ϕ ϕ

ϕ

ϕ

− −

=

=

=≠ and

4 2 2

11 1

1 1

[ , ] [ , ][ , ]

[ , ]1.

c c c cl ll l

ϕ ϕ

ϕ

ϕ

− −

=

=

=≠


Suppose [ , ]a aϕ and [ , ]c cϕ have order 16. Then, there is no positive integer r smaller than 16 such that [ , ] 1.ra aϕ = Since 4 2 '

4 2 (5)a l B−= ∈ and 4 2 '1 2 (5) ,c l B−= ∈ then by

Lemma 1,

4 4 1

4 4

4 4

8

[ , ( ) ] [ , ][ , ( ) ][ , ] 1[ , ] [ , ] 1[ , ] 1

a a a aa a a aa a a aa a

ϕ ϕ

ϕ ϕ

ϕ ϕ

ϕ

−=

=

=

= and

4 4 1

4 4

4 4

8

[ , ( ) ] [ , ][ , ( ) ][ , ] 1[ , ] [ , ] 1[ , ] 1

c c c cc c c cc c c cc c

ϕ ϕ

ϕ ϕ

ϕ ϕ

ϕ

−=

=

=

=

which contradicts the facts that [ , ]a aϕ and [ , ]c cϕ are of order 16. Hence, [ , ]a aϕ and [ , ]c cϕ are of order 8. Besides that,

4 4 4

2 21 1

2 2 11 1

11 1

1 11 1

([ , ][ , ]) [ , ][ , ][ , ][ , ]

([ , ][ , ])

([ ,[ , ] ][[ , ], ])

([[ , ], ] [[ , ], ])1.

a c c a a c c aa l l aa l l aa b l b l ab l a b l a

ϕ ϕ ϕ ϕ

ϕ ϕ

ϕ ϕ

ϕ ϕ

ϕ ϕ

− −

−

−

− −

=

=

=

=

==

Hence, the order of [ , ][ , ]a c c aϕ ϕ divides 4, that is the order of [ , ][ , ]a c c aϕ ϕ is either 2 or 4. But the order of [ , ][ , ]a c c aϕ ϕ cannot be 2 since by Theorem 3,

([ , ][ , ]) ([ , ]) ([ , ])( ( ) ( ))( ( ) ( ))( )( ).

f a c c a f a c f c aa c c a

a c c a

ϕ ϕ ϕ ϕ

µ µ µ µ== ⊗ ⊗= ⊗ ⊗

By Lemma 9, ([ , ][ , ])f a c c aϕ ϕ has order 4. Hence the order of [ , ][ , ]a c c aϕ ϕ is a multiple of 4. Since the order of [ , ][ , ]a c c aϕ ϕ divides 4 but not 2, hence the order of [ , ][ , ]a c c aϕ ϕ is exactly 4.

Moreover, the order of 5 5[ , ]l l ϕ divides 4 since 2 '5 2 (5)l B∈ . Hence

4 2 25 5 5 5[ , ] [ , ] 1.l l l lϕ ϕ= = It means that the order of 5 5[ , ]l l ϕ is either 2 or 4. By Theorem

3, 5 5 5 5 5 5([ , ]) ( ) ( )f l l l l l lϕ µ µ= ⊗ = ⊗ and has order 2 by Lemma 9. So, the order of 5 5[ , ]l l ϕ is at least 2. If the order of 5 5[ , ]l l ϕ is 2, then 2 2

5 5 5 5[ , ] [ , ] 1.l l l lϕ ϕ= = However, the order of 5 5[ , ]l l ϕ cannot be 2 since there are no relation in 2( (5))Bν that allow 2

5l and 5lϕ to commutes. Therefore, the order of 5 5[ , ]l l ϕ is 4.

By homomorphism in Theorem 3 and Theorem 5,


5 2( ) ( ) ,a l Cµ µ⊗ ≅

5 2( ) ( ) ,l a Cµ µ⊗ ≅

5 2( ) ( ) ,c l Cµ µ⊗ ≅

5 2( ) ( ) .l c Cµ µ⊗ ≅

So, the order of 5 5[ , ][ , ]a l l aϕ ϕ and 5 5[ , ][ , ]c l l cϕ ϕ are 2. Therefore,

2 2 22 8 8 4 4 2 2 8 4 2( (5)) .B C C C C C C C C C∇ ≅ × × × × × ≅ × ×

This concludes the proof.

CoNCluSIoN

In this paper, the abelianization and the central subgroup of the nonabelian tensor square of the second Bieberbach group of dimension five with dihedral point group of order eight has been successfully computed. Based on this results, other homological functors such as the nonabelian tensor square, G-trivial subgroup of the nonabelian tensor square, denoted as ( ),J G the nonabelian exterior square and Schur multiplier can be determined.

ACKNowleDGmeNTS

The authors would like to thank Universiti Pendidikan Sultan Idris (UPSI) for the funding of this research under Vote # RACE 2012-0144-101-62 and UTM Vote No. 00M04.

refereNCeS

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Brown, R., & Loday, J. L. (1987). Van kampen theorems for diagrams of spaces. Topology, 26, 311-335.

Eick, B., & Nickel, W. (2008). Computing schur multiplicator and tensor square of polycyclic group. Journal of Algebra, 320(2), 927-944. doi: 10.1016/j.algebra.2008.02.041

Ellis, G. (1998). On the computation of certain homotopical functors. LMS Journal of Computation and Mathematics, 1, 25-41. doi: 10.1112/S1461157000000139

Ellis, G., & Leonard, F. (1995). Computing schur multipliers and tensor products of finite groups. Proc. Roy. Irish Acad. Sect. A, 95(2), 137-147.

Magidin, A., & Morse, R. F. (2010). Certain homological functors. Contemporary Mathematic, 511, 127-166.

Hazzirah Izzati Mat Hassim, Nor Haniza Sarmin, & Nor Muhainiah Muhammad Ali (2014). The abelianization of all Bieberbach groups with cyclic point group of order three. Proceeding of 2nd International Science Postgraduate Conference 2014 (ISPC 2014), 907-919.


Nor’ashiqin Mohd Idrus. (2011). Bieberbach groups with finite point groups (Unpublished Ph.D Thesis). Universiti Teknologi Malaysia, Skudai.

Nor’ashiqin Mohd Idrus & Nor Haniza Sarmin (2010). The nonabelian tensor square of a centerless bieberbach group with the dihedral point group of order eight - theory and calculation. Proceeding of the 15st Asian Technology Conference in Mathematics, 295-304.

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Rohaidah Masri. (2009). The nonabelian tensor squares of certain bieberbach groups with cyclic point groups (Unpublished Ph.D Thesis). Universiti Teknologi Malaysia, Skudai.

Tan Yee Ting, Nor’ashiqin Mohd Idrus, Rohaidah Masri, Wan Nor Farhana Wan Mohd Fauzi, & Nor Haniza Sarmin (2014). On the abelianization of all Bieberbach groups of dimension four with symmetric point group of order six. AIP Conference Proceeding 2014, 1635, 479-486. doi: 10.1063/1.4903625

Wan Nor Farhana Wan Mohd Fauzi, Nor’ashiqin Mohd Idrus, Rohaidah Masri, Tan Yee Ting & Nor Haniza Sarmin (2014). The computation of a central subgroup of the nonabelian tensor square of a Bieberbach group of dihedral point group. Proceeding of 2nd International Science Postgraduate Conference 2014 (ISPC 2014), 709-718.

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