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\c0Gc8ZRUgRUgZZUgZ<BUGKv<<<bbTX<<<GcPPPP&&A Comparison of Pre-Service Mathematics Teacher Education between Malaysia and China
LIM Chap Sam
School of Educational Studies
Universiti Sains Malaysia
cslim@usm.my
Abstract
This paper aims to compare and discuss the pre-service mathematics teacher education between the two countries: Malaysia and China. Based on document study of the syllabus, the comparison will focus on the structure and mathematical content of the programmes offered by two universities in each country. Implications and suggestions that might be learnt to enhance the quality of pre-service mathematics teacher education programme of both countries conclude the paper.
Introduction
This paper discusses part of the findings of a bigger study which aimed to compare and contrast mathematics education in general, and mathematics teaching and learning in particular between Shanghai (China) and Malaysia. This study was made possible with a grant awarded to me by the Asian Scholarship Foundation (ASF) which I spent my sabbatical studies in Shanghai from November 2004 to April 2005.
The basis for analysis and discussion of this paper is mainly based on document study of curriculum documents and syllabus of four public universities, two from China and two from Malaysia. I fully acknowledge that due to time and resources constraints, the findings of this study were not sufficient to be generalized to represent both China and Malaysia. Yet, at least, it should give us a glimpse of the content and structure of pre-service mathematics teacher education in Malaysia and China (Shanghai and Chongqing).
This paper will begin with a brief description of the general structure of the pre-service mathematics teacher education programme of both countries. A comparison of mathematics content and curriculum of pre-service mathematics teacher education programmes between both countries will then be made and implications and suggestions to enhance the quality of pre-service mathematics teacher education programmes of both countries.
Pre-Service Mathematics Teacher Education Programmes
In Malaysia, the training of pre-service teacher for both primary and secondary schools is mainly provided by the 28 teacher training colleges which are under the Teacher Education Division of the Ministry of Education, as well as the 11 public universities.
All the 28 teacher training colleges conduct specialized mathematics pre-service teacher education programmes under their respective mathematics and science departments. These programmes include (i) The Malaysian Teaching Diploma in Mathematics Studies [KDPM]; (ii) The Post Graduate Diploma in Teaching for Primary Education in Mathematics [KPLI-Primary]; and (iii) The Post Graduate Diploma in Teaching for Secondary Education in Mathematics [KPLI-Secondary]. The KDPM is a three years course with minimum intake qualification of SPM (equivalent to O-level) whereas the KPLI is a one year course with minimum intake qualification of a bachelor degree. However, the KDPM course has just ended its last batch in the year 2004.
All the 11 public universities that provide pre-service teacher education programmes, offer a Bachelor Degree of Science with Education (major in mathematics) programme. This is a four-year course with minimum intake qualification of STPM (equivalent to A-level). It aims to produce secondary school mathematics teachers.
Similarly in China, the pre-service mathematics teacher education programme is mainly provided by the thirty odd Normal Universities (^'Yf[). [Note: In China, a Normal university refers to a university which was previously a teacher training college]. These normal universities supply both primary and secondary teachers. Besides these, there are also teacher training colleges (^f[b) and teaching specialist schools (^Nf[!h) that mainly produce primary school teachers. The programme provided by the normal university and the teacher training college takes four years while the one provided by the teaching specialist school takes 3 years. Nevertheless, the recent trend of upgrading teacher qualification to at least bachelor degree has resulted in the gradual diminishing of these training colleges and specialist schools. This is especially apparent in large and more economically developed regions such as Shanghai. As the rate of high school students entering universities in Shanghai is almost 90%, it is not surprising to see that there are at least 90% of the secondary school teachers and more than 50% of the primary school teachers in Shanghai are university graduates.
Curriculum structure of pre-service mathematics teacher education programmes
Generally both countries share many similarities in terms of general content and curriculum of their pre-service mathematics teacher education programmes. Both have the two major components, that is academic/mathematical components and education components. However, a detailed comparison shows significant differences in the emphasis on each component. Table 1 displays the comparison in curriculum structure of mathematics teacher education programmes between two normal universities in China (the East China Normal University, Shanghai & the South West Normal University, Chongqing) and those of Malaysia (University of Science Malaysia, Penang and Mara Technology University, Kuala Lumpur). All these programmes aim to produce secondary mathematics teachers.
Table 1: A comparison of curriculum structure offered by two universities of China and those of Malaysia (number and percentage of units for each component)
ChinaMalaysiaECNUSWNUUSMUiTMAcademic componentMajor (mathematics)57(C)+28(E) [54.1%]49(C)+32(E) [50.6%]52 [40%]39 [30.7%]Minor (non-mathematics)--20 [15.4%]24 [18.9%]Education componentTeaching method course3 [1.9%]3 [1.9%]12 [9.2%]6 [4.7%]Core-professional courses11 [7.0%]-21[16.2%]29 [22.8%]Practical componentTeaching practice6
[3.8%]8
[5.0%]10 [7.7%]8
[6.3%]Project/seminar paper8
[5.1%]6+1
[4.4%]-3 (project)+2 (seminar) [3.9%]University courses/option38 (C)+6 (E)
[28.0%]45 (C) +16(E)
[38.1%]15
[11.5%]16
[12.6%]Total units157 160130127Note: ECNU=East China Normal University, Shanghai, China; SWNU= South West Normal University, Chongqing, China; USM= University of Science Malaysia, Penang, Malaysia; UiTM= Mara Technology University, Kuala Lumpur, Malaysia C= compulsory subject E= elective
Table 1 shows the two universities from both countries allocated more than 50% of the total units to academic component. However, pre-service mathematics teachers in China have single major in Mathematics while its counterpart in Malaysia usually have one major (Mathematics) and one minor subject area (usually science courses such as Biology, Physics or Chemistry). Hence, nearly 50-54% of the courses in China are mathematical content courses but only 30-40% of them in Malaysia. This indicates that the pre-service teacher education programme in universities of China focus much more on mathematical content while its Malaysian counterpart stresses more on educational courses. Malaysia has up to 5-9% of its courses on teaching method and 16-23% on core professional courses, whereas these similar courses only make up the most 2% (teaching method) and 7% (core professional courses) in China. Perhaps this greater emphasis on mathematical content might lead to a higher level of mathematics competency among mathematics teachers in China. Ma (1999) made a comparative study on mathematics teachers in Shanghai and the United States. She found that the Shanghai teachers in her sample were more competent than its US counterpart in terms of mathematics competency and pedagogy. These teachers developed their mathematical competency when they were in schools while their pedagogical competence was mainly acquired during their teaching career. Leung and Park (2002) replicated Mas study on nine Korean and nine Hong Kong mathematics teachers. Teachers in their sample also shared the same view that they usually acquire their teaching ideas from the way they were taught while they were in schools. Thus, Leung (2002) suggests that East Asian students, taught by their competent teachers, acquire competence in mathematics, and when they graduate and join the teacher force, they in turn become competent teachers. So once a good cycle starts, the positive effects cumulate and increasingly reproduce themselves (p.49). This highlights the significant role of competent mathematics teachers in the process of mathematics teaching and learning.
Conversely, the pre-service mathematics teacher programme in China seems to give much less emphasis in teaching practice. As shown in Table 1, 6-8% of the total units are allocated for teaching practice in Malaysia but only 4-5% in China. In Malaysia, pre-service mathematics teachers undergo 10-15 weeks of teaching practice in schools whereas its Chinese counterpart only undergo 6 weeks of teaching practice in schools. The main aim of teaching practice is to provide pre-service teachers with vivid and practical experiences of real classroom teaching in school. With such a short period of only 6 weeks, will the Chinese pre-service teachers be ready for teaching after their graduation?
I have enquired this issue with one mathematics educator in one of Chinas normal universities. According to her, we strongly believe that it is the responsibility of the university to provide students with a strong mathematical content knowledge, while the teaching practice is best learned at the work place. Thus, the lack of teaching practice is supplemented strongly by the school based professional development courses once these pre-service teachers started teaching in schools. However, in Malaysia, the pre-service mathematics teacher programme aims to provide the pre-service teachers with both content knowledge and teaching practice experience so that they are ready to teach in schools once they graduated. Nevertheless, this difference in goals and philosophy of mathematics teacher education could have produced different outcome in terms of quality of mathematics teachers and this should raise concern for both mathematics educators and the Ministry of Education of both countries.
Another significant observed difference in Table 1 is the stronger weight of university or optional courses. While Chinese universities allocated 28-38% but Malaysian universities only placed 12-13% for these courses. A closer review of the course title shows that pre-service mathematics teachers in China are expected to study 12 courses on philosophy (such as basic principles of Marxism; theories of Deng Xiao Ping \s^ and Mao Ze Dong (klN); foreign languages; basic law; moral thinking; career counselling; psychology; sport and basic computer skills. Comparatively, pre-service mathematics teachers in Malaysia only need to take 6 courses which include Asian and Islamic Civilization; English and Malay languages; ethnic relationship and co-curriculum. These observed differences reflect the political and cultural context of the countries.
Mathematics curriculum in the pre-service mathematics teacher education programmes
To gain a better insight on the content details, I have also compared the mathematical content courses offered in both countries (see Table 2). An analysis of Table 2 shows that in all the four universities, mathematics teacher education programmes included six major areas of mathematics: (i) Calculus; (ii) Algebra; (iii) Probability; (iv) Statistics; (v) Differential Equations and (vi) Complex Analysis. Nevertheless, there is a variation in terms of the number of credit hours. Perhaps this is due to the difference in total weight for each component as discussed in the earlier section. It is obvious that UiTM from Malaysia with 31% of total units on mathematics component provided the least number of credit hours for all its mathematics courses as compared to the other three universities. Will the lesser teaching hours on mathematics content courses jeopardise the mathematical competency of the UiTM pre-service mathematics teachers? Further research evidence might be needed to verify the above concern.
Table 2: A comparison of mathematical content courses offered by two universities of China and those of Malaysia (number of credit hours)
ChinaMalaysiaMajor areaECNUSWNUUSMUiTMCalculusCalculus I & II (5+5)Mathematical analysis I, II & III (5+5+5)Calculus for science students I & II (4+4)Calculus I, II & III (3+3+3)AlgebraAdvance Algebra and analytic geometry I & II (5+5)Advance Algebra and analytic geometry I & II (5+5)Algebra for science students (4)Linear Algebra(3)ProbabilityProbability and statistics (4)Probability theory (4)Probability theory (4)Probability (2)Statistics-Statistics (4)Statistics for science students (4)Statistics (2)Differential equationsOrdinary differential equations (3)Ordinary differential equations (4)Differential equations (4)Differential Equations (3) Complex analysisComplex analysis (4.5)Complex variable function (4)Complex analysis (4)Calculus with Complex Analysis (3)Computer relatedC language (3)Modern education technique & courseware (3)Programming for scientific applications (4)Introduction to Mathematical Software (2)Abstract algebraAbstract algebra (3)Abstract algebra (4)Modern algebra (4)Functional analysisFunctional analysis (3)Functional analysis(4)Introduction to analysis (4)Introduction to Numerical Analysis (3)Mathematical modelingMathematical modelling (3)Mathematical model (4)----Geometry Differential geometry (3)College geometry (4)----Calculus vector--Variational calculus (3)Calculus vector (4)--Discrete mathematics Discrete mathematics --Discrete mathematics (4)--Different areasReal analysisReal variable function (4)Advance linear algebra (4)Fourier Analysis (3)Topology (3)Statistical administration (4)Mathematical Foundation (3)Further Differential Equation (3)Foundation of Mechanics (3)Another interesting observed difference is that both universities in China offered geometry and mathematical modelling as two compulsory courses for their pre-service mathematics teachers, however, these two courses were not offered at all by the universities in Malaysia. In fact, geometry is an integral part of Malaysian school mathematics curriculum. Primary pupils in Malaysia are introduced to basic geometrical shapes from first year of their schooling. Geometrical concepts are then slowly expanding throughout the primary and secondary mathematics syllabus. Yet, mathematical modelling is not taught in the primary or secondary school mathematics curriculum in Malaysia. Nevertheless, both geometry and mathematical modelling are inter-related and very pertinent in this technological age and global world. Hence, this comparison might signal the Malaysian universities to provide courses in geometry and mathematical modelling for pre-service mathematics teachers so as to equip them with the necessary competency to teach our future mathematics pupils in these two areas.
Conclusion and Implications
In this paper, I attempt to compare the curriculum and structure of pre-service mathematics teacher education programmes of two universities in two countries namely Malaysia and China respectively. I acknowledge that with such a small number of cases, the findings are not to generalize to represent all universities in Malaysia and China. This is clearly not my aim. As argued by Stigler, Gallimore and Hiebert (2000), Cross-cultural comparison is a powerful way to unveil unnoticed but ubiquitous practices ... Comparative research invites re-examination of the things 'taken for granted' in our teaching, as well as suggesting new approaches that never evolved in our own society. (pp. 87-88). Hence, this comparative study aims to provide a mirror for reflection and suggestions for improvements or enhancement of the quality of pre-service mathematics teacher education programmes in both countries.
From the above analysis and discussion, the following implications are suggested:
The pre-service mathematics teacher education programme in universities in China tended to focus much more on the academic component than its counterpart in Malaysia. This might explain the better mathematics content competency of the mathematics teachers in China than other countries as found by Ma (1999) and Leung and Park (2002). Hence, this might imply that Malaysian pre-service mathematics teacher education programme might need to refocus their academic component so as to focus on single major subject rather than a major and a minor subject as with the existing programme.
In relation to the first implication, more mathematical content courses such as geometry and mathematical modelling might then be included in pre-service mathematics teacher education programme of Malaysia as it is in China. This is in view of the increasing importance of geometrical thinking and mathematical modelling in this global world and technological age.
The Chinese pre-service mathematics teacher education programme seems to give very little emphasis on teaching practice in schools. It is suggested that the period of teaching practice might be lengthen to at least 10 weeks so that the pre-service teachers might have more exposure as well as gain more practical experience of real teaching in the classroom before they graduate.
Nevertheless, as argued by Even (2003), that mathematical knowledge is constructed in ways that do not necessarily mirror instruction and that mathematical meaning is both subjective and sociocultural puts the student and the community in an important place with regard to learning. (p.41). Hence, besides increasing the mathematical content in the pre-service mathematics education programme, it is pertinent to look into the cultural practices of teaching and learning in both school and higher institutions. However, the above comparison was mainly based on document analysis of the syllabi of pre-service mathematics education programmes in both countries. Perhaps further research into the practices of teaching and learning in the universities might help to shed more light on the effectiveness of pre-service mathematics education programme.
Acknowledgement
This study was made possible by the support of the following institutions and peopleThe Asia Scholarship Foundation (especially Dr Salvador, Miss Somkamol & Miss Sasithara), University of Science Malaysia (my dean, Professor Aminah Ayob), East China Normal University (my host institution, especially Prof Li Shiqi, Associate Prof Zhou Xiaoping and Associate Prof Li Jun); Southwest University (Professor Song Naiqing) and the many mathematics teachers, school administrators, students and parents of both Malaysian and Shanghai schools. To all these agencies and people, I express my deepest appreciation and thank you for giving me such fruitful experiences of research, academic and cultural exchange.
References
Even, R. (2003). What Can Teachers Learn From Research in Mathematics Education? For the Learning of Mathematics, 23
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