MD. ABDUL HALIM
Abstract: The study was undertaken for a comparison of primary mathematics curriculum of Bangladesh with that of West Bengal of India in respect of objectives and contents, teaching processes, problems and obstacles in transaction of curriculum in classroom and strengths and weaknesses of the curriculum. Data mainly collected through documents, observations of classrooms and responses obtained through questionnaire and opionionnaire from mathematics teachers, academic supervisors, and experts (curriculum and subject specialists) from both the countries. The review, study and examination of relevant documents, analysis and interpretation of data are used in describing the findings. Significant difference are found in setting objectives and presentation of contents in mathematics of primary level textbooks of the two countries. Difference is also found in transaction of mathematics curriculum in the classroom. Other common areas are: unacceptable ‘teacher-pupil ratio, low ‘contact hours’, and unsatisfactory skill development in mathematics and content integration with socio-cultural aspects and overcrowded classroom in urban areas.
Comparison is one of the conscious human activities; we necessarily and quite often compare in order to make choices and to judge where we stand in relation to others and to our own past (Alexander, 2000). Comparative studies in mathematics education have impact on several areas of education including education policy set of objectives, contents, instructional methods, and the effects of socio-cultural factors on education (Plomp and Loxley, 1993).
There have been great changes in recent decades in mathematics curricula all over the world. Many countries have reformed their mathematics programmes to keep pace with the current developments in various fields of education and technology. Any attempt at reform would take into account local conditions which can vary from one country to another. Nevertheless, reform in all countries finds common difficulties which can be overcome by using the same methods (Aram, 1986).
The universality of teaching of mathematics is a recognised fact. Perhaps no other subject is taught so universally as mathematics and the syllabi, methods and objectives of teaching this subject are quite similar in different countries of the world. The nature of the subject is such that it would easily lend itself to the promotion of inter-cultural understanding.
It was felt that to understand the nature of primary mathematics curriculum and the related aspects in Bangladesh and India; it would be very helpful to undertake a comparative study of mathematics curriculum of primary level of both the countries.
Education System of Bangladesh
The formal education system in Bangladesh begins with a 5-year primary education cycle which is followed by 3-year lower secondary (junior high school), 2-year secondary and 2 -year higher secondary education. The university education comprises of 3 / 4-year Bachelor degree followed by 1 / 2-year Master’s.
The Government approved a New Education Policy (NEP) in October 2000. According to the new policy primary education was to be extended to eight years of schooling in phases by 2010, but no attempt has been made in this regard yet. At the end of grade 10, there is the first public examination, and at the end of grade 12 the second public examination is held. While the bachelor’s degree requires three years for pass and four years for honours courses, the master’s degree extends over two years in the case of pass graduates and one year for honours graduates.
The task of reviewing and redesigning primary curriculum in Bangladesh was initiated in 1986. National Curriculam and Textbook Board (NCTB) designed and developed competency-based curriculum and instructional materials were prepared during 1987 to 1990. The new curriculum was introduced in primary schools from 1992. The existing primary curriculum in grades 1 and 2 include Mother Tongue Bengali, Mathematics, Environmental Studies, Religious Education and Arts and Crafts. Along with these subjects English, Social Studies and Science are compulsory subjects in grades 3 to 5.
Education System of West Bengal of India
All over India, schools which are affiliated to Central Board of Education, elementary education is up to grade-VIII while secondary education is from grades-IX to XII. As per the recommendation of the Education Commission (1964-66), State Government restructured the educational pattern of 10 + 2 + 3 system.
The policy of deciding the number of years for primary level is decided by State Board of Education. However, it differs from state to state. In West Bengal, the elementary education I of 5 years of schooling (grades I-V) followed by Jr. High or Upper Primary Education (grades VI-VIII) provided in all Jr. High, Secondary and Higher Secondary schools. A child enters into the system at the age of 5+ and takes part in the first public examination at the age of 15+ after completion of 10 years of general school education and leaves after completing Higher Secondary stage at the age of 17+ (Government of West Bengal, 1999).
The curriculum is divided into two parts, the thrust is given on the first part. The first (non-scholastic) part consists of (i) activities relating to physical activities, health habits, games and sports. (ii) activities relating to creative and productive works and (iii) activities encouraging understanding own experiences through certain activities pertaining to direct experiences. This part is allotted 45% of the day’s school hours. The second part is related to studies in scholastic areas where emphasis is given on acquiring competencies in cognitive domain of learning. The subjects to be studied in this area are language (mother tongue), Arithmetic and Environmental Studies (Natural Science, History and Geography.)
Rationale of the Study
The aims of mathematics education at primary level could be:
a. providing proper opportunities to learners at school to acquire knowledge and skills,
b. developing logical and rational thinking among learners ,
c. encouraging application of mathematical knowledge and skills in day-to-day life.
The extent to which these aims are reflected in primary mathematics curriculum of the education system of a country is a major consideration for undertaking a study on mathematics. Comparison of mathematics curriculum of primary level of Bangladesh with that of West Bengal of India would enable the researcher to find out to what extent the aims mentioned are reflected in primary mathematics curriculum and these are transacted in primary classrooms of the two countries.
In the absence of any empirical study on primary school curriculum in Bangladesh, it has not yet been possible to evaluate the effectiveness of the existing mathematics curriculum as prescribed by the NCTB, Bangladesh. Even the facilities for implementing the mathematics curriculum in primary schools of Bangladesh are not known due to lack of systematic research. Whereas various research studies in India have been conducted and the findings reported that learning achievement of primary school children in general and mathematics in particular is far from satisfactory (Das, 2000).
Bangladesh and West Bengal of India are geo-politically distinct entities but the two neighbors share common historical, cultural, religious and linguistic heritage. In this context, it is of great importance to study and compare mathematics curriculum at primary level of both the countries.
Review of Related Literature
Studies conducted by Roy et. al. (1996), Amin et. al. (2001), Mollic (2000), Haque (1998), Datta (1998), Borgohain (1999), Tilakratne (1992), Pradhan (1996) provided the information about improvement of teaching mathematics and judged the achievement level of teachers (trained and untrained, in-service and pre-service etc.). Goel (1996) shows that children with arithmetic disabilities make little or no progress and the main reasons for this include poor teaching, ill-prepared teachers, improper materials, and inadequate sequence. Bhatia (1992), Dubey (2000), Tyner (1996) and Hodges (2001), developed instructional technique which can help the students to learn better and also help the teacher to know how the students learn better. Hsieh (1995) revealed distinct patterns in advance and average students’ problem-solving approaches. Lee (1999) identified Chinese second-grade high math achievers and low-math achiever had average or above average intelligence, normal sensory functioning and no emotional disorders. Frempong (2000) identified that socio-economic gradient in mathematics achievement are correlated. Wilson et. al. (2001) identified common features and characteristic routines of mathematics lessons in the North-east of England and St. Peters burg, Russia. Yang and Cobb (1995) conducted a cross-cultural study and found that the arithmetical understandings of the Chinese children were found more advanced than those of their American counterparts. Jacobsen (1996) emphasized on world wide co-operation in mathematics education. ICMI (2001) attempting a comparison between mathematics education in different traditions which will be discovered leading to adequate and effective application of differences, as well as correspondences, in national and international environments. Jean (1998) provided a foundation for further cross-national comparisons between China and U.S. mathematics instruction. Ara (1983) and Shahjahan (1982) conducted cross-cultural study of Bangladesh and India on social science education. In line with the above aspects, the present study is an attempt to compare the mathematics curriculum at primary level in Bangladesh and West Bengal of India.
Objectives of the Study
The objectives of the study are to:
a. critically examine the mathematics curriculum of primary level of education in Bangladesh and in West Bengal of India.
b. identify teaching-learning process of mathematics in classroom of primary schools in Bangladesh and in West Bengal of India.
c. identify problems and obstacles in transacting primary mathematics curriculum in classroom situation in Bangladesh and in West Bengal of India.
d. identify the major strengths and weaknesses of primary mathematics curriculum of both the countries.
e. Compare primary mathematics curriculum of Bangladesh with that of West Bengal of India in respect of above mentioned objectives.
Two types of data were collected – qualitative and quantitative. Data were collected from different sources such as documents on mathematics curriculum, reports of committees and commissions, mathematics teachers, academic supervisors, curriculum specialists and subject specialists. classroom observations were also undertaken.
Sample of the Study
Documents from both countries, such as Curriculum Documents and Implementation Reports, Mathematics Textbooks, Development Plans and Programmes, National Policies on Education, Reports of Education Commissions, and Research Reports on teaching of mathematics were used. Thus, documents became the primary source of information / data for objective one.
Six districts each from Bangladesh and West Bengal were selected purposively. And following the same procedure, two sub-districts (Upazilla / Circle) were selected from each district i.e, a total of 12 sub-districts from each country was selected. Again, 5 primary schools from each sub-district were selected randomly. Thus, a total of 60 primary schools were selected from each country. Further, two mathematics teachers from each school were taken as sample for the study. Thus, the total sample size of mathematics teachers was 240; 120 from each country.
Assistant Upazilla Education Officers (ATEO) / Sub-Inspector (SI) of schools from each country, who were responsible for supervising the classroom activities of the selected sample of the teachers, formed the sample of Academic Supervisors for the study. The numbers of Academic Supervisors selected were 120; 60 from each country.
12 curriculum specialists (6 from each country) and 8 subject specialists (4 from each country) were selected purposively from both the countries to comment on curriculum of primary mathematics.
Sample for classroom observation consisted of 24 primary schools, 12 from each country; covering 120 classes of mathematics teaching – learning process; 60 from each country in primary level (grade I-V).
Two questionnaires, one for primary school mathematics teachers, the other for academic supervisors; one opinionnaire for the experts (curriculum and subject specialists), and an observation schedule were developed. The instruments were given to group experts of both the countries to judge the adequacy and appropriateness of items for the study. As per comments of the experts, the instruments were modified. These modified instruments were given to the respondent categories from Bangladesh and from West Bengal in India to confirm whether the items of the instruments were understood properly by the respondents or not. According to responses especially language ambiguity were checked and the instruments were finalized.
Data were mainly collected through (i) documents, (ii) observations in real classroom situations, and (iii) responses obtained through questionnaire and opionionnaire given to the mathematics teachers, academic supervisors, and experts (curriculum and subject specialists) from both the countries.
The following two technique of data analysis were applied:
Critical examination and analysis of curriculum objectives of both the countries and their comparision with standard set of objectives (RCDICMDCA) were done. Likewise, aims and objectives of curriculum and grade-wise content-areas of primary mathematics from relevant documents and textbooks of both the countries were studied and analyzed.
There were two types of items in the instruments, namely, closed-ended type and open-ended type. The responses to each item of closed-ended type were analyzed in terms of number (frequency) of responses. The frequencies were further converted into percentages. The data supplied by the respondents to each of open-ended items were categorized on the basis of their contents into different clusters along with their frequencies and percentage.
Table-1: Set of objectives
|Objectives of NCTB, Bangladesh||Objectives of BBPE, West Bengal of India||Standard set of objectives prescribed by RCDICMDA*|
|(i)To help develop basic skills related to language, numeracy and counting.|
(ii)To help develop learning skills and attitudes.
(iii) To help develop the habit of solving problems through scientific methods as well as to develop a scientific outlook in life.
|(i)To develop the necessary understanding of basic concepts of mathematics at primary level and to apply those concepts in day-to day life.|
(ii) To develop the ability to perform computations with speed and accuracy.
(iii) To develop reasoning, analytical and problem solving abilities.
(iv) To develop the ability for accurate measurement.
(v) To develop the ability for divergent thinking and creativity.
(vi) To apply the above mentioned mathematical concepts appropriately towards increased efficiency of National productivity and manners and cuostoms of democratic society and to develop this efficiency through necessary practice of the mentioned objectives.
|(i)Development of numeracy and its application to daily life situations.|
(ii) Development of manipulative skills in mathematics, particularly in basic arithmetic.
(iii) Ability to translate simple, real life situations into mathematical terms, thus acquiring an appreciation of the power of mathematics.
(iv) Development of intuitive geometrical notions, and
(v) Ability to draw appropriate inferences from patterns of numbers, reading and writing of pictographs, tables etc.
* Regional Conference on Development of Integrated Curriculum in Mathematics for Developing Countries of Asia, New Delhi, India, December,1975.
Conclusion and Findings
The following conclusions and findings are presented on the basis of review, study and analysis of primary mathematics curriculum of Bangladesh and of West Bengal of India and the opinion and comments obtained from the stakeholders and the findings of class observations.
Set of objectives
• The set of objectives prescribed for primary curriculum by West Bangla Board of Primary Education (WBBPE) is better than the set of objectives prescribed by Bangladesh National Curriculum and Text Book Board (NCTB) of Bangladesh, in terms of knowledge skills, understanding and specific direction to the textbook writers and teachers. But both the sets of objectives fall short of the standard set of objectives prescribed by the experts at Regional Conference on Development of Integrated Curriculum in Mathematics for Developing Countries of Asia (RCDICMDCA).
• Content-areas included in mathematics textbooks of both the countries are almost similar how could it be if set of objectives rifer? , easy to understand and written in regional languages (of both the countries) but the grade-wise distribution of topics differ in the textbooks of Bangladesh and West Bengal.
• Inclusion of introductory discussion, learning objectives/purpose and the exercises given in each lesson/unit in the textbooks of West Bengal are presented systematically and seem to be more effective than that of Bangladesh. However more presentation of contents is found in the textbooks of Bangladesh make it attractive the textbook of West Bengal.
• More emphasis is given on spiral type of organization of the content in the mathematics textbooks of both the countries. However, the focus of this organization for different topics varies in textbooks of both the countries e.g. geometry is spirally distributed in grades-II to V textbooks of NCTB , Bangladesh, while the same is distributed in grades-IV to V textbooks of WBBPE.
• Sufficient information are provided in Teachers’ Manual of Bangladesh and teachers are encouraged to make use of it for effective teaching while the Manual in West Bengal is not good enough for effective teaching.
Competencies of teachers
• More primary mathematics teachers are recruited in West Bengal than in Bangladesh and the scholastic ability of mathematics teachers in West Bengal is much higher compared to the teachers in Bangladesh.
Classroom environment and facilities
• Word problems included in textbooks at grade-I level cause understanding problems for the pupils in Bangladesh and in West Bengal according to the views presented by the teachers, academic supervisors and experts of both the countries.
• The frequency of ‘irregular attendance’ of pupils in classroom is higher in Bangladesh than in West Bengal of India which also creates problem for effective transaction of mathematics curriculum at primary level.
• Teacher-pupil ratio and contact hours are not enough for effective transaction of the curriculum in both the countries.
• Inadequate number of classrooms is found in West Bengal school. The situation is little better in Bangladesh. It is also found that classrooms are highly crowded in urban areas of both the countries.
• In Bangladesh in-service training programmes for primary mathematics teachers are of West Bengal still them of West Bangla teachers demanded more such programmes including the latest teaching techniques used for teaching mathematics.
• Primary mathematics teachers of West Bengal use lesson-plan very regularly while the teachers of Bangladesh are far behind in this respect.
• Teaching-learning processes in mathematics classrooms carried out by teachers of West Bengal are far better, scientific, systematic and effective than. what their counterparts practice in Bangladesh.
• Use of teaching aids for helping learners for quicker and better comprehension of mathematical concepts is satisfactory in West Bengal and to the situation prevailing in the schools in Bangladesh.
• Teachers of both the countries use different methods (such as question-answer method, problem-solving method, discussion method, etc.) except discovery method.
• There is a similar set of beliefs considered by both Bangladesh and west Bangla teachers for the inclusion of socio cultural aspects through illustrative examples for teaching of mathematical content to be effective in teaching mathematics.
Suggestions and Recommendations
• The objectives of primary mathematics curriculum of Bangladesh need to be revised and modified in the light of standard set prescribed by RCDICMDCA.
• West Bengal Board of Primary Education may think of adding two more objectives to the set of existing objectives prescribed for the curricula to allow children learn exact geometrical forms from own environment and stimulate development of spatial perception through intuition, which is very much needed at this level. The two objectives suggested to bee included are culled from RCDICMDCA. There are:
a. Development of intuitive geometrical notions,
b. Ability to draw appropriate inferences from patterns of numbers, reading and writing of pictographs, tables etc.
• Word problems should be deleted from grade-I mathematics textbook of both the countries as it is not suitable for the age group of pupils of grade 1. Also ‘Manipulation of concrete objects and counting’ should be included in textbook (grade-I) of West Bengal which is already present in Bangladesh textbooks.
• Geometry should be included spirally in grades II to V in the textbooks of West Bengal.
• Bangladesh should adopt uniform policy to split the content lists in the mathematics textbooks for grades – I to V.
• Purpose of the lesson /unit should be written in every unit of the textbooks of Bangladesh. Also introduction to each topic in the mathematics textbooks (grades-I to V) of Bangladesh should be included in an interesting way. At the end of each chapter, exercises should be included in the mathematics textbook of Bangladesh systematically.
• More pictorial presentation should be included in primary mathematics textbooks of West Bengal to make learning more interesting and easy to understand.
• Recruitment and placement policies and pay-scale of primary teachers in Bangladesh should be revised to attract and recruit more teachers with sound mathematical background for primary schools. More in-service training programmes should be conducted for mathematics teachers of Bangladesh.
• In spite of adequate number of in-service training programmes in West Bengal, latest development and modernization, latest technique of teaching with IT should be included in training programmes of West Bengal.
• Primary mathematics teachers of Bangladesh should be required to prepare lesson plan prior to actual teaching in classroom and it needs to be monitored by academic supervisors for improving the quality of techniques.
• Bangladesh teachers need to improve their teaching practices in classroom for teaching mathematics effectively with the help of apropriate teaching aids and suitable teaching methods and teaching us
• Sufficient information should be incorporated in teachers’ manual of West Bengal to help and encourage teachers for making the use of the manual for effective teaching.
• Teachers of Bangladesh and West Bengal may incorporate discovery method at the primary level for mathematics teaching as it is one of the best methods suitable for teaching of mathematics which helps the learner to develop imagination and to understand the abstract mathematical concepts.
• Efforts should be made by teachers of both the countries to find out the reasons of irregular attendance of pupils in classroom so that proper measures could be taken to increase regularity of pupils in the classroom.
• Efforts should be made to increase ‘contact hours’, and ‘teacher-pupil ratio’at primary level of both the countries for improving the quality of education at this level.
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Writer: Associate Professor, Institute of Education and Research, University of Dhaka, Dhaka, Bangladesh