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The Republic of Mauritius lies in the south west of the Indian Ocean. It is comprised of the main island of Mauritius and the islands of Rodrigues, Agalega and Saint Brandon as well as a number of outlying smaller islands. The main island of Mauritius is situated about 900 km to the east of Madagascar, at latitude 20 South and 57 East.
Mauritius was an uninhabited island. It never had an indigenous population. The Portuguese first discovered the island in 1513. Then came the Dutch who rediscovered the island in the late seventeenth century and abandoned it around 1710. A few years later the French came and decided to stay. It was during the period of the French colonisation that the island acquired the characteristics of a society and the economical, educational and cultural structures they established formed the base of development. In 1810, the island was taken over by the British. The British introduced changes in the island in many fields especially in the Education Sector. Mauritius became an independent sovereign state on 12 March 1968 and a Republic in 1992.
Mauritius is divided into nine districts. The districts are Plaines Wilhems, Port Louis, Moka, Flacq, Black River, Savanne Pamplemousses, Riviere du Rempart, and Grand Port. The Mauritian society is a multicultural as a result of its historical factors. Its population consists of emigrants and descendants of emigrants from three continents - Europe, Africa and Asia. The variety of ethnic origins coupled with the Franco- British historical background gave rise to a complex language situation. French Creole is spoken by nearly the whole population. English is the official language and medium of instruction for all the other academic subjects in schools and French is the second main language taught in schools. Apart from these, a variety of oriental languages are taught in schools- Hindi, Urdu, Tamil, Mandarin and Arabic.
The network of mass media is efficient. Several daily and weekly papers are printed, mainly in French but also in other languages; radio, and television broadcasts are in English, French and Oriental Languages. The communication network is now further strengthened by the latest information and communication technology (ICT) services like the Internet. All the primary and secondary schools have computer labs and internet services. Some schools even have their websites.
The Mauritian economy is growing rapidly. It is in the process of transformation from a low skill, low labour-cost economy to a much more skill-intensive one in which high levels of education and training are necessary at all levels. It is therefore important to maximise the quality of education provided at all levels and to ensure that students leaving school are equipped with knowledge, attitudes and skills that are appropriate for employment in this changing economy. The population statistics for Mauritius are shown in Table 1.1.1.
Table 1.1.1: Population Statistics for Mauritius.
Under 15 years
Above 59 years
1.2 The Educational System in Mauritius
The struggle for 'Education for All' began in the 1930s and 1940s. With the achievement of the constitutional reforms in 1948, there grew a firm commitment to it. This was seen in the increase of education provision and more school enrolment. After Independence in 1968, the emphasis was on increasing the number of schools and improving the school infrastructure. In the 80's this changed to the improvement of the quality and the effectiveness of those schools. Today, after having achieved the first goal of universal primary education, the shift in emphasis is from enrolment rates and good school infrastructure to quality and relevance of education.
The country's commitment to 'Education for All' is reflected in its Budget Expenditure on Education.
Table 1.2.1: Public Recurrent Expenditure on Education
Special Education Needs
Technical & Vocational Education and training
Schooling in Mauritius is based on the 6 + 5 + 2 system, inherited from the British, with 6 years of primary education leading to the Certificate of Primary Education (CPE), followed by 5 years of secondary education leading to the Cambridge School Certificate (SC) and a further two years leading to the Cambridge Higher School Certificate (HSC) or GCE 'A' level examinations.
1.2.1: Pre Primary Education
Around 95% of our children attend pre-primary schools. In 2008, about 1070 pre-primary schools were officially registered with the Ministry of Education and Human Resources with a population of 29,738 children, 2,541 teachers and 919 non-teaching staff. A pre-primary unit has been established in the Ministry to strengthen the pre-primary sector and to monitor its progress. At this stage itself, the pupils are gradually exposed to English and French languages. The lessons (mainly mathematics and life skills) are conducted in English.
1.2.2 Primary Education
Primary education is free and compulsory, for children belonging to the age group of 5-12 years, in Mauritius. There are 302 primary schools out of which 220 are run by the government and 51 by the Roman Catholic Education Authority (RCEA), 2 by the Hindu Education Authority and the other 29 are Private non-aided schools. Legislation has been introduced since 1991 to make primary education compulsory and a common school curriculum is used. In 2008, the primary school population was 114,007 (58128 boys and 55879 girls). Consequently 98% of the Mauritian population of primary school age attended school. Currently, the subjects taught are English, French, Mathematics, Environmental Studies, Creative Education, and Physical Education. Seven Asian Languages, namely, Hindi, Urdu, Arabic, Tamil, Telugu, Marathi and Modern Chinese are also taught to pupils who opt to study any one of them.
Pupils enter Grade 1(also called Standard I in Mauritius) at the age of five and take CPE examination after six years of schooling. This examination is compulsory and is also used to rank pupils for access to places in the highly rated secondary schools. From Grade 1, the students under the primary education in Mauritius automatically move up to Grade 4. After Grade 4, the students undergo a two-year preparation for the CPE examinations and end-of-year final examinations for both grades 4 and 5 are prepared at national level by the Ministry of Education and Human Resources. Progress towards quality in primary education is seen in high enrolment rates, investment in infrastructure- school buildings, playgrounds, school- gardens, audio-visual facilities, school libraries, decreasing pupil-teacher ratio, control of school transport, school feeding program, school health program, provision of free text-books, teacher education and an effective assessment system. Of the 7542 million of rupees budget in 2008/2009 devoted to education, 24.7% goes to primary sector.
Presently, there are 8090 teachers involved in the Primary schools. In particular, 5454 are teaching staff, 4080 General Purpose Teachers and 1374 Oriental Language Teachers. The remaining 2636 comprised 303 Head Teachers, 918 Deputy Head Teachers and 1415 Administrative and other workers.
Table 184.108.40.206 shows the Certificate for Primary Education (CPE) examination results for last four years. Despite the consistent maintenance of the percentage pass, the high failure rates cannot be ignored.
72.3 Table 220.127.116.11 : Percentage Pass at CPE Examination
1.2.3 Secondary Education
Free secondary education was introduced in 1977. In 2008, there were 69 State Schools and 106 private schools which were providing secondary education. The private schools are also allocated government funds through the Private Secondary Schools Authority (PSSA), which also provides technical advice and guidance. In 2008, there were 112,995 pupils in secondary schools (55 873 girls and 58 730 boys).
Some secondary schools are considered as 'star' schools. This accounts for the high competition at the CPE examination, as only those ranked are chosen to go to these schools. This situation is likely to persist until all secondary schools are considered 'equal' in resources and quality.
To satisfy the demands of the labour market, modifications are being introduced gradually, at the upper secondary level with Business and Technical streams. The Industrial Vocational Training Board (IVTB), which was established in 1989, provides vocational training. Other organisations such as Handicraft Centres and the Lycée Polytechnique also help out in Vocational Training.
1.2.4 Teacher Training
In primary schools, teachers are classified into two categories: the General Purpose teachers and the Oriental Language teachers. The General Purpose teachers have to teach at least four subjects including Mathematics, English Language, French Language and Environmental Science. The Oriental language teacher has to teach only one oriental language. They have all followed a two-year pre-service training course, leading to a Certificate in Primary Education. This course is conducted by the Mauritius Institute of Education (MIE). The course involves pedagogical, teaching methods and regular visit to primary schools. During the training, teachers also have to do teaching practice in schools. There is a major programme for upgrading primary school teachers, leading to an Advanced Certificate. Special training for remedial teaching is also being provided.
Most of the teachers recruited to work in the Secondary Schools possess a Bachelor's degree. Every teacher is required to teach one subject only. However, there are some teachers who possess a diploma only and consequently they are allowed to teach students up to School Certificate; however, these teachers can follow a Bachelor in Education degree at the MIE. Courses leading to Post-Graduate Certificate in Education (PGCE) are also organised for in-service secondary school teachers. Recently, courses leading to Masters Degree Education are being conducted jointly by MIE and overseas universities.
1.2.5 Tertiary Education
Tertiary Education was made free in Mauritius in 1988. This sector comprises the University of Mauritius, University of Technology Mauritius, Mauritius Institute of Education, Mahatma Gandhi Institute and Mauritius College of the Air.
The Mauritius Institute of Education (MIE) runs courses in Pre-School Education and Educational Administration as well as training courses for Primary and Secondary teachers- Certificate and Advanced Certificate for Primary School Teachers; Certificate, Diploma, Bachelor in Education and PGCE for Secondary School Teachers. Recently, it has started a Master in Education course in collaboration with the University of Brighton, UK.
The Mahatma Gandhi Institute (MGI), in collaboration with University of Mauritius (UOM) and the MIE, runs courses at degree level and Teacher Training Certificate courses in Asian Languages, as well as Diploma courses in Indian Music and Dance, the Arts and Hindi Studies. The Mauritius College of the Air (MCA) provides media support in various educational domains, with radio and television programmes at different levels. It is to be used as a Resource Centre for Distance Education. The Tertiary Education Commission (TEC) established in 1988, is the agent for planning and co-ordination of tertiary education. It has established machinery for promoting research in different areas in the different institutions.
Generally, the primary-level teachers join the profession with Higher School Certificate (HSC) as qualification. Nowadays, there are many new teachers who already possessed a diploma or degree from a university (mainly MIE or UOM). Then they undergo compulsory 3-year training at the MIE on full-time basis. During their training, they are also posted to schools under guidance of experienced teachers for teaching practice.
1.2.6 Curriculum Development
The National Centre for the Curriculum Research and Development (NCCRD) has been set up to prepare curriculum materials and disseminate them effectively to schools. The essence in the innovation of setting up a separate centre for curriculum development is that:
It is designed to work with pupils, teachers, heads of schools who constitute the most important part of the system. Ultimately, it is the schools which will make the process of curriculum development an effective means of bringing about reform and change in the system.
It pools limited financial resources in order to work the key issues in curriculum development.
It has become the focal point for partnerships for like-interest groups by tapping the best professional expertise at all levels and in doing so it has become the main source of innovation and improvement in schools.
The innovations undertaken in curriculum development have led to a replacement of inadequate traditional procedures for curriculum formulation through ad-hoc committees, a re-appraisal of the lower-secondary and primary school curricular and in the devise of a new curriculum framework.
For each subject and each level, curriculum panels comprising representatives from MIE, Mahatma Gandhi Institute (MGI), Mauritius Examination Syndicate (MES), Ministry of Education and Human Resources, head teachers and teachers prepare the curriculum materials according to national, educational, pedagogical and psychological norms. These are trialled before final printing and distribution to schools. The NCCRD is governed by a board that controls and monitors book production according to national norms. Textbooks are prepared for all levels: pre-primary, primary, lower secondary and basic secondary schools- for all subjects including Movement Education and Creative Education. Together with textbooks, teachers' guides and other instructional materials are prepared for distribution to schools. Regular sensitisation workshops are held both in Mauritius and Rodrigues on the use of the books.
1.2.7 Examinations and Assessments
Examinations have an important role in improving the quality of education. The Mauritius Examination Syndicate is the main institution concerned with examinations.
At the primary level, for grade 1 to 5, each school has its own assessment practices based on the national curriculum objectives as spelt out in the textbooks. The Ministry of Education, and Human Resources prepares the end of year examinations for grades 4 and 5, however, these are school based. The Certificate of Primary Education (CPE) is a national examination held at the end of six years of primary schooling. It is both a test of the level of attainment of every child as well as a selective device for admission to the best secondary schools. The MES takes elaborate care in the design, administration, marking, security and fairness of the examinations. To monitor learning achievement and to improve standards on education, the MES has developed a Learning Competency Project and laid down Learning Competencies for each age level in terms of Essential and Desirable Competencies. The philosophy behind the laying down of ELCs (Essential Learning Competencies) for all children and DLCs (Desirable Learning Competencies) for those who can go beyond the essential is that no child should be hurried along in order to complete the 'syllabus' without understanding but also that no child should be held back because of others who need a longer time to understand and assimilate what they learn. Thus, the CPE examinations are based on ELCs and DLCs.
As yet, there is no formal system of Continuous Assessment in our primary schools, although there have been a few attempts to introduce it. The new educational reforms emphasise the need for a sound system of Continuous Assessment in primary schools.
At secondary level, the MES organises and conducts examinations in collaboration with the University of Cambridge Local Examinations Syndicate. The examinations are held at the end of the fifth year (16+) of the secondary cycle leading to the attainment of 'O' levels (School Certificate Examination) and the end of the seventh year (18+) of secondary cycle leading to the attainment of 'A' levels (Higher School Certificate Examination).
The MES plays an important role in mauritianising the examinations, thus making the examination geared to the needs of the country as well as keeping international standards. Through the setting up of Examinations Subject Advisory Panels- which comprise all partners in each subject- the syllabus, textbooks, etc. are closely monitored and changes are subtly brought to the system. For School Certificate examinations, seventeen subjects are locally marked. Candidates have a wider range of subjects, 45 at School Certificate level and 40 at Higher School Certificate level. Each candidate chooses 7 to 8 subjects at SC level and 3 main subjects and 2 subsidiary ones at HSC level. Regular training of teachers in the use of the examinations syllabus, marking schemes, paper settings etc. is done and thus making examinations an important means of improving standards and the quality of education.
The term "geometry" simply means "earth measure" ('Geo' meaning 'Earth' and 'metry' meaning 'measurement'). Geometry is one of the longest established branches of mathematics and its origins can be traced back through a wide range of culture and civilisations. Several researchers have defined geometry in their own terms and experience. Some common ones are discussed in this section.
Geometry is the term given to the understanding of grasping space. Such understanding helps students represent and make sense of the world. In order to develop spatial sense, students must do more than learn the names of shapes. They need to analyse characteristics and properties of geometric shapes and develop an understanding about relationships that exist among them (Gould, 2003).
Geometry, says the renowned UK Mathematician Sir Michael Atiyah (2001), is one of the two pillars of mathematics (the other being algebra).
Sir Michael Atiyah writes:
Spatial intuition or spatial perception is an enormously powerful tool and that is why geometry is actually such a powerful part of mathematics- not only for things that are not. We try to put them into geometrical form because that enables us to use our intuitionâ€¦(Atiyah, 2001, p.50)
By concentrating on geometry, the focus is on the development and application of spatial concepts through which children learn to represent and make sense of the world.
"Geometry is grasping spaceâ€¦â€¦that space in which the child lives, breathes and moves.....the space that the child must learn to know, explore, conquer, in order to live, breathe and move better in it"(Freudenthal, 1973, p.403).
Geometry is an abstract branch of mathematics that helps students reason and understand the axiomatic structure of mathematics. It is concerned with finding the properties and the measurement of certain geometric objects. Geometric properties are those properties of the objects that remain invariant under certain transformations when the sizes and measurements of the objects change (National Council of Teachers of Mathematics, 2000).
Godfrey, a leading reformer in England at the start of the 20th century, argued that mathematics is not undertaken solely by logic but that another power is necessary. He called this 'geometrical power', describing it as 'the power we exercise when we solve a rider (a difficult geometrical problem or proof). To develop this power, Godfrey argued, it is essential to train students' "geometrical eye", something he defined as "the power of seeing geometrical properties detach themselves from a figure" (Godfrey, 1910).
Piaget relates geometry as the science of space. He describes the development of the child's representational space as well as the mental image of the real space in which the child is acting where "mental representation is not merely a recall from a memory bank but it is an active reconstruction of an object at the symbolic level.
Thus, geometry is the study of points, lines, angles and shapes, and their relationships and properties. It sounds like a lot to know, but much of it is already in your head. Geometry is all around us. If people didn't think about geometry, they wouldn't be able to build great structures such as pyramids or even simple things that are flat as a table.
1.4 Geometry as a Basic Skill
Geometry is also considered as a basic skill. Sherard (1981) states seven reasons that show geometry is a basic skill:
Its use as an aid for communication.
Its application in real-life problems.
When describing the location of places or when giving directions, geometric terms such as "parallel to" and "diagonally from" are used extensively.
It is used as an application in other topics in mathematics and to prepare students to study courses in higher maths and sciences.
It helps students to develop spatial perception and stimulate & exercise general thinking and problem-solving skills.
It helps students to understand and appreciate the beauty of the physical world.
Many of the terms used to identify, deduce and reason can be used outside of the geometry arena.
As stated, geometry is a basic skill since it is an important aid for communication. Our basic speaking and writing vocabularies have many geometric terms: e.g. point, line, plane, curve, angle, parallel, circle, square, rectangle and triangle. If we are to communicate to others the location, size or shape of an object, geometric terminology is essential. We use geometric terminology in describing shapes of objects: "The floor tiles are spare or the headlights on that model of the car are rectangles" or in giving directions: "Church Street is parallel to Main Street or make a right turn at the second traffic light" (Sherard, 1981).
1.5 Importance and Applications of Geometry
Understanding of shape and space begins with babies as they learn to crawl and walk, discovering the world and space around them (Doverburg & Prambling Samuelson, 2001). Children come to school having some visual and spatial skills. Many children have experienced construction of toys, jigsaw, puzzles, play dough, computer games, climbing, playground equipment at home and kindergarten. Children first develop static strategies as they explore their physical environment and materials. As they notice properties and develop concepts about shapes around them, they begin to understand dynamic imagery and are able to solve spatial problems.
Geometric and spatial thinking are not only important in their own right but also because they provide a foundation for much mathematical learning in other areas (Clements, 2000). An example of this is the use of drawings and manipulatives in the development of understanding of fractions (e.g cut a circle into 4 equal parts to explain one-quarter). The National Council of Teachers of Mathematics (NCTM, 2000) recognises its importance as a foundation:
'As students become familiar with shape, structure, location, and transformations and as they develop spatial reasoning, they lay the foundation for understanding not only their spatial world but also topics in mathematics and in art, science and social studies' (p.97).
Geometry can be used to visualise other forms of mathematics. Rectangles can be used to demonstrate the distributive property during instruction of arithmetic, in general, and to illustrate finding binomial products during instruction of algebra. Using and understanding the properties of geometric figures as manipulatives can help student understand combinatorics, analysis of inequalities, and analytic geometry (Schielock, 1987) and geometry representations are used to understand certain concepts in calculus (Balamenos, Ferrini- Mundy & Dick, 1987).
Willson (1977) further advocates that geometry has an important place in mathematics because it
Enables the study of the Physical world.
Deals with visualisation, drawing, and construction of the figures.
Enables the representation of the concepts in mathematics which are not visual.
Gives us pleasure and it is esthetical.
Hershkowitz et al. (1987) states, "This basic knowledge which comprises geometric concepts, their attributes and simple relationships should, in general, be acquired through geometrical experiences prior to secondary school". In fact, instruction of informal geometry at the elementary level is needed to build a foundation of vocabulary, exploratory skills, intuitive viewpoint, and understanding of geometric relationships, in preparation for studying the formal, demonstrative, geometry offered at the secondary level and beyond (Trafton and LeBlanc, 1973).
Geometry is one strand of mathematics that has application in careers requiring advanced instruction such as art, architecture, interior design and science, but it also has its applications in technical careers such as carpentry, plumbing and drawing as well as daily life. Transformational geometry is seen in art and that concept is integrated into archaeology in the study of the designs applied to pottery and other artefacts in different cultures and different eras. In daily life and vocational career, many concepts and techniques are transferred from the geometry classroom to the field (e.g. carpentry & plumbing).
Geometry is also rich in other applications like
Computer Aided Design (CAD) and geometric modelling (including designing, modifying and manufactured components).
Computer animation and visual presentations.
However, there is an even more important reason for placing greater emphasis on the teaching of geometry. It involves the manipulation of mental pictures, which is often called visual thinking. Problem solving in all strands of mathematics depends on forming mental pictures of the situation in which the problem is embedded and then 'finding' a picture of the mathematical idea that matches. The ability to mentally form, rearrange and match pictures is crucial to all aspects of mathematics, particularly problem solving.
1.6 Aims of Teaching Geometry
The aims for mathematics teaching in general are often listed in terms of
the need of life and work;
the need to develop logical thinking;
mathematics as a form of communication; and
the development of an awareness of mathematics as part of our culture.
Aims which might be appropriate for the geometry curriculum could be a subset or elaboration of these. We might think that geometry is an area of mathematics in which it is particularly appropriate for pupils to
develop the skills needed for the world of work;
develop logical thinking skills;
clarify the precise use of language (e.g. through classifying shapes in a study of transformations);
see the link between mathematics and other subjects;
begin to understand the nature of proof (e.g. through exploring what "being convinced" has meant at different points in history);
understand the central place of problem solving in modern culture, e.g. in a mathematically based design project;
import the knowledge needed to study more mathematics; and
teach the reading and interpretation of mathematical arguments (Jones, 2000, pp. 38-39).
The National Council of Teachers of Mathematics (1989) Curriculum has elaborated on the following geometry competencies that pupils must aim to:
identify, describe, compare, model, draw and classify geometric figures in two or three dimensions;
develop spatial sense;
explore the effects of transforming, combining, subdividing, and changing geometric figures;
understand, apply and deduce properties of relationships between geometric figures, including congruence and similarity;
develop an appreciation of geometry as a means of describing and modelling the physical world;
explore synthetic, transformational and coordinate approaches to geometry, with college-bound students also required to develop an understanding of axiomatic system through investigating and comparing various geometric system; and
explore a vector approach to certain aspects of geometry.
1.7 The Geometry Curriculum at Primary-level in Mauritius
The essential learning competencies for the topic geometry at the primary level are as follows
Recognising, naming and tracing circle, rectangle, square and triangle.
Indentifying shapes placed horizontal, vertical and in oblique (slant) positions.
Recognising and naming the following 3D shapes: cubes, cylinders, cones, spheres and cuboids.
Identifying the above mentioned 3D shapes in different orientation.
Forming patterns with squares, rectangles and triangles (also involves colouring).
Introducing terms associated with cube and cuboids: face, vertex and edge (also include cut & paste to form cubes and cuboids).
Drawing activities involving symmetry.
Drawing and identifying horizontal and vertical lines.
Identifying objects placed horizontally or vertically.
Drawing and identifying parallel lines.
Drawing and identifying diagonal lines in 2D shapes.
Recognising and drawing parallelogram, rhombus, kite, square and rectangle.
Writing properties of each of the five 2D shapes.
Identifying parallelogram, rhombus, kite, square and rectangles from 2D shapes.
Drawing squares and rectangles on square papers.
Exploring symmetry of shapes and geometrical objects. Drawing lines of symmetry on objects in square paper. Completing objects when half of it is given together with the line of symmetry.
Drawing, measuring and comparing angles.
Identifying right angles and complete turns.
Identifying and naming different types of triangles.
Learning the properties of the different types of triangles.
Drawing lines of symmetry for different figures.
Identifying objects with or without lines of symmetry.
Further examples on different types of Quadrilaterals and their properties: rectangle, square, parallelogram, rhombus, kite, arrowhead and trapezium.
Recognising and naming pentagons and hexagons.
Identifying and drawing diagonals in polygons.
Further examples on different types of triangles and their properties: equilateral, isosceles, scalene and right-angled.
1.8 The Decline in Geometry Performance
Research has shown that we can improve students' knowledge and ability to visualise and reason about the spatial world in which they live but are the students achieving this knowledge and these abilities. Third International Mathematics and Science Study (TIMSS) and National Assessment of Educational Progress (NAEP) have collected data that show that student performance in geometry at all levels is quite alarming (Lappan, 1999). To some extent, these problems may be due to the relatively limited quantity of research that has been undertaken into students' thinking in geometry at the school level, which in turn, may stem from a perceived absence of a theoretical framework (Pegg & Davey, 1998).
For instance, according to extensive evaluations of mathematics learning, elementary and middle school students in the United States are failing to learn basic geometric concepts and geometric problem solving; they are woefully underprepared for the study of more sophisticated geometric concepts and proof (Carpenter, Corbitt, Kepner, Lindquist & Rey, 1980; Fey et al., 1984; Kouba et al., 1988; Stevenson, Lee & Strigler, 1986; Strigler, Lee & Stevenson, 1990).
Extensive evaluations of mathematics learning indicate that elementary students are failing to learn basic geometric concepts and geometric problem solving. Apparently, much learning of geometric concepts has been by rote; they frequently do not recognise components, properties and relationships between properties (Clements & Battista, 1992b).
It is observed that children learn little about shapes from preschool to middle school. For example,
About 60% of preschoolers identified correctly triangles and 64% to 81% of elementary students were successful in the same task.
About 54% of preschoolers & 63 to 68% of elementary students were able to identify rectangles. (Clements et al., 1999).
Another major problem, as identified by the International Commission on Mathematics Instruction (ICMI) Study, is that, unlike in numbers and algebra, "a simple, clear, 'hierarchical' path from first beginnings to the more, advanced achievements of geometryâ€¦ has not yet been found and perhaps does not exist at all" (Mammana & Villani, 1998). This means that the relations between intuitive, inductive and deductive approaches to geometrical objects, the use of practical experiments and the age at which geometrical concepts should be introduced are far from clear.
Many researchers (Usiskin, 1987; Swafford et al., 1997; Clements, 2003) have agreed that the level of understanding that students achieve for any concept is limited by the level of understanding of their teacher and the school curriculum.
Anecdotal evidence suggests many teachers do not consider geometry and spatial relations to be important topics which give rise to the feelings that geometry lacks firm direction and purpose. Besides, Porter (1989) reported that the fourth and fifth grade teachers spent virtually no time teaching geometry. Even when taught, geometry was the topic most frequently identified as being taught merely for "exposure", that is, geometry was given only brief cursory coverage.
For instance, the Program for International Student Assessment (PISA) Survey shows that in Belgium, primary school teachers are uncomfortable in teaching geometry. They tend to avoid the subject in the first and second grade and they hardly ever approach solid geometry (Demal, 2004). Besides, the need for improvement in geometry teaching and learning in the primary , middle and high school grades is clearly evident in international comparisons such as Trends in International Mathematics and Science Study and PISA.
The report on the teaching and learning of geometry by the Royal Society and Joint Mathematical Council (2001) argues that "the most significant contribution to improvements in geometry teaching will be made by the development of good models of pedagogy, supported by carefully designed activities and resources" (p.19). In fact, a primary cause of this poor performance in geometry may be the curriculum; both in what topics are treated and how they are treated.
The failure of existing pedagogic models for geometry means that across many countries important aspects of geometry (such as work in 3D) are omitted, there is an over-reliance on teaching methods that rely solely on memorization. It is claimed that current primary geometry curricula neglects and do not promote opportunities for students to use their basic intuitions and simple concepts to progress to higher levels of geometric thoughts. This problem becomes more apparent in high school where students are required to employ their deductive reasoning (Hoffer, 1981; Shaughnessy & Burger, 1985). As the ICMI Study details, the main consequences of these problems have been that many countries have tried to bypass the obstacles by cutting down the amount of geometry taught or resorting to pedagogical approaches that rely heavily on memorisation. As a result, there is not much in the way of a base if good practice on which to base development. This is why the Royal Society and Joint Mathematical Council (2001) report argues that there is a further problem: "We believe that there are many teachers who have been taught geometry through styles of teaching which we would not advocate as appropriate" (p.19).
1.9 Significance of the Study
This study will represent an overall analysis of teaching and learning of 2D geometry among upper primary level in Mauritius. The relevance of the actual teaching and learning of geometry will be discussed.
As such, this study will make a significant contribution to our theorising with respect to classroom teaching and learning of geometry, to our understanding and optimization of the practices employed in classroom settings and to our understanding of those aspects of learners and teacher practices (and their interrelationship).
It will help to determine whether the use of inquiry-based teaching along with concrete materials and manipulatives can improve learning of 2D geometry.
It will also help to analyse the impact of language and socio-economic status of pupils on learning of 2D geometry.
2.0 Research Questions
A series of main research questions together with their sub research questions are addressed in this study. Each sub research question is described along with a brief summary of how it will be addressed.
Research Question 1
Is the 2D geometry curriculum at the upper primary level in Mauritius appropriate and relevant? Are there ways to further improve it?
This main research question is further divided into a more specific set of questions.
1.1 What is the level of 2D geometry acquisition among upper primary pupils in Mauritius?
This research work will assess the pupils understanding of the different content areas of 2D geometry via the experimental teaching and their performance in the multiple choice question paper and open-ended question test. The pupils' van Hiele level of thinking in different 2D geometry items will be tested. Misconceptions about 2D geometry will be detected and remedial actions proposed. The retention ability of the 2D geometry lessons taught to the upper primary level pupil will be examined.
1.2 Is the upper primary 2D geometry curriculum meeting its goal? Are there ways to improve it?
This study will involve a scrutinize analysis of the content areas of the 2D geometry curriculum at the upper primary level. All its positive and negative aspects encountered in the experimental teaching will be discussed. Ways to improve the 2D geometry curriculum will be proposed.
1.3 Do the pupils' gender and/or grade level influence their learning of 2D geometry lessons significantly?
This study will also test whether learning of 2D geometry is perceived differently by boys and girls and whether the retention ability of pupils is gender dependent. Both fourth and fifth graders are taught the same 2D geometry lessons. It is further targeted to analyse whether maturation (gradewise) has a significant impact on performance and retention ability of the 2D geometrical concepts.
Research Question 2
Can the use of different teaching strategies improve the teaching and learning of 2D geometry at the upper primary level in Mauritius?
This main research question is further divided into a more specific set of questions.
2.1 Can the uses of manipulatives, concrete materials and inquiry-based teaching methods significantly influence 2D geometry learning at the upper primary level in Mauritius?
This study will compare teaching of 2D geometry using usual teaching methods (use chalkboard and notes from textbook for explanation and do exercises from textbook for consolidation of learning) and use of investigation and inquiry to teach 2D geometry lessons with the additional aid of concrete materials and manipulatives. The efficiency of the methods will be first judged using 2 instruments. Firstly, 2 geometry tests will be conducted, one involving multiple choice questions only and the other involving open-ended questions only. Secondly, the pupils' involvement, interest, interaction in class with teacher and friends, participation and enthusiasm in the geometry lessons will be determined. For this purpose, the lessons will be videotaped so that the pupils' reactions, interest and gestures during the lessons can be analysed.
2.2 Does the use of different teaching strategies influence the pupils' retention ability significantly?
The two instruments used for comparison of learning through different teaching strategies will be again conducted after 7 or 8 weeks in order to test which of the methods better help to retain the lessons taught.
2.3 Do gender and/or grade level interact significantly with the different teaching strategies in the learning process of 2D geometry?
It is also aimed to test the multivariate interaction between the 4 teaching strategies, grade level and gender in the process of learning 2D geometry. It will examine whether boys and girls from grades 4 and 5 interact differently with the teaching strategies in their performances.
Research Question 3
Is language a barrier to learning of 2D geometry?
This main research question is further divided into a more specific set of questions.
3.1 Does the use of mother-tongue Creole influence the learning of 2D geometry significantly?
Creole is the most commonly spoken language in Mauritius whereas the foreign language English is the official language used in teaching at schools. This study will test whether the involvement of a foreign language in the teaching of 2D geometry increase its difficulty. Since Creole is not yet a language with its proper grammar for writing, it is only widely spoken. Thus, the geometry are written in English but explained in Creole. The aim is also to find if the use of Creole helps the child to better retain the lessons.
3.2 Does language factor combined with different teaching strategies improve learning of 2D geometry significantly?
English and Creole are combined with the 2 teaching strategies proposed (usual classroom teaching using textbook only and inquiry-based teaching with concrete materials and manipulatives) to analyse whether language interact with the teaching strategies to improve performance in 2D geometry significantly.
Research Question 4
What are the relative impact of home and pupil characteristics in determining performance of pupils?
This main research question is further divided into a more specific set of questions.
4.1 What are the crucial home-related factors influencing performance of pupils?
Based on extensive research available on impact of home environment on scholastic performance, home-related indices (concerning child SES, availability of educational resources at home and parent attitude towards educating children) will be constructed from a questionnaire filled by the parents of all surveyed pupils. Using structural equation modelling (AMOS in this study), the crucial home-related factors will be extracted to create latent variables in order to better measure their impact on children performance.
4.2 What are the crucial pupil-related factors influencing performance of pupils?
It is well known that pupil's personal characteristics contribute enormously towards his/her academic success. Based on a questionnaire filled by surveyed pupils, pupil-related indices (concerning pupil attitude towards homework, school and teacher; reading corner; pupil reading materials at home and pupils' language ability) will be constructed. Using structural equation modelling (AMOS in this study), the crucial pupil-related factors will be extracted to create latent variables in order to better measure their impact on children performance.
Taking these research questions in combination, this research work seeks to determine the teaching and learning practices of 2D geometry in the upper primary schools in Mauritius. It also involves testing of new experimental teaching strategies in order to optimize learning of 2D geometry locally. As Mauritius is a multiracial country where the social background of the children can play a very crucial role in their learning process, the study will use the data collected to draw conclusions concerning critical contextual factors influencing learning.