This project is based on the use of technology to improve mathematics in secondary schools of Mauritius. It discusses about the various theories associated in the application of new means of communication and teaching-learning mathematics, as well as the available technological tools and their applications. After much research work, this project has been successfully completed and applied on a sample of ‘Lower six’ students.
PURPOSE OF THE STUDY
Mathematics is a very important subject at the primary and secondary educational level. The subject finds its own place in all sciences, accountability, economics and technology. To be able to understand concepts or application of statistics in the latter subjects, a good foundation in mathematics is highly recommended. Also, after completion of secondary education, a student is required to give evidence of a good analytical and numeracy skill through his/her mathematics results so as to qualify for a seat for most of the field of the tertiary education locally or overseas. Consequently, teachers and the school administration should leave no stone unturned in creating an efficient teaching-learning environment and incentives for their students.
Mathematics is a subject which has been regarded as being very difficult by many students and parents. This stereotype way of thinking has acted as a demotivating factor and has lead to a downfall in the performance of students in mathematics, especially in upper secondary classes (Form 4 – Upper 6). Many students take the subject as a burden since it is a compulsory subject to their study stream. Hence, Mathematics, including Additional Mathematics, is neglected resulting in homework undone or uncompleted and poor performance in assessments and exams.
JUSTIFICATION OF THE STUDY
At the start of every academic year, lots of problem are faced by teachers and school administration to convince students and explain to them the importance of mathematics in their subject combination for Lower Six. Also, after the first few weeks of following Additional Mathematics classes, many students wish to drop the subject, but since the subject is mandatory for science, economics and technology streams, students find no alternative. This situation arises because students are being exposed to more abstract mathematics than the basic. As a solution to this mathematics crisis, efforts have to be done to develop the educational psychology and mathematical pedagogy.
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Technology is the tools or the ways used by individuals to improve the standard of living or comfort of living in their civilization. The youngsters of this era are highly and easily fascinated by technology. In other words, it can be said that it is the ‘fashion of technology’; consequently, technology can be more easily used as a teaching-learning tools to achieve educational goals.
SIGNIFICANCE OF THE STUDY
The use of technology in teaching mathematics will attract students towards liking the subject, thus motivating them to work harder, get a clearer understanding of concepts, develop their reflex, logical thinking and problem-solving skills, and improve their performance as a whole in the subject.
LIMITATION OF THE STUDY
Despite all the theories and technological tools existing, it is very depressing that due to limiting resources, materials and finance in our educational system, it is very difficult to apply all instantaneously. Also, though technology is reaching the society very fast, there are still families who cannot afford to provide their children with all technological facilities. Therefore, children from such families would feel very underprivileged if technology is fully applied to teaching and learning. For instance, these children will be deprived if any computer-based or internet-based homework is given.
Hence, the project is based on “theoretical approach” so that students interact “on this strategy” with the following “learning activities”â€¦.
SUMMARY OF THE CHAPTERS
(Yet to be written)
PSYCHOLOGY AND PEDAGOGY IN MATHEMATICS EDUCATION
Piaget and the learning of Mathematics
Jean Piaget (1896 – 1980) was a Swiss developmental psychologist and philosopher known for his epistemological studies with children. He placed great importance on the education of children. Piaget’s theory is a theory of intellectual development rather than a theory of learning, teaching, instruction or curriculum in general or with respect to mathematics in particular. But much writing and many investigations have been directed toward hypothesized implications of Piaget’s theory for mathematics learning, teaching and instruction, for the nature and sequence of curricular content, and for classroom structure, organization and management. Also, concerns have been expressed regarding ways in which Piaget’s theory has been applied to different aspects of education and mathematics.
Very often it has been suggested that certain Piagetian tasks (conservation tasks, for instance) provide a good basis for determining students’ willingness for learning one aspect or another of school mathematics. But Hiebert and Carpenter (1982) have indicated that the available research evidence suggests that Piagetian tasks are not useful willingness measures. The hypothesis was that Piagetian tasks can be used to identify children who would be unable to benefit from instruction in mathematics, but all the available evidence clearly suggested that the hypothesis was null. Instead, many children who fail Piagetian tasks are able to learn mathematical concepts and skills.
Kirby and Biggs (1980) indicated that “Cognition returned to psychology in the 1960s and flourished in the 1970s, permeating most areas of psychology. Its metaphor, information processing, became dominant in that discipline”.
More directly to the point, Groen and Kieran (1983) pointed out that “A few years ago, research on children’s mathematics was dominated by Piaget. To many in the field, the task was to extend Piaget’s theory or reinterpret it. Information-processing theory, broadly conceived, has replaced the Piagetian framework as a broad explanatory model. The significance of information-processing theory in cognitive development has grown concurrently with a retreat from the Piagetian framework”.
Within the present-day context of cognitive science, emphasis is placed upon understanding and comprehension. The learning of mathematics and research associated with such learning is more and more commonly being described or explained in relation to a system that includes provision for the intake of information, for its compilation within a working memory, and for interaction with other information stored within and retrieved from a long-term memory.
Latest research associated with the learning of mathematics is much more likely to focus upon individuals than upon groups. It looks beyond observable performance related to behavioral objectives for its data base. Romberg and Carpenter (in press) have indicated that “internal cognitive processes are acknowledged. Rational task analysis, which is based on a logical analysis by experts, has evolved to empirical task analysis, which focuses on what children actually do when they solve mathematics problems”. Some of this “doing” may be observable in a student’s explicit actions, but much of the “doing” may be not only terms of a student’s observable but self-reportable thinking.
The term metacognition refers to a person’s awareness of and sensitivity to her or his own thought processes, and includes the ability to monitor and control such processes to some degree. There is growing evidence that learning associated with problem solving is facilitated or enhanced by a student’s increased awareness of metacognitive aspects of the problem-solving process. Also, there is evidence that some of the differences between expert and novice problem solvers may be attributed to differences in metacognitive skills.
Romberg and Carpenter (in press) believe that “We currently know a great deal more about how children learn mathematics than we know about how to apply this knowledge to mathematics instruction. Research is clearly needed to explore how knowledge of children’s learning of mathematics can be applied to the design of instruction”. Furthermore, “Although the emphasis in research on learning has changed dramatically in the last 15 years, the connection between theories of instruction and theories of learning remains an issue”.
Cognitive Guided Instruction
Cognitively Guided Instruction is a professional development program based on an integrated program of research on
the development of students’ mathematical thinking;
instruction that influences that development;
teachers’ knowledge and beliefs that influence their instructional practice;
the way that teachers’ knowledge, beliefs, and practices are influenced by their understanding of students’ mathematical thinking.
CGI is an approach to teaching mathematics rather than a curriculum program. At the core of this approach is the practice of listening to children’s mathematical thinking and using it as a basis for instruction. Research based frameworks of children’s thinking in the domains of addition and subtraction, multiplication and division, base-ten concepts, multi-digit operations, algebra, geometry and fractions provide guidance to teachers about listening to their students. Case studies of teachers using CGI have shown the most accomplished teachers use a variety of practices to extend children’s mathematical thinking. It is a belief of CGI that there is no one way to implement the approach and that teachers’ professional judgment is central to making decisions about how to use information about children’s thinking.
The research foundation on children’s mathematical thinking upon which CGI is based shows that children are able to solve problems without direct instruction by drawing upon informal knowledge of everyday situations. For example, a study of kindergarten children (Carpenter, et al., 1993) showed that young children can solve problems involving what are normally considered advanced mathematics such as multiplication, division, and multistep problems, by using direct modeling. Direct modeling is an approach to problem solving in which the child, in the absence of more sophisticated knowledge of mathematics, constructs a solution to a story problem by modeling the action or structure.
The motivation for learning
Another crucial assumption regarding the nature of the learner concerns the level and source of motivation for learning. According to Von Glasersfeld (1989) sustaining motivation to learn is strongly dependent on the learner’s confidence in his or her potential for learning. These feelings of competence and belief in potential to solve new problems are derived from first-hand experience of mastery of problems in the past and are much more powerful than any external acknowledgment and motivation. This links up with Vygotsky’s “zone of proximal development”, where learners are challenged within close proximity to their current level of development. By experiencing the successful completion of challenging tasks, learners gain confidence and motivation to embark on more complex challenges.
The term educational technology is often associated with, and includes, instructional theory and learning theory. Educational technology, also known as e-learning, instructional technology and learning technology, is the use of technology to support the learning process. It is an innovative way to design, deliver, facilitate, and manage instruction for learners of all ages, whether it is face-to-face in a classroom, online, or a combination of methods. While instructional technology covers the processes and systems of learning and instruction, educational technology includes other systems used in the process of developing human capability. It includes, but is not limited to, software, hardware, as well as internet applications and activities. Although technology is widely used in the administration, management of education and in research, educational technology is only concerned with the impact of technology on the learning process. In other words, technology is used as a tool or support to deliver learning materials, to facilitate communication and to provide assessment and feedback. In this present information age, the demand for knowledge is growing at a very fast rate leading to the emergence of e-learning at a much higher pace.
Some of the various types of technologies which can be used in today’s traditional classrooms are:
With a computer in the classroom, a teacher would be able to demonstrate a new lesson, present new material, illustrate how to use new programs, and show new websites.
In today’s society, children know how to use the computer and navigate their way through a website.
Therefore, a class web page is an easy way to display students’ work. Once a web page is designed, the teacher can post homework assignments or other student works.
Class blogs and wikis
Blogs allow students to maintain a running dialogue, such as a journal, thoughts, ideas, and assignments. They also provide for student comment and reflection. Wikis are more group focused to allow multiple members of the group to edit a single document and create a truly collaborative and carefully edited finished product.
Wireless classroom microphones
Noisy classrooms are a daily occurrence, and with the help of microphones, students are able to hear their teachers more clearly. Children learn better when they hear the teacher clearly. The benefit for teachers is that they no longer lose their voices at the end of the day.
Mobile devices such as clickers or smartphone can be used to enhance the experience in the classroom by providing the possibility for professors to get feedback.
An interactive whiteboard provides touch control of computer applications. These enhance the experience in the classroom by showing anything that can be on a computer screen. This not only aids in visual learning, but it is also interactive, that is, students can draw, write, or manipulate images on the SmartBoard.
Streamed video websites can be utilized to enhance a classroom lesson, for instance, United Streaming, Teacher Tube, etc.
Podcasting is a relatively new invention that allows anybody to publish files to the Internet where individuals can subscribe and receive new audio files from people by a subscription. The primary benefit of podcasting for educators is quite simple. It enables teachers to reach students through a medium that is both the new style of today’s youngsters, as well as a part of their daily lives. For a technology that only requires a computer, microphone headset and internet connection, podcasting has the capacity of advancing a student’s education beyond the classroom. When students listen to the podcasts of other students as well as their own, they can quickly demonstrate their capacities to identify and define quality and develop their creativity. This can be a great tool for learning and developing literacy inside and outside the classroom. Podcasting can help sharpen students’ vocabulary, writing, editing, public speaking, and presentation skills. Students will also learn skills that will be valuable in the working world, such as communication, time management, and problem-solving.
There are many other tools being utilized depending on the local school board and funds available. These may include digital cameras, video cameras, document cameras, or LCD projectors.
Educational leadership, also known as school leadership, is the process of enlisting and guiding the talents and energies of teachers, pupils, and parents toward achieving common educational aims. Educational leadership came into attention in the late 20th century since demands were made on schools for higher levels of pupil achievement, and schools were expected to improve and reform. These expectations were accompanied by calls for accountability at the school level. The concept of leadership was favored because it conveys dynamism and proactivity. The school head is commonly thought to be the school leader. However, school leadership may include other persons, such as members of a formal leadership team and other persons who contribute toward the aims of the school.
RESEARCH AND METHODOLOGY
THE MAURITIAN EDUCATIONAL SYSTEM
The education system in Mauritius, prototyped after the British model, has improved greatly since independence. After the country became independent in 1968, education became one of the main preoccupations of the Mauritian Government to meet the new challenges awaiting the country. New dimensions have been added to education, which have gradually democratized the whole system. The government made an effort to provide adequate funding for education, occasionally straining tight budgets. Considerable investment of resources, both human and material, has been put into the Education sector and impressive progress has been achieved in terms of free and universal education. Since 1976, education has been free for all and from the year 1991, education has become compulsory for both boys and girls. As from the year 2005, with the introduction of 11-year schooling, education has been free at all levels and compulsory for all up to the age of 16.
From Primary school onwards, education has been structured in a 6-5-2 system, whereby a child follows a minimum of 6 years’ free and compulsory Primary Schooling leading to a Certificate of Primary Education (CPE). This is followed by a minimum of 5 years’ Secondary Schooling which is free and, compulsory until the age of 16. This 5 years’ schooling leads the pupil to a School Certificate (SC) or General Certificate of Education (GCE) – Ordinary Level, which henceforth enables him to pursue another 2 years’ schooling leading to a Higher School Certificate – Advanced Level (HSC), which is the key towards Tertiary Education, either locally or overseas.
Students who fail to attain a CPE are admitted to pre-vocational schools set up specially by the government to enable them to learn only basic subjects such as Mathematics, English and French, and some skilled works such as plumbing, electrical, handicrafts, art and painting, agriculture, etc.
Today the education sector is being marked by a series of reforms based on innovation and creativity from pre-primary to tertiary level. The reforms are aligned on developments worldwide and they focus on empowering the Mauritian child to face the challenges of the new millennium and to use information and technological tools available. One of the main components of the reforms is the National Curriculum Framework for primary and secondary education. It brings about an all-around development of the individual, hence allowing him to lead a balanced, active and productive lifestyle together with an understanding of the biological, physical and technological world. Education would also make the child conscious of the notions of equity and social justice.
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As concerns secondary and tertiary education, innovations brought are mainly designed to enable schools and institutions to respond effectively to local, national and international priorities. Further, the new reforms 2010 aim to meet individual learning needs of all students, provide a strong foundation for lifelong learning and instill in all learners the skill they need to adapt to an ever-changing world.
The curriculum framework for secondary education is based on the need to engage students in meaningful and integrated learning experiences. Sustainable development, citizenship, developing and maintaining a culture of peace and coping with stress are elements that will cut across the learning process. The curriculum base programme at the secondary level has been broadened with emphasis on the teaching of science and technology to those not intending to take science as their field of study in higher classes. General Science will become compulsory till Form V for students not opting for a pure science subject in view of the increasingly important role of science. Changes at the secondary level also comprise the vocationalization of the curriculum through the introduction of new subjects like Travel and Tourism, Physical Education, Marine Science and Environmental Management and the pedagogy will be reinforced by the use of ICT and multimedia.
The inclusion of extra and co-curricular activities for all in secondary schools is also proposed by the Ministry of Education, Culture and Human Resources. Thus students will have activity time during which they can choose from a range of co-curricular activities. These activities include arts and crafts, computing, debating, drama, dance, music, singing and a wide range of physical activities.
Students at the end of Form III will be initially assessed at national level in literacy in English and French, Numeracy, ICT and Social Studies, leading to a National Certificate of Achievement. This certificate will provide a statement of the level achieved by each student in these core competencies.
The new secondary education curriculum has been developed by keeping in view the following key characteristics:
Promoting global awareness
Integrated with other disciplines
Acceptable to the community
Thematic / Spiral in approach
Fair to the learner
Despite the fact that major innovations have been introduced into the system, there are still a number of challenges that need to be faced and overcome as a complement to the reforms undertaken. Today, the major challenge is the reorganization of the secondary education to ensure the fostering and development of the skills and knowledge required for socio-economic growth.
Since the year 1991, all state schools have been equipped with a television set and VCR player so that educators could make the most of the tools in the process of teaching and learning, by providing more visual support. Lately, the VCR players have been replaced by DVD players and schools have been provided computers and projectors. For the past 5 years, most schools even have internet connection to enable teachers to do their research work in preparation of their lessons. Also, students are allowed to use internet in school libraries to improve their research skills. However, only 33% of secondary schools in Mauritius have ADSL connection and others are still using the dial-up connection.
In 2009, the Ministry of Education launched the EDU-WEB project. This project enables live broadcast and interactive session in real time between the Minister and senior officials and heads of both primary and secondary schools and the education staff.
Furthermore, two State Secondary schools have been equipped with Interactive Whiteboards by the Ministry of Education on a pilot base. Subsequently, the government, in collaboration with the Sankoré Project, is coming with the setting up of at least one Interactive Whiteboard in each of its primary and secondary schools by the end of this year. The Sankoré Digital Education for all in Africa programme is part of the French contribution to the Franco-British partnership designed to achieve the Millennium objectives in education in Africa. In its 2010 – 2015 programme, the Sankoré project is providing digital classroom equipment, resource creation and sharing, professional and schoolmaster training. The equipments provided include computers, projectors and Interactive Whiteboards (IWB).
There is a growing body of evidence that young children invent or construct much of their own mathematical knowledge, and that they come to school with some well-developed, although understandably immature ways of dealing with various mathematical situations. We do not seem to take full advantage of children’s conceptions in our programs of mathematics teaching and instruction.
EMPHASIS ON TECHNOLOGY EDUCATION
The ultimate objective of any educational enterprise is to improve student achievement so that individuals may fulfill their personal aspirations and become contributing members of society. This requires meaningful change in the way educators do their work. It requires new structures, new tools and new knowledge. But more than anything, the culture of the education system must change. And creating a culture of achievement throughout an education system requires a different mindset altogether.
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