To begin with, all the trainees, of the Boys Department, had a meeting with the rector, who told us a bit about the college and its staff members. He, then, pointed out some rules that the teachers must abide to, for example, the male teachers should wear a tie and the female ones should avoid dressing in jeans or trousers. Afterwards, he leads us towards the staff room and we introduce ourselves to the teaching staffs. We, the mathematics trainees, were told to relax for the first day and so, we stay in the staff room till the school ends. The second day, I followed Mr Gaudy’s lower six class and two of Mr Navin’s class. On the third day, I was transferred to another department.
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There, I followed Mr Inder’s class and most of the time I actually did his class. He had classes with the Form III and Form IV students. With the Form IV students, he was explaining a topic on absolute error and the Form III students were studying matrices. However, as Mr Inder had only a few classes, it meant that I was free most of the time and so, I proposed to Mr Saidoo to allow me to follow his classes. Mr Saidoo was a prevocational teacher. It should be noted that most of the students of this department were prevocational ones.
I participated in an inter-department Quiz competition where I was given the role of the time-keeper. Before the Quiz competition, Mr Inder told me to make a quick revision with the two participants and the latter actually won the competition by beating the Form IV boys from Department A. I also attended two causeries, one on smoking and the other was about the problems facing the youth.
My Experience as a Replacee Teacher
After my graduation from university in July 2008, I had the opportunity to work as a replacee teacher at Hamilton College (Boys) till the end of the school year in October 2008. There, I had the opportunity to work with the students of Form III up to Form VI. The subjects that I taught were English and Mathematics. Overall, it was a very fruitful experience as I had the occasion to work with the HSc students, both boys and girls. Furthermore, I learnt that teaching is not a simple job as a lot of preparation is needed so as to make the teaching and learning experiences a success. One other experience I gained was about how to conduct examination and all the difficulties it entails regarding planning the examinations as well as the invigilation schedule.
My Experience as a Full-Time Teacher
In January 2009, I joined Dar-Ul-Ma’arif Secondary School where I taught Mathematics and Additional Mathematics with the Form 4 and Form 5 students, boys and girls separately. The school population was about 110 students and there were not many teachers working there. So, any teacher had a heavy timetable and had many responsibilities. For instance, I was responsible to prepare the scheme of work for Mathematics and Additional Mathematics for the Form 4 and Form 5 despite being a novice in the profession.
Moreover, during my say at Dar-Ul-Ma’arif, I did a six month course at Mauritius Institute of Education for the Educator’s Licence which helped me a lot to understand the students. In February 2010, I joined the Doha Academy Secondary School.
Chapter Two – The Bachelor in Education (B.Ed) Course
Besides submission of a dissertation and the portfolio at the end of the academic year, the B.Ed course comprised of the following modules:
Sociology of Education
Philosophy of Education
Education Psychology
Introduction to Curriculum Development
Assessment and Evaluation
Education Management and Supervision
Instructional Technology
Trend in Pedagogy
Educational Research
Subject Didactics (Mathematics)
Functional English
In the next parts of this chapter, issues raised in five of the modules will be discussed and reflected upon.
2.1 Philosophy of Education
This module enabled me to have a deeper insight about what education is. Dr Rassool, the lecturer, made us reflect upon our own philosophy of education and without a doubt, it helped us to better understand ourselves as teachers. A teaching philosophy statement is “a systematic and critical rationale that focuses on the important components defining effective teaching and learning in a particular discipline and/or institutional context” (Schonwetter et al., 2002, p.84).
2.1.1 My Teaching Philosophy
“Teaching should be such that what is offered is perceived as a valuable gift rather than a hard duty” – Albert Einstein
Being a mathematics teacher as well as a lover of the subject, there are some features of mathematics that makes it a very special discipline. To name a few:
Mathematics is an excellent intellectual game where all the players win.
Mathematics is also a model that can be used for developing independent and critical thinking.
Mathematics can be seen as a language that allows us to communicate ideas precisely between ourselves.
Lastly, mathematics is a tool used in natural sciences and, thus, a required discipline for many students.
The above statements alone motivate me to share my mathematical knowledge, among others, to my students. However, my goals for teaching mathematics are many. Firstly, communicate to my students that mathematics is a fun and improve their confidence about mathematics as well as reducing their anxiety about mathematics. Other goals are:
Develop a mathematical sense about quantities, geometry, and symbols as well as a variety of problem-solving strategies and basic computational skills
Enable students to make judgments based on quantitative information, to prove basic results, to read mathematics effectively and to understand their own thought processes
Ensure that students really understand concepts
Establish constructive student attitudes about mathematics
Facilitate acquisition of life-long learning skills
Foster a desire to ask mathematics questions, critical thinking, student discovery of mathematics and foster understanding of the proofs of key theorems
Teach the beauty of mathematics
Help students learn the key theorems and their applications
Improve students’ understanding of technology
Increase the number of mathematics majors as well as the students’ mathematical knowledge
Model expert problem-solving
Motivate students to make an effort to learn mathematics
Open the doors to other opportunities for students
Prepare future mathematicians, students for technical careers and students to be knowledgeable adults
Teach applications to other fields; especially for abstract subjects like vectors whereby students often ask the question: “where will vectors used us in our life?”
Teach calculator and computer skills, fundamental concepts, generalizing, logical reasoning, mathematical writing, predicting, problem-solving and proof-reading of mathematics
Teach students how to translate back and forth between words and mathematics
Teach students to work collaboratively
My mathematics classroom features multiple methods of instruction that depends mainly on the topic to be taught and my experience with how individual student best learn mathematics. On some occasions, the student-centred approach is undertaken while on other occasions, small-group investigations, among others, are carried out. These various classroom practices help address the varied learning styles found in the mathematics classroom.
Furthermore, I prepare my classes meticulously, but I like to improvise whenever possible. I dislike being interrupted during my explanation but I love it when the students ask questions afterwards; and I congratulate them for any good questions and comments.
Prophet Muhammad (Peace and Blessing of God Almighty be upon him) once said: “Facilitate things to people and do not make it hard for them” (Sahih Al-Bukhari). Since I learnt about this saying, I try effortlessly to apply it in my daily life and especially in my teaching.
2.1.2 Criticism
The positive aspect of this module is that it makes one reflect a lot on issues related to education. However, compared to other modules, this one is more bulky and we have too little time to cover everything. Furthermore, this module was presented by Dr Rassool who had three modules with us and many a time, we could not figure out what module that we are actually doing. In my opinion, this module cannot be assessed through examination as it is too abstract a subject.
2.1.3 Self-Reflection
The first important aspect of the course was to help us understand better what education is. Previously, I thought that education was only transfer of knowledge from the teacher to the students. But, at the end, of the course, I realised that education is much more than a transfer of knowledge. Among the various definitions of education that I came across throughout the course, there is one put forward by Dr Sohawon that I really appreciated and upon which there is a lot to reflect. According to Dr Sohawon, education is “the deliberate and systematic influence exerted by the mature person upon the immature, through instruction, discipline, and harmonious development of physical, intellectual, aesthetic, social and spiritual powers of the human being, according to individual and social needs and directed towards the union of the educated with his creator as the final end.”
2.2 Instructional Technology
Upon further reading regarding articles related to this module, I came across a term that caught my attention. The term was coined by Professor Prensky (2001, p.1) who stated that, today, school students are “digital natives” and they “are all ‘native speakers’ of the digital language of computers, video games and the Internet”. The different lectures provided with further insights about the use of information and communications technology (ICT) in the field of education.
2.2.1 Application of ICT in Education
Ertmer et al. (1999) identified three levels of teachers’ computer use, varying in their relationship to the existing curricula. These involve using ICT as:
a supplement to the curriculum,
a reinforcement or enrichment of the curriculum, or
a facilitator for an emerging curriculum.
The emerging ICT tools that may be useful in the teaching and learning of Mathematics can be subdivided into two main categories:
Mathematics software
For the lower secondary students, the freeware Graph can be used for the topic Coordinates Geometry to draw simple linear graphs in the form . Thereof, students shall be able to identify the different points on the line. This very light but useful software can also be used with the Form IV students to draw quadratic curves as well as other functions like cubic, trigonometric, logarithmic and exponential.
For 3-D representations of objects, the freeware Microsoft Mathematics 4.0 can be used. It has many features from different important Mathematics topics ranging from statistics to trigonometry to calculus among others. This freeware may also be used to explain “perfectly” the topic on drawing simple linear inequalities and hence to find the required region satisfying two or more inequalities.
The Yenka freeware is another great mathematical software that incorporates different aspects of mathematics and especially the topics in Statistics. Explaining the concept of probability becomes much more easier with it as animations are also provided. For instance, when explaining about the different outcomes possible when tossing two coins, Yenka provides a 3-D animation whereby two coins are tossed. At the same time, a tree diagram is constructed.
Social Media
The different social media that I find reliable to incorporate in teaching and learning are:
Blog
A blog can be created by the teacher whereby notes on specific topics may be posted as well as related videos can be embedded. Blogs also offers the ability to post photos. Useful links can also be shared. Another benefit is that it offered the participants, that is, the students the possibility to post comments and so, students can give their feedbacks and share their views.
Wikis
Like blogs, wikis can be created to post important information about Mathematical topics. But unlike blogs, participants can also edit the post by adding other useful information. However, the danger is that can delete any information or post information not related to the topic.
Social Networking Sites (SNS) such as
The different features offered by Facebook make it a very useful tool in the teaching and learning of Mathematics. Some of these useful features are
For teachers
BookTag: This app offers a great way to share and loan books out to students, plus create helpful quizzes for studying.
Webinaria Screencast Recorder: Record a video for students, and share it with this application.
Mathematical Formulas: Distribute formulas, solutions, and more with this application.
SlideShare: Create presentations to send to students with this slideshow application.
For students
Books iRead: Share the books you’re reading, and see what others think of books with this application.
Notely: Organize your school life with Notely, an app that helps you wrangle your calendar, notes, assignments, and more.
Study Groups: Get everyone together on your group project by collaborating with this application.
HeyMath!: These mini-movies explain difficult math concepts, so these are great to share with students or use on your own. (Monaghan, 2008)
A ‘fan page’ can also be created to promote Mathematics. Each ‘Like’ will increase its popularity.
Concerning its educational use, it may enable the teacher to ‘tweet’ useful links and reminders to his students, for instance, about an assessment to be done in the coming week or to do a research on a particular topic. Furthermore, it has the feature of opinion poll. This may benefits the professional growth of the teacher.
Vodcast
The use of Vodcast might benefits student that were absent for a particular lesson or have not fully grasped the different concepts in a lesson. It may also be an advantage when doing revision. The teacher can use the video to evaluate his own teachings.
2.2.2 Criticism
This module was as interesting as all other modules but I believe that this module needs to be accompanied with practical exercises and lesser literature. These practical exercises could be assessed and evaluated.
2.2.3 Self-Reflection
The ‘Instructional Technology’ module provided us with innovating ideas to enhance the teaching and learning experiences as well as to motivate students and teachers. While researching on the topic, I came to realise how powerful a tool technology can be and also how the worldwide web can be a way of reaching out to different kinds of students. For instance, Facebook has got many applications that would make Mathematics much more easier and enjoyable. I sincerely believe that technology can be an integrating part of the teaching and learning experience but before its integration, there needs to be a change in the curriculum, especially for the use of technology in exams. What is the point of using a lot of technology in teaching and learning but in exams, only very few pieces of technology are allowed? At the same time, I fear the misuse of technology and its impact on society.
2.3 Introduction to Curriculum
This module helped many of us students to understand the concept of curriculum and at the same time, to clearly differentiate the curriculum from the syllabus. Tyler (1949) defines the curriculum as ‘all the learning of the subjects which is planned by and directed by the school to attain its educational goals’. The different types of curriculum were also discussed.
2.3.1 Types of Curriculum
Curriculum is subdivided mainly as
Official curriculum
According to Posner (1992, p.10), the official curriculum, also known as the written curriculum “gives the basic lesson plan to be followed, including objectives, sequence, and materials. This provides the basis for accountability.”
It can be said that the official curriculum consists of the syllabus and content of different subjects, the legal framework, the examinations, the school and its infrastructure, the administration amongst others.
Taught curriculum
The taught curriculum, also known as the operational curriculum is “what is taught by the teacher, and how it is communicated. This includes what the teacher teaches in class and the learning outcomes for the student” (Posner, 1992, p.10-12).
Therefore, the taught part of curriculum involves all the teaching and learning experiences that take place in the classroom when educators interact with students and vice-versa. Personally, I usually adopt different teaching strategies with my student. The learner-centred teaching approach and the team teaching approach are favoured for the upper classes while the authoritative style is favoured with the lower classes as it is a democratic approach in which the rights of both the teacher and the child are recognized and respected compared to the authoritarian style (Shaffer& Kipp, 2007). Formative assessments are performed during the lessons so as to obtain feedbacks to both the learner and myself and thereof, teaching strategies are altered accordingly.
Hidden curriculum
According to Horn (2003, p.298), hidden curriculum is defined as “the unrecognized and sometimes unintended knowledge, values, beliefs that are part of the learning process in schools and classrooms”.
It can be deduced that the hidden curriculum refers to those things which students learn indirectly at school. For example during a lesson, different teaching-learning strategies are used for active participation. This indirectly inculcated values and skills in them such as:
Maintaining discipline
Obedience
To be democratic, that is, freedom of opinion to give answers without any fear of being wrong
Tolerance and patience towards others’ opinions to become good listeners
To be critical, they are asked to comment on their friends answers in case they don’t agree
Social interactions through group discussions and whole class discussions
Communication skills are developed
Null curriculum
According to Posner (1992, p.10-12), the null curriculum “consists of what is not taught”. Eisner’s (1995) position on the “null curriculum” is that when certain subjects or topics are left out of the overt curriculum, school personnel are sending messages to students that certain content and processes are not important enough to study.
When the Mathematics syllabuses of Cambridge for the O-level and A-level as well as that of the National Assessment at Form III, prepared by the Mauritius Institute of Education, are thoroughly analysed, it is observed that two very important components of Mathematics have not been included, namely
History of Mathematics.
The mathematician Glaisher once said that “no subject loses more than mathematics by any attempt to dissociate it from its history.”
Hayes (1991) stated: “I believe that it is a grave mistake and error of strategy to attempt to teach mathematics without reference to its cultural, social, philosophical and historical background”.”
Application of Mathematics in real life situations for complex topics.
From past experience, when teaching complicated topics, like “Vector of Plane”, students often asked the question: “Why should we study this topic?” as for them, they do not understand the importance of such a topic as the problems they are faced with are sometimes too abstract. But, when they are made aware of its importance in real life, they are more eager to do the topic.
2.3.2 Criticism
Understanding the concept of curriculum and all that it entails was a very important step in the career of an educator. However, knowing all this and consequently, identifying the various flaws of a curriculum can be seen as a loss of time as we, as educators, cannot do anything to change a curriculum, especially for S.C and H.S.C, that is prepared by an elite group in England.
2.3.3 Self-Reflection
Besides having had a deeper insight of education, the concept of curriculum became much clearer. I realised that when following a particular curriculum, it is not only completing the different topics involved in the syllabus. In fact, the syllabus is only one part of the curriculum and there is more to a curriculum. We have the aims and objectives that also need to be achieved. In fact, these curricula that we normally follow are the official curricula. However, there is one other type of curriculum that is equally or more important than the official curriculum. It is the hidden curriculum. It is through the hidden curriculum that moral values and ethics are passed on. Therefore, this helped me to be even more cautious in class as behaving badly or weirdly would result in the students behaving as such. Sometimes, when I observe a student behaving badly, I say to myself that maybe the student is behaving like this because of his teacher who was rude. Also, upon further reflection, on a larger scale, I came to realise that maybe the way ordinary people behave may be the result of how those who are governing them behave.
2.4 Education, Management and Supervision
Among the many important concepts learnt in this module, there is one that I think is essential for every teacher to possess – managerial skills in the classroom.
2.4.1 Managerial Skills Required by Teachers in the Classroom
Mintzberg (1973) identified the following managerial skills:
Leadership Skill
This skill is concerned with the ability of the teacher to motivate and help his students and at the same time, to deal with their problems effectively. For those students who are intrinsically motivated, the teacher only acts as an initiator and a facilitator. However, for those students who are not motivated, the teacher’s leadership role is vital important to motivate them.
As a Mathematics teacher, the following strategies can be adopted to motivate the students:
The teacher himself/herself must be seen as being motivated
Find suitable ways to make students love the subject
State the aims and objectives of the subject matter
Let the students know that the teacher is always available whenever someone is having difficulties in his studies.
Set-up the classroom rules and regulations in collaboration with the students.
Use different teaching styles in order to match the diverse learning styles of the students.
Peer Skill
Peer skill would refer to the ability of the teacher to act, at one time, as a manager of the classroom and at another time, as a friend to his students. This friendly relationship should be to some limit and the students should be made aware of it. Otherwise, being too friendly would cause chaos and indiscipline in the class and subsequently, the learning environment of the class would be heavily and badly affected.
Conflict Resolution Skill
Life in a classroom is not always sweet. On and off, things get sour between the students or even between the student and the teacher for diverse reasons. Classroom conflicts, may it be a minor or a major one, must be dealt with as soon as they arise so as to prevent the situation from getting out of control. Otherwise, they would spoil the teaching and learning environment of the classroom.
Information Processing Skill
This skill is about the teacher’s ability to extract, collect and share information relevant to the subject matter or topic. In the traditional view of teaching and learning, the teacher was the sole source of knowledge and hence, the class was dominantly teacher-oriented. However, despite the fact that this approach to teaching and learning is regarded as being obsolete, some subjects, like mathematics, are most of the time teacher-centred. But, a good mathematics teacher would find ways to make his class an enjoyable and fruitful experience.
A good mathematics teacher should be able to use a variety of teaching styles in order to make the subject appear interesting and easy, and at the same time, cater for the different learning styles of his/her students.
Resource Allocation Skill
This skill deals with the teacher’s ability to manage his time properly and to reach out to each student’s encountered difficulties. The best way to achieve these is through proper lesson planning. From past experience, the following should be taken into consideration when preparing a lesson plan:
Carry out one lesson at a time
The aim and objectives of the lesson should be well set and the students should be made aware of it
Since nearly all topics in mathematics is based on some pre-requisites, always recall those previous knowledge in order to get the students in the mood
Based on the difficulty of the topic, take a considerable amount of time to fully explain the topic, taking into consideration the problems students are having and waste no time to clear these misconceptions
Allow students to have sufficient amount of time to practice some problems in class and at the same time, use this ‘free’ time to deal individually with those having further problems
Summarise the whole lesson
Give a reasonable amount of homework
Reserve the next session for correcting homework and for further practice (remedial works if needed)
A well-prepared lesson plan not only involve the resource allocation skill but also the entrepreneurial skill of the teacher-manager as the latter deals with the ability of the teacher to look for problems and opportunities that may arise during a lesson and thereof, implement the necessary change smoothly.
2.4.1.6 Introspection Skill
This maybe the most important skill needed by a teacher-manager. It deals with the teacher’s ability to reflect upon his own work and the impact it has on his students. In other words, after each lesson, the teacher needs to self-evaluate himself. Successful evaluation would be that teaching and learning has occurred and each student has understood the lesson and all works have been completed. Else, the teacher needs to change his teaching strategies and/or behaviour in class.
2.4.2 Criticism
Dr Sohawon made this lecture lively through his various real-life cases and so, it was an enjoyable and enriching experience. However, some aspects of the module, I believe, are out of reach of a teacher, for instance, the concept of quality control. I think that these concepts should be taught to a group of experienced educational officers that solely has for job to monitor the performance of teachers and students.
2.4.3 Self-Reflection
At the beginning of the module, I thought that the topics were beyond me as I am relatively new to teaching and the lecturer was talking about being a manager, a supervisor or an inspector and how to manage or supervise. But, as the module was dealt further, these managerial styles and skills are as important for a teacher as they are for a manager. This is because, in the class, I concluded that the teacher has multiple roles. Moreover, since I have been appointed as Section Leader for Form 4 and Form 5 (Boys), I am realising the importance of the different theories learnt in the module regarding managing and supervising.
2.5 Trends in Pedagogy
This module, according to me, is one of the most important modules of the whole course as it covered very important topics which are directly related to the teacher and his teachings. Among the many fruitful topics, I would like to share my views on teacher motivation as it is a topic that is not often talked about.
2.5.1 Teacher Motivation
A definition of teacher motivation, according to me, would be a force that drives a teacher to do his best so as the best learning environment is formed for students. Associated to teacher motivation are a low level rate of absenteeism and a good disciplinary record of the teacher. According to Michaelowa (2002, p.5), teacher motivation can be defined as “willingness, drive or desire to engage in good teaching”. Hence, mathematically speaking, teacher motivation is equivalent to efficient teaching and consequently, efficient learning.
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Some people believe they are born to be teachers. Others believe they have the necessary qualities for being a teacher. Normally, these people are intrinsically motivated teachers. No external factors, positive or negative, would affect their determination to give their best as they care for the students and they want to see their students achieve in their studies and in life. For doing so, they are willing to do a lot of sacrifice and use a multitude of strategies for the gain of the students.
The majority of teachers need to be motivated extrinsically, that is, their level of motivation is based on some external factors which may be directly related to the school environment or related to personal issues in their private life. A first issue that can help in motivating a teacher, in my opinion, is a fair and equitable timetable. Being a mathematics teacher, it would be very difficult and demotivating to work too many periods per week, especially if there are a lot of lower secondary classes. This is because to teach mathematics, one needs a lot of preparation, concentration and energy so as to foster a fruitful and dynamic learning environment whereby students are active and interested in the subject. Otherwise, from past experience, students are easily bored in mathematics classes that have a monotonous learning environment. Furthermore, teachers are motivated when they have students who make effort and work well as well as participate in class. According to Csikszentmihalyi (1990), a person who is involved in an activity and is working at the peak of his abilities reaches a state of happiness and satisfaction. Schonfeld (1989) claimed that being satisfied with one’s job is an index of morale and motivation.
Another element for teacher motivation is being praised and rewarded by the management or inspectors/supervisors. Bamisaye (1998) found that unfair administrative and supervisory practices tend to undermine teacher morale. Moreover, according to Nwankwo (1984), teachers feel highly motivated when they are consulted about decisions regarding their work. One further element important for motivating teachers would be a better remuneration. It is often argued that teachers are not being salaried for what they are really worth. The student-teacher ratio in a class should also, according to me, be reasonable. Just imagine teaching mathematics with forty students in a class. Will the teacher have sufficient time to look at each of his students individually?
To further motivate teachers extrinsically, all educational facilities should be offered to the teacher to fully express himself appropriately in class. For instance, in mathematics, while explaining the topic ‘Transformation’, a set of geometrical instruments is needed to enhance teaching and learning. Apart
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