Biography of Dr. Payer Ahmed
Teaching Philosophy & Methodology
My philosophy in teaching is to inspire students as William Arthur Ward stated “The mediocre teacher tells. The good teacher explains. The superior teacher demonstrates. The great inspires”.
Mathematics is the mother of science and a tool of scientific and technological efflorescence. It has been a demanding subject across disciplines. Numerous research Centre and companies have always been searching for graduates in computational mathematics, first to absorb and then to train them to suit their requirements. As a mathematics instructor, one attempts to reinforce the analytical and problem-solving skills to a broad range of academic areas. In all subject contents and other educational endeavors, the applications of basic mathematical principles, deduction, and the scientific method militates the disciplined-reasoning abilities that one strives to develop.
Since I started my academic career as a teacher of mathematics, my goal has been to become an effective teacher with a positive attitude towards students and colleagues. The substantive indication of the students from the student evaluation reports demonstrate that my teaching is on the right track. This longstanding evidence has been a continuous source of encouragement that keeps me moving forward on the road to be an efficient teacher. My interaction with my teachers during my student life, and now my interaction with students as an instructor have both helped me to rediscover the knowledge of the subject and enthusiasm for teaching.
Students need to be encouraged to ask questions. They need to receive genuine appreciation for their ideas, talents, and learning abilities. My experience has shown that prompt feedback, participation during their individual and group projects, flexibility in setting individual and group requirements, fair evaluation and grading, all help to a large extent to motivate them to meet their individual and group objectives. These in turn help me to meet my objective of being an efficient and effective teacher.
On a continuous basis, my students contribute a lot to make me understand their needs and my own limitations as their facilitator in the learning process. Another reason for my dedication towards excellence in academia is my keen interest in research publications and books. I have enjoyed my teaching profession over the years by being able to teach. Hopefully, one day I will perfect my teaching techniques and will become an “ideal” teacher.
I usually present course materials by uploading these on WebCT. I follow the content of the text book, enriching them by some annotations from my personal notes and efficiently integrating it while lecturing through the smart classroom facilities. I organize my lecture notes in three ways. For service courses in mathematics, I concentrate to calculus and prefer to explain rationale behind mathematical theories for a wide spectrum of students. Emphasis is given on the understanding of real world phenomena, the formulation of mathematical methods by using intuitive arguments and thereby making meaningful decisions.
Lecture notes are typed up, projected on the screen and then explained during every lecture. They are organized in a way that motivates students. In service courses, I start to motivate students with an easy problem and in so doing the underlying theory is exposed. Students actively take part in the process of formulation of the theory.
Some typical questions that may help students understand the material are projected on the screen and explained with reference to the particular section of the lecture material or the particular formula being employed. At the end of every chapter, I encourage students to solve some typical questions prepared as Practice Problems, uploaded on WebCT or Blackboard, projected on the screen and explained in the class.
In certain courses, I give instructions to the students in the use of Mathematica, Fortran, Matlab etc. while teaching computational mathematics. I believe it helps students to read outputs from mathematical packages.
I have always been attempting to improve my service to students. Invariably the course schedule is distributed on the first day of the course. I always offer a minimum of 5 office hours per week, maintain an open door policy and encourage students to contact me at any time during working days. I encourage them to ask questions by telephone or email.
The decision to base grades on computerized marking of multiple-choice questions is very detrimental. Thus, I like to do the marking of answer sheets myself so that I can know the level of my students after completion of the first mid-term exam. I then try to reach their level. To be fair with the students, I always mark one question at a time for all the exam booklets which reduces some sort of bias in marking, let alone the managerial time per exam booklet. Moreover, I set a broad range of questions, which requires putting ideas together to solve.
Teaching Style in the Classroom
Mathematics is one of the subjects that almost everyone dreads. Students have lot of anxiety about the subject and most of the time they start the course with fear, disappointment and nervousness. However, it is the instructor's responsibility to make sure that the course is taught in an easy to understand language and make it fun. Below are some of the ways I apply so that these can make the mathematics class very fun and interesting and will increase student participation.
Encouragement: On the first day of the class, I encourage the students to learn the particular course by explaining its importance by a simple example drawn from their area of concentration of study and making a connection between the two. I tell students that the class will be an entertaining one. Also I assure students that I will do my best to make the concepts easy to understand with interesting examples and exercises. This helps student develop a passion for learning. I also encourage them to carry a laptop or other multimedia devices where lecture materials are downloaded, calculator, pencil, eraser, ruler and most importantly a school-bag with them.
Importance: I tell students the importance of the subject and why they should work hard in a disciplined manner to learn. I provide the reference that the use of mathematics can be found in almost every newspaper, magazines and other media outlets. I tell that understanding mathematics on different media will ensure their success in their personal life. The subject will create a skill in using information around him to take right decisions in the face of uncertainty in their professional life.
Motivation and Discovery: I try to motivate students by a real world example that is close to their life, say to their cars, computers, fridges, mobile phones etc. I pose a problem. Instead of solving the problem, I try to brainstorm the solution based on their past background and further motivation, helping a little by little, formulate the problem, and together we discover a well known formula. The joy of excitement and team work will leave impeccable impression in their mind. They will enjoy solving problems with that formula. It will be part of their life, rather than a formula imposed on to them, or rotten by them without interest.
Accommodation: I discovered through my experience that while learning a subject students strive to add on their existing knowledge. This requires a special care of knowing and accommodating their background in order to help facilitate learning. For example, in teaching probability theory, some may prefer Venn diagram for showing a sample space while others may like tree diagram, tabular representation or set theoretic representation. Similarly a flow chart of concepts or stages of an experiment, a mesh, lattice work or trellis diagram may facilitate learning for many.
Two Innovative Methods: While preparing lecture notes or power point presentations, I use a method “Simplification Through Colors (STC)”. The part of a mathematical equation in a line that needs to be simplified is colored. In the following line its simplified version is also represented by the same color. The use of different colors for different simplification problems make the material visually pleasing, much more readable and easily understood. I also use another method “Engagement Through Filling in Activity (ETFA). My lecture notes or tutorials have blank spaces to be filled in by understanding the material during lectures or tutorials. Students feel special eagerness to improve his or her own note.
Package: I prepare the lecture notes in some electronic format. I upload them in the Blackboard or WebCT. I also prepare home works in a way that contains problems that can be solved by the skills achieved during lecture, problems that need to put ideas together, and problems that are a bit challenging. I also set the other exams keeping in mind the outcome of learning.
Presentation: Sometimes, I give them the assignment of picking an article from Newspapers, Magazines or other academic journals that has mathematical problem and ask to present their finding in the class via a short 10 minute presentation. This provides them an opportunity to pick their favorite article and discuss their finding with the class. I also sometimes provide Lab Projects.
Interaction: I allow students to interact. I wander around the room so that shy students can also pass comments when I am closer to him or her. Their comments help me assess where they stand with respect to the content. Often I need to move back and prepare them for moving forward through an example or recapitulating the material.
Humor: I tell stories and jokes about mathematics. If there are interesting videos about mathematics, I show them during the class.
Software Package: I try to teach basic course in a lab. Ideally basic math courses should be taught in a lab environment.A mathematical software / package has been essential to understanding the subject. The other alternative is the strong background in analysis. However visualization gets permanent impression on any mind.
Lifelong Learning: I try to provide the impression that by taking a course in mathematics, they did not learn everything of it, rather they started becoming a better learner of it, and it will continue. He or she may lose the teacher’s lecture note but internet facilities, books and journals will be around him to enrich his or her knowledge, to help him /her to take the right decision in the face of uncertainty.
Research Interests
Research Fields: Mathematics, Solid State Physics
Research Groups: Mathematical Systems, Quantum Materials Science
Dynamical Systems: Chaos, Fractal, Mandelbrot & Julia Sets, Population Dynamics, Applications of Chaos Theory in Natural and Other Sciences), Computational Mathematics, Functional Analysis, Topology, Measure Theory,Fundamentals of Mathematics, Advanced Calculus, Real & Complex Analysis, Linear Algebra,etc.
More Interests: Differential Equation, Numerical Analysis, Fluid Dynamics, Theory of Relativity, Semiconductor Physics (Quantum Material Science), Mathematical Statistics, Probability and Statistical Modeling,Basic Statistics, Bio-Statistics.
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