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Muhammad Ashfaq Bokhari, PhD
Associate Professor
Department of Mathematical Sciences
King Fahd University of Petroleum & Minerals
Dhahran Saudi Arabia
Contents
Introduction
Communication Experience
Pakistan
Canada
Saudi Arabia
Nature & Level of Courses Taught
BZU (Pakistan)
UWO & U of A (Canada)
NUST (Pakistan)
KFUPM (Saudi Arabia)
Teaching Philosophy and Goals
Teaching Methods
Use of Technology
Exams
Grading Policy
Interaction with Students & Feedback
Involvement in Curriculum Development
Teaching based Projects/Research
Seminars/Workshops on Teaching
Thesis/Projects Supervision
Student Evaluation at KFUPM
Introduction
I started my teaching career in a Pakistani University (Bahuddin Zakariya University [BZU]) in December 1975 after my MS in Mathematics. In 1979, I left for Canada for my higher studies. During the period of my MA and PhD studies at the University of Western Ontario [UWO] and University of Alberta [U of A] respectively, the source of my income was merely Teaching Assistantship. After completion of my PhD, I rejoined BZU in 1985. I moved to King Fahd University of Petroleum & Minerals [KFUPM], Saudi Arabia in 1988. In 1997, I was on a 1-year teaching assignment at the National University of Sciences & Technology [NUST], Pakistan. Since 1998 to date, I have been teaching at KFUPM.
Communication Experience
As indicated above, I happened to teach in various academic set-ups in 3 different countries. Throughout my teaching career, although I was engaged in the institutions having English as a medium of instruction, I came across students of various nationalities with different mother tongues. In a way, I had to pay specific attention to the communication part of my career. A brief description in this regard is as follows:
Pakistan
The students entering the university complete their early education partly in their national language Urdu. A significant number of these students in the MS program face a difficulty in the comprehension of English during their initial classroom lectures. Here, I learnt how to make the students understand my lectures.
Canada
The students I came across in the Canadian universities had various mother tongues ranging from English to Chinese, and some with South Indian languages. It was, indeed, an experience of listening to a mixture of different accents in the classroom. Here, I developed my listening ability to understand them.
Saudi Arabia
Almost all the students entering to BS programs at KFUPM come with high school education in Arabic medium of instruction. Most of these students have difficulty of communication as well as following the class lectures during the initial weeks of their study at KFUPM. Only a caring instructor can cope with this type of students. Teaching experience at KFUPM helped me to understand the importance of patience while dealing with students.
Nature & Level of Courses Taught
I have taught a wide variety of courses which range from Pre-calculus to Graduate level courses. The detail is as follows:
BZU (Pakistan) [1975-79 & 1985-88]
Here, my teaching was confined to math graduates. The courses, which I was assigned at BZU, dealt with Pure and Computational Mathematics.
UWO & U of A (Canada) [1979-85]
Here, for the first time, I got an experience of dealing with students of different disciplines. I taught calculus and differential equations to undergrad engineering, medical and computer students.
NUST (Pakistan) [1997-98]
NUST comprises of several army institutions having a quite rigid and ambitious programs in engineering and computer science. Here, I had to cover the usual 3-term calculus material in 2 terms. Also, I happened to teach a course on applied math to BS students. This course covered a variety of topics: linear algebra, vector calculus and partial differential equations. In addition, I taught a Numerical Analysis course to MS electrical and computer engineering students. Computer programming (Fortran 90 & C+) was a vital component of this course.
KFUPM (Saudi Arabia) [1988-97 & 1998 to date]
Although KFUPM is an engineering institution, it has BS, MS and PhD programs in physical sciences, industrial management and environmental design as well. I have availed the opportunity to teach not only to math major students but also to the students of other disciplines. I have taught
Pre-calculus to Prep-Year students;
Calculus (single variable, multivariable and vector), Differential Equations, Linear Algebra and Complex Variables to BS engineering and computer science students;
Applied Calculus to BS business & management students;
Advanced Calculus, Complex Analysis, Topology, Numerical Analysis, Linear & Nonlinear Programming to BS math major students;
Optimization Techniques, Linear Algebra, Approximation Theory, and Real Analysis to MS/PhD math students.
Teaching Philosophy and Goals
I base my teaching on the belief that the only way to learn mathematics is to do mathematics. This is achieved mostly through class assignments, and also through in-class discussions and exercises. I view my role as a facilitator for this process. I try at my level best to design the framework in which learning can take place, and then stimulate and nurture the students' development, giving help in terms of knowledge, techniques, and encouragement.
My goals in teaching are not just to promote learning of the subject matter. I also try to help the students learn to think logically, learn problem-solving methods and techniques, and improve writing skills. In addition, I try to help students understand how the lecture material links to various concepts they took in their earlier courses.
Teaching Methods
I usually begin each class with a brief summary of the previous class session, and a reminder of where we left the topic we are currently working on. After this, I briefly outline the new material and list its objectives. My teaching style varies according to the nature of the course.
In the lower level courses, I always subdivide my lecture into various concepts related to the topic and append a number to each one for quick reference. After explaining the concept, I demonstrate its application to an appropriate exercise of the text. I usually break the solution of an exercise into various steps and seek the input of the students while moving from one step to another. I encourage questions and pause in the lecture to answer them. Depending on the time and topic, I may then have an in-class exercise, usually involving cooperative learning with a follow-up discussion to end the class. I always assign practice problems and reading at the end of each lecture.
As much as possible, I try to present course material in analytical, numerical, and graphical contexts. This approach of course depends on the particular topic, but it is particularly valuable in calculus, differential equations, and numerical analysis courses. I am especially conscious of using geometrical figures and graphs to illustrate different concepts. This helps most of the students develop intuitive understanding of the concepts in the class.
In the Pre-calculus and Calculus courses, I incorporate cooperative learning techniques into the class sessions, particularly during the recitation hours. I involve the students to work in pairs or groups of three on a short problem, with specific instructions on how to share ideas and come up with a common solution. While the students are working, I move around the classroom to help various groups.
My strategy in the senior and graduate courses is a bit different. Here, I try to motivate the students towards self-learning. The class size at this level is usually small. Therefore, I invite the students to initiate proof/solution of the result/problem under discussion on the blackboard. Towards the end of the course, I also direct them to research material that is closely related to their course contents. However, this exercise is only up to getting exposure of some research articles.
Use of Technology
I have used computer for demonstration purposes in many courses. I usually design the courses like Numerical Analysis, Linear Algebra and Differential Equations, in such a way that a significant portion is to be completed using numerical software like MATLAB. In calculus courses, the students are advised to use a graphing calculator for in-class exercises and homework.
Depending on the nature of a course I often demonstrate some of the material by transparencies, laptops, and/or graphing calculators in my lectures. This approach, particularly in the low level courses, not only gives me ample time to cover the course material but also provides my students a comprehensive exposure of the topics that involve
Problems with numerous steps and lengthy calculations, e.g. higher order system of linear equations, solution in series of 2nd order LDE, solution of IVP by techniques like Runge-Kutta method etc;
Weird behavior of the graphs of some functions near specific points, e.g., EMBED Equation.DSMT4 near 0;
3-D visualization, e.g., quadric surfaces, solids of revolution, graphs of the functions of two variables etc;
Abstract concepts like EMBED Equation.DSMT4 definition of limit, evaluation of definite integral by Riemann sums etc;
Approximation problems dealing with several fractions or irrational numbers, e.g., Linear approximation of functions of several variables, approximation of infinite series and integrals etc;
Word problems (applications of mathematical concepts that involve maxima minima, differentials, etc) and mathematical models that lead to a system of linear/nonlinear equations or differential/integral equations etc.
Exams
When I create an exam, I try to follow several guidelines. First, I try to test over a reasonable range of class material, and I try to stress the important concepts. I do not include non-essential items or problems, which require some "trick" that the students may come across rarely. I also include problems of varying difficulty and critical thinking. Before each exam, I spend some time in class discussing what topics will be covered and which are the most important. I usually go into more detail for undergraduate courses, especially the lower level courses. I also try to be careful not to make the exams too long.
I always keep my old exams, and I notate them if they are too long or if a certain problem was not formulated properly or was not a good question for this particular class (i.e., if most of the class missed this question). When I teach the same course again, I do not usually ask the same questions but I often modify the statement and numerals without changing the underlying concept.
A part of the purpose of my exams, especially a midterm exam, is to help the students learn. It shows the students what they really know and what they dont, so that they can go back and work harder on the areas in which they are having trouble.
Grading Policy
In order to keep uniformity, I always specify suitable credit to important steps that lead to a solution of an exam question. The key to the exam with grading policy is displayed for guidance of the students. This practice helps them in two ways: first, it provides them the reason(s) of their mistakes; second, they can easily figure out an abnormality, if any, in the award their solution.
I take specific measures while grading midterm exams: be fairly strict while at the same time avoid discouraging the students. In fact, this exam gives a signal to the students who are not paying due attention to the course, or for whom the course material is too difficult. Therefore, they have an option either to drop the course or make the decision to devote more time and effort to the course. Also, the midterm exam gives the students a good idea of where they stand in the course, so that there are no surprises at the end. And finally, it provides me a feedback regarding the general weaknesses of the students.
I spend quite a lot of time in the process of figuring and deliberating final grades. As a result, I very rarely have any student who thinks that his final grade is unfair or unexpected.
Interaction with Students & Feedback
I encourage my students to discuss their academic problems during my office hours, which I designate five to six times a week. I make myself available at other hours as well. I have tried to increase communication with the students as well as get their feedback. I collect the email addresses of all students at the beginning of the semester so that I can quickly notify them of changes or hints on assignments, temporary changes in office hours, etc.
In graduate and senior level courses I have a small discussion with each student, usually midway through the semester. I tell them my view on their work and try to give them suggestions for the material in which they need improvement.
Involvement in Curriculum Development
I have been the chairman of the department undergraduate committee that reviewed the entire BS Math Program of KFUPM during the period 1993-1996.
I have served on several committees charged with designing, reviewing and developing math major/service courses. While dealing with any service course (calculus, linear algebra, differential equations or numerical methods), I usually discuss the matter with some faculty members of other departments to determine what they expect their students to know after taking this course. This experience helped me understand the math component and its level required for the engineering, computer science, and business management programs of KFUPM.
Last year, I chaired a department standing committee on calculus. This committee after deliberating over a period of one year made recommendations regarding adjustment of the calculus sequence contents, prerequisite material for each calculus course, appropriate use of recitation classes, in-class use of technology, and selection of appropriate calculus text.
Teaching based Projects/Research
I am usually involved in the projects that deal with the use of technology or innovative teaching methods. Two years back, I made an experiment in collaboration with a colleague about the use of computers in the pre-calculus courses. We have submitted our findings in the form of a research paper Computer Aided Learning of Mathematics: The case of software evaluation, to Mathematics and Computer Education Journal (under review).
Currently, I am a part of a team that submitted a project to the Deanship of Academic Development (KFUPM) entitled Students Learning Process in Pre-Calculus and Calculus Courses at KFUPM: Identifications of Problems and Possible Remedies. It is a funded project in which I shall be the principal investigator.
Seminars/Workshops on Teaching
I have been a regular participant of the workshops, which are organized from time to time by the Deanship of Academic Development (KFUPM). These workshops concentrate on new trends in teaching, designing objective-oriented courses, evaluation methods, exam item analysis, students learning outcome, course assessment and adjustment of course objectives. A keynote speaker in these workshops is an educationist usually invited from the Europe or North America.
I participate in the weekly seminars held under the auspices of the Department Teaching Committee. Recently, I presented a talk at this forum entitled MATH 202 (Elementary Differential Equations): A course amid expectations and obligations.
During the academic years 2000-2002, I was the coordinator of KFUPM Prep Year Math Program. This program involves 20 to 25 instructors who teach preparatory math courses to the fresh undergrad students. I used to organize a one-day instructors workshop at the start of each academic term. The workshops provided a forum to the instructors to express their views and experiences related to teaching methods, use of teaching aids, mode of recitation classes, and students academic problems and possible remedies.
Thesis/Projects Supervision
I have supervised MS thesis at KFUPM (Saudi Arabia) and MPhil survey thesis at BZU (Pakistan). In addition, I supervised a project oriented senior course at KFUPM in which the math major students select a math topic and prepare a comprehensive report which includes historical perspective of the topic, explanation of related concepts along with illustrative examples, detailed proof of relevant theorems, and current status of the topic in the literature. The topic supervisor reviews the report prepared by a student and then the student presents it in a seminar, which is evaluated by an examining committee.
Student Evaluation at KFUPM (1988-1997 & 1998-2003)
On a scale of 10 (highest) to 1 (lowest), my student evaluations have fallen in the following ranges:
Level
Courses: MATH ---# of OfferingsAverage EvaluationPre-calculus001, 00247.36Calculus101, 102, 011, 201348.42Applied Math202, 260, 280, 302108.32Senior Math311, 411, 412, 421, 430, 472, 48088.86Graduate531, 550, 575, 59558.87
Students generally comment positively on my class presentation, organization, fairness, and availability.
Some of the negative comments are that I go fast in class and try to cover too much material (of course, for some courses I have no choice in this matter), exams are hard, and there is too many quizzes.
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Introducing word problems in the class demands a significant planning from an instructor. After having abstract concepts and complicated mathematical computations, the students of applied sciences usually look forward to have an exposure of real life problems where these concepts and techniques are applicable. However, they are not aware of complexity of the procedure that let them derive a relevant mathematical equation. To achieve this end, an instructor has to narrate and explain the statement of the problem, identify its known and unknown quantities, and finally, use appropriate physical/mathematical laws/rules that relate these quantities with each other. In some cases, geometry of the problem also proves helpful to understand an analysis of the problem statement. Even in simple calculus applications, this process turns out quite lengthy. Therefore, an instructor cannot merely rely on chalk-board facility to accomplish his task. In my opinion, use of laptops or transparencies is a suitable and effective approach to handle this type of problems in the classroom.
Teaching Portfolio/M.A.Bokhari
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