STEP – Science, Technology, and Education in Pakistan

The following article is heavily influenced by Paul Lockhart’s brilliant article, ‘A mathematician’s lament’. I only hope to add my experiences as a Pakistani student to back his stance in the debate over Mathematics Education.

Throughout my life I have hated mathematics with a passion. I hated its rules and notations. I hated the fact that I had absolutely no say in whatever was going on in the class. I just had to sit there and listen to my math teacher go on and on about formulas, notations needed to write these formulas, practice questions which would help us memorize these formulas and eventually “practical problems” which were supposed to exhibit the relevance of these formulas in everyday life although even the eight year-old me could tell that these were merely the same practice questions loosely disguised in the most unlikely of social situations known to man. And frankly, I didn’t care. I didn’t care where x was, or how much older Mary was than her brother Mark or when train A would reach London. As far as I was concerned math was an obsolete science to which I didn’t want to contribute to and which, for the most part, didn’t really want me to contribute to it anyway.

Therefore it comes as a surprise to many people that I am currently a Computer Science major focusing on theoretical computer science, which is basically a branch of mathematics. I, who had once famously given a speech to my seventh-grade math class about the pointlessness of mathematics, am now the one trying to explain to other people the beauty of Erdos’ brilliant proofs. And it all started with the following beautiful proof of the infinity of prime numbers:

For any finite set  {p_1,p₂…p_r} of primes consider the number n= p_1..p_2..p₃…p_r +1. This n has a prime divisor p but this is not one of the {p_1,p₂…p_r}, otherwise p would be a divisor of n and the product  p_1..p_2..p₃…p_{r ,} and thus also of the difference n-( p_1..p_2..p₃…p_r) =1, which is impossible.  So a finite set {p_1,p₂…p_r} cannot be the collection of all prime numbers.

I first heard of this proof in the first lecture of a discrete mathematics course I took during my sophomore year at university. The instructor didn’t even write the proof down, with all its messy set notation. He just told us about the idea of putting the prime numbers together in a group and showed us what goes wrong if we assume the group to be finite. At first I thought this was one of those introductory shenanigans professors deploy in the first class to get students interested. How could something so simple be counted as math? Where were the fancy symbols and the list of variables with their definitions? Where was the list of steps used to reach the conclusion? Where were the ten similar questions I needed to solve at home for practice? This was simply a clever idea used to solve a problem. Surely, this couldn’t be math! But, as I have learnt in the past year, this is basically what math is: a set of simple ideas used to solve problems. Sometimes the problems can be simplified to older problems for which people have already come up with solutions. Sometimes ideas which have been used to solve a certain problem can be used to solve an unrelated problem. But the simplicity of the process remains intact. It is the ‘idea’ which is at the heart of all mathematics, and to come up with ideas you just need creativity (and maybe a pencil and a notebook).

If a course can change the path of a person’s life, then this discrete math course changed mine. In the course of nine weeks, I was introduced to the kind of math I hadn’t even known existed. For the first time in my life I didn’t feel like a robot while doing math. I actually had to think about the problems and figure out strategies for solving them. While I was introduced to techniques like induction and graph theory, for the most part my assignments and exams required me to come up with my own strategies based on these techniques and my own logical arguments and common sense. Math was like an elaborate game and finally I felt like it actually wanted me to take part.

So, this brings us to the central question: why did I, and countless other students, hate elementary and high school math? What needs to be done to make mathematics more interesting to students? Although I do not have any experience teaching mathematics, I do remember the reasons why I hated it so much and know exactly what eventually made me realize that I wanted to study a branch of mathematics as my major. For the sake of this article, I am going to ignore factors which affect all subjects alike and focus on why math has become such a hated subject.

Looking back at my years of struggling with high school math the first word that comes to mind is boredom. And this was not caused by a lack of interest in school because I was generally a very enthusiastic kid. I loved studying languages, history, and science. It was just math that I dreaded. And looking back at the way math is taught it comes as no surprise. While all other subjects are taught as an amalgamation of the history, foundations, rules and applications of the subject, math is mainly limited to the rules of the subject. Take a typical sixth grade science class. I remember learning about the effect of different factors on the rate of evaporation by placing different shaped beakers filled with water all over the school campus. What followed was a memorable class in which we all had mock “evaporation races” as we timed the beakers to see which one would lose its water first.It was only once we had made our own conclusions about which factors affected evaporation, that our teacher explained Brownian motion to us. She also mentioned factors such as surface area and wind-speed, which most of us had been able  to conclude for ourselves based on the observations we had made.

Now compare this to a typical sixth grade math class. Looking back, sixth grade was when some of the most wonderful mathematical concepts were introduced to us. It was in the sixth grade that we first encountered the idea of a variable and started to really analyze shapes. Statistics was introduced, and we started manipulating probabilities to get results which even now give me the feeling of being able to predict the future. But in the midst of all these amazing ideas, this is how a typical math class would go:

Teacher: An isosceles triangle is a triangle which has two sides of equal length. Okay?

Students: YES!

Teacher: So what is an isosceles triangle?

Students: A TRIANGLE WHICH HAS TWO SIDES OF EQUAL LENGTH !

And you can bet one of the questions on the progress test would be: “What is an isosceles triangle?”. In such a situation who would be interested in math? And these are not just two extreme examples I have mentioned to prove my point. Science that year continued to keep us hooked: we grew plants in inky water, caught insects in jars, experimented with mirrors and discovered the material we were supposed to learn, while in math we moved on to triangles which had no sides of equal length (I honestly don’t remember what they were called, though I think it begins with an s) and other lexical atrocities.

You may argue that science is an extreme example and that math just doesn’t have the exciting material needed to keep students hooked. While science teachers can use models, take their students outside or perform simple experiments to demonstrate their material, math teachers have nothing to interest a group of thirty kids. Not only do I disagree with this, I actually claim that it is the other way round and that it is the math teachers that have it good. While science teachers need extensive (and often non-available) funding to buy lab equipment and take their students out on field trips, all a math teacher needs are thirty pencils and notebooks. And how does he keep them interested? Well, he actually asks them to do some math. Do you remember the puzzle we probably all tried as kids in which we had to draw a house without lifting our pencils. That is just a simple example of a Eulerian path. And those complicated strategies for winning card games that our older siblings tried to explain to us were mostly simple applications of probability. The tower of rings of increasingly small diameters which we had to shift to another peg is the most common example given for recursive algorithms. The list of interesting mathematical problems which we solved willingly as kids is endless. Nim, Hex, magic tricks, and riddles in which we had to find loopholes in logical arguments are all example of the math we enjoyed as children and it is these problems which should be bought to the classroom to make math classes more interesting.

Another issue which I find with the way mathematics is taught, which is closely related to the first, is the extreme and almost exclusive emphasis on the utterly mundane aspects of mathematics. Take the isosceles triangle example above. Would it really have mattered if we had called the triangles, “triangles with two equal sides”? Maybe shortened to TWTES (pronounced tevtes). What’s important are the properties of these triangles. Instead of asking a child to spend time trying to memorize the pronunciation and spelling of this weird word, she should be asked to think about how they are made, and how the angles inside this triangle are related to each other. I am pretty sure if a child made a dozen different TWTES’ she would figure out most of their  properties for herself and she would actually enjoy the mental excursion of discovering these properties instead of hastily be given a list of them in the last fifteen minutes of class.

Admittedly, there are some terms and jargon that a student of mathematics must learn in order for the classes to be held smoothly and for the students to eventually take part in the wider mathematical discourse. But no other subject puts even half of the emphasis that math places on its lexicon. Take the example of chemistry. If a subject has the right to focus on terminology it is chemistry, with it’s multitude of  symbols, chemical formulas and specific reactions. But not once do I remember a chemistry teacher reciting the names of the elements along with their atomic symbols. Instead, we focused on the elements and their reactions and any time we needed help deciphering a symbol we could simply look it up on the huge periodic table taped to the classroom wall. Maybe that is what mathematics needs: a periodic table of shapes and functions which would be taped to the wall of every classroom. Then, children all over the world could forget about mathematical terminology and actually do some math.

And by ‘doing math’ I don’t mean the mindless repetition, or solving exercise problems at the end of every chapter. As a result of school mathematics, most people end up believing math is the application of known rules to problems that we know the rules can solve. That is the job of an accountant or a cashier or an insurance planner. A mathematicians  job is much simpler. He must come up with the rules that other people are to use. When faced with a problem, he is not told that it can be solved using the second trigonometric identity; that is what he must figure out. And while this is harder than simply applying a set of rules, the result of coming up with a solution is infinitely more rewarding. You can compare the two as the difference between the joy a child feels in having an adult place him on a bike and push him along, and the joy he feels when he races through the park himself. It is hard to teach him how to ride and it might take him ages to learn but all parents understand that the end result is worth it. Math teachers should definitely do the same with their students.

And if difficulty was such a major barrier, why doesn’t it stop teachers of other subjects from trying to get their students to appreciate the beauty of their fields? By the end of high school most of us have faced the toughest aspects of most of the other subjects. We have read Iqbal’s poetry and critiqued it with our peers. We have a deep understanding of how the major systems of the body work. We have built electrical devices and have made original pieces of art in a range of different mediums. Then, why is it that most of us only experience the joy of coming up with a true mathematical proof well into our undergraduate programs? Surely there is something wrong going on here.

Nature’s recent article on higher education in Pakistan has re-ignited the debate on higher education reform, evoking strong responses from both supporters and critics of the HEC. Recently, we interviewed the lead author Dr. Athar Osama, to learn more about his wider conclusions, and his response to some of the criticisms of the methodology used in the Nature article.

To seed this discussion, we present commentary from Dr. Pervez Hoodbhoy and Dr. Atta-ur-Rehman. Dr. Hoodbhoy presents his opposing point of view, arguing that the measures presented in the article were inadequate, and further that the conclusions drawn from the metrics were flawed. Dr. Atta-ur-Rehman, founding (and former) chairman of the HEC, who led the higher education reform effort during his tenure, responds by pointing to data that, in his view, shows the depth and breadth of the reform’s success.

We invite our readers to contribute their thoughts on what metrics are appropriate for measuring the success of higher education within the context of Pakistan.

NOTE: Both commentators have significantly shaped the landscape of Pakistani education over the last few decades. We request our discussants to avoid personalizing the discussion and to maintain a civil and constructive tone.

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Dr. Pervez Hoodbhoy has reproduced his email but not my subsequent response to it.

There are four aspects of the comments of Dr. Pervez Hoodbhoy that need to be considered:

1. Firstly, Dr. Hoodbhoy himself admits that there has been a huge increase in international publications at QAU after HEC came into existence when he mentions the number of international publications in the two time periods. Strangely, he picks a six year period, 1998-2003, and then compares it with the subsequent 4.5 years (?) , 2004 to mid 2008, (the correspondence occurred in August 2008, so he could not possibly have had access to the figures for the entire year) I can only assume that he has mentioned 2003 by mistake in the second “5 year” period as there is no reason to include the publications of the year 2003 in both time periods, which he has done. It is clearly unfair to take two time periods of different durations and compare them.

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This communication is concerned with “Pakistan’s Reform Experiment” (Nature, V461, page 38, 3 September 2009), and the response to my critique by its lead author.

Unfortunately, I find the response as unsatisfying as the original article. Since Nature is unwilling to accord me a chance for a satisfactory reply on its pages, I shall clarify the basis of my criticism in some detail here.

In the said article, strong conclusions have been derived from weak data. The authors have not dared to ask the basic questions whose answers are essential for ascertaining whether there has been actual progress in Pakistan’s higher education system and, if so, by how much. Instead, in giving a thumbs-up, numbers have been quoted that have doubtful significance. Take, for instance, the claim that:

“In mathematics, for example, an average paper by a Pakistani author is cited around 20% more than the worldwide average for the discipline”.

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Pakistan has been rated a ‘Rising Star’ in research multiple times over the last couple of years by ScienceWatch.com, a Thompson Reuters website which tracks trends and performance in research by analyzing its database of scientific papers and citations. The ‘Rising Star’ rankings are published every two months to acknowledge new entrants, by identifying the scientists, institutions, countries, and journals which have shown the largest percentage increase in total citations.  In the May issue of the ratings, Pakistan was named a ‘rising star’ in two areas, ‘Materials Science’ and ‘Plant & Animal Science’. Read the rest of this entry »

Editor’s Note: Since the establishment of the Higher Education Commission (HEC) in 2002, the higher education sector in Pakistan has undergone a transformation both in its size and its nature. Dr. Sohail Naqvi, the Executive Director of the HEC, has been at the helm of many of these changes. STEP’s student editor Mariyam Khalid recently sat down with Dr. Naqvi to learn more about the HEC and its mandate. In the first of this two-part interview, the performance of the HEC, the local relevance of research and other key issues regarding research in Pakistan are examined.

STEP: You have worked as a professor, as a dean, as an industrial entrepreneur and now as a policy-maker in the government. Which of these roles did you find the most rewarding?

SN: I find the one that I’m doing now the most rewarding because of its ability to influence so many factors pertaining to education in Pakistan. But I do miss the university environment, especially the interaction with students. I’ve always loved teaching and being in the classroom. In fact, I sometimes catch myself talking to my colleagues as if I’m lecturing them! So that’s definitely something that I do miss. There is a freedom in being a professor that is simply not available in any other job. When I’ve had it with administration, I can always go back to being a professor. Read the rest of this entry »

IEEE INMIC 2009 is being organized once again, this time by the folks at MAJU and UET, Taxila:

IEEE INMIC is held every year and INMIC 2009 will be the 13th in the series. INMIC has become Pakistan’s flagship technical conference with a broad scope, thereby inviting interest of a large audience. The conference targets research presentations by academic and professional researchers, and also includes a series of tutorials, enabling participants to learn about the latest trends in technology. Research contributions are expected from the participants, covering various disciplines under IEEE’s domain, including technical papers, panel discussions, tutorials and project exhibitions. For all submitted papers, the review criteria include significance of the problem, novelty, clarity, completeness, and accuracy.

As a venue for research, a multi-topic conference like this one is necessarily going to have substandard work: researchers with good work aren’t going to publish here because the audience will not be able to fully appreciate their contribution, and the related scientific sub-community (who would cite their work) aren’t going to be in attendance and therefore won’t be aware of the research. Read the rest of this entry »

The Khwarizmi Science Society is organizing a series of Astronomy Fairs to celebrate the International Year of Astronomy, 2009.  The society has organized three fairs till now. The first was held at the Punjab University in Lahore. For the subsequent ones, they ventured out to smaller cities, having one at Government High School, Phool Nagar (about 50km from Lahore, formerly known as Bhai Pheru) and the most recent one at District Public School, Okara.
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House Resolution 1886, known as the Pakistan Enduring Assistance and Cooperation Enhancement PEACE act, introduced on April 2^nd, 2009 by Rep. Howard Berman authorizes President Obama to dramatically increase non-military assistance to Pakistan – $1.5 billion a year for five years. The scope of the act includes strengthening democratic, judicial, and government institutions, support for public education, the establishment of a human rights commission, healthcare development and cultural and educational programs. This is the House version of the Kerry-Lugar Bill, currently referred to committee; it still has to be voted in the House and in the Senate before reaching the President.

This bill constitutes the clearest articulation yet of the direction the United States wishes to see Pakistani civil society take. It reflects an understanding on the part of the US leadership that the military engagement of the Pakistan army is just one of many fronts that the battle against the Taliban is being waged. Education takes a central role in the bill, requiring the regulation of madrassas (enforcing existing Pakistani law) and advocating the development of a comprehensive national curriculum, framed on “modern” principles, particularly in FATA. The bill highlights a number of urgent national educational needs including women’s literacy (current adult literacy rate of females as a percentage of males is 59%, among the largest differentials in the world [3]), increasing teacher salaries and training, and linking education more closely with employment. In Section 102, the details of public education reform are outlined:

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