What follows is a story I have told only to a few of my closest friends (and probably not in its entirety), because of its complexity, personal nature, and my own confusion. It’s taken me a long time to formulate this into a coherent message to share. I think it is worth reading for anyone who is considering a career in (or at least an academic foray into) the field of Engineering.  I apologize in advance for the length, as this may read more like a journal than an essay. I hope, though, that you will appreciate the sentiment behind the words.

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High School Blues

It was the final year of high school. Some say it’s the best year of their life – not yet an adult, but old enough to do all the cool things you never could when you were ‘just a kid’.  I, however, spent most of this year in confusion and stress. Up to this point, I had been fairly academically accomplished. I’d been regularly getting those revered 90’s in all of my classes. I’d written all the toughest math contests and placed well. I’d just placed in the top 60 in the Canadian Computing Competition. Actually, I was really bored by school. It provided no challenge, and it gave me no direction.

I was stressed because I needed to make a choice that I had been avoiding for years. What is it that I want to do? I sought advice from friends, teachers, family, and anyone else who would listen. None of it helped, and all of it was contradictory. My mom wanted me to do Biology; my dad was indifferent; my friends thought I made a great programmer; other friends thought I should take a stab at business; my teachers suggested Engineering.

The last of those seemed intriguing. Engineering? What on Earth was Engineering? It intrigued me because it seemed so foreign. What do Engineers do? Why should I have anything to do with them?

Engineering, according to my high school teachers, was the place where the smartest people gathered. All the students who had the best math grades and the best science grades and some desire to get a real job went into Engineering. This is, of course, a terribly short-sighted view of the diverse profession.

I had no particular desire to save the world, or to invent the wheel. I just took the suggestion because it seemed like a good fit. Math grades? Check. Science grades? Check. And then I was off. But like all things I do, I didn’t start with the easiest of paths. I chose the most difficult. I entered the vaunted Engineering Science program at the University of Toronto, upon the suggestion of my Calculus teacher.

Engineering Science – A Proving Ground

The Engineering Science program is no cakewalk. When you hear the oft-repeated ‘horror’ story of a professor telling you to look to your classmates to your left and right, and saying that only one of you will make it through four years in the program, there is no doubt in my mind that such a story could only be true here. It is an unadvertised fact that first year Engineering (and especially Engineering Science) at the University of Toronto is tougher than all other Canadian undergraduate programs, bar none. There is nowhere else where the material will be as challenging, the courses more packed, and the workload more demanding, than here. It’s even been said that first year of EngSci, as it is known here, is more challenging than its counterpart at the more famous Massachusetts Institute of Technology.

I took on this challenge with glee. I had never failed to meet a challenge.

So it was with this intention of ‘proving myself’ that I entered into the toughest period of my academic career. My previous math and science training had paid off. I had no problems transitioning into university-level courses, and met the challenge with gusto. I was able to do most of this without much thought, without much hard work. I wasn’t used to doing hard work. I had gone through all of primary, middle, and secondary school without doing any hard work. At the end of the first term, I was ranked 18th in a class of over 300. In a class that started with 334 students and would eventually dwindle to just over 170, I considered that one of the greatest accomplishments of my academic life.

A Slippery Slope

It all went downhill from there. It turned out I was just ahead of my time, and it would all catch up to me.

You see, I had always been told that at some point in my life, I would actually have to work hard for results. I’d been told that natural intelligence would only get me so far. Being the arrogant kid that I was when I first heard this in elementary school, I ignored the advice. After all, it had gotten me results in the past, and it had worked until even the first year of university. I never believed otherwise.

Then second year came, and where everyone else had by now fully adjusted to the work, I had just begun to reach the limits of what my so-called intelligence could handle. I could no longer spend just an hour or two reviewing for an exam the night before and expect to get my 90’s. Nor could I afford to skip doing homework and expect to remember anything of value.

It was during this turbulent second year that I encountered numerous personal troubles as well, further eating into my academic life. I entered a funk, and into a greatly reflective mood.

I decided that I hated math and everything associated with it. It was so dry, and tedious, and mechanical, that I could find no joy in doing this for a living. I was greatly depressed by this because the one thing that everyone had told me I was really good at – math – turned out to be something that I hated. I never realized this before, because I never really had to work at it. This is incredibly selfish, I realize too, but alas, I cannot be everything to everyone.

Second, I was not enjoying my time at school by focusing only on academics. In my entire first year, I lived inside this protective shell, meeting only a few new people whom I kept touch with regularly. I had joined little to no extracurriculars, despite my extensive involvement in various activities throughout high school, and most of all, I felt I was wasting my time with university. I asked myself, what does going to university contribute to my life? Why go through all this trouble?

A Search for Passion

It was at this point that I reached out to some friends in various places, began talking to lots of upper years, and some grizzly old professors. What was generally acknowledged was that school is sometimes a necessary evil on the way to a career – but it doesn’t necessarily have to be evil. Having never thought of school as much of a chore, I had never really thought much about this problem.

I began to get out of the academic shell, and look for other things to do. This, in itself, was not a solution to the academic problem I was having, of course – you may even think it would exacerbate the problem. However, my goal at this stage was not to be ‘the #1 student’ – marks were now a secondary concern, and my main purpose was to meet as many people as I could.

The result was a newfound perspective of my situation. While I had always lived in the upper echelons of academia, I had been completely ignorant of, well, everyone else. I had set such high standards for myself that I had been unable to see where I really was.

At some point, everyone gets lost. We get lost in the midst of our midterms, or in times of personal crises. What sets you apart from everyone else is how you choose to play the cards in your hand. Sure, I could complain about life, or get all depressed about everything – but these choices are mine to make, and I could now see how I could turn things around.

Having met so many people, I found that I was not unique. Engineering is tough. But everyone here has a reason to go through the trouble.  What sets Engineering apart from almost any other profession, is that while most people claim to be doing the world a service, only Engineers can really say this with any conviction. If Engineers don’t go through the trouble, who will?

Engineers are immensely practical – we can see through lies, and we know what we want. Underlying the philosophy of Engineering is that we can not only learn about nature’s forces, but also that we can use it to our advantage to improve humanity. Thus, engineers can invent awesome machines, design more efficient systems, and construct civilizations. I had come one step closer to figuring out why I was in engineering.

A Choice and a Path

One more decision had to be made. After 2 years of Engineering Science, we were expected to choose an Option (or a Major, so to speak). Of these, I had identified Computer Engineering and Infrastructure Engineering as my frontrunners, but for extremely contrasting reasons.

I was interested in Computer Engineering because my entire life, I had been fascinated with computers. They are so essential to our daily lives now I can hardly imagine anything without them. I had learned most of my knowledge through computers, and spent a great deal of time with them. I was good at all things computing, and this should have been an easy choice. I could probably excel in Computer Engineering without much trouble – it would probably even solve my academic issues.

But then there was Infrastructure Engineering. Nothing in my first two years of university had stoked my passion as much as this field of Civil Engineering – of bridges and buildings. In my reflection, I had found that I had the most fun in my Civil Engineering design projects – those involving bridge designs and such. I had spent countless hours with these projects, and it felt like no time at all. It was one of the few things I enjoyed in my coursework.

So here we were, at another crossroads. Should I choose what I was ‘good at’, or should I choose what I can be passionate about?

There were many factors to consider, of course, like coursework, class sizes, difficulty, career prospects, and such – but for me, there was one last motivating factor. What impact do I want to have with my education?

This made my solution clear. I could learn computer engineering anywhere. In fact, I was well on my way through my adolescence in learning all this, without the help of school anyway. But if I really wanted to do something useful with university, and to not make the same mistake I had made two years earlier in high school, this was it. This is how I decided to be an Infrastructure Engineer.

In retrospect, I probably should have chosen the more direct path through Civil Engineering to begin with, rather than go through the charade of Engineering Science – but naturally, I hadn’t gone through this whole thought process in high school. I had no such guidance, and no such experience. Part of the reason I was so enthused by Alex’s idea of the RHHSAA was that I probably could have benefited from something like this in my own days as a student. Alas, we had to start somewhere, and now was as good as any.

Having said that, it’s not as if my studies are going perfectly as planned. There are still courses I don’t enjoy, and subjects I cannot comprehend, but at least I know why I want to do it. And that is the biggest lesson of all – I found a good reason for making a choice, and having such a reason, I can deal with the hardships that might come of it. Motivation is thus created by the mind.

Normally, I don’t have too big a problem with strikes – certainly unions have had their place in bringing much needed job security and improved working conditions – but in this instance, it was nigh impossible to feel any sort of sympathy for this union strike.

As a TA in the University of Toronto, I made $28.50/hour – a fairly hefty amount for little work and admittedly low standards of qualification. Granted, I am still an undergraduate, meaning my wages are lower than those of my graduate counterparts – who earn $36/hour plus health benefits (amounting to about $400 in medical coverage per year). York TAs, who work comparable hours in comparable situations, are paid a whopping $63.29 per hour. That’s right. Even as a graduated student, working in a full-time engineering firm, I would make no more than $40 an hour to start with – and that’s if I’m lucky.

CUPE3903’s demands have been wholly unreasonable, from the massive wage increases (they want in excess of 10% in the next 3 years – during the worst recession in decades, no less) to what they call “job security”. Let me elaborate on this point. The union wants part-time professors on one-year contracts to be given lengthier contracts based only on seniority, not qualifications. Many of these part-time professors lecturers are Ph.D. candidates or recent postdocs. The union claims it unfair that they don’t get the same security as tenure-track professors who have their Ph.D.s and established research fields.

On the face of it, increased job security seems something worth fighting for – something that even the students suffering from the strike could support. However, this demand of longer contracts comes with a condition of a shorter collective agreement. CUPE3903 refuses to sign a collective agreement longer than 2 years, while demanding that their faculty receive lengthy contracts of up to 5 years. Though unpublicized, most people know that the reason CUPE refuses to sign a longer collective agreement is so that their next round of bargaining in 2010 will coincide with all the other university CUPE unions province-wide. They’re just itching to go back to the picket lines in less than two years, along with a cohort of colleagues from around Ontario. With contradictory demands like this, it’s hard to take them seriously.

Moreover, CUPE3903’s hardline position has managed to drive a stake into Ontario politics. While McGuinty’s Liberals are in a no-win situation – alienating either the students or the unions, he can at least claim public opinion support in bringing back-to-work legislation to Parliament. The New Democratic Party, on the other hand, has been smoked out by CUPE to do something brazenly unpopular amongst us students. NDP Leader Howard Hampton has declared his support of the unions, and is solely responsible for holding up back-to-work legislation at Queen’s Park. In doing so, he has alienated one of his largest group of supporters – the students – in order to appease his core power base – the unions. It is yet to be seen how big of a political impact this will have on the NDPs, but needless to say, it won’t make the students any more likely to vote for them in the next election.

If the NDPs take a political hit in the next election, their already fragile existence may become life-threatening for the party – and CUPE3903 will have had no small part in making the NDPs look irrelevant to the public in the midst of a massive recession. NDPs losing power means less sway for CUPE, and some would wonder how they’ve gotten themselves in such a mess. It all seems to me like the unions have bitten off more than they can chew, asking for the moon when we can’t even see the sky.

I wonder, too, whether CUPE3903 really represents the graduate students and the TAs and the contract faculty. In my experience, having attending a couple of union meetings for the sister union at the University of Toronto, the meetings are dominated by the union leaders, whose jobs are paid for by the union, and whose only tasks are to fight for more demands and get more publicity. There is no room or any voice for dissent, and generally, the leaders are preaching to the converted. The people who attend union meetings are usually the most hardcore, or even militant. These are the ones who really believe in striking until all their demands are met. Most of the moderate or conservative types stay away from union meetings because of these attitudes. With such a biased attendance, it was no surprise to me when I read news reports of CUPE3903 members voting to reject York’s latest offer. What I wonder is whether those who voted even bothered to read the contract, or just decided to do what their all-too-aggressive leaders told them to do.

What’s even more puzzling is the lack of student input in the whole issue. When a striking union of less than 5000 members holds over 50000 students hostage in a 3-month long strike, one would think there would be more of an outcry in the media – but reports have been mostly docile from the students, not outraged. If I were at York right now, I would be demanding a full refund from the university, and in addition demanding that the union compensate me for lost time – the opportunity cost of a few lost months of education plus lost time in the summer for employment. Not to mention all those people who still have to pay their loans, or the exchange students who have become disgusted at the whole system in the ordeal.

Have the unions become irrelevant? What are the students doing? Will there be another strike in 2010?

Props also to Alex Leung, the 2008 valedictorian, whom, despite a rather unconventional speech with lots of shouting, did a great job describing their trials and tribulations over at the ‘ol high school. I was worried Dr. Chan would die in shock when Alex L started shouting stuff like “we were the last to have grade nine camp!”, but she took it all in stride, probably savouring the fact that she got a promotion to work at the board instead of the high school. The new principal, too, sounds rather Mr. Leonard-like, cutting his own speech short for the sake of the obviously bored and antsy grads.

But on to the main point of this particular post. At commencement, I saw a great handful of my past teachers, and it led me to some reflection. As I saw one of them walk by, I felt guilty at not having said “thanks” to him.

Now, of course, I’m not the most sentimental of people, so I’ll have you know, I never actually thanked any of my high school teachers (I did, however, give the favour to Mr. Crawford my grade 8 teacher). That’s not to say I didn’t appreciate their work, just that I never felt compelled to say so formally. On this occasion, however, it might be worth backtracking.

At RHHS, I’ve had some of the greatest of them, and many deserve at least a note here. These great teachers include: Mr. Brar, the fierce calculus teacher who never stopped his relentless attack on the limits of my ability, which to this day has yet to be matched (regardless of EngSci); Ms. Ireland (now Mrs. Doganoglu), the oh-so-nice science teacher who never said a bad word about even the worst of her students, and undoubtedly my favourite teacher through high school; Mr. Ross, the vaunted discrete teacher who made mathematicians cool, and made math class a passionate experience to remember; Mrs. Kennedy, the loud-but-endearing chemistry teacher who we could hear across a wall, but always made chemistry make so much sense; Ms. Martin, the eccentric chemistry teacher who tried to teach us how to make fireworks before she taught us how to titrate; Mr. Ridout, who, despite my misgivings with his rather rigid class, laid down the best computer science foundation any high school computer science teacher could lay for a student; Ms. Sudy, who despite never having taught any of my classes, was one of the most amiable and down-to-earth people I’ve ever met.

All of these teachers made a remarkable impact on my high school education, but there was one in particular I never mentioned, and one I would never have expected to have such a lasting impression. Enter Mr. Pomakov. The Head of English would never have crossed my mind, during any time of my high school career, as the teacher who would have the most impact on me.

Why Mr. Pomakov? I was never comfortable with his class – grade 12 English, nor will it ever be near the top of my favourite subjects list. In fact, I dreaded his class when I went into my senior year. But it was perhaps the fact that I was never quite comfortable with English (both the language and the subject), that his extraordinary character affected me so.

Imagine the scene. It was grade 12, and I was a self-professed science-and-math-loving nerd and english-hating student, entering the dreaded grade 12 english class, with the teacher who had become known for giving out a legendary amount of work load. There was every reason for me to become disinterested, as I had done in all my previous english and language classes.

But his classes were remarkable. They always fluttered around the boundaries of my comfort level, what with the regular journal entries, impromptu discussions, almost weekly presentations, and of course, essays. This is what made his class great. I never cared for presentations, and before this point in my life, I had always approached any kind of public presentation with a sense of dread and reprehensiveness. But, after the last of his classes, I could prepare for a presentation not with fear, but with passionate anticipation. It was as if he tuned into my mind, full of relentless ideas, and opened up an outlet for me to stream them.

Admittedly, he never did much directly. I didn’t become a confident speaker because he told me things; I became one because he let me. It was as if he knew just how to let me express myself, without too much control, and without too much freedom. The man was intelligent, and knew how to provoke conversation at just the right times and on just the right topics. I never knew it, but it was perfect. I learned, in that class, the art of giving a good presentation. I became passionate about it, and I have been great at it ever since. (Still working on it, of course.)

For all your efforts, and sorry for being so late: thank you, Mr. Pomakov.

(Click for a larger version!)

All of these changes were designed to simplify the curriculum, or perhaps, in their mind, to make the curriculum more ‘relevant’ to students. The ministry cited increasing failure rates in mathematics, and the low enrollment numbers into the Calculus and Geometry courses. There was some noise made by students and parents, as well as the Ontario Society of Professional Engineers. To this end, I wrote the ministry a letter, which I subsequently posted on my blog (click to read). [For the record, after they replied with their initial acknowledgment of my letter, I never heard back from them.] After hearing the complaints, the ministry decided to postpone the proposed changes for a year, while creating a special task force to investigate the changes to the curriculum.

I, for one, was hoping the ministry would scrap the changes completely, and realize the mistake they had made. Unfortunately for me, that didn’t happen. While I occupied myself with the various activities at university, I forgot about this issue during the past school year. So when I visited my high school again, I was shocked to hear that new changes were to be implemented next year which would have a dramatic effect on current secondary school math students.

The changes made were:

• Grade 11 Functions and Relations became Grade 11 Functions
• Grade 12 Advanced Functions and Introductory Calculus became Grade 12 Advanced Functions
• Grade 12 Geometry and Discrete Math was basically removed, making room for a new course, called Grade 12 Calculus and Vectors
• The third senior math course (and generally recognized as the easiest), Grade 12 Data Management, was essentially untouched

Now, it would appear that Calculus remained in the curriculum, and that the only real casualty was the Geometry and Discrete portion of mathematics. Upon closer inspection, in fact, both calculus and geometry+discrete were dumbed down and/or removed. Vectors, which made up about one-third of the old (and difficult) Geometry course, was added onto the already packed Calculus course, while some of the Grade 11 Functions and Relations content was moved to the new Grade 12 Advanced Functions course.

What did all this accomplish?

• Grade 11 students who don’t intend to take calculus now have a much easier course;
• Grade 12 students who wished to take calculus, but not the more difficult geometry course must now take an extra course to get their credit;
• Stronger grade 12 math students who wished for a challenging course to stimulate them are now simply out of luck.

Not to mention, of course, the problems that they caused for all the students going into this ‘transition’ year. (Namely, all the students who took Grade 11 Functions and Relations last year will have to take Grade 12 Advanced Functions, which repeats some amount of material, before they can take Calculus)

Now, I am sure the Ontario Ministry of Education had the students’ best interest at heart when they implemented these changes, but they have gone about it in a completely backwards way. To put it bluntly, in order to curb failure rates of senior mathematics students, the ministry has decided to dumb down the curriculum. Simple, right?

Well, as I wrote previously in my letter to the ministry, the failure rates, in fact, are representative of a larger problem, and that is the growing incompetence of our educators and the use of particularly bad learning material (anyone who remembers the Quest 2000 series of textbooks introduced by Harris will understand what I mean). Kids are no longer learning the fundamentals properly – of course they’re having trouble in upper years.

I’d love to get into how the education system is flawed, but that’s a topic for another day. Most of it, of course, has to do with most educators teaching all the wrong things, and the mostly forceful rote memorization and inherent boring-ness of the assigned work. If we start teaching people to ask why and motivate instead of lecture, we might actually see some positive results.

In any case, the fundamental flaw behind this new series of courses is that instead of fixing the fundamentals from the ground up, they have decided to build another obstacle and hoping for the best. Seriously, will requiring an extra math course before calculus really improve students’ understanding of the concepts? Surely, those who were having trouble with calculus aren’t going to suddenly get better at it just because they’ve been given more math.

A second fatal flaw in the new courses lies in the lack of a true mathematics course. Anyone who has taken high school calculus knows that for the most part, this is a course about memorizing techniques and, well, methods of differentiation. For the most part, students taking calculus don’t realize its significance, nor do they expect to use it in any facet of their life after the course. Most merely enroll in the course to get the prerequisite for their university program. The only real mathematics course for senior students, Geometry and Discrete Mathematics, has been all but destroyed.

Sure, the ministry did note that the “Discrete” course was getting low enrollment numbers – but for good reason. It was a course designed, and in that respect, designed very well, for students who were genuinely interested in mathematics or were at least skilled in the subject. I say without hesitation that content-wise, it was definitely the most challenging course I took in high school, but it was also very enlightening, from a mathematics standpoint.

Geometry and Discrete brought everything we learned in mathematics together, from basic number theory to algebra to geometry. It required connection between concepts, and a deep level of understanding of what mathematics is. If nothing else, it was an unbelievable learning experience. The sheer elegance of mathematics was brought out in the course, and for those so inclined, it was even enjoyable.

Beyond just the learning experience, Discrete provided a solid basis upon which science, math, and engineering students could build during their postsecondary education. Without taking the Discrete course (which was not a requirement for my engineering program), I would surely have done far worse in both my Vector Algebra and Linear Algebra courses. Ironically, the only reason I had a vector algebra course at all in my first year was because it was removed as a prerequisite for entry into the program last year. The class average in that course was very high this year – and not because the material is easy, but because most of the students there had already learned the material.

Now, engineering at the University of Toronto is a rather diverse group. I would venture to say (although I do not have solid statistics here at the moment) that somewhere between a third and a half of the students in my program was from out-of-province, and yet, most still had the background knowledge for that course. This proves only one thing – the rest of the world is at least on par with the Ontario education system. Now, with the removal of the more challenging course, Ontario has surely fallen behind.

As an aside, but perhaps not so off-topic, AP Calculus in Ontario has all but hit an end. The flagship course of the American Advanced Placement program is a course which teaches university-level calculus to high school students who wish to get a head start, or wish for a truly challenging learning environment. With the addition of a second prerequisite to calculus, it essentially forces all secondary schools to semester their grade 12 math programs, and run calculus in the second semester. Thus, if AP Calculus classes were to be run, it would have to be in the second semester as well. Typically, schools in Ontario have their second semester from February to June. Unfortunately, the Advanced Placement exams run by the college board in the States is held in early May. That leaves only three months for AP Calculus to teach students all they need to know for the AP Exams in May, on top of all the other curriculum-required material. This little logistical problem has rendered AP Calculus virtually useless in Ontario. Now, it will only be a matter of time before that is ultimately canceled, leaving Ontario students further behind their counterparts from the rest of Canada as well as the United States. Oh, and not to mention the more impressive European education systems, and the ever-competitive Chinese students. So much for having a good and competitive education system.

Canada was recently ranked one of the worst in terms of innovation among modern industrialized countries around the world. Now, with Canada’s largest province deciding to dumb down the education system, Canada will fall even further behind in innovation. Without solid mathematical foundations in secondary school, the postsecondary institutions will now have to shoulder the burden of teaching students these subjects, in an environment that is generally harsh for learning (for one, if you fail in university, you’ll now have to pay for it – is that any incentive to take a challenging course?). With our mathematics lagging behind, it is no wonder that we’re not innovating – how long will it be until our economy begins to suffer because our students have been denied the opportunity to excel in a global context?

Yesterday, amidst a rather empty convocation hall, I attended the Engineering Science overture lecture for the 2007 Winter Term, themed “Systems and States”. Giving the lecture was one Professor Thomas Homer-Dixon. The director of the Peace and Conflict Studies Program, and an MIT graduate, Mr. Homer-Dixon’s lecture for the day had a sobering message. By all scientific accounts, modern human civilization is heading towards collapse in many different directions. The time to act against it is now. Yes, climate change is occurring. Yes, population growth is at an unprecedented high. Yes, energy production is slowing down. There are numerous factual evidences that support these phenomena. It’s happening. Now.

—

Not too long ago, I was contemplating what I would do after high school. For me, there was almost no doubt I was going to be doing something science-related. Being practical, I chose to study engineering rather than purely theoretical science. I wanted to do something with knowledge. Learning is exhilerating, but alone, it serves no greater purpose.

Something else had always been troubling me for a while. Why aren’t the smartest people in the world making the decisions about the world?

Our world, for the large part, is run by the great democratic political machines of industrialized western nations. Yet this same political machine regularly fails at recognizing what I feel are the most important issues of today – the human impact to environment.

Now, I’ve never called myself a tree-hugger, or anything of the sort. I don’t have that sense of activism. But, I do maintain that many governments of today seem only to be concerned, with great hubris, about their own infinite ‘economic’ growth.

I am fascinated by politics. I read the newspaper regularly, just to catch up on the latest political scoop. I am fascinated, by the way politicians continue to sidestep real and important issues, with great deftness of words. Politics, to me, is nothing more than a play on words with some basic economic management.

So I figured long ago, that democracy is broken. Sure, if you ask me now, I’ll tell you that I’ll go out to vote, but for me, the impact of government is too slow, and too little. There are things going wrong with the world today, and political manuevering is not the way to solve it.

I was shocked, one day, about a year ago, to learn that there were still a great many important international figures who contest the notion of global warming, or even climate change. (Here’s a list of some: http://www.sourcewatch.org/index.php?title=Climate_change_sceptics) It shouldn’t take so much work to convince the public. And it sure as hell shouldn’t be so hard to realize how it’s bad for the Earth.

With my faith in politics and the media shaken, I resorted to the conclusion that the only way to get things done is to do things yourself. Of course, it’s a long road, and it’s hard to see where to begin on something so monumental.

—

Professor Homer-Dixon listed the problems, and offered a great many solutions. He articulated what I had been thinking, unconsciously and in abstract. But now I see it more clearly.

As an engineer, in the 21st century, these problems will be up to us to solve. So we can avoid a catastrophe in the future (near or far). Will we be able to engineer ourselves out of this problem? Well, we can only try and see now.

What I write here will pertain to the teachers for which I have the utmost respect for, but apparently do not understand the idea that embodies “Freedom of Information”, and also to the students (but also teachers) who do not quite grasp the concept of what education should be.

The tests and assignments which I have put up, on the “School” section of this website, are all from my various years of high school. They have been scanned and made available to students everywhere to see. This practice is not new. I have been in school long enough, and I am sure all of you have seen enough with your own eyes to know that old tests have been passed along for years. Students often have siblings, or older friends who have taken a course that they are currently taking. Thus, past tests and assignments such as those which are found on this site are quite readily available to them. Furthermore, I have been to several paid “tutorial” classes run by private organizations, who also seem to have repositories of old test and exam papers from various schools and various years. This information is not unique, nor is it a secret. If you must consider it an advantage to the students who have access to this material, then you must also consider it an unfair advantage, because not all students will have access to such material. Don’t pretend like it’s never happened before, because everyone IS aware of it.

What I have done is simply to level the playing field. This site is not only available to me, to my friends, to my classmates, but to the world. This information is something which I have shared with many people, regardless of whether or not I have shown my tests. The information in itself is free. If I am asked a specific question for a specific test or assignment, I will repeat almost exactly what I have written on said test or assignment. Why should I repeat myself dozens of times, when I have the facilities to make such information free?

Now, I mean no offense to any teacher who has found this availability disturbing. Anyone who has had a decent conversation with me will know that I don’t think these tests will help a student learn. And isn’t learning what school is about? The marks, the assignments, those are all just subjective obstacles that monitor (albeit very poorly) the progress of such education. A teacher who has done his or her job should not have any qualms about their tests being available. I, like many others who have gone through high school, can just as well tell the difference between a good and a bad teacher – and I am blessed to have had classes with some of whom I think are the best high school teachers in the region (a few weeks of university has shown me that quite vividly). A good teacher won’t mind, because it simply won’t matter. If the concepts are taught well enough, then any test question should be a walk in the park. It shouldn’t matter if the class average becomes artificially high, as long as the students have learned. And perhaps, too, it is time for an exercise in thinking – a creative problem is a hundred times more satisfying to do and solve, and when designed properly, a solution cannot simply be memorized. It must be understood. [Specifically, if math teachers are able to create problems that are unique and creative every year, then science teachers ought to be able to do the same thing, such is the expanse of the field.]

Likewise, to the students who have used these tests – understand that tests, assignments, and examinations are in no way any indication of what you have learned, it is simply an indication of what you can regurgitate. You want to learn the material? Don’t just read it, don’t just memorize the questions and solutions I have posted (and will explain by request), but be able to explain it yourself. I’ve spent a good portion of my time in high school explaining problems to others, not necessarily because I knew the ideas better than others, but because that truly is the only one way to learn. If you’ve learned it enough to teach it, you’ve truly mastered it, and the matter of tests and evaluations become trivial. Only by necessity must I care about marks. The purpose of school is to learn, and learn how to learn. I’ve been asked once or twice how I can be so nonchalant about marks. Why is it? It’s that I realize it doesn’t matter how others evaluate you subjectively, so long as you know you’ve learned from everything you’ve done.

Students – here’s a word of advice. I’ve never studied from past tests and assignments. I find it a useless endeavour. I daresay that in fact, many of the top students at RHHS also find this to be useless. Questions on tests and assignments can, and will be changed. Using this as your only resource is a sure path to disaster and failure. You’ve failed as a student if you haven’t learned. So get studying if you still don’t understand. Use the tests, but only to test yourself – not so you can memorize the formulas and methods. Otherwise, you’ve only wasted your time.

This isn’t meant to be inspiring, or even meant to be of any use in guidance. This is simply the facts, as they are, from my point of view. It is an opinion, and it is a freedom (of speech and of information), which I choose to share with the world.

I’ve said the same thing for over two years, and I’m not about to change. Got comments? Hit the comment button right below here.

For those who are unfamiliar with Calculus, it is a small strand of mathematics that essentially studies the rates of change of variables, but is often extended to include broader concepts such as functions and relations and equations on the Cartesian plane. Its ideas have been around since the ancient Greeks, but were not formalized in the 17th century by Newton and Leibniz. It has been used since the 17th century by various fields of science and mathematics to solve difficult problems and develop new concepts.

Early in the 2005-2006 school year, the Ontario Ministry of Education held a review of the secondary school curriculum in Ontario, particularly in the mathematics area. Among the most notable changes was the removal, or indeed, substantial reduction, of calculus from the grade 12 curriculum. The primary reasons given for the sweeping changes in the grade 12 math program were that dropout rates were increasing, enrollment into certain mathematics courses (particularly the infamous Geometry and Discrete Mathematics) were decreasing, and rates of failure in grade 12 Calculus were increasing. The proposals also noted that there was ‘not enough time’ to teach Calculus in a 4-year high school system, and that the subject was only necessary for careers in engineering, science, political science or physics. These proposals not only do not make any sense for the advancement of education, but will also hinder the future of Ontario’s workforce.

First, the allegation that Calculus is too difficult a course for high school students is ridiculous. Calculus has been around at the high school level for several decades. Ask your parents, and they have probably sat through a Calculus class, or at the very least, had the option of doing so during their high school years. Calculus is also offered worldwide in high school, and in almost every other province in Canada. So what has changed in the last few years in Ontario that has caused an increase in the failure rate of Calculus students? Well, to answer that question, we will not look at the Calculus course, but at the foundations of mathematical education in Ontario. In Ontario, mathematics is often unfairly treated as an extraneous subject that is ‘feared’ by students. This attitude of education has caused a dramatic lag on the teaching of mathematical concepts in early education. Simple concepts of counting, addition, and subtraction are often left out in kindergarten and are sometimes taught as late as the second grade, usually out of fear from the teachers that students will find the subject “too difficult” for them. In turn, there is a cascading effect on the rest of the student’s life in school. By the time students reach the sixth grade, they have learned only the bare basics of mathematics, but have developed a culture of fear around the subject. Back to Calculus, the subject itself requires a few mathematical concepts to have been learned by the student. They include an understanding of equations, functions, the Cartesian plane, and the ability to manipulate algebraic expressions. These skills are not very difficult to master, and generally do not require much conceptualization on the part of the student once it has been taught. Therefore, it is not much of a stretch to say that these concepts should have been taught from grades 9 through 11. Unfortunately, because of the culture of fear of mathematics and the delay of its teaching, students are still learning about fractions and division in grades 9 and 10. Thus, it is easy to see how students are going into Calculus without the necessary skills, and will naturally find the subject difficult. Calculus teachers are left with no other choice but to reteach these concepts and skills, thus leaving no time for the actual “calculus” part of the course. The fault in the system here is that mathematics is being dragged along the curriculum too slowly at the elementary level, leaving students wholly unprepared for the real world of math by the time they reach high school. Therein lies the biggest problem in the approach to this problem by the Ministry of Education – instead of starting at the root of the problem, they are only attacking the symptom, and the fatal flaw remains. Indeed, a change from the bottom up would take some time and considerable effort, but with the advancement of the modern world, it is inevitable that changes will happen, and if the current trend continues, Ontario’s education system will lag far behind the rest of the world, and schools will not be prepared for the future.

Recently, Calculus has been used as a convenient excuse for students dropping out of school, due to its irrelevance to the students and its level of difficulty. This is no more convincing than the student’s popular “I left my homework at home” excuse. It may be true that dropout rates are increasing in high school, but this fact is completely independent of students taking the Calculus course. In Ontario, Calculus is only offered as a ‘12U’ course, meaning it is geared towards more hard-working, intelligent students aiming towards post-secondary education in university. In any graduating class, the number of students heading towards university and college are about the same (although the trend is leaning towards the university side of things due to parental and educational pressure). The system is designed in such a way (like it or not) that only the more academically inclined half of students from grades 9 and 10 move on to grade 11 and 12 ‘U’ level courses. Generally, students who drop out of high school are failing courses, and by the same token, if a student has bad grades during their first two years of high school, they are strongly encouraged against or even prevented from taking ‘U’ level courses in the senior years. Thus, although it is more difficult to prove statically due to the lack of information at this level, it is probable that of the students who drop out, only a very low percentage have taken Calculus, and were not influenced by the subject. The reasons behind the dropout of students vary, but they will not be discussed in the space of this text.

The extent of use of Calculus in various fields has been debated by the Ministry of Education and their study, and they have come up with only a short list of careers that require the study of the strand of math. Those include engineering, science, political science, and physics. As a Calculus student, I find that list highly selective and is a gross misinterpretation of the flexibility of Calculus. In fact, many concepts and skills learned in Calculus are essential to business, medicine, and even certain arts, like architecture. Those who believe otherwise do not understand the essential concepts behind Calculus and do not realize its power. It is inconceivable that students will enter university programs without learning any calculus, even though it is an integral part of modern science. Where I will concede to changes in the curriculum is in its focus, but I will propose an alternate method of changing grade 12 math. Currently, Calculus is the focus of the grade 12 mathematics curriculum, and the main mathematics courses in grades 9 through 11 all gear students toward grade 12 Calculus. Although Calculus is very powerful and can be used for a great many purposes, it should still remain an optional course reserved for students who are interested in the subject, or have a need for it in the career path they choose (particularly for computing, engineering, physics, and mathematical studies). In place of Calculus, a fourth grade 12 university level mathematics course should be implemented. This course would include in it the concepts of algebra, equations, graphical analysis, and more real-world applications of mathematics, which could mean a movement of the current grade 11 finance unit into this new grade 12 course. Other changes to grade 12 math could potentially include the removal of the last unit of Geometry and Discrete, as it overlaps with the Data Management course and is often not taught, and the movement of Conic Sections into the grade 12 Geometry & Discrete course. These changes would allow teachers in grade 11 to focus on the development of vital mathematical skills required for all of the grade 12 math courses, and allow more time in earlier grades to cover geometric and algebraic concepts that have been neglected in the current curriculum (these include Euclidean Geometry and trigonometry). The choice of four different grade 12 mathematics courses for university-bound students with the new focus on the algebra skills course would make much more sense than cramming many unrelated concepts into the Advanced Functions and Introductory Calculus course as it is being done currently, and would leave Calculus as the third or fourth math course behind the new proposed Algebra course and the current Data Management course, the latter of which has had a reputation of being the ‘easiest’ of the three current senior math courses, and is often taken by students in grade 11. The Calculus course and the Geometry & Discrete course would thus be left only for stronger math students and those who are motivated for a challenge. This solution allows more flexibility and choices for the average student, while both reducing the focus on Calculus as well as keeping the course available for students who require it.

Moving forward, it is important for Ontario’s Ministry of Education to realize that removing Calculus from the curriculum will not solve the problems they have identified themselves. The problem should be attacked at its root, that is, the culture of fear that has developed around mathematics, even with its simplest concepts and skills, especially in early education. Without a solid foundation of the concepts behind math, it is inevitable that students will find Calculus and its related subjects hard to understand. The focus of Calculus in the grade 12 curriculum should be reduced, and deferred to a new course which will encompass and bring to a closure all the algebraic skills that will be useful in practically every career path. Calculus should be kept as a third or fourth senior mathematics course, for students who still need it for their post-secondary education or have strong interest in the subject.