Tuesday, September 28, 2010

Philosophy 101

Well, it's that time again...for one reason or another, I've found it necessary to update my "teaching philosophy," that nebulous document no one's really sure how to write.

I find that the older I get, the less patience I have for philosophies which read like litanies of pedagogical tricks, no matter how clever those tricks are. I see no reason anymore to brag about "use of technology" or "co-curricular activities" or even "inquiry-based learning" in my statement of teaching philosophy. It's not the place.

For what it's worth (I've nothing to hide), here's my current philosophy, version 2010.1.2 (or thereabouts):

My philosophy of teaching, like my teaching itself, has undergone many changes in the years past. Like those of many novice teachers, my earliest philosophies were tailor-made to fit one or another job description and often relied on catch-phrases like “use of technology” and “collaborative learning.” Embarrassingly recently my teaching philosophy read like a behaviorist’s manifesto, a long list of actions typically taken by me or by my students, actions which merely indicated a certain philosophy at work without getting at the heart of that philosophy. As I’ve grown as a teacher (and scholar of teaching and learning) I’ve been better able to tease out from those actions their essential qualities in order to understand why it is I do what I do, and what it is I hope my students will do with me when we work together in and outside of the classroom.

As a result my philosophy has become more streamlined and systematic, and while it is on its face less “practical,” it still has profound practical implications when put into action. It is no longer so describable by a few pages filled with phrases like “co-curricular activities,” “writing-to-learn,” or even the loftier “inquiry-based learning.” Though all of these feature prominently in my teaching, none is the prime mover, none is the ultimate reason why I do what I do.


If not these things, then what is it that guides my teaching?


My primary goal is to address my students’ affective needs as well as their cognitive ones. Put simply, I believe, and the literature on teaching and learning bears me out, that how my students feel about what they do is as important as what they do in the first place. Students who feel confident about their abilities will pursue greater challenges and aspire toward greater goals than students who lack that confidence. Moreover, confident students will strive toward their goals far more effectively than will unconfident ones. Therefore, instilling a sense of security and confidence in my classes, and in all other interactions with my students, is of paramount importance.


To help my students feel secure and confident, I aim to create a safe learning environment characterized by openness, honesty, and friendliness. Such an environment cannot help but lead to a shared sense of respect and understanding. Such an environment relies on a commitment to clarity and transparency, and this I keep in place by maintaining open lines of communication. I go to great lengths to make sure that my students are always able to get in touch with me in a timely manner, and that the concerns they raise in their correspondence will be met with legitimate concern and care. In this way open communication fosters a deep sense of mutual trust.


Once I have my students’ trust, and once they are convinced that they have mine, we can work more effectively together. But working effectively requires that we have a shared sense of purpose, and I cannot presuppose that my students will come to class with the same purpose I will. Some work is needed on all of our parts to align our purposes. I spend a great deal of time early in the semester learning as much as I can about my students and their academic and life goals, so that I can better make the case that what we will learn together will be useful to them: every aspect of every subject I teach I try to imbue with relevance and applicability. Here my aim is to instill in my students an intrinsic desire to learn, rather than an extrinsic one, for their learning experience will not fail to be a richer one if they see how what we study is inherently useful to them. Put another way, it’s better that my students see how useful a subject is, in actual practice, than that they merely be told of its usefulness, in theory.


Once students are intrinsically motivated to learn, it’s up to me to place before them challenging opportunities for deep learning. These opportunities are often driven and directed by the students themselves. While it is difficult to characterize broadly the activities in which my students take part, they are as a rule

  • active and not passive,
  • guided by discovery and not prescription,
  • concept-driven and not computational, and
  • authentic (that is, "real-world") and not artificial.
In every one of my courses, from the first day of class, my students do rather than see. They are encouraged to cooperate and collaborate, and competition of every sort (including for grades) is minimized. I prod them to be skeptical and to ask probative questions, like “why should I care?” and “why is that true?,” and I encourage them to answer these questions themselves before looking to me for a response. With a bit of practice, they end up learning more from each another than they learn from me.

If I am successful in my efforts, my students soon become (often very literally!) the authors of their own knowledge. They allow themselves to become the experts and are no longer beholden to an intermediary who stands between them and their engagement of new ideas.


Of course, no two students are alike: some develop more quickly than others, some are more or less astute, observant, or mathematically apt. Moreover, students at varying stages in their academic careers exhibit a broad variation in maturity and intellectual development. When put into practice, my philosophy must take these variations into account, and I do this by adopting a sort of “dialectical” approach to teaching, engaging in frequent conversations with my students about the pace with which we proceed and the direction in which we travel. What do my students need from me, as individuals and as a class, this week, on this day, at this moment? I can never plan more than a class or two in advance, knowing that on any given day we might linger longer than I’d anticipated on a surprisingly challenging concept, or that an interesting conversation will spiral outward into an engaging and enlightening example.


For the same reason, no two iterations of the same course will look at all alike, and no amount of experience or preparation will fully ready me for the next time I teach a course. Herein is the true challenge my philosophy must face: meaningful teaching is time-consuming and work-intensive. It requires constant vigilance and refinement, because midcourse adjustments are almost unending. It requires humility, and a rather thick skin, because mistakes are often made, and it’s often hard to not take them personally. Finally, it requires seemingly limitless patience and flexibility, because to teach well I must be ready to work effectively with every sort of learner I can imagine…and a few I cannot.

Why work so hard?

I can think of no better way to affect the world in a positive manner than to teach, and to teaching meaningfully. I can think of no better way to spend my time. Indeed, I feel blessed that I get paid to do something which I do well and which I love to do anyway. When I reflect upon my experiences with my students, I realize that I truly am one of the luckiest people on Earth.

6 comments:

maxx said...

"How my students feel about what they do is as important as what they do in the first place." - I cannot agree with this more.

Overall, what I really like about your teaching philosophy is that it is deeply practical. Everything is done with the ultimate goal in mind: to foster learning. It is stupefying how many miss this point: that the goal of teaching is to teach. Sometimes, our perception of what teaching *is* gets in the way of what teaching is supposed to *do*.

Dirk Awesome said...

Love it.

Nick Galatos said...

Patrick, my enjoyment while reading your statement was only surpassed by my amazement on how much I agree with what you wrote. The fact however that what I was reading was almost the same as my teaching philosophy put me into introspective mode. Indeed, I am also very practical in my approach -- and your philosophy is most practical, contradicting your early disclaimer -- and also very concious of my attempts to motivate my students. This is the part that I want to criticise; not the discovery method, the cooperative environment, the active learning or the concept driven approach.

Why do I try so hard to motivate my students? Why do I struggle to provide the sense of security and feeling of confidence that you referred to? I say, it’s because I teach to the unmotivated, or hard to motivate student. Not that the easily-motivated student does not benefit from this approach; she does. But she has not been my main focus, I realize. Why? Well I suppose because students like her are fewer than students of the other kind. I want to make this clear, though: the distinction between easy-to-motivate and hard-to-motivate is very, very different than that of likes-math and doesn’t-like math, or is-diligent and not, and the list goes on.

Then, while reading your philosophy, I got worried. Do I provide a good service to the hard-to-motivate students? I mean the easy-to-motivate students would benefit either way, and the hard-to-motivate ones get interested in the subject, they become willing to learn and they do learn. But, do I reinforce in this way their attitude to need well-motivated introductions in things?

The problem is of course systemic to our society. In a world of video games and instant messages for teenagers (which by the way reinforce limited attention span) people learn to prioritize things in terms of relevance to their lives, applicability and usefulness (three terms used in your teaching philosophy). Subconciously knowing that these are their criteria, I rely on that to be able to approach them and motivate them, by providing examples, applications and situations that indeed relate to them, are applicable and can be perceived as useful. But, even though I succeed in teaching them the material (and also, and more importantly, the methodology and the tools and the way of thinking about the material), I still do so by “cheating” them (the term used in a very, very loose sense). And I do it by reinforcing their “addiction”. (Continued...)

Nick Galatos said...

(...Continued) I am often surprised when during a course in which I failed to provide the above-mentioned “motivation” there are many, if not the majority of, students (not “math-oriented,” by the way) who -- I suppose because of the other parts, like active learning, the discovery method, etc -- get very much into the course and end up being motivated. Motivated not because I linked the course to their lives, or provided any hint of applicability, but because, I believe, they “motivated themselves.” Or rather, because no motivation was needed. Just the enjoyment of discovery -- of pure discovery, and often of abstraction -- with no relevance to usefulness, or to their lives or to applications, is enough to get them interested.

There is an article, I forget by whom, that claims that math (beyond basic arithmetic) is not needed in everyday life by the majority of people. Exceptions include mathematicians, and other researchers. Most people, will actually even use a calculator for basic arithmetic, and definitely no farmer will ever have really limited amount of fencing and want to enclose a maximum area; and even if he needs to and even if he had Calculus, most likely he will not differentiate any function to find the maximum. Although I do not quite agree with that article, I am convinced that we do not (or at least I do not) teach math because the facts will be useful to the students in their lives, or because they are applicable to so many areas related to our lives, which they indeed very much are. I teach math because of the training it provides (to the human brain, and also to other aspects of human development), because it teaches abstraction, and because it is fun! I think that this last thing is what my students (who end up being “self-motivated”) discover (via the discovery method etc.). It is, I believe, inevitable. [By the way, I believe that all human constructs (computer hardware and software included) are designed very mathematically, just because math is natural in abstract thinking, and in some sense innate to us.] In other words, I appeal to very primitive instincts of my students: it all amounts to just exposing them to and revealing to them the math and beauty behind all those symbols and behind that foreign language we use. (After all I am a hedonist, as we have discussed in the past, and I treat my students as such, as well.)

I think next time, I will make a consious effort, an experiment of sorts, where I will try to completely abstain from “artificial” applications, or any reference to usefulness, and just try to capitalize on the hedonistic nature of my students, who I believe will love the subject, not because they will think they will make use of it in their busy lives, but just because they will discover that it is fun. (As I said I believe that it will also be beneficial to their thinking, but I won’t mention that either.) I will let you know how it goes. Thanks for the opportunity you gave me to do some thinking.

DocTurtle said...

Nick: Wow! I've never received this sort of extensive feedback on a blog post before!

You've given a lot of food for thought...I'd like at this time only to play devil's advocate regarding a couple of things you've said:

1. Stanislas Dehaene makes a very cogent argument (see my post from a few years back, under the tag "Dehaene," on his book The number sense) that mathematical thinking is actually very unnatural, and that is why many (most?) people have a very hard time doing it. This might stand in contradistinction to your assertion that people think mathematically without thinking it.

2. There are a number of studies (none of which, sadly, I have handy at my fingertips) which show that there is very little "portability" to mathematical thinking, including the sort of abstraction that you and I do in our research every day. That is: when attempting to translate the skills (in "critical thinking" or "abstraction") students pick up in our courses to other domains of knowledge, generally some or all of the efficacy of those skills is lost. This fact makes the argument that "math teaches critical thinking skill which we can all use in daily life" an untenable one. I've shied away from this sort of argument for "what we do" in recent years, because of this reality of apparent "domain independence."

That's not to say we shouldn't do what we do, but that we should be cautious about how we defend/explain it!

I'm definitely going to have to think more deeply about your insightful comments. I'd forgotten how exciting our philosophical discussions in grad school always were! :)

Nick Galatos said...

Patrick, I miss our discussions (on philosophy, mathematics, politics, linguistics to name a few) a lot, too!
Just to defend myself to devil's comments that you are relaying...:

1. The language we use in math is, I agree, very unnatural, as we are not used to that level of precision (and our natural language partly reflects that), or the associated abstraction, in our everyday life. Once this language is mastered, though, I don't know. It's the same with all kinds of puzzles and (say board) games. Maybe the 'rules of the game' are strange, most of the time artificial, and often hard to comprehend or explain to others, but once people get them, they spend endless hours playing those games, or solving those types of puzzles. Unfortunately, we (as math teachers) do a very bad job at even explaining the language, so I have to take devil's argument with grain of salt, here.

2. Again I believe that very few math educators spend as much time and energy as you in making sure that the students get the 'rules of the game,' (and to make it clear that math is fun) let alone develop "critical thinking" or "abstraction." In other words, it may be the case that these studies usually assume that these skills exist at point A when studying their "portability" to point B.

Cheers.