Philosophy of teaching
A very committed lecturer and friend of mine recently sat in on one of my lectures. She is taking a course essentially designed to make her an even better lecturer than she already is, and she needed to listen to someone else give a lecture, then ask some follow-up questions. I found the experience terrifying to begin with - it is so hard to be natural in front of one’s peers, where by natural I mean the completely unnatural persona one puts on in order to both entertain and inform a class. I soon forgot she was there and got into the usual swing of things.
Her follow-up questions were really illuminating for me. They centred around what one might call my philosophy of teaching. I might paraphrase them as What did I see as my job in the classroom? What is my approach to teaching? Why did I become a lecturer?
Another question can by email and I would like to share my response and invite yours. She asked
I remember you saying that the course I sat in on today is taught by mathematicians but designed by engineers. So do you feel that this influences what you teach and how you teach it? Have you ever felt competing pressures from the context vs. your personal views of teaching and learning? Have you found a way of resolving them?
My response was
You do ask interesting questions! I think my main aim is to show that mathematics is a way of thinking and working rather than a set of rules or results. Math is something you do and there is no substitute for rolling your sleeves up and getting dirty with it. (”Mathematics is not a spectator sport” someone once said.) I also think it is beautiful, challenging, pleasing, and fun, a product of hard work and creative people.
That said, in this particular course I am supposed to equip engineers with a set of tools to help them be better engineers. Modern engineering is suffused with mathematics, and they need to be fluent both in the mathematical way of thinking and in a particular set of tools. So, due to time restrictions and their own needs and interests, I skip over some of the challenging stuff, and some of the most beautiful parts (like proofs), and concentrate on using the ideas. But “in the margins”, so to speak, I always try to link the ideas to things they know, things they might have heard of, and cutting-edge stuff which builds on what we are learning. This way they at least see a hint of what drives weirdos like me to be mathematicians.
I think these questions touch on some fascinating aspects of the teaching and learning experiences. If you are a teacher, how would you respond? We are all learners; how do you think a teacher’s philosophy of teaching influences your ability to learn?
Filed under: big picture | Tagged: learning, teaching
All too often education and training is designed for the convenience of the teacher. Lecture is easy on teachers but hard on students. When you look at retention rates, lecture is always at the bottom.
It’s one of the reasons why so much of what you learn in school you never use on the job or in real life.
Thanks for your comment, Steve. I’m not sure I agree that lecturing is “easy on the teachers”, but I think I know what you’re getting at. It doesn’t take much effort to read out (i.e. lecture) a prepared book-like set of notes. It does take a lot of effort to engage the imagination and learning faculties of a roomful of people. But I think that attending a lecture can be a wonderful learning experience - if the lecturer is good and if the student applies themself. It certainly is a two-way street.
Lecturing is now a very old way of imparting knowledge - but it has undoubtedly worked for all those many years and I am hesitant about rushing to change it.
Your blog looks very interesting; I’ll be sure to read it more carefully soon.
I am reminded of work by Hanson, Silver and Strong — The New American Lecture… links to more info on this lecture technique and others can be found here:
http://facit.cmich.edu/instructional-support/links/effective-lecturing.html
An effective lecture presentation is a highly skilled craft — one not to be taken lightly. Unfortunately, many prof’s, perhaps a bit arrogant concerning their command of and knowledge of a subject, or as I would guess is more frequently the case, simply because of time constraints, neglect to apply the same rigor and dedication to lecture as they do to clearly presenting an important paper to peers.
A vital consideration for any presentation is the audience…a love and respect for the audience is one key to success.
Just a thought
You do have a nice way of phrasing ideas! I have an undergraduate degree in math and continually regret that I did not go further. The reasons were/are mostly my own, but one of them was the type and style of lectures I sat through at university. There was almost nothing “in the margins” and the style was from the 19th century or earlier.
Anyway, the part of your response that really caught my attention was “mathematics is a way of thinking”. Despite (and because of) my experience with math, I now take great pleasure in my two children who are studying math at university and higher levels. To me, this establishes that they are learning to think like mathematicians. They are learning to step back to see the big picture and to zoom in to focus on the details that need work. They are learning the value of abstraction and simplicity and how to leverage what they already know.
I tell them that I don’t care if they do not become mathematicians (a parental fib) but only that they learn to think like one. Certainly other ‘disciplines’ benefit from the same ways of thinking, but in mathematics, in a sense, that’s all there is.
Back to the topic - I am sure that a lecturer could stop at some point in every talk, step into the margins, and explain why this or that is beautiful or how it links to an apparently unrelated concept. Isn’t that the fun part?
Brad.
Hi Edward, and thanks for your comment.
The summary of the New American Lecture sounds very interesting - unfortunately, the link leading on from the page you give does not work. What an annoying name, though. I’m not particularly sure it is new, and what makes it American?
But I quite agree with you about the skill required to craft an effective lecture. (Although I’ve seen too many mind-numbingly dull conference presentations to believe that there are many academics who bother about good presentation skills.)
Moreover I think you are right about the love and respect for the audience, even if at first it seems like a strange idea. Eagerness to open someone’s mind to the wonder of one’s subject is a kind of love, and if one does not respect the point from which the student begins one cannot hope to lead them to the scenic point on which you stand.
Hi Brad, and thanks for your input. You have a nice way with words yourself! You say that “other ‘disciplines’ benefit from the same ways of thinking, but in mathematics, in a sense, that’s all there is,” and I agree with you. Of course there is more - vastly more - to mathematics: its utility in application to the world around us and the mystery surrounding this, for example, but at its core is this near-magical link between our finite brains and the stupendous mathematical world. In other words, this wonder of mathematical thought.
In answer to your final question: yes! Of course, it’s also fun to impart something which you think is pretty cool, but if you think it is cool then you must think the way it all hooks up with other things to be even cooler, and that the very fact that everything is connected up is even cooler still! So why not say it?! I share your exasperation.
Love the blog, I’m a student in your EMTH 210 class so I find this very interesting!
Thanks Adam! Not long to wait for the test marks either, I hope!
kindly copy mails of teaching philosophy to me