The theme underlying this blog is that of Self-Directed Learning. The specific example is that of my efforts to Learn calculus (again). But the psychological theory that provides me with my direction is constructivism, an increasingly popular perspective within the cognitive (a word worth looking up in the OED)tradition.
I have always had a cognitive orientation, which was reinforced when I was a graduate student in the late 1960's. I remain deeply indebted to three professors at the University of Alberta at the time: Steve Hunka, Don Fitzgerald & Tom Maguire, who provided the support and encouragement to swim against the current and who exemplified the notion of Self-Directed Learning 40 years before the term became common. The constructivist philosophy became the heart of my approach when I became heavily involved with children and Logo in the early 1980's. I continue to believe that Logo was a superb idea and am still saddened when I realize how badly Education dropped the ball by failing to realize that it was an approach to mathematical thinking and not just another computer language.
The above reflections were precipitated by the second edition of "Constructivism: Theory, Perspectives, and Practice" (2005) edited by Catherine Twomey Fosnot. I ordered this book a couple of weeks ago and had my first look at it yesterday while sipping a coffee, alone, in a local cafe. The short opening chapter by one of the leading proponents of constructivism, Ernst von Glasersfeld, is stunningly simple. Drawing on Piaget's epistemology (another word worth looking up in the OED), Glasersfeld says, "... what we see, hear, and feel - that is, our sensory world, is the result of our perceptual activities and therefore specific to our ways of perceiving and conceiving. Knowledge ... arises from actions and the agent's reflection on them" (p. 4).
Glasersfeld continues, "... the way we segment the flow of our experience, and the way we relate the pieces we have isolated, is and necessarily remains an essentially subjective matter. ... The conceptual structures that constitute meanings or knowledge are not entities that could be used alternatively by different individuals. They are constructs that each user has to build up for him- or herself. And because they are individual constructs, one can never say whether or not two people have produced the same construct." (p. 5)
The above quotes have been yellow-highlighted in my copy of the book.
All of the above applies seamlessly to my efforts to Learn calculus. And it is worth noting that fundamentally ALL such efforts must be Self-Directed. The term Self-Directed Learning is redundant, but the emphasis is worth repeating.
I am also reading a novel, "The Master" by Colm Toibin, which is a fictionalized biography of the writer Henry James. Here is a quote from that book that I noticed yesterday which reinforces the above comments by Glasersfeld: "The gap between these two desires filled him with sadness and awe at the mystery of the self, the mystery of having a single consciousness, knowing merely its own bare feelings and experiencing singly and alone its own pain or fear or pleasure or complacency" (p. 167).
I have an appointment in a coffee shop within the hour with a colleague who has also purchased the book on constructivism and we will attempt to communicate with our individual minds. Such social events are another way to engage in Learning.