Friday, July 22, 2005


Although my primary goal for the next year or two is to become reasonably proficient in calculus, and perhaps also in number theory, I am equally interested in the psychology of Learning. There are obvious extensions to education where my focus is on the use of technological tools to facilitate and enhance Learning.

The above paragraph is my personal road map to the future. It is also a map of the present and without much additional thought, a map of the past. The map is created by myself and is self-referential in that it is continually being referred to and modified as time progresses.

While I have stated my preference for a constructivist approach to Learning, and have used that as a guidebook for the last 30 years, I continue to enjoy reading, studying, and thinking about the topic. My three favorite authors are Jean Piaget, Lev Vygotsky and Jerome Bruner. My favorite sources for information specifically on constructivism are Ernst Glasersfeld, Paul Cobb and Seymour Papert. Cobb has written extensively on constructivism and mathematics learning whereas Papert has emphasized the role that technology can play in learning to think mathematically.

I recently purchased the book "Constructivism: Theory, Perspectives, and Practice. Second edition" (2005) edited by Catherine Twomey Fosnot. The second chapter provides an introduction and overview of constructivism. I began reading this chapter about an hour ago and quickly realized that I needed a map to envisage the overall structure of the chapter. I immediately quit reading and opened up my MindGenius software.

It only took about 15 minutes to create a chart based on the headings and subheadings of the chapter.

As a result of creating the image, I was aware that the chapter contained a fairly traditional and reasonable structure consisting of a brief review of theories of learning, and of biological approaches to learning, followed by a major section on constructivism and then a very brief section on education and a concluding paragraph.

The short concluding paragraph contains only 4 sentences, the third one being "It is a theory based on complexity models of evolution and development." For me, this is an important sentence. I am familiar with complexity models and the important idea of emergence but this is the first time that I have seen these models explicitly utilized as the framework for understanding constructivism. I suspect that I have been falling behind the current literature on constructivism - this is a bit of a wake-up call. I have yet to read the chapter, but I now have a good sense of what to expect. Reading for me is an example of a constructivist activity where I first try to imagine/create a structure that captures the overall framework and then I begin to actually "read" the words and yellow-highlight important passages. Yes, I mark up my books. The action of highlighting forces me to slow down and reread a section while also allowing me to review the book later more efficiently. If I decide it is appropriate I can also use this highlighting to efficiently extend my cognitive map that I have created with the MindGenius software. Then I can refer to this map at a later time when for some reason I wish to review this material.

My next step was to read the short section on education. Once again, a sentence jumped off the page at me: "Constructivism is a theory about learning, not a description of teaching." That is my interest and the central theme of this blog. I am interested in how I, the learner, can learn. And in my case this learning is totally self-directed. I am learning about learning and about calculus simply because I find it enjoyable. It engages my mind.

Now to sit back with a fresh cup of coffee, my mental map of the chapter, a yellow highlighter and the book and see what flesh I can attach to the bones.


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