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October 8, 2008

Teaching to Transgress

I read this book, “Teaching to Transgress" by bell hooks (1994) about ten years ago. I remember hooks talked about “engaged pedagogy"; this concept has really stayed with me. hooks (1994) writes the following:

"To educate as the practice of freedom is a way of teaching that anyone can learn. That learning process comes easiest to those of us who teach who also believe that there is an aspect of our vocation that is sacred; who believe that our work is not merely to share information but to share in the intellectual and spiritual growth of our students. To teach in a manner that respects and cares for the souls of our students is essential is we are to provide the necessary conditions where learning can most deeply and intimately begin." (p. 13).

As I re-engage myself in teaching, I am reminded of this idea of “engaged pedagogy." Most universities (especially research one universities) have a focus on research and not on pedagogy or, for that matter, “engaged pedagogy." With teacher training, I think there is a parallel process of engaging future teachers in the pedagogy of pedagogy.

Good teaching is about being present, being active (in all respects), being authentic, being transparent, being patient, being creative, being flexible, and being engaged (on all levels) – all in a safe, nurturing, theatrical, and exploratory environment. With these conditions, education can be about “the practice of freedom." If learning is about taking risks, good teaching should be about creating spaces for risk-taking. If learning is a process, teaching is a process.

August 14, 2008

The identity matrix: Semiotics or mathematical theory?

Based on the definition from Wikipedia – http://en.wikipedia.org/wiki/Identity_matrix, an identity matrix can be defined as follows:

“In linear algebra, the identity matrix or unit matrix of size n is the n-by-n square matrix with ones on the main diagonal and zeros elsewhere. It is denoted by In, or simply by I if the size is immaterial or can be trivially determined by the context. (In some fields, such as quantum mechanics, the identity matrix is denoted by a boldface one, 1; otherwise it is identical to I.)

The identity matrix also has the property that, when it is the product of two square matrices, the matrices can be said to be the inverse of one another."


The names of other matrices in matrix algebra all make sense and are easily defined (e.g. square matrix, upper/lower triangular matrix, diagonal matrix, tridiagonal matrix, diagonally dominant matrix), yet the identity matrix seems to be embedded in a deeper symbolic and/or cultural meaning. What would Jung have said about this as an archetype?

Which mathematician named this particular kind of matrix an “ identity matrix" – and why don’t other matrices bear more interesting and culturally symbolic names?

August 4, 2008

Long live D.W. Winnicott!

Thanks to object relations and the work of Winnicott (1951), we have all come to know a transitional object as occupying a “transitional space" between a mother and child – a replacement object (e.g. often a favorite blanket or cuddly) for the mother-child bond to soothe the child in “the transitional experience" of separation. Two days after the tribe departed, my daughter had the brilliant idea to buy a kitty “cuddly" to remember the tribe. So the next day, we went in search of our transitional object. At first, we found an orange and white tabby cat at our local flower shop. This cat was quickly rejected – as it didn’t remotely resemble any of the four cats in the tribe. But then thanks to our local power house chain, Barnes & Noble, we found several options that looked remarkably similar to the tribe. Two cats were initially purchased – one resembling Pookie and one resembling MacKenzie. But that evening, we all decided that we’d return to our local Barnes & Noble and bring Shadow and Sadie home as well.

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Alas, the tribe has returned via transitional objects; long live D.W. Winnicott! While born out of modernist psychodynamic theory, even transitional objects can be postmodern in scope - as we all have multiple realities.

Who would even know the difference?


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