Philosophical Foundations of My Teaching
My teaching and learning philosophy developed through the interaction of my own teaching and learning experiences, the theories of Whitehead, Dewey, and Heidegger, and education research conducted by myself and others who seek to understand the complexity of our profession and overcome its challenges. Furthermore, contemporary educational thinkers such as Jayne Fleener, TJ Murphy, Anne Reynolds, Bill Doll, and Brent Davis have influenced my thoughts about what it means to teach and learn. The endeavor of teaching is foremost an activity of human being for human beings. Heidegger’s (1996) intricate notions of Da-sein and authenticity continue to weave a resonating fabric from which I make my own teaching from my being-in-a-world while being-with-others.
Engaging others in learning and thinking, with authenticity, is a complex task. By doing so you are asking them to challenge some part of their being-in-the-world. In this sense, the learner is one who accepts that their being and world are interconnected and incomplete. The world that is understood is that world which is lived with, learned with, engaged with, and authentically connected with. In moments of authenticity we find ourselves learning through our temporality. Through this learning we know more about ourselves, our world, and our incompleteness because we have made the connections by our own being. By our very being we have become a clearing that reveals. Learners, being as such, make problematic the notion that one has control of knowledge and understanding. Each learner has a temporal-being and hence the resonant emergence of authentic knowing cannot be prescribed as if there were some direct linear causality.
Though some wish to reduce teaching to a set of pre-decided curricular activities or a logical sequence of well-developed expositions such reductions miss the shades of meaning for being. Each learner is already a being-with-world. To treat them as dissected from it is to take away what they have to say in the moment of authenticity. The philosopher John Dewey once said that “There is all the difference in the world between having something to say and having to say something” (Dewey, n.d.). The one who is coming to know things authentically has something to say. Creating dynamic classroom environments and engaging students in spaces that allow them to generate and pursue the “having of a voice” streams through all of my teaching.
It is by these means that my end-in-view for teaching seeks to perturb thought and action from each student asking them to consider in each moment of being the danger of our modern instrumentalist tendency toward inert ideas. Though Whitehead (1967), among others, warned long ago about the dangers of inert ideas, human beings find themselves perpetually at the very doorstep of inertness with knowledge. We wager in each moment of life whether to “receive [ideas] into the mind without being utilized, or tested, or thrown into fresh combinations” (pg. 1) or to refuse the path of apathy and deal with the ambivalence through all aspects of our being-as-resolute.
Engaging learners in this way overcomes traditional either/or dualism of practice that continue to ensconce our educative policies. As Da-sein in-a-with-world our classroom community engages in thought about educational and mathematical spaces. Through my teaching, I seek to give learners opportunities to authentically “have something to say” about mathematical ideas and being.
Seeking Authentic Moments through Teaching
In order to promote authenticity among my students I seek to design classroom environments that encourage them to dance on the edge of the Mandelbrot fractal (Mandelbrot, 2004). http://www.youtube.com/watch?v=gEw8xpb1aRA
The Mandelbrot fractal is a mathematical structure that has been used as a visual to understand what we mean by complexity and its role in recapitulating different ways of approaching how and why we educate (Fleener, 2002). The fractal itself holds infinite complexity in a finite space and yet it is really something quite simple, being generated from one of the most simple of mathematical formulas. To understand what it means to dance on its edge one must wrestle with the fact that its edge is ever changing depending on the level of zoom from which we choose to view it and furthermore as we change our level of zoom its level of complexity does not change. For example, looking at the picture provided above gives the allure of seeing what might be considered mathematically definable edges. However, what appears to be an edge from this perspective is actually an intricately connected complex arrangement that is not at all what one can call an edge via the typical Euclidean definition.
In my middle and secondary mathematics methods courses I use this fractal as a metaphor for teaching and learning. We take the connotation of the black interior part of the Mandelbrot fractal to be knowledge and learning that is considered to have declared meanings set by various communities, while the outer and colorful reaches are considered to be knowledge and learning in which meaning is creatively derived. Pedagogically then, for a teacher to dance on the edge of the Mandelbrot fractal is to provide engagement in learning through the dynamic interplay of these shades of meaning. It is in this dance of complexity that we find the resonant emergence of authenticity in learning (Matney, 2004). The idea of teaching and learning on the edge of the Mandelbrot fractal is then no longer a linear and casual relationship but must be viewed as one in which each level of scope contains infinite complexity, from the state level all the way to the individual child.
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