I have been brushing up on some earlier readings in preparation for the Quizzes which are due to be completed tomorrow, and I stumbled across some interesting information by Luis Mateus Rocha talking about the phenomenon of self-organising learning processes emerging from random initial conditions (1998).
This set some mental bells ringing, as it sounded like one of my favorite TED talks ever. I've popped the video in down below if you'd like to watch it yourself, I highly recommend it to anyone with even a passing interest in the latest educational theories. In his TED presentation, Sugata Mitra outlines an experiment he and his colleagues have undertaken in a poor region of India, where good teachers are loath to venture. The exercise involved putting an internet-connected computer in a "hole in the wall" of a public space and giving children access to the mountain of resources that are available online... with astounding results.
The experiments have shown that, even without supervision or a teaching professional, learners are able to teach themselves and each other, drawing their motivation from competition with their peers and curiosity alone. A similar approach could be successfully implemented in my Math class by assigning tasks such as; "who was Fibonacci, for which mathematical concept is he famous, and what are some examples of its use by man and occurrence in the natural world?" Students could be given the opportunity to develop higher-order thinking and demonstrate their declarative and procedural knowledge through activities such as:
- Racing their peers to tabulate up to a certain level in the series.
- Formulating ideas as a group as to why the golden ratio might appear with such frequency in nature, followed by research to discover the veracity of their hypothesis.
- Additional group work could involve students working together to apply their newly acquired knowledge by having them analyse potential uses for the series and design, implement and evaluate practical, real-world situations in which it may be applied.
- The Fibonacci activities can provide a convenient segue into fractals, where further activities can be undertaken.
It is evident upon reflection, that an exercise structured in this way walks students through almost every thinking-skill set in Bloom's taxonomy, starting from the basic level of discovering and remembering what the Fibonacci series is, how it works, where it can be found in nature and its usefulness, and progressing on through understanding, applying, analysing, designing and evaluating its potential implementation. A similar approach could be adapted to subject areas as diverse as Pascal's triangle, Pythagoras' theorem, the Mandelbrot set. The list extends ad-infinitum, a useful tool indeed.