Problem-solving is arguably at the core of mathematical teaching and learning. That is, various concepts and skills are taught/learned in the hope of solving more and more complex problems. Logic is very much valued.
I have always sensed that mathematics (re: Logic) and creativity are contradictory.
I just read an interesting article on observations on Real Science : sometimes (often even) logic stumps scientists and creativity paves the way to solve problems. The article talks about diversity-induced far view talk reliant on metaphors and analogies. I learned today that the idea of far view, or distancing oneself via abstraction, is a strategy for creative thinking (read more on Scientific American). The way I see it, it’s a logical way of thinking outside the square or taking on a different perspective.
My point is, logic does not necessarily clash with creativity. Used in tandem, the likelihood of finding solutions is increased.
The challenge now is translating this into practical applications in the classroom! I already use metaphors and analogies in teaching (re: Analogies and Algebra post). I must encourage students to think of their own. Also, I need to harness more the potential brought by the innate diversity of every class – this means, at least, more opportunities to work in group to solve problems…futuristic perhaps?