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Abstract
The AHA! experience – the moment of illumination on the heels of lengthy, and seemingly fruitless, intentional effort – has long been the basis for lore in mathematics. Unfortunately, such lore is often restricted to the discussion of these phenomena in the context of great mathematicians and great mathematical advancement. But are such experiences reserved only for the upper echelons of mathematical practice? This study focuses on the impact of these AHA! experiences on undergraduate mathematics students’ affective domain. In particular, the role of the positive emotion that accompanies such moments of illumination in changing the attitudes and beliefs of ‘resistant’ students is examined. That is, pre-service elementary school teachers who deem themselves to be incapable and/or phobic of mathematics and the learning of mathematics but are forced to take an undergraduate mathematics course as qualification for entry into a teacher education programme. The results indicate that an AHA! experience has a transformative effect on ‘resistant’ students’ affective domains, creating positive beliefs and attitudes about mathematics as well as their abilities to do mathematics.
Notes
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From the movie The Proof (Nova Citation[1]).
Of course, there were a few exceptions to this. If the details of the problem were so intricate that they could not be remembered the problem was provided in writing. Also, if there were details that were beyond the scope of getting into the problem, such as submission guidelines and instructions pertaining to journalling, then written instructions of those details were also provided.
The students journaled about their problem solving work, in general, and their AHA! experiences in particular using two very different types of journalling techniques. The first type is a simple reflective journal in which they respond to prompts such as: tell me about your problem solving techniques, reflect upon any AHA! experiences that you may have had, what makes a good problem, etc. The second type of journalling is more real-time and is based on the writing style of Douglas Hofstadter Citation[22] in which the writer adopts a trinity of personas to more accurately convey their efforts, failures, and successes in solving challenging problems Citation[23].