Provocative mathematics questions: drawing attention to a lack of attention
- Sergiy Klymchuk * Sergiy Klymchuk is an Associate Professor of mathematics in the School of Computer and Mathematical Sciences, Auckland University of Technology, New Zealand. He has 33 years of experience in teaching university mathematics in different countries. His PhD (1988) was in differential equations and recent research interests are in mathematics education. He is an author of more than 200 publications including the Counterexamples in Calculus book that received an Outstanding Academic Title Award from the Choice magazine of the American Library Association in 2010, Paradoxes and Sophisms in Calculus book that made the cover of the 2014 Publications Catalogue of the Mathematical Association of America, and Money Puzzles book on popular mathematics that has been published in nine countries.
+ Author Affiliations
- School of Computer and Mathematical Sciences, Faculty of Design and Creative Technologies, Auckland University of Technology, Private Bag 92006, Auckland 1142, New Zealand
- Received June 2014.
- Accepted July 2014.
The article investigates the role of attention in the reflective thinking of school mathematics teachers. It analyses teachers’ ability to pay attention to detail and use their mathematical knowledge. The vast majority of teachers can be expected to have an excellent knowledge of mathematical techniques. The question examined here is whether this kind of knowledge might structure their attention in such a way that the emphasis on procedures deflects their attention from the essential details. Four groups of participant teachers from New Zealand, Hong Kong, Germany and Ukraine were given a mini-test containing seven simple mathematics questions. Most questions in the test were provocative in the sense that they looked like routine questions but in fact had some catch. The results of the test were startling—the vast majority of the participants gave incorrect answers to most questions in the test. After the test, the participants were given a short questionnaire to reflect on their performance on the test. Their responses were analysed using the theories of selective, divided and focused attention and Mason’s concept of the discipline of noticing. Implementations of the results of the study in assessment and professional development are discussed.
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