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Optimistic problem-solving activity: enacting confidence, persistence, and perseverance

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Abstract

Optimism supports creative mathematical problem-solving. To elaborate its nature, empirical data were analyzed to identify relationships between optimism and more commonly researched constructs, confidence, and persistence. To do so, theoretical links between these constructs were first explored. Theoretically, confidence and persistence were found to be mutually exclusive personal characteristics possessed by optimistic students. Then, five elementary school students were purposefully selected from a broader longitudinal video-stimulated interview study of the role of optimism in collaborative problem-solving to find whether all combinations of confidence and persistence existed. Activity of students possessing different combinations of confidence and persistence was analyzed to determine whether there were differences in their problem-solving activity. Perseverance emerged as a third mutually exclusive characteristic within optimism. By distinguishing between persistence and perseverance, the crucial nature of perseverance in creative mathematical thinking was illuminated. These findings should inform teachers, teacher educators, and researchers interested in building optimism to increase problem-solving capacity.

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Notes

  1. http://www.oxforddictionaries.com/definition/english/optimism.

  2. Transcript protocol key for all transcripts: ‘…’ omitted text that does not alter meaning; [text] researcher comments/clarifications; ‘italics’ emphasis by speaker.

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Acknowledgments

David Clarke at the International Centre for Classroom Research (University of Melbourne) hosted this study funded by the Australian Research Council (DP0986955). Special thanks to Cam Mitchell and Reggie Bowman (ICCR Technical Team) for their high quality collection of data. Thankyou to the reviewers for their thoughtful and insightful comments.

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Authors and Affiliations

  1. School of Education, Deakin University, Burwood Campus, 221 Burwood Highway, Burwood, VIC, 3125, Australia

    Gaye Williams

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  1. Gaye Williams
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Correspondence to Gaye Williams.

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Williams, G. Optimistic problem-solving activity: enacting confidence, persistence, and perseverance. ZDM Mathematics Education 46, 407–422 (2014). https://doi.org/10.1007/s11858-014-0586-y

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