Abstract
The present study aims to examine mathematical creativity in students’ work in geometry. Research conducted was based on two aspects: (a) examining the influence of geometrical figure apprehension on the production of multiple solutions and (b) how the necessity to construct auxiliary lines in the given shape promotes the production of multiple solutions and the variables of creativity. Data was collected from 243 tenth graders (15 and 16 years old); all participants were asked to complete a 2-part test, a multiple solution problem solving test, and a geometrical figure apprehension test. The analysis of the results primarily shows that the way through which students perceive the geometrical figure and their ability to process it, is an important factor in predicting their mathematical creativity. Furthermore, it became evident that only perceptual apprehension of geometrical figures is not a reliable predictor of creativity variables, as opposed to operative apprehension of geometrical figures that positively predict the characteristics of creativity: fluency, flexibility, and originality.
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28 May 2022
A Correction to this paper has been published: https://doi.org/10.1007/s10763-021-10210-0
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Acknowledgements
This research is carried out / funded in the context of the project “Multidimensional approach to mathematical creativity as a tool for learning and using geometry with applications in the teachingof fractions, in problem solving and problem posing in the transition from primary to secondary education” (MIS 5050336) under the call for proposals “Supporting researchers with an emphasison new researchers” (EDULLL 103). The project is co-financed by Greece and the European Union (European Social Fund- ESF) by the Operational Programme Human Resources Development, Education and Lifelong Learning 2014-2020.
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The original version of this article was revised: The original version of this article unfortunately contained incorrect Acknowledgements.
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Gridos, P., Avgerinos, E., Mamona-Downs, J. et al. Geometrical Figure Apprehension, Construction of Auxiliary Lines, and Multiple Solutions in Problem Solving: Aspects of Mathematical Creativity in School Geometry. Int J of Sci and Math Educ 20, 619–636 (2022). https://doi.org/10.1007/s10763-021-10155-4
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DOI: https://doi.org/10.1007/s10763-021-10155-4