Abstract
The paper analyzes the results of activities undertaken by Mathematics students enrolled in a pre-service teacher-training program. Students were given the task to describe the way of building a figure from which one could get a box, to identify the geometric properties that allow producing the box, and to propose new models from which new boxes can be obtained. For creativity analysis, a cognitive flexibility framework has been used, within which students’ cognitive variety, cognitive novelty, and their capacity to make changes in cognitive framing are analyzed. The analysis of some specific cases led to the conclusion that creativity manifestation is conditioned by a certain level of expertise. In the process of building a solution for a nonstandard problem, expertise and creativity support and mutually develop each other, enabling bridges to the unknown. This interaction leads also to an increase in expertise. Moreover, in order to get individual relevant data, the identification of creativity should take place based on tasks situated in the proximal range of the person’s expertise but exceeding his/her actual level of expertise at a time.
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Annex
Annex
1.1 The Given Task
From the figure below one can get a “fantasy box” [a.n. the box was presented “physically” by the teacher].
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I.
The first two questions constitute a group task (2 people). For this part, the group members will receive the same score.
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Write specific instructions for constructing this figure. The instructions will contain only words, no drawings, diagrams or pictures.
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Give these instructions to another person who does not know what you want to achieve. Ask that person to follow instructions. Do not interact with that person, do not give indications, or help. Note (or record) what happens. If the person has difficulty in representing the figure, or something unforeseen happens, it’s OK: this only shows that your instructions are not enough precise and should be reviewed. You will not be penalized if the first set of instructions is not quite accurate.
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Write a report as detailed as possible (but no longer than 3 pages!) about what happened;
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Write a revised instruction list and possibly repeat the experiment with another person.
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Answer the following 3 questions individually.
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What geometric properties are used in the construction of this box? Explain your answer.
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The fantasy-box has a “squared” shape ☺. How could you modify the original drawing to get boxes of other shapes? Build two new figures and make sure you can get boxes starting from the figures you indicated.
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Do the proposed figures above use other geometric properties than the ones of the original box? Explain your answer, and if it is yes, please specify which are these properties.
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3.
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Singer, F.M., Voica, C. (2017). When Mathematics Meets Real Objects: How Does Creativity Interact with Expertise in Problem Solving and Posing?. In: Leikin, R., Sriraman, B. (eds) Creativity and Giftedness. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-38840-3_6
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DOI: https://doi.org/10.1007/978-3-319-38840-3_6
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