Abstract

The study aims to define the processes of pre-service mathematics teachers in reaching spatial visualisation generalisations within the context of drawing surface nets of solids. Two theories, Polya’s problem-solving steps and novice-to-expert problem-solving schemas, were used as reference frameworks to describe the participants' spatial visualisation generalisation processes. The research methodology employed in this study was a qualitative theory-testing case study design, in which hypotheses based on those two theories were generated and tested. The sample consisted of 44 participants who completed low- and high-complexity spatial visualisation drawing tasks and attended task-based interviews. The findings obtained by qualitative data and verified with quantitative data revealed participants’ problem-solving processes involved a series of steps, including the creation of a mental representation of the problem situation (comprehending the configuration and the requirements of the task), devising an appropriate strategy to unfold the surface of the solid, implementing the strategy enabling to draw one of the nets of the solid, and finally evaluating the accuracy of the net drawing representing the opened surface of the solid. The participants’ three developmental spatial visualisation stages (novice, competent, and expert) were identified based on their spatial visualisation problem-solving performances in low- and high-complexity tasks.

Keywords

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References

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