Abstract
We apply theoretical tools from the onto-semiotic approach to present skill levels on tasks requiring visualization and spatial reasoning. These scales are derived from the analysis of visualization and spatial reasoning skills involved in solving a questionnaire supplied to 400 pre-service primary teachers. In order to set skill levels, we describe different types of cognitive configurations considering the network of mathematical objects involved in solving the items. The results show that there may be several configurations at each level and the levels depend on both certain conditions of the task and the visualization skills required. In most cases, the ratio of students expressing high level is significantly below than those of exhibiting low level. The analysis manifests that students put into play variety and quantity of visual objects and processes; however, most did not reach the solution successfully. This leads to the need for specific training actions.
Highlights
According to Cunningham (1991) the reinstatement of the visual and intuitive side to mathematics, started decades ago, opens up new opportunities for mathematical work
We present each one of the seven items that make up the questionnaire and includes a schematic description of the different cognitive configurations detected for each item
In this study we have applied the notion of cognitive configuration, through the onto-semiotic approach to mathematical knowledge (OSA), to describe and interpret student responses to tasks requiring visualization and spatial reasoning in terms of geometrical objects which are involved in their resolution, in order to establish a type of scale on VSR
Summary
According to Cunningham (1991) the reinstatement of the visual and intuitive side to mathematics, started decades ago, opens up new opportunities for mathematical work. This leads us to think that the teaching of visualization involves learning new pedagogical skills and that we must understand mathematics and learn to communicate our mathematics visually. In the field of Mathematics Education, the works by Battista (2007), Blanco (2013), Clements (2014), Gutiérrez (1996, 1998), Mix and Battista (2018), Nemirovsky and Noble (1997), Phillips, Norris, and Macnab (2010), Presmeg (2006, 2008), and Rivera (2011) provide us with a tour of the state of affairs in visualization research
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