Visualizing Mathematics

Abstract

Visualization abilities and complexity of reasoning in mathematically gifted students' collaborative solutions to a visualization task. A networked analysis. In K. S. S. Mix & M. T. Battista (Eds.), Visualizing mathematics. The role of spatial reasoning in mathematical thought (pp. 309-337). Cham, Switzerland: Springer.

Factors Affecting Success in Solving a Stand-Alone Geometrical Problem by Students aged 14 to 15

“…These visual skills are crucial for the process of SA problem solving; lacking the necessary skills, the participants were unable to find the path to the solution. These results are comparable with other researchers' findings, which also emphasise that visualisation skills are not innate but have to be learned and developed (Duval, 1999;Rellensmann et al, 2017;Sinclair et al, 2018). Although many use the saying 'Geometry is the art of reasoning well from badly drawn figures' , this ability to reason well cannot be expected from students lacking visualisation skills and the confidence in their knowledge.…”

“…All aforementioned difficulties that students experienced throughout the problem-solving process indicate that the learning and teaching of geometry should emphasise the visualisation skills (drawing, interpretation, formation of connections among different notations, etc.) (Duval, 2014;Sinclair et al, 2018) and systematic notetaking. This skillset can be learned and developed by solving geometry problems of different cognitive requirements.…”

“…The previous two decades of educational research, specifically research focused on the role of visualisation in learning and teaching mathematics, has uncovered anew the potential of visual reasoning in discovering, describing, debating, and evaluating mathematical results (Duval, 2014;Presmeg, 2006). Therefore, a new idea has gradually developed, suggesting that an overemphasis of abstract and analytical thoughts can have an adverse effect on mathematics teaching and indicating the importance of developing students' visualisation skills (Gal & Linchevski, 2010;Rellensmann et al, 2017;Sinclair et al, 2018).…”