Investigating the use of spatial reasoning strategies in geometric problem solving

Abstract

A core aim of contemporary science, technology, engineering, and mathematics (STEM) education is the development of robust problem-solving skills. This can be achieved by fostering both discipline knowledge expertise and general cognitive abilities associated with problem solving. One of the most important cognitive abilities in STEM education is spatial ability however understandings of how students use this ability in practice are currently underdeveloped. Therefore, this study aimed to investigate how levels of spatial ability impacted both performance and approaches to problem solving. In the context of graphical education, selected due to its significant overlap with technological, mathematical and engineering knowledge, a repeated cross-sectional study design was implemented to gather longitudinal data of student approaches to problem solving. A battery of psychometric tests of spatial ability was administered to two cohorts and problem solving was examined through a variety of graphical problems. The findings illustrate a relationship between attaining higher levels of spatial ability and performance. Participants with lower levels of spatial ability evidenced the utilisation of models to a greater extend with a particular emphasis on models with the capacity to alleviate the need for spatial reasoning.

Survey on Individual Differences in Visualization

“…Though there is no consensus on precisely which mental abilities are encompassed by this general term, commonly referenced components include spatial orientation, spatial location memory, targeting, spatial visualization, disembedding and spatial perception (for further detail on these concepts, please see [Kim00]). Individuals with high spatial ability tend to excel in scientific and engineering fields [WLB09] and exhibit stronger problem‐solving skills for various tasks [WHA*02, CKT16, SDL*18], including solving mathematical [YLM18] and geometric problems [BSC19]. Some commonly used tests for spatial ability include the paper folding test [EDH76] and mental rotation test [VK78].…”

Skill Levels on Visualization and Spatial Reasoning in Pre-service Primary Teachers

“…According to Gorgorió (1998), in order to solve a spatial task, it is possible to follow a kind of strategy that is not grounded on visual objects and processes. Participants with lower levels of spatial capacity tend to use models allowing them to avoid spatial reasoning (Buckley, Seery, and Canty, 2019). In the analysis performed on the configurations, all the configurations obtained are visual configurations (Godino et al, 2012) and it has been observed, through their cognitive configurations, how the students have mostly used visual arguments when solving the tasks proposed.…”

“…From a more interdisciplinary point of view, spatial ability has been shown to correlate with academic performance in multiple areas -including other domains in mathematics, as has been said-and postulated as one of the most important cognitive abilities in STEM education (Lubinski, 2010;Rafi, Anuar, Samad, Hayati, & Mahadzir, 2005;Verdine, Golinkoff, Hirsh-Pasek, & Newcombe, 2014). However, a deeper understanding of how students use this ability in practice is still necessary (Buckley, Seery, & Canty, 2019).…”

“…Our particular interest lies in research related to teacher training in visualization and spatial reasoning (VSR), specifically in pre-service teachers. Several studies have addressed problems of this group as representation of three-dimensional objects (Gaulin, 1985;Malara, 1998), acquisition of basic concepts of geometry (Hershkowitz, 1989;Tatsis & Moutsios-Rentzos, 2013), concept of symmetry (Son, 2006), identification and classification of solids (Guillén, 2005), development of three-dimensional solids (Cohen, 2003), or problem-solving strategies in relation to levels of spatial ability (Buckley, Seery, & Canty, 2019). Other studies have focused on the mathematical specialized knowledge (Hill, Ball, & Schilling, 2008) on the specific content of visualization (Godino, Gonzato, Contreras, Estepa, & Díaz-Batanero, 2016;Gonzato, 2014;Miragliotta & Baccaglini-Frank, 2017).…”

Enhancing 3-D Spatial Skills of Engineering Students Using Augmented Reality

“…Spatial ability or visuo-spatial ability is the capacity to comprehend, reason and remember the spatial relations among objects or space 1 . It is of value for the success in engineering and other technical fields.…”