Efficacy of Instructional-Based Learning (IBL) on Learners’ Geometric Spatial Cognition in South Africa: Parallel Approach to Enhancing Use of Dynamic Geometric Environments (DGES)

Spatial skills, cognition and geometry’s connection is owed to their characterisation with space and spatial orientation, consequently, the duo is seen as a tool for human cognitive development, particularly true in geometry application and cognition. Such a view is anchored on the fact that for most science, technology, and mathematics (STEM) disciples, spatial skills have primarily been used as and described as the ability to mentally or physically orient 3D objects in space. Evidence also suggests that strong spatial and geometric senses correlate positively with high achievement in STEM disciplines. On the other hand, while geometry is exclusively devoted to Euclidean geometry, which employs geometric ideas, axioms, and theorems in solving geometric-proof related problems (such as cyclic quadrilateral theorems), regardless, there are still deep rooted challenges, which contribute significantly and warrant the current research: For instance, even though the mechanism responsible for spatial skills and geometry relationship with mathematics aptitude is still unclear for a number of candidate reasons (such as but not exclusively mixed results based on gender) yet, research has evidenced that spatial skills is trainable through geometric interaction. Yet, it has also been demonstrated that solving geometric-proof related problems simultaneously requires spatial skills and a deep of not simply understanding of geometric ideas, but instructional based learning (IBL) or dynamic geometry environment such as GeoGebra. Unfortunately, limited studies on IBL this far has been employed as a pedagogical tool for teaching and learning Euclidean geometry (exclusively cyclic quadrilateral theorems), and its effect on spatial skills and geometric thinking. Consequently, the goal was to examine efficacy of IBL cyclic quadrilateral theorems on the development of learners’ spatial skills and geometric cognition. Based on the challenges and the goal, the experimental study was anchored on the conceptual frameworks of Van Hiele (1999) theory of sequential geometric understanding and Zazkis et al. (1996) visual-analysis model. Anchored on the goal too, a mixed method (qualitative and quantitative) was employed to collect data from randomly selected 50 grade 11 pure mathematics learners from one of the high schools in South Africa, analysed using independent sample t-test. While the qualitative finding was able to explain the conceptual employs geometric ideas, geometric-proof, axioms, and theorems in cyclic quadrilateral theorems, the inferential analysis demonstrated that an IBL cyclic quadrilateral theorem significantly affects grade 11 pure mathematics learners’ spatial skills and geometric thinking. The ramification thus is that the development of learners’ spatial skills and geometric cognition is best achieved through cyclic quadrilateral theorems which is acquired through IBL.