Instructional-based learning of cyclic quadrilateral theorems: Making geometric thinking visible and enhancing learners’ spatial and geometry cognitions

Abstract

Geometry learning has a long history with the connection to human cognitive development. The ability to mentally or physically orient 2D shapes or 3D objects in space is believed to support achievement in science, technology, engineering, and mathematics (STEM) disciplines. Thus, geometry by its description is characterised by space; hence its conceptualisation requires deep spatial and geometry sense which can be developed through instructional-based learning (IBL). While the current study supports the evidence of educational technology tools in support for effective teaching and learning, it explores IBL as an alternative source of enhancing learners’ spatial and geometry cognitions and making geometric thinking visible to learners in the classroom. The experimental design research applied a mixed method to collect data from randomly selected 50 Grade 11 Mathematics learners from one of the high schools in the Cetshwayo district, South Africa. Quantitative data were collected through a pre-test-post-test design and analysed using independent sample t-test whereas qualitative data were collected using content analysis and analysed using descriptive analysis. The analysis was guided by the theoretical frameworks of Van Hiele theory of levels of geometric understanding and Zazkis et al.’s visualisation-analysis model. Based on the data set collected, the review of literature, and the theoretical frameworks, the ramification is that IBL has a positive effect on learners’ spatial and geometric cognitions and makes geometry thinking visible to learners in the classroom.

Contribution: The recommendation is to explore the effect of hybrid learning design, thus the integration of IBL and dynamic geometry environments on the development of learners’ spatial and geometry cognitions.