The purpose of the study is to perform a less-dimensional thorough visualization process for the purpose of determining the images of the students on the concept of angle. The Ward clustering analysis combined with Self-Organizing Neural Network Map (SOM) has been used for the dimension process. The Conceptual Understanding Tool, which consisted…

This article presents results of a research study. Sixty-one first graders' responses to interview questions about negative integer values and order and directed magnitudes were examined to characterize the students' mental models. The models reveal that initially, students overrelied on various combinations of whole-number principles as…

This article explores the inter-relationship between the embodied processes of pattern generalisation and the visualisation of pictorial cues. A research framework is established for analysing pupils' multiple visualisations of figural cues in the context of pattern generalisation. The research framework centres on a novel combination of three…

Immersive 3D worlds can be designed to effectively engage students in peer-to-peer collaborative learning activities, supported by scientific visualization, to help with understanding complex concepts associated with learning science, technology, engineering, and mathematics (STEM). Previous research studies have shown STEM learning benefits…

This article argues for a shift in how researchers discuss and examine students' uses of representations during their calculus problem solving. An extension of Zazkis, Dubinsky, and Dautermann's (1996) Visualization/Analysis-framework to include physical modes of reasoning is proposed. An example that details how transitions between visual,…

Continuity of functions appears throughout the grades in South African high school (FET (further education and training)) topics as prescribed by the final draft of the Curriculum and Assessment Policy Statement. This article reports on the use of a combined framework of APOS (action-process-object-schema) and DCT (dual coding theories) to analyze…

Contemporary trends in education reflect a shift from traditional teacher-centered approaches to more student-centered approaches to learning. Empowering students in their own learning is facilitated by teaching them effective meaning-making strategies that support active participation in their own learning. Making this happen requires using…