Evolution of Pre-Service Mathematics Teachers’ Spatial Visualisation Skills During a Cognitive Load Theory-Based Education

Abstract

This study explores how pre-service mathematics teachers’ spatial visualisation skills evolved during a Cognitive Load Theory (CLT) based education. The study used the qualitative theory-testing case study method, which guided the identification of participants, the design of technology-supported education, and the data collection and analysis process. The four participants meeting specific criteria were selected as the study sample. A CLT-based education equipped with technology was provided to help participants overcome difficulties in spatial visualisation problems, improve their existing schemas, and build higher-order schemas. Various teaching approaches (e.g., worked examples) were applied to optimise participants’ learning in CLT-based education. The study data (e.g., transcripts of interviews) were analysed using the pattern-matching technique, in which the observed patterns were compared with the derived hypotheses from the theoretic models regarding the problem-solving process and novice-expert schemas. The study achieved remarkable results: In CLT-based education, where teaching approaches have an important role, the improvement in their spatial visualisation skills happened as the participants overcame their challenges in problem-solving steps throughout their cyclic problem-solving processes and gained more knowledge and skills. The participants’ acquisition of expertise in spatial visualisation skills went through various developmental stages. They strengthened their initial spatial problem-solving schemas by completing the deficiencies in their prior knowledge. They gained practicality in same-category tasks and constructed higher-order problem-solving schemas when dealing with high-category tasks by activating their assimilation and adaptation processes. Keywords: Cognitive Load Theory, the development of spatial visualisation skills, theory-testing method, acquiring an expert spatial problem-solving schema

Introduction to the Geometrical Objects and Axioms: Conceptual, Didactical and Historical Considerations

“…It represents the first and fundamental step which progressively led to a formalized language for mathematics. For the students to acquire a satisfactory view of geometry and of the other mathematical abstractions, we consider it crucial that they are introduced to this discipline through two historical-methodological lessons (for the importance of the history of mathematics in an educative context, see, e.g., Bussotti 2012Bussotti , 2013Bussotti , 2017Bussotti , 2021 With regard to the methodological aspects of mathematics education, see e.g., Mudaly & Mpofu 2019, Ersoy & Drağyar 2022, Kurban 2024, whose development has been described here.…”