Abstract
In traditional mathematics education, especially in multiplication, a predominant emphasis on rote memorisation and procedural learning has led to a significant gap in students’ conceptual understanding. By integrating spatial reasoning and embodiment through spatial analogies, this study explores an innovative instructional model to foster visualisation in support of mathematical abstraction, especially in the less inherently spatial aspects of multiplication concepts, to enhance conceptual understanding and problem-solving strategies.The study utilised a mixed-methods approach, involving a convergent model of triangulation design, to assess the effectiveness of the instructional model. The instructional model encompassed twenty-seven learning tasks distributed over seven lessons and was implemented with 24 Year 3 primary students in Indonesia (9- to 10-year-olds).
The quantitative analysis revealed remarkable improvements in students’ mathematical performance post-intervention. There was a noticeable enhancement of the students’ ability to correctly solve multiplication problems, with a substantial increase in the usage of visual-spatial representations, particularly schematic ones. This advancement was closely linked to better problem-solving skills. Additionally, a significant shift was observed in the students’ approach to multiplication, moving away from traditional algorithmic strategies to more conceptual methods such as the distributive property, indicative of a deeper comprehension of multiplication concepts.
Qualitative insights from the study highlighted the instrumental role of spatial analogies, like array and bar models, in aiding students to visualise and conceptualise multiplication’s structure and relationships. While stimulating spatial reasoning, these tools effectively facilitated the transition from tangible representations to abstract conceptualisation. Moreover, embodied learning activities, encompassing physical manipulation of objects and drawing spatial models, markedly reinforced conceptual understanding. This approach enabled students to bridge their physical experiences with abstract mathematical concepts, fostering active learning and engagement.
The study conclusively demonstrates that the integration of spatial reasoning and embodied learning into multiplication teaching significantly enriches students’ understanding and problem-solving capabilities. The findings have significant implications for mathematics education, advocating a shift in teaching approaches toward strategies that emphasise conceptual understanding through interactive and tangible learning experiences. This research provides valuable insights for curriculum development and teacher training, promoting more effective and engaging mathematics teaching approaches.
Despite its effectiveness, the focus of the current study on a specific student group and the absence of long-term retention data highlight limitations in its generalisability and sustained impact. Future studies should explore broader applications and long-term effects to enhance the effectiveness of the learning model in diverse educational contexts.
| Date of Award | 2025 |
|---|---|
| Original language | English |
| Supervisor | Sitti PATAHUDDIN (Supervisor), Tracy LOGAN (Supervisor) & Tom Lowrie (Supervisor) |