Visualizing Algebra: Exploring a Gifted 3rd Grader's Problem-Solving Techniques for Enhanced Conceptual Understanding in Algebra Education


  • Harvinder Kaur Singh 1.School of Mathematics Education, Australian Catholic University, Melbourne, Australia. 2.Sri Dasmesh International School, Kuala Lumpur, Malaysia
  • Hazeeq Hazwan Azman Centre for Foundation and General Studies, Universiti Selangor, Selangor, Malaysia.


Algebra, Problem solving, Gifted, Visualization


This study delves into the world of mathematical giftedness by examining the problem-solving strategies of a gifted 3rd grader in the context of algebraic equations. The research highlights the student's proficiency in creating visual representations of mathematical problems, emphasizing the potential of visualization as a valuable teaching strategy. Notably, the use of diagrams and sketches as substitutes for traditional variables like  and  has been instrumental in aiding comprehension. The gifted student's unique fluency in solving equations is noteworthy, showcasing a strong grasp of underlying principles. The paper underscores the potential for a transformative shift in algebra education by introducing visual representations at an early stage, prioritizing conceptual understanding. However, it's important to acknowledge that the study's focus on a single gifted 3rd grader might limit the broader applicability of its findings to more diverse student groups. Consideration of external elements, including the student's unique background and resource constraints, could potentially influence the observed outcomes and their generalizability. While the findings suggest that the use of visual representations may offer an effective strategy for improving algebra instruction, it is important to approach these implications with caution, recognizing the need for further research and evaluation to fully understand the impact of this approach.



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