Figural Representations on Theory of Mathematical Representations: Operational Diagram and Ways to See

บทคัดย่อ

In this article, the Theory of Mathematical Representation (Isoda, 1990) was applied to distinguish different types of pictures, drawings, and figures that can be regarded as mathematical representations, alongside algebraic and other forms of representation. To clarify the unique interpretation of written mathematical representation, Isoda defined its nature in terms of context/objective, focused symbol, and focused operation. And to explain ‘focus,’ the ways to see is explained by using Curriculum Framework to develop mathematical thinking (Isoda, Teh, Gan, 2024)). Using this framework, some figural representations can also be recognized as a form of mathematical representation when used as tools for thinking. This perspective highlights the necessity of teaching figural representations in Japanese origin mathematics textbooks (Isoda & Maitree, 2013), not merely as explanatory tools used by teachers on an ad hoc basis, but as essential thinking tools for students’ future learning.