Communicating in Mathematics beyond Symbols

I believe generalization and abstraction are fundamental elements of mathematical expressions. While engaging with the article "Crest of the Peacock," I was captivated by the rhetorical techniques employed by the Babylonians because, rather than simply breaking down information with words, they utilized geometric properties, such as length and area, to signify unknowns. This suggests that, beyond the familiar algebraic notations we often rely on, mathematics can also be conveyed through a combination of diagrams, symbols, and verbal descriptions, enabling students to grasp concepts as effectively as those in Babylonian times. This is a demonstration of the beauty of mathematics in the recognition of patterns and abstract reasoning, whether in the usage of words, symbols and diagrams.

 The question that lingers in my mind is whether mathematics might be more accessible to us when approached through the manipulation of figures alone. It leads me to ponder why my students often struggle to piece together figures and derive meaning from them, or could these rhetorical methods, occasionally intertwined with syncopated algebra, serve as a valuable bridge to close this knowledge gap? For example, the connection between the nodes of a graph could be represented with diagrams rather than symbols, and the rate of change could be described with words and curves before applying derivatives. I recall that while teaching Pythagoras' theorem, before stating the formulae using the symbol  , I can say the square of the longest side is equal to the sum of the squares of the other two sides and diagram-wise, my students usually prefer using this method below, when practicing during the lesson.

 

From both historical and practical illustrations shown in the article, it is glaring that mathematics is not limited to symbolic algebra and that even without the aid of these symbols, generalization and abstraction can be effectively utilized to assist learners in understanding principles, reasoning logically and recognizing patterns.

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  1. MaliheSeptember 22, 2025 at 11:30 AM

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  2. MaliheSeptember 22, 2025 at 11:33 AM

    You wove together the Babylonian methods, your own teaching practice, and the broader theme of generalization and abstraction very well. I especially like how you connected Pythagoras’ theorem and your students’ preference for diagrams — it shows a clear link between historical practices and present-day pedagogy. To make your reflection even stronger, you could briefly consider how relying too much on diagrams or words might also create challenges, just as symbols sometimes do.

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