The first point that made me stop was that the core mathematical idea can remain the same even when the notation are different. The Babylonians did not use modern symbols such as x,y, or x^2, but they could still solve equations by using words such as “length,” “breadth,” and “area.” Their methods for solving linear and quadratic equations were very alike to the methods we use today. So, mathematical symbols can be convenient or not, and we can also discuss whether a number system or notation is well designed. However, no matter which notation we use, it should serve the same mathematical logic.
That inspires me the way students learn mathematics now. I think students should also begin by focusing on the principle, instead of paying too much attention to mathematical symbols at the beginning. In my own teaching, I can use more words at first and let students explain what the quantities and relationships mean. After they have a general understanding, I can introduce the corresponding mathematical notation. This does not mean that symbols are not important. Standard notation is necessary because it makes mathematical ideas clearer and easier to communicate. However, if students only memorize symbols and procedures without understanding the meaning behind them, they may not really understand the mathematics.
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