One of my favourite quotes about mathematics: **“Mathematical notation no more is mathematics than musical notation is music. A page of sheet music represents a piece of music, but the notation and the music are not the same; the music itself happens when the notes on the page are sung or performed on a musical instrument. It is in its performance that the music comes alive; it exists not on the page but in our minds. The same is true for mathematics.”** — Keith Delvin

Are your students really DOING mathematics, or just working with notations on a page?

Mathematically yours,

Carollee

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Ah an interesting quote, and one that brings up some philosophical questions. I suppose my experience has led me to believe that the relationship between the language of math and the concepts themselves is extremely similar to natural language and its relationship to ideas in the real world. Certainly, there are different ways to say or write “dog” in many languages, but these are merely descriptions of a general idea or phenomenon. That leap from notation to concept I believe is the biggest hurdle. The conventions in math are merely the way we express it. Ancient Greeks expressed mathematical concepts from prime numbers to angles in terms of lengths of lines and their relationship between each other. It influenced human thought for millennia as evidenced by Euclid’s Elements. But it gets deeper, and I think that is where it gets much deeper. Is all math the manipulation of symbols in the human mind or does reality better reflect Platonism? Are well just chained in the allegorical cave? I guess that’s for another discussion đź™‚ good post.