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Given that mathematics is not about number, and that it is not even about the cryptic notation used to describe mathematical problems, how much of mathematics could be taught without reference to mathematical notations?

When I ask "how much", I'm thinking of the progression in which mathematics is taught to children. Could you actually teach the patterns and concepts of mathematics up to university entrance level?

I realize that mathematical notation is an essential tool for communicating mathematical ideas, however it is a rather cryptic and convoluted way of talking about things, and one in which similar things do not necessarily use similar names and notations. As a result, the language can be a barrier to understanding for many people.

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  • $\begingroup$ I don't think this is really an appropriate question for MathOverflow. It probably be better for somewhere like sci.math. See the FAQ mathoverflow.net/faq#whatnot $\endgroup$
    – Ben Webster ♦
    Commented Nov 3, 2009 at 15:00
  • $\begingroup$ This does not seem to go against the FAQ section on what not to ask. Why did you close this? Shouldn't you have at least waited to see what others think of the question before closing it? $\endgroup$
    – Michael Dillon
    Commented Nov 3, 2009 at 15:24
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    $\begingroup$ I think Ben is saying this is more a "discussion" question, although if you rephrase it you can make it more appropriate: something like "what's an example a curriculum that can be taught at an elementary level without numbers?" so that there are specific answers. For example, the Davydov curriculum in Russia begins teaching mathematics without counting: maa.org/devlin/devlin_01_09.html $\endgroup$
    – Jason Dyer
    Commented Nov 3, 2009 at 15:45
  • $\begingroup$ I'm definitely with Ben here: off topic, more suitable elsewhere. No one can, even in principle, give a definitive answer, and you're not asking for a sorted list of resources, so it's out. $\endgroup$
    – Kim Morrison
    Commented Nov 3, 2009 at 18:15

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