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I'm looking for references about activities that encourage elementary school students to create or evaluate mathematical notations. do you know any?

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    $\begingroup$ I'm confused, actually. Creating notations is very different than evaluating notations. I think creating notation might be a cool activity. But evaluating? Isn't that what we always do/teach? $\endgroup$
    – Sue VanHattum
    Commented May 23, 2023 at 18:23
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    $\begingroup$ @SueVanHattum I'm not so sure. It looks reasonable, for instance, that denoting the sides of a triangle $a,b,c$ and the opposing angles $A,B,C$ is slightly better than denoting the sides $x, w_3, r'$ and the angles $U, F_8, \lambda$ respectively unless the triangle is just a small part of a big diagram and the latter notation is forced by the prevailing logic of the rest of the diagram. But do we really teach that? Of course, the verb "to evaluate" has several meanings, so, maybe, we are just using different ones. :-) $\endgroup$
    – fedja
    Commented May 24, 2023 at 3:22
  • $\begingroup$ I personally think the way we denote fractions is problematic, and would be curious what other invented notations students might create. But ... perhaps not too useful... $\endgroup$
    – Sue VanHattum
    Commented May 24, 2023 at 6:11
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    $\begingroup$ I agree with @fedja that evaluating an expression does not mean evaluating its notation. However, by "evaluating notation", I was thinking more of judging how well a system of symbols has been designed (for concision, intuitiveness, readability, universality, etc., how well it highlights interesting features, how organic/amenable it is to developing results, etc.) rather than labels per se. $\endgroup$
    – ryang
    Commented May 24, 2023 at 6:55

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