Grade-school elementary algebra presented in an abstract-algebra style?

It is a parody, but "Mathematics Made Difficult" by Carl Linderholm is this, using concepts from category theory in order to explain things like "counting" and "subtraction". The presentation is not strictly correct in terms of the mathematical concepts being wielded, so it's not a great source to actually learn about category theory or elementary arithmetic. People who do know about those things may appreciate the humor.


Hardly "requires no prior knowledge," but:

Klein, Felix, M. Menghini, and G. Schubring. Elementary mathematics from a higher standpoint. Berlin/Heidelberg: Springer, 2016. Springer link.

         


You might ask Mark Sapir. I understand he had a series of lessons on words in semigroups with a 4th grade audience in mind. (I don't know which country.) He might know of similar efforts.

Gerhard "For Me , It Was Latin" Paseman, 2019.05.21.

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