You mention Eastern Europe, are you by chance familiar with the Hejný method of math education in Czechia? Because that introduces some "math beyond mere arithmetics" concepts to the elementary school education.
Sometimes, it is possible to create a less abstract version of a more abstract thing, and thus introduce the seeds of the concept to children much younger. For example, "solve the equation 2x+1=7" is abstract, but "Peter decided to use a # symbol for a specific number, and he didn't tell us which one, but we found in his notes that # + # + 1 = 7; can you figure out which number is # ?" is simple to understand for a very young child, even if the child can only solve it by trial and error.
Sometimes, it is possible to create a less abstract version of a more abstract thing, and thus introduce the seeds of the concept to children much younger. For example, "solve the equation 2x+1=7" is abstract, but "Peter decided to use a # symbol for a specific number, and he didn't tell us which one, but we found in his notes that # + # + 1 = 7; can you figure out which number is # ?" is simple to understand for a very young child, even if the child can only solve it by trial and error.