"Algebraic reasoning" in this context is a (AFAIK) sort of fuzzily defined thing, but it's a reference to generalized algebra- of which the "algebra" high-schoo

"Algebraic reasoning" in this context is a (AFAIK) sort of fuzzily defined thing, but it's a reference to generalized algebra- of which the "algebra" high-school students encounter is a specialized part. Arithmetical expressions like you describe aren't what is meant there.