Yes, there are many types of “manipulatives”, and they have value as pedagogical tools, but most of them tend to be rather slow and ineffective practical tools,

Yes, there are many types of “manipulatives”, and they have value as pedagogical tools, but most of them tend to be rather slow and ineffective practical tools, unlike an abacus (of either the counting board or sliding bead varieties) which is as or more efficient than pen and paper, or a slide rule, which is more efficient.