I think arithmetic has a lot of merit in the teaching process, and shouldn't be dismissed. Maybe it's overemphasized, but it does have value.
Arithmetic can help show some deep mathematical concepts that might not be obvious if you study theory alone. For example, the advantages of arabic numerals over roman numerals. There are important mathematical distinctions between the two representations, but without actually using them both, it's hard to understand why arabic numerals are so much more useful for so many purposes.
I think it's best to switch between concepts and practical applications. I also don't think there is a problem with memorization. In any field, to exercise good judgement or gain deep insight, logic and reason are not enough. You need a collection of facts to guide you as well as other people's ideas to draw from.
Arithmetic can help show some deep mathematical concepts that might not be obvious if you study theory alone. For example, the advantages of arabic numerals over roman numerals. There are important mathematical distinctions between the two representations, but without actually using them both, it's hard to understand why arabic numerals are so much more useful for so many purposes.
I think it's best to switch between concepts and practical applications. I also don't think there is a problem with memorization. In any field, to exercise good judgement or gain deep insight, logic and reason are not enough. You need a collection of facts to guide you as well as other people's ideas to draw from.