I would also agree that separating the conceptual stuff from the computation can be very helpful for some kids who are at different levels in the two. Keep working on the basic arithmetic by all means, but let her move ahead in parallel, at her own comfortable pace, with the conceptual stuff as well.
You may find, as we have have, that she actually does a lot better learning/ memorizing the basics when they are part of more substantive and complex problem solving, rather than isolated factoids. For us, for example, the best way to learn times tables was to use them incessantly in simplifying fractions and equations, and finding common multiples, divisors, prime factors, etc.
