When we start a lot of things are interrelated and unless you a bare minimum is committed to memory, it's difficult to start.
It is akin to learning a language where one need to cram the basics building blocks i.e. words and grammar rules before applying them. I think idea of trying to understand before remembering ends up impairing learning at least in my case.
I have a two year old and I see this process in action. She will first cram things like counting and then start attaching meaning to it slowly.
When it comes to addition however, any attempt to learn addition by tabulation and memory would clearly be futile.
I certainly don't mean to suggest that one should study a theorem in a particular corner of mathematics from fundamentals up; rather understand it "one level down", to something previously interned in a similar manner (and since forgotten because one no longer had need of it) or to somemething axiomatic.
For example, say I come across an equation for the area of a right triangle for the first time. I've previously understood and accepted some other problem that I can reduce it to - area of a rectangle, say, or integration - so I can do so and actually understand why, and be able to reproduce it. Easier to learn, recall, and apply than rote memorisation in my opinion.
I suppose people's methods differ, but personally I don't think I could have an effective memory without understanding, and that my memory follows understanding.
By "effective memory", I mean that I could actually apply some definition, not merely remember the pattern of notation on the page. I fancy if I learnt it from a flash card I'd struggle when variables were named differently, or with the slightest variation in form.