I know exactly what you mean about words not 'looking' right. I think the more 'successful' students become with numeracy, the more their confidence increases and the same thing happens when the answer to a given problem just does not 'look/feel'' right. Again, it's hard to explain as this ability has become so automatic to me.
yes the memory still haunts me but from that experience i certainly remember them. whilst learning the times tables in groups we could learn from each other aswel.
in regards to my own area of music we have a saying for the cirlce of fourths and fifths, 'father charles goes down and ends battle and in reverse 'battle ends and down goes charles father' this is something i learnt over and over again and have continued to use it with my own learners in music theory sessions.
Repetition within learning can become boring but from experience it sure does stay with you.
It is one of those activities we all have early memories of. I am not sure for learning basic times tables there are many other effective ways execpt to do the sums everyday until you can mentally, recall the answers.
Apart from this case parrot fashion learning is likely to have as many resistors as followers. I am a great believer that even if what to be learned is repetitive and/or sequentially linked, learning should be linked to something real. In engineering, students have to learn about percentages of carbon and other elements for a variety of steels. They could learn them parrot fashion, but having a wider understanding of how each element effects an alloy mixture will help them build core knowledge to make a pre-conditioned prediction rather than abstract memory recall.
As Piaget reminds us .. linking together facts helps many of us expand schemas.