As an educator, it is a mystery as to why some students learn the basic operations much more fluently than others. I will, however, say that some of these processes do need to be drilled in order for children to show automaticity in that skill.
My own experience with math stems from my ability to create a vivid mental picture of what the problem looks like. For some reason, because of my own internal pressure to be "good at math", I would lie in my bed, look up at the ceiling and paint the numbers and operations in my head. I would sit up and write what I remembered on a blank piece of paper to see if it was correct. I was lucky - at seven years old I realized that I tricked myself into learning something that many others had memorized.
When children need to learn something, whether it be math or spelling or the names and capitals of states and countries, they need to discover their own personal and unique way of learning. For me, it's a skill that I share with my students and feel very passionately about. When you find it, you'll never want to give that Secret of Memorization away.
Instead of focusing on the "what" focus on the "how" of learning. We'll always need to learn something new - whether it's an appliance that you just purchased or a new teacher that your child has to encounter. It's your job to help yourself learn how to commit these things to memory.
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