I agree with the writer(sorry, I don't keep track of the names - this board is so prolific I have trouble getting it all read) who stated that we need to teach what we use-paper/pencil and mental. I put mental at the top of the list. I memorized my facts as a child - in fact it was the worst experience of my life and I can't believe I ended up in mathematics after the humiliation and frustration of learning the facts. I didn't really understand the concept of number and work well mentally until I was an adult in a mental math workshop (Paul Trafton) when we all were doing mental math activities and then explaining how we figured things out. It was mind-expanding. I learned number tricks based on place value. I picked up strategies from the other teachers and since I've picked up slick mental math strategies from students. It was talking about computation and playing with number that helped cement it in my mind. I still mentally count on my fingers when I subtract 13-8. I literally do not have it memorized like I have 6*5 memorized, but I've been very successful getting a PhD in mathematics education and doing quite well in all the advanced math courses I've had to take. I think memorizing is important, but agree with those who say it needs to go hand-in-hand with concept building activities.