When I was in third grade, I had no choice but to memorize the multiplication facts using flash cards. My parents would practice with me at home, we would also practice at school, then I would get tested by the teacher on how well I knew them. I had to know one set before moving to the next. I remember the 8s and 9s kicking my butt. I also remember my mom giving me a little prize, like a book, after I'd mastered the harder ones.
These days I notice that public and private school kids alike don't know their facts. I remember trying to do it with Joel and failing miserably. Kids in school have a handy dandy multiplication facts table like the one below (you can print one out bigger in PDF version here). I think the reasoning is that they will learn them this way if they have to look it up over and over.
Some kids easily memorize the facts. Michael, for instance, my 9-year-old son (this was originally posted in 2012), can pop off that kind of thing from memory. I also still have them in my brain. Joel, who is 11 and struggles with it a little bit, can benefit from a table like this. It takes more thought than just using a calculator, and hopefully he will pick up the facts after looking them up for his IXL.com "test" questions daily.
How do you teach multiplication?
Updated 9/28/17 and my sons use this like crazy now for their Teaching Textbooks lessons. Now that they are 14 and 16, they are doing different things than IXL.com and Teaching Textbooks is an investment that I can spread over five kids and then sell to someone else later. It's a great and fun program. Check it out!