Yes, today they seem to spend an aeon getting through the table up to, possibly, 12. Do it quickly when young and kids won't forget. I did it myself with my daughter - don't rely on schools.
Turning logs into dates is an interesting mnemonic technique - you must have a lot of spare mental energy! You're a biologist, is that right? What field?
A local fellow I know had a math teacher who was paying attention. The math teacher noticed that this guy had an easy time with multiplication tables and so he made him memorize them up to 50x50! I wish I'd had a teacher who had pushed me like that!
I don't know about spare mental energy... it's more like I'm prone to distractions. My family just thinks it's funny that I'm distracted by math!
I started off wanting to be a desert ecologist, so I went to work with a big-name desert ecologist and discovered that digging ditches in the hot desert sun was not going to work for me. After that I went into lab work, and gradually made my way from evolutionary biology to microbial genetics. The most exciting thing I did was probably working in a Biosafety Level 3 facility with things like Western Equine Encephalitis. Now I teach at a community college. It's not as dangerous, but seeing the students make connections is in some ways more exciting than making connections myself!