By the way, "one-ten-two" and "three-ten-thee" is literally how the Chinese would pronounce their numbers (一十二，三十三）. In a way I think it's helped me understand place values earlier.
I think my wife and I use that teaching method quite naturally. I'm never inclined to just give our children the answer; they only learn when they arrive at the answer themselves.
Teaching my then 4yo the decimal system I dropped in some binary, in a similar way to this class - except for him we called it "robot language". He knew it from watching a few (PG!) episodes of Futurama. Hey, if Bender talks it then it's cool and that's enough to spark some interest.
I try to get him to interpret 12 as "one ten and two ones" or "one ten and two more" and say then they we just call it 12. In the same way 1100 in robot language is "one 8, one 4 and 0 twos and 0 ones".
When I'm president of the world number-names are up for reform!