I was trained in CGI when I taught kinder. I learned a lot and changed the way I taught math. I didn't do it exactly the way we were taught - I altered it to fit my style of teaching and my students. My kinders were able to multiply and divide (didn't call it that though). An example: When we studied the farm, I would ask something like "There are three cows on the farm. How many cow legs are there?" Students could choose how to figure it out, but most of them drew pictures. For division I would say something like "There are eight chicken wings. How many chickens are there?" And they might have drawn too many chickens, but then would go back and count eight wings, cross off the extra chickens, and count how many were left. We also used the calendar to count on and count back. Example: "Today is the 11th. We have a field trip on the 24th. How many days until our field trip?" And the students would count the calendar squares until they got to the 24th. Math was so much easier for them when there were word problems. It made sense to them. After practicing with word problems, presenting the problems as math problems like 4+3=? was a lot easier for them. By the end of the year, I would give them problems like 27 minus 9 and they'd be able to count back (using their fingers) to get the answer.

Blue, you've got the idea. It is basically teachers making a decision about student's learning based on how that student thinks about math. It really is the concept that is focused on rather than the procedure.