how does elementary education teach us to be analytical thinkers?

I'm not sure that "elementary" education needs to approach more than a bare hint of critical thinking. By definition, this is the time for building the foundation on which all other learning will take place, and whether the education establishment likes it or not, that foundation is built on memorization of facts, practice, and drill work. A recent newspaper column criticized an elementary school math book for asking questions like, "If math were a color, what color would it be?" The vehement negative reaction to silliness like this is well justified. In the name of "critical thinking," the students are being asked to philosophize about the nature of a subject they actually don't know anything about. Students taught from that book may have wonderful, creative, analytical skills, but won't be able to perform calculations. Critical thinking belongs in the curriculum, certainly. But it belongs at the point where the students have enough foundation knowledge of facts that they are in control of something to think critically about.

Based on the students that I see moving through the system and evaluating them in HS and when they get to my door in college, I would say that the primary education system fails in that regard. Students have the bearest concept of logic and analytical thinking. We're too busy with recess and extracurricular activities.