Why are manipulatives (how about "real life objects") considered lower-level thinking? You got me to actually look up what manipulatives are, I think they should stay in the classroom all the way until high school (and into college). Students would probably end up with much stronger imagination skill (and how else would someone strengthen thier imagination?
Most calculus TEXTBOOKS introduce the derivative with a formal definition of speed. I can't think of a single person who would call that approach "lower-level thinking".
In fact, the "battle" you described continues into college:
Some physics professors deny the existence of the centrifugal force, and insist that there is only a "centripetal" force. Which is true...sort of. The funny thing is, approaches like the one I just described at the college level end up actually being an insult to (underestimation of) students' intelligence. Whoever teaches introductory physics assumes that those kids are too stupid to understand the idea of accellerating reference frames (if you are driving around a bend, you are in an accellerating reference frame, your speed in any set direction is changing. Yet, within this reference frame, you feel pulled OUTWARD (centrifugal force), not inward, or straight ahead) If the teacher could just take time to introduce the accellerating reference frame, people would not have to defy thier senses by telling themselves that they had just been experiencing a 'fictitious force'.
My conjecture is that real-life objects are classified as lower level thinking because a lot of N's (who are the majority of curriculum/test developers) didn't need them a whole lot, i.e., my INFP son saying "Why do I have to move around pieces of pizza if I can see them in my head?" Most are banned from test situations so teachers want kids off using Cuisinairre rods, color tiles, fraction circles, counting blocks, etc., as soon as possible. Once you watch films of students who develop deep understanding while using this stuff--and how they sometimes have to try it a bunch of different ways before they're convinced they've got it, which we seldom allow for--you realize how this teaching norm can hose them.
As far as high-level and low-level...one university changed its physics class sequence so the first 2 for engineering were more practical/lab oriented and less theoretical-see-it-in-your head stuff and equalized the graduation rate between S and N students whereas before the S's were dropping out. I've seen the same thing in calc classes. There's this bias that you should be able to see the stuff in your head if you're really smart...
A note to members: this "typist" shit will not fly here. We have rules against insulting members that we enforce in order to be able to discuss things openly and maintain a community where people feel welcome and accepted and are encouraged to post. Veiled attacks against certain types won't be tolerated here. There are ways to say things, and there are ways to say things.
A note to members:We have rules against insulting members that we enforce in order to be able to discuss things openly and maintain a community where people feel welcome and accepted and are encouraged to post.
You forgot to mention that the rules defeat themselves.