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As it can be seen, the point is not to teach or not to teach geometry. The point is to teach geomety as mathematics and to teach mathematics as geometry. That is to see mathematics as a lively connected knowlege. This is what most curriculums and accordingly most teachers fail to do so.
First of all, consider that the title speaks itself. Separating the teaching of geometry from the teaching of mathematics (including calulus) reflects the belief of most teachers. Indeed, whatever a mathematician may say in favour of teaching geometry falls into disfavour from teachers' point of view: Geometry is problem based, each problem could have several solutions, solving most problems needs creativity (and you cannot teach creativity), geometry has a unity (that is to say its different parts are closely related to each other) and so on.
@ToddTrimble Dear Todd. The research I mentioned is an unpublished master thesis I supervised in 2009: (Leila Mansouri), The differences between the teaching of geometry and the teaching of mathematics in highschool! Unfortunatly, the result is not available in English. Thus, let me summerize the results here, hoping that it comes handy.
@BenjaminDickman Yes, and No. Yes, human-wise, No, professional-wise! I always enjoyed your answers. In this case, I shall add that I have some ideas (at least, practice-wise) about gifted education. But, I am not aware of any research on phenomenonally gifted people. Any idea in that direction is very welcomed. Best regards :)
@AakashM Maybe! But, if you had ever met a young natural talent who wasted her youth to prove Goldbach's conjecture without learning anything new on the way, then you would believe that "maybe" much more cautiously.The week before, I met such an untrained prodigious natural talent!
