Wayne Bishop postedMar 25, 2013 10:10 PM: > > Failure to understand the exponential function > primarily due to poor > preparation prior to that. > > W Bishop > Well, that's true enough, but not adequately helpful (I believe) for the student-teacher's expressed needs.
In order properly to arrive at an adequate 'system understanding' of why 'learners' may fail "to understand the exponential function", we would need to investigate the 'contributory factors' for stated "poor preparation prior to that".
Why do learners fail to understand the 'exponential function'?
Usually (in no particular order):
- -- Because they have been inadequately taught (i.e., 'prepared') about the exponential function;
- -- Because their preparation did not expose them to sufficient number of meaningful examples and instances of the exponential function in such a way as to enable them to understand its importance;
- -- Because the 'teachers' did not themselves properly understand the exponential function in all;
- -- Because the 'teachers' taught the 'learners' the 'exponential function' purely as a theoretic math construct;
- -- Because the examples provided were not 'directly meaningful' in terms of the learner's own background and experience;
- -- Because of lack of effective exploration of the background and theory of the exponential function, properly related to the student's personal background;
- -- etc, etc, etc.
Yes, all of the above do fall under the rubric of 'inadequate preparation', but these factors above-named do try to go a step or so further, in order to suggest to the 'teacher' what he/she might do to rectify some of the defects of his/her teaching of the exponential function. (Above is a very cursory explanation indeed. A professional teacher would do much better than I've been able to).