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GS Chandy
Posts:
7,942
From:
Hyderabad, Mumbai/Bangalore, India
Registered:
9/29/05


Re: Mean, Median and Mode  the threeheaded monster
Posted:
Apr 11, 2014 4:59 AM


This is in response to the posts appearing for some reason in 3 'minithreads' comprising this thread:
1) http://mathforum.org/kb/message.jspa?messageID=9372443 (8 posts) 2) http://mathforum.org/kb/message.jspa?messageID=9432449 (2 posts) 3) http://mathforum.org/kb/message.jspa?messageID=9432489 (3 posts) [It is possible I might have mixed up the 'minithreads' containing 2 and 3 posts respectively]. AND Donald Sauter's web page (Mean, Median, Mode... mean, schmedian, schmode...  http://www.donaldsauter.com/meanmedianmode.htm).
I have read Mr Sauter's web page carefully as well as all the responses (quite carefully) to the original post from Mr Sauter.
(I should confess that I needed to refresh my own understanding of 'mean, median and mode' at 'Purple Math' and Wikipedia).
A: I largely agree with Donald Sauter that most of this is not useful to the beginning student  who really needs to get the underlying concepts of arithmetic (+,, *, and /) firmly fixed and usable in his/her mind. The underlying issue for the beginning student is that he/she must do enough examples, instances and meaningful problems so that these pretty sophisticated concepts become *effectively* usable in real life. How is that to be done?  THAT is the issue!
B: I strongly agree with Robert Hansen (RH) that there is nothing like the 'raw data';. It's the teacher's huge responsibility to get the concepts *effectively into the students' minds* so that they are able to put them to use in their daily lives. Some teachers do that very successfully; many teachers do not. Which indicates that there's a lot of 'rectification' to be done with the 'teacher education system'.
C: I also take mind of Richard Strausz's somewhat cryptic (but most meaningful) instance about the costs of houses on the block where his cousin lives (more or less alongside Mr & Mrs Bill Gates).
However: After ALL of that, what I do not yet perceive is a clear answer to these quesitons:
a) WHAT specifically is the arithmetic that a beginning student should get, at various levels, in order that he/she may 'cope *effectively* with life' after school?
b) HOW specifically should the various parts of arithmetic be 'taught' (followed by beginning algebra; slightly more advanced algebra; etc, etc)??
I'm ENTIRELY in agreement with Mr Sauter's several claims in his first pargraph.
So, now, what's to be done about this fairly sorry situation?
Keep in mind that *effective* education is critical to the future of the human race (if we have a future at all) AND that early math is a critical part of education.
I don't believe we here at Mathteach have adequate answers yet to these real issues. I don't believe the 'educational system' as a whole has adequate answers.
I suggest that some 'systems modeling' based on the late John N. Warfield's contributions to systems science would help very significantly. In fact, that's the 'whole ball game' if I have the 'US expression' right.
To provide some 'light refreshment' after all that heavy lifting, here are a couple of problems that someone recently challenged me to do:
1) What is the number (say 'N') that, when the 'units digit' is put as the 'inital digit' of the number (as we write it out) becomes = to 2*N?
2) Your doctor gives you a bottle of liquid medicine with the STRICT instruction that you must take EXACTLY half a drop of the medicine three times a day. How do you manage to do this?
(I succeeded in doing No. 1 [with some trouble]; didn't succeed with No. 2).
[I am not directly involved in teaching myself  though I do conduct workshops on 'systems' for teachers].
GSC
Message was edited by: GS Chandy
Message was edited by: GS Chandy



