While re-asserting my claims that Robert Hansen (RH) has systematically been wrongly crediting some Germanic 'Kahn' or the other for the works of the proud Pathan 'Salman Khan' and the 'Khan Academy' in the teaching of ALGEBRA (thereby causing Mr Khan some degree of ANGST), I believe that RH is in essence correct in his statement (at his post dt.Aug 27, 2013 10:33 PM - http://mathforum.org/kb/message.jspa?messageID=9236330) to this effect: >> >> Algebra is not about predicting and measuring. It is >> about symbolic reasoning, period. These "busy work" >> examples are no substitute for building symbolic >> reasoning. I am open to an amount of operational >> stuff in the class. But not to the point where there >> isn't any symbolic reasoning left. I think my rule of >> thumb where 25% of the class can be operational while >> the other 75% should be symbolic reasoning is a >> pretty fair and decent standard. >> True.
RH's 'rule of thumb' of 25% 'operational' Vs. 75% 'symbolic reasoning' seems to be more or less valid. (But this ratio already contains a major difficulty, which I touch on below).
I don't know that Dan Meyer is doing it all wrong (as RH claims he is) or that Salman Khan is doing it all correct and perfectly A-OK - but I do believe that in general RH is correct in his claim that "algebra is symbolic reasoning": in any case, that is the impression I've always had.
Underlying questions, to my mind, are: +++++++ Why do so many school students not 'get' algebra at all?
How many out of each hundred? I don't know - but from my memories of school I believe it is quite a sizable number. +++++++
The issues to be resolved in the case of algebra lie in the questions: ++++++ How to help the student build his/her skills to reason symbolically (algebraically)? (I believe it is possible to enable *most* students to do this - at least a great many more than the educational system is currently succeeding with).
Is it possible to do this for *most* students - or is this something beyond the abilities of *most* students? (I believe this is NOT beyond the capabilities of *most* students). ++++++
I believe that the 'math educational system' does need to find out WHY so many students fail to understand how to reason symbolically - and then to create practical means to overcome this grave deficiency in the process of teaching a very important part of math - in fact, I claim this should be considered a part of 'general critical reasoning'.
I believe that this may be the problem what Dan Meyer is trying to 'fix'. He may not yet have 'resolved' that problem. Is he on the right track? I do not know: RH claims he is not.
But neither has Salman Khan resolved that problem! The problem Salman Khan has resolved is something else entirely!
Salman Khan has, I believe, more or less satisfactorily resolved the issue of how to help students improve their proficiency who already 'get the underlying idea of algebra'. (This is my understanding, from only a very cursory glance at the Khan Academy works).
Salman Khan has not found out how to help students who do not at all 'get the idea of algebra' to resolve that very serious difficulty.
I believe that the answer goes back a considerable way - in that many students are turned off math right to begin with: they have been turned off LONG before they ever got to 'algebra'! That ratio of 25% operational to 75% symbolic (mentioned below) is of little use to students who have already been totally turned off the whole idea of math (as difficult/ boring/ fearsome/ loathsome).
THAT is the real problem the 'math educational system' has to learn to fix (or otherwise resolve) - and it doesn't seem to have the slightest clue of how to go about doing it.
Robert Hansen may like to observe that I am NOT accusing teachers of making students fear/loathe math (though they may play some part in this sad scenario): I AM accusing the entire 'math educational system' of doing that.
I don't know if RH will be able to understand the distinction between what he has been suggesting I claim and what I actually do claim. The underlying difficulty is, RH has this habit of *arguing from falsehoods*, so one does not really know how seriously any of his statements should be taken.
*Here are a couple of RH's false arguments that I've encountered:
1. OPMS is just petty list-making (words/ideas to that effect).
2. GSC accuses teachers of making students fear or loathe math.