Robert Hansen (RH) posted Jun 30, 2013 10:22 PM (GSC's remarks interspersed): > > On Jun 29, 2013, at 4:04 PM, Joe Niederberger > <email@example.com> wrote: > > > Logic is that which seeks to understand the "laws > of thought", independent of subject matter. So if > > we agree that the following is logical: > > I would say the "laws of proof" rather than the "laws > of thought". > Broadly, I agree with RH. Perhaps the book might have better been titled "An investigation of the Laws of Logic": the difficulty here is that many people might have been turned off by that. I suspect, also, that 'marketing concerns' might have played a part: the publisher would rightly have wanted something 'snappier'. Almost EVERYONE would be interested in the "Laws of Thought"; how many would be interested in the "Laws of Logic" or in the "Laws of Proof" ??? Thus it was (I surmise) that we got "Laws of Thought". > > Thought is based on many elements and > "logic" is just one of those elements. > Indeed. Unfortunately, in conventional circumstances, we tend not to look at all those elements in any 'integrated way' - and, in the process, 'logic' often suffers as well. We see this happening in practicall all our forums when we discuss societal issues.
For instance, in much of the 'traditional teaching process', the teacher's main concern is to discuss the topics of the curriculum. He/she is interested is in 'teaching', and only incidentally with how the student learns! (At least, that is the process as it is formally practiced [so I believe, from my personal observations]).
While the teacher certainly should pay adequate heed to the topics of the curriculum, it is equally important - possibly more important - that he/she understands (clearly and *effectively*) just how each of the students is 'imbibing' his/her lecture.
I accept that most teachers intuitively understand that (and do succeed to an extent). This is part of human nature: it cannot be driven out, regardless how much we may try to do that by way of the inadequate and utterly ineffective design of our 'systems'! (Of course, there are some 'rules' such as: "Capture the attention and interest of students", etc, etc - but these are, in the main, just rules that can be safey treated as an 'add-on').
However, it is only the 'great teacher' who adequately understand their separate students' interactions with the material being taught. I believe the schools of education do have some quite complex and complicated theories and processes to bring about such understanding. (I have read only very little about these theories). Actually, using the OPMS process, this is a very simple and natural thing to do - the 'understanding by students' is built right into the process that we refer to as the fundamental 'teaching + learning dyad'. We should NEVER think of the process as being just 'teaching'.
The 'One Page Management System' (OPMS) - a 'systems aid' to problem solving and decision making that I often discuss - can help ensure that many more teachers naturally become 'great teachers' rather than just the VERY rare exception as at present [and in the past]. Such was the case even when I was in school umpteen years ago: for instance, right through my school career, I encountered only ONE 'great teacher'; some of the teachers ranged from 'OK' to 'quite good'; the majority were not satisfactory teachers at all. The only assumption that OPMS makes is that the teacher MUST love teaching in general - and in particular teaching the specific age-groups he/she may be entrusted with. Without a passion for teaching, no teacher can be even an 'adequate' teacher. (For instance, I am most conscious that I'd never be even a minimally competent teacher of children at any level!!! However, I believe I have been a reasonably good teacher with my own children years ago and more! recently with my grandchildren - but that was because of my personal relationships with them, not because of any passion I had for teaching).
Brief information about the OPMS is provided at the attachments to my mail heading the thread "Democracy: how to achieve it?" - http://mathforum.org/kb/thread.jspa?threadID=2419536 . (In order to keep things straight, I note that Robert Hansen [and Haim] had a number of objections to the OPMS process: I claim that ALL their objections are entirely spurious). > >To say that > one "thinks logically" is to say that one applies the > rules of logic to their conclusions. Not just the > final ones, even the little ones along the way. But > the majority of "thought" is in the space between > those conclusions and it is not "logic". It is > instinct, intuition and habits of mind, for lack of > better terms. But logic plays an important role in > developing those skills. Think of logic as a harsh > environment to which your instinct, intuition and > habits of mind must evolve and adapt to. > Yes - agreed in most part. > > The statements of mathematics (its conclusions) are > logical, but mathematics itself is much much more > than just its statements. > ENTIRELY TRUE!!