Robert Hansen (RH) posted Aug 24, 2013 3:57 AM, http://mathforum.org/kb/message.jspa?messageID=9231571: > > This is not rat-sense or log-sense. Order of > magnitude just works, it is very concrete, it is > convenient, it is syntactical and is easily shared. > (Words or phrases enclosed within stars (*...*) contain some meaning which is based on - but which is somewhat deeper than - the meaning available in the conventional dictionary. Such meaning may not be readily accessible to those who propound the naive belief that the 'Holy Grail' of management is encompassed in PERT Charts or in the relationship "PRECEDES" within 'systems').
> very concrete, convenient, syntactical > and (are) easily shared
- but I observe that Joe Niederberger (JN) had NOT claimed that it WAS "rat-sense or log-sense" ('existentially', so to speak). As evidence, I quote JN's post launching the thread (dt. Aug 23, 2013 10:37 PM, http://mathforum.org/kb/message.jspa?messageID=9231062), in which he had clearly stated: > >>"Related to the talk about "Rat-sense", estimation, and such, but logs certainly deserve their own topic. In my estimation, log sense can be strengthened and developed long before it is formalized in arithmetic".
(All of which is entirely different from the claims made by RH).
(Specifically, the suggestion is that "log sense can be strengthened and developed long before it is formalized in arithmetic" [or via algebra, for that matter]).
In any case, I do believe Philip Ball's column provides plenty of excellent food for thought - and it fully justifies his suggestion: >>> "The tendency of 'uneducated' people to compress the number scale for big numbers is actually an admirable way of measuring the world, ..."
I am aware that not all here will agree with the following statement (or the implications of the statement) in the article: > >>>That's why a new claim that logarithmic mapping of numbers is the natural, intuitive scheme for humans rings true. Stanislas Dehaene of the Federative Institute of Research in Gif-sur-Yvette, France, and his co-workers report in Science1 that both adults and children of an Amazonian tribe called the Mundurucu, who have had almost no exposure to the linear counting scale of the industrialized world, judge magnitudes on a logarithmic basis. > But these are just claims that Stanislas Dehaene is making: 'proof', if any can be brought about, is still far away.
As suggested above, this 'is not proof' (in any existential sense) of something that we can claim IS 'log sense' in children (and other 'primitive folk') - but it does suggest that 'log sense' may well be more deeply ingrained in us than we readily imagine or understand per the best available theories.
(By and large, the 'best available theories of learning (and teaching)' are by no means written in stone yet. We (human beings/science) are still just about starting to understand what 'thinking' really may be.
(To the best of my knowledge, Maria Montessori had made some seminal advances late in the 19th or early 20th centuries - upon which we have unfortunately not built adequately. Doubtless there have been advances - and some serious regressions, such as the 'behaviorism movement and its derivatives' - but we do need to admit that we do not yet know everything [notwithstanding some of us who like to pretend they do].
(In this context, Shakespeare had given Hamlet some profound ideas to speak: "There are more things in heaven and earth, Horatio, /Than are dreamt of in your philosophy. - Hamlet (1.5.166-7), Hamlet to Horatio).
In any case, irrespective of any 'log sense ingrained in us' which I agree may need to be proved more rigorously, what IS ingrained in every 'normal' child is the 'propensity to learn' (anything that the child can be convinced would be useful) - see below. > > Again, if this was truly related to logarithms then > why do students suck at them (logarithms) when they > get to algebra? > My claim: Students often "suck at them (logarithms)" precisely because the education system sucks at teaching them (logarithms) - and even at enabling whatever 'natural sense' that we may have about them (logarithms) and, indeed, whatever 'natural sense' that we may have about learning itself! (I am NOT denying that many teachers do teach very well indeed - that occurs because they intuitively use the child's ingrained 'propensity to learn'). > >They are good at other things and > don't all of sudden suck at them later on. > Possibly because none of those things is treated in schools as 'damagingly' as is math?
Math is, after all, THE subject ('par excellence' so to speak) that the great majority of students learn to fear and/or loathe by the time they leave school. > > Which > brings to mind, instead of fantasizing about a sense > that children do not have, fix the real problem > instead. Teach students logarithms in algebra. > Why do we not just:
"Teach students math *effectively* (including algebra, logarithms in algebra, geometry, etc, etc)" ??? > > I am positive that the reason these "Chariots of the > Gods" fantasies see the light of day isn't that the > have a modicum of truth. The last 50 years are full > of failed attempts to pre-charge students up for > algebra. The reason is simply that these fantasies > are more salable than saying the truth which is > "There is no secret." > I entirely agree that there is no "Chariots of the Gods" secret behind children learning (or not learning) math ideas and concepts such as algebra, logarithms, etc.
(More or less) the ONLY needed 'secret' (which every mother knows right when her child is born and brought to her to hold) is:
"My child needs ENCOURAGEMENT (not PUSHING) to learn practically all the things it needs to learn in life" > > This goes under the chapter "Ants doing Trig" > You think so? I believe not.
It goes under the chapter "How Children ACTUALLY Learn". Check out the attached document "How a Child Learns".
Subheading: "Children don't need to be PUSHED to learn (unless the parents/teachers have already screwed up their minds by PUSHING and not ENCOURAGING!)"
GSC (Still Shoveling! Not PUSHING!") > > On Aug 23, 2013, at 1:07 PM, Joe Niederberger > <email@example.com> wrote: > > > Ever heard the expression, "like a lump on a log"? > (A favorite of certain old nuns...) Well I represent > that! > > > > Related to the talk about "Rat-sense", estimation, > and such, but logs certainly deserve their own topic. > In my estimation, log sense can be strengthened and > developed long before it is formalized in arithmetic. > > > > > http://www.nature.com/news/2008/080529/full/news.2008. > 866.html > > > > Cheers, > > Joe N