Rote Learning Vis-à-vis Physical Comprehension

#15 Posted by iron_mask:

"we can see the significance of this wrt to a the number lines! "

Perhaps. But I find it very difficult to understand "negative numbers" and therefore by extension the number line. Perhaps, one can try to understand it as "negation"(as used in logic). If so then we can 'understand' what -(3/2) is. As such we can use "equivalence" to understand what 3/(-2) is. But on its own 3/(-2) is a difficult concept. I, at least, won't be able to explain it to my daughter.

#15 Posted by iron_mask:

Iron:

At the apex (of the tent map) we have non-differentiability not dis-continuity. But your example of the curvature as an approximation is very nice indeed. As the approximation becomes sharper and sharper what do we get:

We get differentiability at the limit! But in truth at the apex we have non-differentiability.

Excellent example!

Masada Complex you are a sorry case of a man.

You give the mentally disabled people a bad name.

You stink.

Get lost.

Re: # 12

This is a problem which many face. If we start of with a gradient

Grad= (y1-y2)/(x1-x2)

if it is a straight line it is a constant. If it it is tent like function (couldnot resist the temptation GT!), then the magnitude of Grad remains the same, there is a sign change as we cross the apex (ofcourse assuming the tent is symmetric).

Now add a cruvature to the apex - thus is it no longer a point but a gradual change (note - above I have not considered the fact that the apex is a point of discontinuity). You will find that Grad is no longer a constant as we approach the top. AS we approach the top we have to take smaller and smaller steps (i.e (x1-x2) approaches epsilon) only then will we get an accurate measure / value for Grad. (we get a series of tangents). Again this would be syymetric. The problems becomes even more accute if instead of a smooth quadratic type curve at the apex we change it to a higher-order polynomial. At this point, how small should epsilon be becomes the question - indeed Grad might have to take on instantaneous values. In a way dy/dx is like that - an instanteneuous value. This is more clearly understood if we take velocity into consideration - where we can talk of instantaneuous velocity (not speed). dS/dt is a vector (note the above on sign changes), it provides us with information on speed and direction. If distance travelled is a staright line we get one value. If distance travelled is plooted against time and its a curve you get speed (if we are not interested in direction) but just magnitude, velocity (speed and direction (this need not be direction of travel but could be normal to it)), and acceleration as well!.

You say

1. We do not quite understand what 3/(-2) means. Yet we may use it as a 'step' to 'solve' a simple linear equation whose solution we understand quite well.

Clearly if we reqrite this as
(3-0)/0-2)
we can see the significance of this wrt to a the number lines! Am I wrong?

for your (2) see the instantaneous thing above - dx=x1-x2 = epsilon (epsilon small but greater than zero.)

who knows.....god knows!

#5 Posted by masadi

Asadi sahib:

Aap bohot gusse mein ho. I think you are pissed with Gill sahib for the wrong reasons. Even if the reasons were to be true they do not merit so much of anger. If you were to calm down (after all chowk is just a chowk), and communicate with Gill, both Gill and you could have good discussions from which many of us can learn some.

#4 Posted by khurram:

Kurram sahib,

You do not forget do you? :) But you should go a bit easy on khuram. There are several mathematecians with only one degree of separation from khuram. These are the ones who find it very difficult to accept the application of Zorn's Lemma (and hence the Axiom of Choice) in proofs.

Dear Gill,

It was a very nice read. Limiting approximations are actually quite difficult to fathom. Hence I, like you, believe it could be difficult for a person to understand phenomena if the person were to start from fundamentals (I may be wrong). For example, in dy/dx, where say y=f(x), delta x is never "actually" zero! Yet we can intuitively 'understand' (visualize) limits quite well and use dy/dx to verify other intuitions (hypotheses) that we may have. Let me give you 2 examples:

1. We do not quite understand what 3/(-2) means. Yet we may use it as a 'step' to 'solve' a simple linear equation whose solution we understand quite well.

2. Let y=constant for all x, and forget the definition of a 'limit' for the time being. Why choose 0 as the value of dy/dx if delta x were indeed to be equal to zero. Yet intuitively we have no problem with our choice as deltay/delta x would indeed be 0 no matter how 'small' delta x is.

Of course there are problems with this approach and the problems usually manifest when we integrate instead of differentiate. My view is that integration should be taught from first principles instead of teaching it as some sort of "inverse of the differential" as is often done. Would like to know your views on this.

Again nice read.

Re: # 8 -
masadi aka 'joker' - with every snide comment you make - I believe more in Mohammad Gill Sahab ( I am sure everyone else will agree ) .
I happened to check your blog - and I fail to get the proof! what excatly is your point?
kindly ( I am sure your can't be kind to anyone ) but for the sake of the forum - do email your content and whatever proof you have to the chowk staff and I'm sure they will respond and take action .
Here I would like to request Mohammad Gill Sahab to come up with his version .

Is this guy Masadi for real? If this is the state of the educated, god save the rest of us.

Is this guy Masadi for real? If this is the state of the educated, god save the rest of us.

IB writes " if you don't I wish I could punch you now "

Look you little rat, my article was submitted months ago and was censored by this a-hole. Regarding proving myself, you can read that article and the date on which it was published at the alternative site http://articles.asadi.org

As for my claims about the "parrot" mentality of Gill, read my comments on his 1001 previous articles. The guy can't think worth a fart....

Re: # 5
masadi
you are wrong gill sahib is not the editor.
the editor is an Indian P**** and she has over dozen nics.

Re: # 5 - masadi - I had a fair idea about you as a 'as*****' - now its confirmed!
kindly prove - what you said about a respected person - whom I had been reading from almost 6-7 years or more I guess! if you don't I wish I could punch you now .

Gill writes " was inspired to write this article by an interview of Professor Eric Mazur, Gordon McKay Professor of Applied Physics at Harvard"

The guy is a liar, my article which the GOP is now adopting, which I submitted to Chowk earlier this year, and which this pervert censored talked about the rote learning methodology and its origins and effects in Pakistan. The guy evidently read it, censored it and then composed his own piece of bs. Like I have been writing before about this person he merely reproduces what he has read in books without any iota of thought involved in it, and then claims to relate his "teaching methodology" to real life experiences. He is a tape recorderesqe, parrot, rote spitting out "scholar". All he is interested in is self promotion and abusing his office of editor at Chowk. People like him are a miserable disgrace to the world of education.

Where is our friend khuram (with the single 'r')? He would have loved this stuff about dy/dx .

Rote learning is something which I feel is being passed on from generation to generation. During my four year 'ordeal' in an engineering university, I was constantly surrounded by people whose attitude towards serious study was rather retarded. They believed strongly in rote learning, in obtaining better marks so that they could get better job opportunities in places where employers are more interested in your detailed marks certificate, and not in what you have learned. A terrible outcome of this easygoing laidback sort of attitude which has been passed on from generation to generation of students is the reduced number of engineering graduates who really are engineers, and not just exam clearing experts.

I believe that this problem has to be corrected at the grassroots level. The way you manage an institution and create an environment of learning is very important for young impressionable minds. Without a properly managed system, idle teachers, century old books and notes, the students would feel unimportant, as if they are here to merely go through the course, clear the exams, and get a job. This results in change in attitude of the students, and they feel lost. The students too should root out the ills and the traditions that have plagued engineering institutions and should try to make themselves better.