Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Mental Reflexes
Replies: 5   Last Post: Feb 26, 2012 10:00 PM

 Messages: [ Previous | Next ]
 Robert Hansen Posts: 11,345 From: Florida Registered: 6/22/09
Re: Mental Reflexes
Posted: Feb 26, 2012 10:00 PM

In this last post I talked about speed and to clarify I am really talking about cognitive processes that take virtually no time at all (speed is essentially infinite). The basis of these processes is instinct.

For example, when Kasparov played Deep Blue in 1997, the results of the match was Kasparov 1, Deep Blue 2 and 3 draws. Deep Blue was able to look at 200 million moves a second while Kasparov could look at maybe 3 in the same amount of time, yet Kasparov managed to beat Deep Blue once and draw 3 times.

In "plodding" time, Deep Blue was roughly 100 million times faster than Kasparov, but Kasparov was still able to hold his own because of instincts. It is these instincts that need to be developed as you move deeper into artful subjects. Plodding will not suffice. In fact, even moderate problems in algebra will not succumb to (human) plodding because there are simply too many permutations to cover. In human time it would take an infinity to solve the problem. In each second of thought, Kasparov's instincts allowed him to reduce 200,000,000 possible moves to 3.

Bob Hansen

> I wasn't particularly saying that one must "catch on"
> in a set amount of time, and in my replies to Haim
> and Wayne I think I was pretty explicit about not
> closing doors at any particular grade. Catching on
> appears to me to be as normally distributed across
> the dimension of time as it is across any other
> dimension. Which means, as we advance in grade, the
> number of students crossing that threshold is
> reduced, and at some point to a trickle, but not all
> at once. The fact that catching on is normally
> distributed is an indication that many factors are
> involved in some form of a probability function and
> it would seem natural to me that time be one of those
> many factors.
>
> But there is certainly an issue of time involved,
> although different than a time limit of "catching
> on". There is in these things a speed requirement
> that if not overcome will be an absolute blockage to
> passage.
>
> When one learns to catch a ball thrown to them
> (actually, at them) you cannot slow the act of
> catching the ball down (like slow motion). You can
> talk to the kids about catching but when you hit the
> field and start throwing actual balls, physics as it
> is, does not allow you to slow the balls down so that
> the kids can plod through the act of catching. That
> talk you just had becomes rather useless when
> everything is occurring in realtime. The reality is
> that you must throw the balls to them and hope that
> after enough iterations they learn to catch. In this
> sense, catching a ball is not teachable. It isn't
> something you teach them and then they go do it. It
> might be coachable, but it is not teachable.
>
> I started this thread on "reflexes" but I must now
> add "instincts" to the mix.
>
> You often read that lion's teach their young to hunt.
> My theory on this, and it may very well be a common
> theory, is that they don't actually teach them how to
> hunt but instead simply show them hunting. I am
> saying that the instinct to hunt, in particular to
> hunt with speed, claws and fangs, to hunt like a lion
> hunts, is so instinctive in lions that showing is all
> the teaching they need, especially when the showing
> is being performed by another lion. And even if that
> showing does not occur, I think most of them would
> pick it up just from their own instincts. Those
> instincts are simply that strong and they have to be
> that strong because without them we would not have
> lions.
>
> Examples with humans would be talking and walking. We
> are not taught how to do either. Example is all we
> need. In fact, we would eventually do them even in
> the absence of example, it is who we are. Like the
> lion hunts, we talk. Someone once debated with me
> that if a baby was without examples of humans walking
> then they themselves would never walk. I (and
> probably everyone here I suspect) would find that an
> absurd conjecture. Our musculature, our skeletal
> frame and our nervous system is designed to walk and
> eventually we would stand and eventually we would
> walk. We are fated by design to walk.
>
> Where am I going with this? If walking was not
> instinctive do you realize how difficult an activity
> it would be to teach? It would be like teaching
> people to ride a unicycle on a tightrope, without a
> balancing pole. It would be in all practical terms,
> impossible to teach. I have to go that far with a
> difficult example in order to exemplify just how
> difficult a task even standing up is, if it were not
> for our prewired instincts, reflexes and sense of
> balance. And even with our sense of balance, the only
> way to learn to ride a unicycle on a tightrope is to
> try to ride a unicycle on a tightrope and hope that
> your mind and body reacts to the challenge in a
> positive way.
>
> Catching a ball is similarly not teachable. Without
> the requisite reflexes and instincts, the kid will
> not catch the ball. The instinct that will emerge is
> not the instinct to catch but the instinct to duck.
> You can have them hold their glove up to the side and
> throw the ball into it, but this is not catching. In
> these seasons of baseball this is what I have
> observed. I have always been good at sports and I can
> catch pretty well and I display this catching ability
> naturally during practice with the kids. I make it
> look easy. All of the kids start off with high hopes,
> thinking that it is as easy as I make it look, until
> they realize it isn't. At first, the reaction is
> pretty uniform. Upon realizing that catching is not
> as easy as I make it look they begin to try (I love
> this stage btw). In the beginning all of the kids
> catch equally poorly and are equally ignorant of what
> it feels like to catch a ball right out of the air
> with a glove. Over time though, some of the kids are
> able to turn some of their attempts into near misses
> and then turn some of those near misses into actual
> catches. Meanwhile, the other group is still
> ignorant. They are not even exhibiting what you would
> consider near misses let alone actual catches. They
> are trying, but catching is not something you can
> practice if you can't even catch at all. There is too
> much detail to the art of catching that simply isn't
> even there for discussion if you are not at least
> almost catching.
>
> Throwing is another activity that exhibits this. Many
> boys "throw like a girl" when they first start off
> but some outgrow this pretty quickly just through
> association with someone that is throwing properly.
> They seem to resonate with the physiology and physics
> of throwing a ball and example is enough to move them
> along. When this doesn't happen I must say that the
> training looks more like rehabilitation in that you
> are trying to replace instincts and reflexes that
> aren't there. The outcomes can be very weak. And
> these are brand new kids, not kids that have acquired
> some sort of baseball anxiety disorder.
>
> Mathematics requires cognitive instincts and reflexes
> as well. There is a part of it that you cannot slow
> down and at some point you must be able to throw the
> problems at the student and they catch them. Having
> them hold their glove off to the side and throwing
> problems into it does not count. One cannot read a
> novel if they are plodding through the words nor can
> one perform a piece of music if they are plodding
> through each note or chord.
>
> I don't think teaching is what it is portrayed to be.
> I think all teaching with all species works like it
> does with the lion. We (when we teach) do not create
> ability, we only resonate with it when it is there. I
> can accept that the ability can be dormant and a
> teacher must bring it to the surface but I don't know
> of any pedagogy that actually creates it.
>

> > I question, is it always a requirement that those
> "practicing to catch the ball better" catch on
> quickly?
>
> I do not claim there is a time limit to "catching on"
> but I do claim there is such a thing as "catching
> on".
>

> > I have a number of students who think things out
> well, but slowly. They consider multiple
> perspectives carefully and often excel on the finals
> I give, yet do poorly on any pop quizzes.
>
> Lacking any details I wouldn't be able to comment on
> your case but I can sense when my son is "plodding"
> and it is usually not a good sign. It is a sign that
> he has not sufficiently developed his instincts.
> Those instincts are critical for the later levels.
>

> > Also in regards to reflexes and catching balls -
> the player's visual depth perception is a variable.
> How can a player's reflexes come into play when maybe
> the position of the ball is fuzzy?
>
> If there is an impediment then you can either correct
> it (give the player glasses) of if it is not
> correctable, find something else, maybe even another
> sport, to do. It depends on the nature and
> seriousness of the impediment and the ability of the
> player to overcome it.
>
>
> My point to this discussion is to make the case that
> when you run away from the notion of talent you are
> also running away from very necessary ingredients for
> success, like reflexes and instincts. Our model of
> teaching is too one sided and puts all of the
> emphasis on the teacher with the supposition that
> something flows from the teacher to the student. I do
> not think anything "flows". It is more a matter of
> resonating.
>
> Btw, my son did not do well with catching but I was
> able to overcome this at home. Without going into
> details, I replaced his instinct to duck with the
> instinct to catch.:)
>
>
> Bob Hansen
>
>
>
>
>
>
>
> On Feb 25, 2012, at 4:55 PM, roys.anna@gmail.com
> wrote:
>

> > I question, is it always a requirement that those
> "practicing to catch the ball better" catch on
> quickly? I have a number of students who think things
> out well, but slowly. They consider multiple
> perspectives carefully and often excel on the finals
> I give, yet do poorly on any pop quizzes. Perhaps
> the quick "reflexes" are not the only consideration
> for judging student performance. Also in regards to
> reflexes and catching balls - the player's visual
> depth perception is a variable. How can a player's
> reflexes come into play when maybe the position of
> the ball is fuzzy?

Date Subject Author
2/25/12 Robert Hansen
2/25/12 Anna Roys
2/26/12 Robert Hansen
2/25/12 Joe Niederberger
2/25/12 Haim
2/26/12 Robert Hansen