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Topic: Creative Math. on Zim Mathematics Web Site
Replies: 40   Last Post: Mar 8, 2003 12:15 PM

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Newton Liebniz

Posts: 15
Registered: 12/8/04
Response to S. Jystad Part I
Posted: Aug 28, 1999 12:25 PM
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S. Jystad says:

My version of constructivism says that (biochemically) (I think
this
corresponds to Jack's 'real world') a student constructs their
own
synapses which constitute the students knowledge. I challenge
both NL
and Jack to come up with a means to construct meaningful
synapses in
a student's brain by a method external to the student. The
ability to
give a student a shot which would replace a year of instruction
would
be an educational panacea, and a bit frightening.

I say:

1. Here we go again. Redefine the term constructivism and call me an
idiot. I thought I already went through this with you guys. Thank
you for at least specifying your new way of defining constructivism.
Now I can at least make a few comments about it.

2. "A student constructs their own synapses?" I could get nit
picky with that statement but I wont. I am not an expert in how the
brain works, and I suspect that you aren't either. I did, however,
read a few chapters about the brain in a good Physiology textbook. I
also asked a doctor of medicine. While synapses are created
throughout your life, most are created in the brain during infancy and
early childhood. If the child is not exposed to an enriched
environment, then the brain `throws away' this extra structure for
reasons of economy (If you don't need the extra structure, why support
it?) . To quote the text,

"Brains of subjects in an enriched environment (vs. impoverished
environment) had more neuroglial cells, a more complex branching of
neurons' dendrites, an increase in the spines on nerve-cell processes,
which serve as sites for synapses, and a change in the synapse
structure. This ability of neural tissue to change because of its
activation is known as *plasticity*."

Platicity accounts for the brains ability to learn (its potential to
learn). Studies show that young animals in rich environments learn
faster than those in impoverished environments. So science concludes
that there are indications that structural changes may be associated
with learning. They use the analogy at this point that the brain is
analogous to a muscle -- the more you use it, the more plastic your
brain gets. (aside: I think Jack talks about this sometimes.)

Scientifically, you were talking about placity and the potential for
kids to learn, not what happens when students learn. The answer to
what happens in the brain when people learn is far more complicated
then you make it seem. For that, I give you this quote from the text:

"Neural circuits in the central nervous system connect the sensory
reception of the new information to be learned with the behavioral
response. For example, if an animal learns to blink its eye in
response to a tone, neural circuits must in some way connect the
auditory pathways from the ear to the motorneurons controlling the eye
muscles. some molecular or cellular change has to take place
somewhere along these neural circuits if learning is to be achieved.
This change is called the *memory trace*. It is important to
distinguish between the entire neural circuit necessary to demonstrate
learning, which usually involves a sensory and a motor component, and
the memory trace, which is the part of that circuit that shows the
training-induced changes. JUST WHERE THE MEMORY TRACE OCCURS AND WHAT
FORM IT TAKES ARE PARAMOUNT QUESTIONS IN THE STUDY OF LEARNING, BUT
UNFORTUNATELY, THE ANSWERS TO THESE QUESTIONS ARE STILL
DISAPPOINTINGLY VAGUE." (capitalization was done by me for emphasize)

To paraphrase this quote, we don't know yet how people learn. These
are extremely deep and hard questions, and while scientist are working
very hard at them, we just don't know a whole lot about how the brain
works.

So do you really want to base the theory of constructivism on how the
brain works when we don't know how it works? It is like putting the
horse before the cart. I think what you meant to say, and I am
honestly trying to work with you on this one, is that some type of
chemical change happens (we don't know what, but we don't care) in the
brain when we learn. I think everyone agrees with this statement.
But this is hardly revolutionary and certainly not worthy of attaching
a name such as ``constructivism'' to this fact. The fact fits under
the better named title, "Duh!"

3. Okay, so now that we got the science issues out of the way, we can
focus on the educational issues of this paragraph. I think you were
trying to communicate a very important message, but you mangled it by
misrepresenting science. The educational issue I think you were
trying to communicate is that students must internalize mathematics.
This is obviously true! As a teacher, I can't physically force
students to internalize mathematics I am teaching them, they must do
this for themselves. Again, everyone would agree with the statement
that learning requires the engagment of the learner.

a. Do you see what you did here in your argument? You saw that I was
attacking constructivism, this upset you, and so instead of attacking
my arguments, you state something which is obviously true, and then
claim that I don't understand this or think its false. So you see,
you are the one setting up the straw man by claiming I don't believe
an absolutely true statement. Here, let me try one on you. The Earth
is spherical! I would like for S. Jystad to present evidence that the
Earth is flat which is what he believes.

b. The irony of me paraphrasing your paragraph has not been lost on
me. You may think I have done exactly what I just slammed you for.
But I merely gave interpretations of what you actually said (since it
was a bit convoluted), and I offered multiple interpretations to
account for possible misinterpretations. I did not put false ideas
into your head like you did to me. You do the same thing to me in
your next paragraph, but I will come to that in part II.

c. By the way, IF you mean the definition of constructivism (and I
don't think you do for reasons below) to be based on students needing
to internalize mathematics, then we are all constructivist. But
constructivism has a definite theme and not everyone, me included, are
constructivist. So constructivism is more specific then the general
need for students to internalize mathematics. I will talk more about
this theme in part II.




Date Subject Author
8/12/99
Read Creative Math. on Zim Mathematics Web Site
Zim Olson
8/12/99
Read Good intentions, but `Zim mathematics' is not mathematics.
Newton Leibniz
8/12/99
Read I see wholes in all Mathematical theory also
Zim Olson
8/14/99
Read Math and the dangerous Mr. Zim Olsen
Jack Jersawitz
8/15/99
Read dangerous ideas
Victor Steinbok
8/15/99
Read Huh? Whatchu talking about Willis?
Newton Leibniz
8/15/99
Read The central question
Jack Jersawitz
8/15/99
Read dangerous ideas and dangerous "mathematicians"
Jack Jersawitz
8/15/99
Read dangerous ideas and dangerous "mathematicians"
Jack Jersawitz
8/14/99
Read Mathematics and theory of knowledge
Jack Jersawitz
8/16/99
Read Math. Art dangerous to NCTM???!
Zim Olson
8/16/99
Read A full blown example
Jack Jersawitz
8/17/99
Read The GRAND FINALE to this topic!
Newton Leibniz
8/17/99
Read Why a Creative Axiom for Mathematics
Zim Olson
8/17/99
Read The pity of it is..
Jack Jersawitz
8/17/99
Read I'll buy that
Jack Jersawitz
8/17/99
Read The GRNAD FINALE: A Jack in every stable
Victor Steinbok
8/17/99
Read Snake oil and apricot pits
Jack Jersawitz
8/17/99
Read Snake oil and apricot pits
Jack Jersawitz
8/19/99
Read My last reply to Vic.
Newton Leibniz
8/19/99
Read Nonetheless
Jack Jersawitz
8/27/99
Read The straw man
Steve Jystad
8/28/99
Read Response to S. Jystad Part I
Newton Liebniz
8/28/99
Read Response to S. Jystad Part II
Newton Leibnitz
8/29/99
Read And classroom examples
Jack Jersawitz
8/29/99
Read And classroom examples
Jack Jersawitz
3/8/03
Read Re: The straw man
xfly
8/17/99
Read The GRNAD FINALE: A Jack in every stable
Victor Steinbok
12/15/02
Read Re: Math. Art dangerous to NCTM???! w/ new web address.
Zim Olson
8/16/99
Read Math. Art dangerous to NCTM???!
Zim Olson
8/27/99
Read Your philosophy site
Kirby Urner
8/28/99
Read Lack of Standard for Creative Mathematics for NCTM
Zim Olson
9/13/00
Read Re: Creative Math. on Zim Mathematics Web Site
wil
9/14/00
Read Explanation of some of Zim's ideas.
Zim Olson
9/24/00
Read Re: Explanation of some of Zim's ideas.
wil
9/24/00
Read Further explanation: Old paper of mine, 1997.
Zim Olson
9/30/00
Read Another example, Creative Math, Old Paper of Zim's Apr. 2000
Zim Olson
9/30/00
Read Re: Creative Math. on Zim Mathematics Web Site
Jack Jersawitz
10/8/00
Read System - Subsystem; Hierarchy & Definition. Answer attempt
Zim Olson
12/15/02
Read Re: Creative Math. on Zim Mathematics Web Site.(New Address)
Zim Olson
1/17/03
Read New Zim Mathematics Web Site
Zim Olson

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