Why do some students fail to improve?
- Thread starter Brian Manzella
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shootin4par said:
Neil,
Ok, here is my interpretation of what you are saying. There are some implict steps in your logic that should be spelled out:
a) student trusts teacher
b) student grows through counseling of teacher
c) student realizes they have grown and continues to trust teacher
d) steps b-c repeat until student loses trust
If I understand you correctly, you're saying that as long as student trusts the teacher, it stands to reason that the student will be improving because if they were not growing, they would stop trusting the teacher.
I'm saying the same thing, I just choose to focus on step (b) as the primary "role" because it is less dependent of the student's perception.
Lou
shootin4par
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Lou, B and C dont happen till A is established, A is NOT established when the teacher and student shakes hands. SOmetimes A is never established, therfore B and C never happen. The teachers role is getting A established as quickly as possible and from there B and C happen much more rapidly.
neil
neil
Saying the same thing
My graduate school advisor (a member of the National Academy of Sciences) and I were finalizing a proposal for a government-sponsored research grant. We disagreed on how to approach some facet of the document. After discussing our opinions for a while, the conversation went like this:
Me: "I'll defer to you because you have more experience than I do with these things."
Advisor: "It's not that I have more experience, it's just that I've done this a lot of times before."
Loubert said:
This is a true story ...Brian Manzella said:
My graduate school advisor (a member of the National Academy of Sciences) and I were finalizing a proposal for a government-sponsored research grant. We disagreed on how to approach some facet of the document. After discussing our opinions for a while, the conversation went like this:
Me: "I'll defer to you because you have more experience than I do with these things."
Advisor: "It's not that I have more experience, it's just that I've done this a lot of times before."
birdie_man
New
Brian Manzella said:
Hooozaba??? Whatawaka? (more jibberish)
Is this like moving the box forward? ("hit the box")
Or is this a Pink Floyd deal.
rundmc said:
Yes. Here are selected definitions from the the Random House Dictionary[1].
Notice that the definition for "counsel" extends the definition of "teach" to include "advice" and "opinion" in addition to "instruction."
Here is an example. You come to me and say "I was shopping for a stereo equipment and I kept seeing things 'dBs.' I looked up dB, which uses logarithms. How do I calculate a logarithm?"
As your "teacher", I now have a couple of options.
Option 1: I could help you understand everything in the next quote [2]. Then we could move on to power series.
Logarithmic function
It may be shown, by Mathematical Induction, that the Geometric series has the indicated value:
1 + x + x^2 + x^3 + ... + x^i + ... + x^n = (1 - x^(n + 1)) / (1 - x)
The limit, as n increases without bound, is 1 / (1 - x) provided that x is inside of its circle of convergence: abs(x) < 1.
We define the logarithmic function as the inverse of the exponential function; hence, the derivative of the logarithmic function is d ln(x) / dx = 1 / x. Thus, the indefinite iintegral of 1/x is ln(abs(x)) + C. In passing, we observe that, for real a and b, the logarithm of the complex number a + ib may be expressed as ln(a + ib) = (1 / 2) ln(a^2 + b^2) + iArctan(b / a).
Let us integrate the infinite Geometric series to obtain:
- ln(1 - x) = x + x^2 / 2 + x^3 / 3 + x^4 / 4 + ... + x^i / i + .... provided abs(x) < 1
Replace x by its additive inverse (that is, by -x):
ln(1 + x) = x - x^2 / 2 + x^3 / 3 - x^4 / 4 + ... - (-x)^i / i + .... provided abs(x) < 1
Take half the sum:
(1 / 2) ln((1 + x) / (1 - x)) = x + x^3 / 3 + x^5 / 5 + x ^7 / 7 + ... + x^(2i + 1) / (2i + 1) + .... provided abs(x) < 1
Let y = (1 + x) / (1 - x); then x = (y + 1) / (y - 1). This transformation is called "bilinear"; because it is the quotient of two linear expressions. It has many interesting properties: for instance, it maps conic sections into conic sections. We may employ this transformation in the foregoing to obtain the logarithm of y provided that the real-part of y is strictly positive, which we write Re> 0:
ln
Of course, we would square x once, then employ that value in the series. The ratio of the i-th term to the (i- 1) term is x^2 2i / (2i + 1). See the evaluation of a power series, for a practical method of evaluation of a power series.
In passing, we observe that the logarithmic function has an essential singularity at the origin.That means that the limit of the logarithmic function, as x approaches zero, depends upon the angular direction of the approach.
Option 2: I could show you the "ln" and "log" buttons on your calculator.
In each case, I will have taught you something, but to counsel you, I need to make a decision on what is best for you. For most people, option 2 is all they need, but if you were studying to be a math major, we would need to take the time to do option 1.
Lou
Citation:
[1]"counsel", "teach." Dictionary.com Unabridged (v 1.0.1). Based on the Random House Unabridged Dictionary, © Random House, Inc. 2006. 11 Oct. 2006. <Dictionary.com http://dictionary.reference.com/browse/teach>
[2] Excerpted from http://www.geocities.com/ResearchTriangle/2363/logarith.html Copywrite (c) 1997 R. I. 'Sciibor-Marchocki
shootin4par
New
you being a scientist is good and will help you figure out certain things that need it, but when conversations are broken down scientifically, maybe that is a little much?
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