Teaching "Critical Thinking" in Education
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07-02-2013, 07:31 PM (This post was last modified: 07-02-2013 07:48 PM by Zat.)
RE: Teaching "Critical Thinking" in Education
I can't resist giving an example, from my own book, on what I think "Critical Thinking" in education could look like.

In essence it is not just accepting the imparted knowledge, but examining it from every possible angle, making sure that we know what it is we are talking about.

Sample from my book:

"I always had a problem with Newton's Second Law: F = m * a

We have an equation with three values in it. I know one of these three: I know what acceleration is and how to measure it.

I have an instinctive ‘feel’ for the concepts of mass and force, but I have no idea how to measure them and without measuring instructions, no concept in Physics has any practical value (an essential part of most experiments in Physics is the measurement of the values that play a role in the observed process).

How do we measure this inertial mass: m and force: F?

Any time I asked my teachers what mass was, I was told that it is the measure of an object’s inertia (force divided by acceleration). And when I asked what force was, I was again told, predictably, that it was mass times acceleration.

Finally, years later, I read a few books that satisfied my curiosity. One of the best: Richard Feynman’s “Lectures on Physics” recognizes the validity of my question:

Let us ask, "What is the meaning of the physical laws of Newton, which we write as F = ma? "What is the meaning of force, mass, and acceleration?" Well, we can intuitively sense the meaning of mass, and we can define acceleration if we know the meaning of position and time. We shall not discuss those meanings, but shall concentrate on the new concept of force. The answer is equally simple: "If a body is accelerating, then there is a force on it." That is what Newton's laws say, so the most precise and beautiful definition of force imaginable might simply be to say that force is the mass of an object times the acceleration.”

Then Feynman states the same problem I was struggling with at University:

If we have discovered a fundamental law, which asserts that the force is equal to the mass times the acceleration, and then define the force to be the mass times acceleration, we have found out nothing.…Now such things certainly cannot be the content of physics, because they are definitions going in a circle….. One might sit in an armchair whole day long and define words at will, but to find out what happens when two balls push against each other or when a weight is hung on a spring, is another matter al¬together, because the way the bodies behave is something completely outside any choice of definitions.”

Finally, Feynman tells us the solution to the dilemma:

The real content of Newton’s laws is this: that the force is supposed to have some independent properties in addition to the law F=ma; but the specific independent properties that the force has were not completely described by Newton or by anybody else, and therefore the physical law F=ma is an incomplete law.

As far as “what use is Newton’s Law” is concerned, Feynman states that:

In order to use Newton’s laws, we have to have some formula for the force; these laws say pay attention to the forces. If an object is accelerating, some agency is at work; find it. Our program for the future of dynamics must be to find the laws for the force. Newton himself went on to give some examples. In the case of gravity he gave a specific formula for the force.

When I read all this, my philosophical problems were solved: Now I knew what Newton meant and how to use his law to solve practical problems. Once you substitute the formula for the force (be it gravity, tension in springs, etc) then I could easily determine the motion of any object subjected to the force if I knew the mass of the object. "
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RE: Teaching - fstratzero - 08-02-2013, 02:44 AM
RE: Teaching "Critical Thinking" in Education - Zat - 07-02-2013 07:31 PM
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