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Re: [Phys-L] Conceptual Physics Course



-----Original Message-----
From: phys-l-bounces@mail.phys-l.org
[mailto:phys-l-bounces@mail.phys-l.org] On Behalf Of Bernard Cleyet
Sent: Saturday, May 19, 2012 1:04 AM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] Conceptual Physics Course


On 2012, May 18, , at 09:38, Jeffrey Schnick wrote:

John,

I've interspersed some comments below but first: Thank you
so much for a useful and thoughtful answer. Your response shows that:
1. You read the original question carefully so you knew it
was about x+y vs. 1/(1/x+1/y) rather than x+y vs. 1/x+1/y.
2. You comprehended the question so you knew it was about
convincing people in a lasting manner rather than providing a proof.
3. You gave some thoughtful, thought-provoking, and
potentially useful suggestions.
I am truly grateful.


Proofs are not lasting?

Your question makes me all that much more impressed that John Denker and Robert Cohen knew exactly what I was getting at in that your question makes me aware that the wording in my original question was not ideal. I'm going to take another shot at it. My original question was "... what do you do to convince a person in a lasting manner that the reciprocal of (1/x + 1/y) is not, in general, x+y?" My new version is:
What do you do to make it so that a person who has a tendency to replace 1/(1/x+1/y) with x+y gains the understanding and habits of mind that result in that person not replacing 1/(1/x+1/y) with x+y ?

Here's a scenario in which the question can crop up. A physics teacher, teaching a physics course, reviews algegra with the people taking course by testing them repeatedly on various algebra skills and discussing their mistakes in one-on-one conversations. Among others the mistake, in the case of less than half of the people, 1/(1/x+1/y) -> x+y, crops up. By the end of the algebra review period which lasts a month and is actually going on outside of class, no one is making the mistake 1/(1/x+1/y) -> x+y. Some months later in the context of resistors in parallel, the teacher notes that the mistake is being made again, this time by fewer people than were making the mistake in the first place. The mechanism automatically triggering one-on-one consultations is no longer in place so only some of the people still making the mistake get one-on-one discussions about it and others just get some written feedback on the same page on which they made the mistake and perhaps get to hear a mini-lecture on the topic in class. The process later repeats itself in the context of capacitors in series, and still later, in the context of thin lenses. Each time, the number of people making the mistake is fewer than the last, but the number is never reduced to zero. The teacher would like to reduce the number to zero by the end of the algebra review period.

The particular mistake in question is just an example, call it a poster child for the subject at hand. The ideal solution would work in the case of the poster child even if the teacher never addressed the poster child specifically, beyond being marking it wrong. Thats why John Denker's suggestions, no matter how obvious and banal at first glance, seem so valuable to me. A scenario in which the people in the class discussed above developed habits of checking their work and making connections such that despite the poster child mistake never being addressed by the teacher, the mistake never reappears after the first month, does seem possible.

Now I want to highlight the poor wording in my original question by means of an example. About seven month's after Brian Whatcott's post, <http://www.phys-l.org/archives/2008/4_2008/msg00262.html>, I decided to use SuperMemo to attack my old junior high to first year of high school nemesis, Spanish. I'm over three years into my learning Spanish hobby now and I'm at some intermediate level that Spanish speakers on the list might be able to judge by looking at my writing at <http://diariolecturajeff.blogspot.com>. Within the first couple of months I learned that the word "and" in Spanish is "y" unless the next word begins with a sound like that of the word "y" in which case the word for "and" is "e". I would say that I was convinced of that long ago in a lasting manner and yet, just last week, a Spanish speaker kindly pointed out that I was consistently using "y" where I should have been using "e". The point is that knowing something is not the same as applying that something on the fly. If someone asked me to fill in the blank with either y or e in the expression "español __ inglés" I think I would get it right but apparently, at least up till last week, if in the course of writing some prose, I wanted to include that expression in what I was writing, I would get it wrong. I think it is conceivable that a student could get the question about the building block "is 1(1/x+1/y) equal to x+y ?" correct and still get it wrong when using the building block to build something else with. I think this just highlights another point that John Denker has stressed, namely that if the goal is to get students to be able to build the building, don't just ask questions about the building block--it's okay to start there, but there is more to do.