IMO, JDs post below relates to a comment I was going to make:
Namely that those of us who like to laugh at the "three forms of Ohm's law" (and I've been known to disparage this) tend to forget that knowing only one form carries with the implicit corollary that you are also completely comfortable with Algebra. Many for which the "three forms" are intended are not.
The above does disagree with the sentiments below in any way, shape or form.
|-----Original Message-----
|From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of John Denker
|Sent: Saturday, June 29, 2013 12:27 PM
|To: Phys-L@Phys-L.org
|Subject: Re: [Phys-L] playing for keeps
|
|On 06/29/2013 06:34 AM, Dan Crowe wrote:
|
|> V = IR, I = V/R, and R = V/I is not a set of three equations: it is a
|> set of three representations of one equation.
|
|++ You see it that way.
|++ I see it that way.
|-- Other people do not necessary see it that way!
|
|
|On 06/29/2013 06:34 AM, Dan Crowe wrote:
|
|> found a lengthy explanation to help learn "the three equations" of Ohm's
|Law.
|
|That's what I was alluding to. But wait, there's more. If you are interested in
|power dissipation (as well as voltage, current, and
|resistance) then there are 24 equations to memorize (not just three).
|
|For only $24.95, you can get a poster to hang in your classroom, to help people
|learn all 24 equations by rote.
| http://www.etgiftstore.com/24-classroom-charts-your-choice-of-ohms-law-
|charts-ac-or-dc-ohms006-detail.htm
|
|There was a time in my life when I could not have imagined any such poster
|could exist. But it does exist. I regularly attend seminars in a community
|college classroom where such a poster hangs on the wall. It's for the "avionics
|technician" training program. This is a /postsecondary/ training program. You
|might think that high-school algebra would be a prerequisite, but it is not.
|
|You can understand the situation as follows: Some of these students don't
|understand algebra, and this program is not going to teach them algebra. It
|teaches them how to plug numbers into a formula, not how to perform
|abstract manipulations on algebraic symbols.
|
|I reckon at least 90% of the students in this program could learn algebra, and
|would be better off learning algebra. However, the college doesn't want to
|spend the time and money it would take to teach them algebra ... and it
|doesn't want to wash out the 10% or so who have some disability or phobia
|that would interfere with learning algebra.
|
|I know people who are never going to learn algebra. They are never going to
|be physicists, but they are perfectly nice reasonable people who hold high-
|paying professional jobs. Note that according to BLS statistics, on average, an
|avionics technician gets paid slightly more than a school teacher.
|
|Bottom line: There are two sides to the argument:
| *) I am glad there is a career path for people who are never
| going to learn algebra.
|
| *) On the other hand, algebra is a prerequisite for HS and college
| physics. These students will be better off if we insist on the
| algebraic approach to Ohm's law and everything else, rather than
| the rote equation-hunting approach.
|
| The rote approach to Ohm's law is a crutch. People with a
| disability may need a crutch, and I'm OK with that ... but
| everybody else is better off not using crutches.
|
| This is only the tip of a super-important iceberg, namely the
| idea of teaching them to learn, to remember, and to think. And
| as explained previously, by "remember" I mean a deep, powerful,
| intellectual, richly-connected memory, the kind of memory that
| is good for figuring things out (not a rote memory).
|
|=============================
|
|Speaking of figuring things out:
|
| 1a) Can you tell me the mass of the proton, right now, without
| looking it up, accurate to better than 1%?
|
| 1b) If not, can you tell me how much a mole of protons weighs?
|
|
| 2) What's the square root of 50, accurate to better than 1%?
|
| I can think of two ways of figuring this out in my head,
| either one of which is faster than using a computer or
| hand calculator.
|
|
| 3) Given an ellipse with semi-major axis "b" and semi-minor
| axis "a", what's the formula for the area of the ellipse?
| I don't remember this formula, but I can figure it out in
| less time than it takes to ask the question.
|
|
| 4) How much water flows down the Mississippi in a year? Pick
| a spot such as New Orleans and tell me how much river water
| flows past that spot. Figure it out, without looking anything
| up.
|
|
|================================
|
|Sometimes there are techniques that help with this
| -- expanding stuff to lowest order
| -- scaling laws in general;
| dimensional analysis as a weaker corollary
| -- symmetries and conservation laws
| -- et cetera.
|
|... and sometimes the only thing that matters is the /habit/ of figuring stuff
|out. If you do it a lot, you get better at it. Education should be about forming
|good /habits/ ...
|habits that remain for the long term. This is what I mean by playing for keeps.
|If at some point you decide that you would rather figure stuff out than look it
|up, the habit reinforces itself.
|
|On 06/28/2013 07:29 PM, Bruce Sherwood wrote:
|>
|> Apparently it is well established by experiment that in general
|> forgetting follows a fairly universal power law.
|
|Habits are exempt from this law.
|
|
|On 06/29/2013 09:32 AM, rjensen@ualberta.ca wrote:
|
|> You look up data! (And numerical data changes over time.) I don't ask
|> my students to memorize physical constants, I teach students where to
|> find the data and how to assess the quality of the data.
|
|Sometimes you look up data ... but sometimes it's quicker and better to figure
|it out. Figuring stuff out is a good habit, because it allows you to see the
|relationships between things.
|
|At the 1% level of accuracy, the mass of the proton does not change over
|time.
|
|Some people say that principles should be learned, and details can be looked
|up whenever necessary ... but the concept of /figuring stuff out/ blurs the
|distinction between principles and details.
| -- The mass of the proton is a detail. It could be googled.
| -- The definition of dalton is worth remembering. There's a concept
| involved, something to do with connecting mass to baryon number in
| atoms. The mass of the proton is not exactly 1 u, but it's within
| 1%. Actually it's off by about 0.7%, which is interesting unto itself,
| because it tells you something about the order of magnitude of nuclear
| binding energies.
|
|It is good to cultivate the /habit/ of figuring stuff out. If you are stuck waiting
|somewhere, practice figuring stuff out.
| -- How many ways can you think of for figuring out the square root of 50?
| -- How many ways can you think of for proving the Pythagorean theorem?
| Hint: I've seen about 100 different proofs.
| -- What's the density of air? What's the mean free path? How is
| the speed of sound related to the speed of smell (i.e. the rate of
| diffusion)?
| -- Why are meteor showers typically best seen in the wee hours of the
| morning?
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