is one I think is OK; what really gets my goat is books that give a range formula . . .
I always put the starting location and target at a different location on test questions to see if they memorized the same elevation range formula, usually half the class or so somehow plugs into the range formula and do not get anything but a miniscule amount of partial credit on that problem . . .
| -----Original Message-----
| From: phys-l-bounces@mail.phys-l.org [mailto:phys-l-bounces@mail.phys-
| l.org] On Behalf Of Joe Wise
| Sent: Wednesday, May 16, 2012 1:07 PM
| To: Phys-L@Phys-L.org
| Subject: Re: [Phys-L] proportional reasoning, scaling laws, et cetera
|
| I have and have found it very exciting.
|
| The equations generally taught are for specific contitions that the
| students never see. They constantly used to plug instantaneous speeds
| into equations requiring average speed etc.
|
| I make students create a graph sketch of the problem and then derive
| the equation that represents that graph.
|
| They complain a lot, but understand much more. They also start looking
| for salient points vs superficial elements.
|
| In alg based physics we are more often than not, solving for a slope,
| axis, or area under the curve.
|
|
|
| Robert Cohen <Robert.Cohen@po-box.esu.edu> wrote:
|
| I have a simple question I now ask students who struggle with algebra:
| which is larger, 3/5 or 8/9, and how do you know? It is amazing how
| well this gets at the heart of their struggles and how they've managed
| to "tread water", so to speak, through algebra, calculus, physics, etc.
|
| In my own physics book, I no longer include any of the "magical"
| kinematic equations (like x = x_0 + v_0 t + 1/2 a t^2) as I find they
| just allow students to bypass understanding. Without them, students
| must solve problems based on scientific laws (like Newton's laws) and
| definitions (like average velocity). At least that is my intention.
| Has anyone else tried this?
|
| Robert A. Cohen, Department of Physics, East Stroudsburg University
| 570.422.3428 rcohen@esu.edu http://www.esu.edu/~bbq
|
| -----Original Message-----
| From: phys-l-bounces@mail.phys-l.org
| [mailto:phys-l-bounces@mail.phys-l.org] On Behalf Of John Denker
| Sent: Tuesday, May 15, 2012 9:49 PM
| To: Phys-L@Phys-L.org
| Subject: Re: [Phys-L] proportional reasoning, scaling laws, et cetera
|
| On 05/15/2012 10:40 AM, Bill Nettles wrote:
| > I have found very few students who can do proportional reasoning when
| > they arrive, and they are very resistive to using it to solve
| > problems. For example studying Kepler's Laws, having them work
| > examples using ratio & proportion in class, I ask them on a test to
| > find the period of an asteroid orbiting the Sun at a distance of 3.5
| > AU. They ask me what the mass of the Sun is. I tell them they don't
| > need it. They stare at me like a calf looking at a new gate
|
| I would love to see more discussion of this point.
|
| There is a problem here that we should be able to solve. I don't
| pretend to fully understand the problem, let alone know the
| solution(s),
| but I know this is important.
|
| Oddly enough, this topic is not covered in the typical physics text ...
| even though it is more important than 99% of the stuff that is covered.
|
| Some miscellaneous thoughts:
|
| Remark: It is interesting -- and encouraging -- that even though they
| ask for the mass of the sun, they don't ask for the mass of the
| asteroid. That suggests that they have internalized the principle of
| equivalence, or something like that. Not bad!
|
| Question and/or possibly-constructive suggestion: Students probably
| don't consider cosmology important to their daily lives. So perhaps
| when broaching the subject of proportional reasoning and scaling laws,
| would they do better if we start with something closer to home? For
| example: Consider a skateboarder starting from rest at the top of a
| half-pipe.
| Neglecting friction, calculate the gee-force (in gees) he will
| experience at the bottom. It turns out you do not need to know the
| radius of the pipe.
| Note that the skateboard problem has direct application to
| cars, and has life-and-death application to airplanes.
|
| Another remark: Perhaps I'm missing something here, but I don't think
| proportional reasoning is a substitute for algebra, or in any way
| easier
| than algebra. It is *part* of math, and not even the easiest part.
| For
| example, I don't remember the exact form of the Kepler 1-2-3 law. I
| don't even try to remember it, because I can rederive it when needed.
| For me, the effort of rederiving it is negligible compared to the
| effort
| that would be required to memorize it verbatim. However, rederiving it
| requires algebra.
| I decided long ago that if I'm going to go to the effort of
| learning something, I will learn things that have the most
| power and generality. If I know algebra, dimensional analysis,
| the law of universal gravitation, and a couple other similarly
| broad ideas, I get the details of the 1-2-3 law for free.
|
| I am quite aware that it is possible to perform proportional reasoning
| without algebra. Euclid did it and Galileo did it, to great effect.
| Similarly, I am quite aware that it is possible start a fire by rubbing
| two sticks together ... but I would rather not do so. There exist more
| modern techniques, which are considerably more convenient.
|
| I reckon trying to get by without algebra is a fool's errand.
| High-school algebra is a prerequisite for high-school physics, not to
| mention college physics, and it would be madness to pretend otherwise.
| I am not interested in hearing pseudo- Piagetian claims that students
| "can't" do algebra. That's a lame excuse. There's a big difference
| between "never bothered to learn it" and "can't possibly ever learn
| it".
|
| ============
|
| Maybe I'm off base here, but my first instinct would be to /not/
| require
| students to remember the exact form of Kepler's
| 1-2-3 law. That seems only fair, given that I don't remember it
| myself.
| Similarly, I would not expect them to memorize the loop-de-loop scaling
| laws. Instead, I would want them to learn that:
| a) There are lots of scaling laws. They are very
| convenient and very powerful. They have have been central
| to physics for nigh on 400 years, and will remain so.
| b) If you have never seen the scaling law that you need,
| or if you have seen it but forgotten it, you can figure
| it out on the spot. In simple cases you can use dimensional
| analysis. In more challenging situations, you might need
| non-dimensional scaling.
| http://www.av8n.com/physics/dimensional-analysis.htm
| http://www.av8n.com/physics/scaling.htm
|
| =============
|
| Again I recommend picking some random adult non-scientists and asking
| them what they remember from physics class. Most likely they will say
| "Oh, let me think ... I remember there was something about
| monkey-shooting, but I don't remember the details."
|
| We can do better than this. We /need/ to do better than this. It is
| an
| enormous waste of time and money to teach stuff that students will not
| remember and/or not find useful.
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