Re: [Phys-L] widget rate puzzle ... reasoning, scaling, et cetera

[Robert Cohen <Robert.Cohen@po-box.esu.edu>]

On Friday, January 02, 2015 4:22 PM, I wrote:

> How about the following?  Students frequently have trouble with it.
>
>     An ohmic resistor of resistance 10 ohms allows 1 A of current to flow when a voltage of 10 V is applied across it.
>     What is the resistance of the SAME resistor when  a voltage of 100 V is applied across it?
>
> How would you help students who have difficulty with this question?

My purpose was to show that some students tend to interpret any problem that has numbers into a "math" problem that does not involve any interpretation or reasoning.  I was hoping that this problem was simple enough to illustrate this.

I asked this forum the following question: "How would you help students who have difficulty with this question?"

Several people responded.  I have taken the liberty of extracting a couple of quotes.  I apologize in advance if they are too far out of context.

On Friday, January 02, 2015 5:39 PM, Richard Tarara wrote:

> It is quite likely that students having problems with this are too focused on the algebraic
> equation...Ohm's Law...without much understanding of what the three quantities in that equation actually are.

On Friday, January 02, 2015 7:08 PM, Philip Keller wrote:

> By this time of the year, they know that I would LIKE for them to think
> about proportions and ratios, but they don't know what stays constant.  
> To settle the question, we do an experiment.  

On Friday, January 02, 2015 9:01 PM, John Denker wrote:

> This is practically the definition of a "sophomoric"
> mistake:  Overconfidence resulting from inexperience.
> This includes assuming that a rule that applies in one case "should" apply in all cases.
.
.
> The only cure is to get some perspective on the situation. There are lots of scaling laws in this world.
> Not all of them follow the trivial raisin-bread pattern.  That is, if you increase one variable by a
> factor of x, it does *not* mean that all the other variables go up by the same factor.

To help clarify the issue, I gave the following question on the first day of class to students enrolled in the second semester of our algebra-based physics sequence. I changed the question in terms of mass rather than resistance because one would think that by the end of one semester of physics the students should be pretty familiar with mass (they've already taken chemistry also).  This should show whether the presence of the algebraic equation makes students focus exclusively on the equation rather than on any interpretation of the variables.

There are about 85 in the class.  I've scored 62 so far (I won't have the others until tomorrow).

1. According to Newton's second law, F=ma, where F is the net force acting on the object, m is the mass of the object, and a is the acceleration of the object.  Suppose an object of mass 1 kg is placed upon the floor and experiences an acceleration of 1 m/s2 while a net force of 1 N acts upon it.  What is the mass of the object when a net force of 10 N acts upon it?
A. 0.1 kg
B. Between 0.1 kg and 1 kg
C. 1 kg
D. Between 1 kg and 10 kg
E. 10 kg

22 chose C (37%)

And, just for reference, I also asked a ratio question (to be done without a calculator).

2. Which of the following is largest?
A. 5/7
B. 23/25
C. 0.80
D. Two have the same value
E. All three have the same value

30 chose B (48%)

Robert Cohen                 Department of Physics              East Stroudsburg University
570.422.3428                   http://www.esu.edu/~bbq     East Stroudsburg, PA 18301