Re: [Phys-L] Evaluation tests

[brian whatcott <betwys1@sbcglobal.net>]

On 12/16/2013 7:32 PM, Bernard Cleyet wrote

> >   On 2013, Dec 16, , at 15:23, Robert Cohen <Robert.Cohen@po-box.esu.edu> wrote:
> >
> > We have found a very strong correlation between students passing this course with a C or better and our own survey, which is based partly on Jerome Epstein's "Basic Skills Diagnostic Test" (BSDT) and focuses a great deal on proportions and the meaning of algebraic letters (variable and unit abbreviations) vs. numbers.  The key is to ask as simple a question as possible that still reveals the weakness.  For example, without the help of a calculator, which is bigger: 25/27 or 15/17?
>
> That’s hard for me.  I had to think:  2/17 is larger than 2/27.  Therefore, 15/17 is further from one than 25/27.
>
> Does everyone else just know it automatically?  Or is there another method?
>
> bc fails in a timed test.
You might have been helped to think which  is larger, a number that's 
two big chunks less than its denominator, or one that is two small 
chunks less than its denominator?

But if *you* thought that you had hit a salutary test, here was mine, 
this evening:
In logic, if a variable, say x is defined as equal or greater than a 
number - say 5, then NOT x is defined as less than that number. This is 
something used in math models, and is well-known to math programmers. So 
I was checking some homework. The task was drawing the line graph of the 
area of interest, and symbolically showing where the inequality relation 
was valid. In the case mentioned above, it would be indicated by a line 
with values marked on it, 3,4,5,6,7... and a circle symbol showing the 
valid limit of the relation, in this case 5 with an arrow indicating the 
valid direction, in this case to the right ("greater than") and there 
was one more symbolism: if the boundary included that number (=>), the 
circle was to be filled in to make a dot, otherwise it was to be left as 
a circle, meaning (>) Still with me? :-)

All was going well with correct answers for X>1,   A>=2,   v < 5,  b <=6 
featuring a numbered line and a bubble or dot with an arrow going the 
correct direction. THEN came a different style of question like this 1 
>= x. This looked like a regular inverse to me (for some reason!): if 1 
>=x, then x must be < 1 (thinking of x and not x). however after a 
couple of young women shouted at me for a sufficient length of time, I 
came to realize that the relevant inequality is this: if 1 >= x then x 
<= 1    (NOT if 1>=x then x < 1.) What IS true is if 1 >= x, then 1 < 
not x. And that is a level of abstraction at which 14 year olds are 
working, I am pleased to say!!!


In the spirit of the Season:

Brian Whatcott   Altus OK