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Re: [Phys-L] Evaluation tests



Consider the following task:
a) Add 198 plus 215.

You can easily do it in your head if you re-arrange it as
215 + (200 - 2).

As an exam question, this has the weakness that it can be
done by brute force, by direct long addition, so you don't
entirely know whether the student used the clever, indirect
method or the brute-force direct method.

I mention this because on 12/16/2013 04:23 PM, Robert Cohen wrote:
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?

Call that question (b).

It's an excellent test question, although it suffers from
same bug as question (a): It can be answered by brute force,
by direct long division.

Also I'm not sure I would classify (b) as being "as simple as
possible" since it is clearly more complicated than (a). Both
call for an indirect approach, but (b) requires stringing together
a somewhat longer chain of ideas, including the idea that _inverse()_
is a monotonic function.

So I see two issues here:
-- direct versus devious reasoning
-- one-step versus multi-step reasoning

These are both important skills, but they are not entirely the
same skill. (OTOH they are not entirely different, because
almost any indirect solution requires extra steps.)

These skills are learnable and teachable. This is discussed at
http://www.av8n.com/physics/thinking.htm#sec-devious

Students who show up for physics class have been trained for
10+ years to expect problems that can be solved directly in a
single step, or not at all.

As I have said before, I reject the notion that kids are unable
or even unwilling to engage in indirect, multi-step reasoning.
They do it all the time in the games they play; they just don't
do it in class.