[Phys-L] Re: Goals of the Introductory Course

[John Clement <clement@HAL-PC.ORG>]

Well if it were nonsense then why were teachers so surprised when they found
their students couldn't pass the FCI?  If it were easy to construct a
problem solving test that assesses conceptual understanding as well as the
FCI, then why hasn't one been published by now?  The sort of work required
to create a good test is actually quite large.  Just look at what was
necessary to create the FCI or FMCE.

The problem with using problem solving to test conceptual knowledge is that
problems can often be overcome by rote memorizing equations.  Also if
students lack the conceptual skills to solve problems, they can understand
the concepts, but lack the problem solving skills.  It appears that the two
types of testing are actually testing fairly different skills.  But once one
has both skills, then expert problem solving is possible.

Mehl found that the following problems blocked problem solving, even when
conceptual understanding was OK.
1.  Lack of visualization of the physical situation.
2.  Lack of qualitative evaluation of the situation.
3.  Poor quality of sketches when present.
4.  Lack of identification of implicit data.
5.  Lack of goals
6.  Inability to elaborate on the information.  Could not find the cues
necessary to suggest an approach.
7.  Excessive impulsivity, Unsystematic and incorrect data analysis.

These are closely related to the problems noted by the psychologist Reuven
Feuerstein as characteristic of the deprived individual.  He divides
cognition into input, elaboration, output.  He characterizes the problems
as:
A. Input phase
i.  Blurred and sweeping perception
ii.  Unplanned, impulsive and usystematic exploratory behavior.
iii. Lack or, or impaired, receptive verbal tools and concepts which affect
discrimination.
iv. Lack of, or impaired need for, precision and accuracy.
v. Lack or, or impaired use or, two sources of information.
B. Elaboration phase
i.  Inadequacy in experiencing the existe of, and in subsequently defining,
an actual problem.
ii.  Inability to select relevant as opposed to irrelevant cues in defining
a problem.
iii. Lack of, or impaired, spontaneous comparative behavior.
iv.  Lack or, or impaired, iteriorization.  (ability to abstract and use
information in mental acts, is limited.  Perceived experiences are usually
concrete in nature.)
v.  Lack of, or impaired, planning behavior.
C.  Output phase
This affect the ability to communicate results.

Notice that it is perfectly possible for students to always answer correctly
when asked to compare the force on one object with the reaction force on
another object, while still not being able to use this information in a
problem.  OTOH if the appropriate equation is memorized, momentum
calculations can be performed correctly without any understanding of
Newton't third law.

Now by deprived Feuerstein meant that the individual was not subjected to
the necessary mediated learning process to be able to overcome these
problems.  This is very similar to the Piagetian idea that students will not
gain understanding of proportional reasoning without the necessary physical
challenges.

Good evaluation can be done without the FCI, but not by just problem
solving.  Mazur also included conceptual questions the required
explanations.  The act of explaining in a coherent fashion demonstrates
understanding much better than any problem solving.  The best evaluation
would include both types of questions.  And the best teaching would aim at
both skills.

John M. Clement
Houston, TX


> > Sadly, I don't believe the ability to solve a problem or set of
> > problems, no matter has carefully crafted, will tell you if students
> > understand the content.  There is lots of data, not just the FCI which
> > strongly suggests that students can solve the problems at the end of the
> > chapter and not understand the conceptual content.  I suspect problem
> > solving is a necessary but not sufficient indicator of learniing.
>
> I would say that this is nonsense.  If one can construct a way to assess
> conceptual content--FCI for example--and one can construct problems (every
> text book known), then certainly one can craft problems that contain both,
> and both at the same time.  This may not be easy and may certainly not
> look
> like standard back of chapter problems, but I can see no fundamental
> hurdle
> to doing so.  To be sure, it is usually easier to separately test
> conceptual
> knowledge and problem solving skills, but there is no reason such can't be
> combined.  In fact, one can see aspects of the FCI questions in many
> problems--net force = 0 at constant velocity is a concept hit hard in the
> FCI and is an integral part of many problems.  What good assessment
> problems
> have to avoid is being structured exactly like example problems in the
> books--such that memorized algorithms can be used to solve them.  This
> takes
> some effort, but it is not all that difficult.  Now how well students fare
> with such questions.......;-(
>
> Rick
>
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> Professor of Physics
> Saint Mary's College
> Notre Dame, Indiana
> rtarara@saintmarys.edu
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