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Re: [Phys-L] kinematics objectives

The problem is not algorithms vs concepts, but algorithms in place of
concepts. That is the problem that Benezet noted. Students didn't think,
they just calculated and gave nonsensical answers. Physicists pick the line
of attack by looking at the concept. Students pick the attack by equation
hunting. So algorithms have a lot of value, they need to be brought in
after the concepts. And they need to be brought in as something that is
understandable rather than as a rote procedure. Notice my "just" in the
original statement.

When you emphasize problem solving over concepts, the students just discard
the concepts and memorize the methods. But if you make concepts the core,
and then bring in methods afterwards, the students can learn efficient
problem solving. I would strongly disagree with the idea that thought is
brought in afterwards. That is the currently conventional approach to math
and it is not working well. Whitehead might have changed his mind if he saw
the research that we have now.

As to grinding through algebra, you have to know what concepts you use
before you pick the algebra to use. I have given the Mirands & Joey problem
to many students, and even physics teachers. Look at activity 16 at
http://www.srri.umass.edu/mop/MOPSamples . Most can not solve it by
algebra, but all can solve it by methods a and c. Indeed even advanced
students, and students who have had several semesters of calculus have
difficulty using algebra. 99% of students who have had just algebra are
stumped. Of course I always point out that once you have the graph, you can
write the equations, and they all agree. At that point a few students (very
few) will actually do it. The activity is always done in class and if they
don't have a clue about part B after 10min, they are told to move on. But
some students have difficulty with A & C such as being able to visualize the
motion. Some actually make Miranda's graph go past the 15m mark, so there
is no solution. With a little prompting they eventually get it. Part A
poses a difficulty because they have to label the markers coming back and
then look at the numbers carefully. But once they have done this some
actually use it for solving problems. Then they are capable of solving very
difficult problems.

Sure math can be used to get answers when you can't pre-visualize the
answer. But you have to understand the math and be able to interpret the
answer. Algorithms are like computers GIGO.

John M. Clement
Houston, TX


On Wed, May 08, 2013 at 04:53:18PM -0500, John Clement wrote:
But the problem with emphasizing problem solving is that it
perpetuates the idea that you just learn algorithms. The
antidote to
that is to emphasize concepts and more difficult problems
that need to
be solved in groups.

The "algorithms" vs. "concepts" distinction sounds like code
for "math chunk size". For example, if a student can grab
some law, and start dropping terms they realize won't matter
(proportional analysis?), that counts as "conceptual", but if
they can't see that right off the bat and have to grind
through some algebra, that counts as "algorithmic". On the
other hand, maybe I'm just reacting to what seems like an
overly negative take on algorithms, and was primed by looking
up Whitehead's [1]

Civilization advances by extending the number of important
operations which we can perform without thinking about them.
Operations of thought are like cavalry charges in a battle-they are
strictly limited in number, they require fresh horses, and must only
be made at decisive moments.

Cheers,
Trevor

[1]: Alfred North Whitehead. An introduction to mathematics. 1911.
http://archive.org/details/introductiontoma00whitiala
The quote's on p. 61

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