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Re: [Phys-L] kinematics objectives



Yes this is a problem, but it is the first problem after 16 other activities
which are aimed at conceptual understanding. It is followed by a set of 6
problems which require careful thought. So the problem solving is
subordinate to the concept building. The following page of problems have
some that can not be easily solved using algebra, and are easily solved
using graphs. But some are easily solved using simple arithmetic. Then
following that the students go back to building concepts (tools?). Notice
the problems are limited in number, but higher in difficulty. The last one
is purely an exercise in keeping the facts straight and need a bit of paper
and pencil work along with possible a timeline. The arithmetic is actually
simple.

While one can craft good problems, they must be preceded by good conceptual
understanding. Actually this problem is not designed to be just a problem.
It is designed to help break down the student tendency to plug and chug. It
is also designed to introduce alternate methods for solving problems that
have strong intuition connections. This is actually also an attack on a
misconception that you have to always use memorized equations. To use
equations you have to write them. Unfortunately the standard HS math
teaching never gets around to using the X intercept. Indeed it never builds
good understanding of why the slope intercept formual works. So it has some
strong conceptual links but in the form of a problem.

As to the statement that algebra was not the easiest it is a bit of clusure,
or a minilecture in print. It is designed to prod the students to consider
other methods of solving problems. As to memorization, I don't consider the
idea that algebra can be difficult as a memorized concept that will cause
difficulties. The learning cycle can have lectures in the middle part.
Actually activity 16 & 17 together form a learning cycle. In 16 the
students explore other methods for solving problems, then in 17 they have
the application phase. The little paragraph at the end of 16 and the
reflections all form the middle part of the learning cycle where you have
concept development. So I always give A16, then A17 for a complete learning
cycle.

So I am not against problems, but I am against just basing the course on
problems. But I am against the over-reliance on algebra when there are
alternate methods. The Modeling program has found that students who are
taught geometric methods end up being better problem solvers. The research
going back at least 20 decades shows that students need to have multiple
representations graphical, pictorial, descriptive, and algebra. But the
algebra should come last to combat the tendency to be equation hunters.

John M. Clement
Houston, TX



A question about the below Miranda/Joey exercise that you
used as an example.

In the reflection section I am quite bothered by the "final
note" section where the authors tell the students what the
correct answer is for their own self-reflection!

"In this context, using algebra was not the easiest."

This strikes me as reinforcing a memorize "the correct
answer" mode of thought amongst students. And goes against
the idea of self-reflection being a personal view based on
one's own personal experience. Just curious about your
opinion regarding this minor point.

Incidently, I consider this exercise to be a problem and not
a conceptual question. Or at least it is a reasonable
example of what I was referring to in a previous post about
the use of well written problems also testing for concepts as
well as problem solving ability. (in particular, in that
post I suspect that a lot of the denigration of problems are
really straw-man type arguments, based upon poorly written problems.)