Re: Setting up problems

[Aaron Titus <titus@MAILAPS.ORG>]

On Wednesday, October 8, 2003, at 02:00 PM, AGraham wrote:
> I had 3 years of high school algebra from a very experienced teacher
> who
> retired at the end of my senior year.  He was supposed to teach set
> theory
> our third year (for college prep).  He refused, and spent the whole
> year
> working on word problems.  He required us to begin our solution of a
> problem
> by listing the known quantities (or "givens" as he called them), and
> then
> the unknowns (or things we were asked to find).  Failure to do this
> earned a
> zero for that problem, even if we had the correct solution.  I believe
> this
> method is very effective in teaching students to structure their
> approach to
> solving any problem.
>
> andy graham


This approach is useful for solving problems where you are given
certain things and need to solve for x -- this is typical of algebra
word problems and is typical of "traditional textbook" exercises.

However, this is not the typical format of "real-world problems" where
you are given nothing but a question and you have to decide what
quantities are needed and then make measurements to get the quantities
you need.

For example, if you were to set up a smooth inclined ramp and put a
ball at the top, let it roll down the ramp, and ask students "What is
the speed of the ball at the end of the ramp?"  Allow students to use
whatever tools they need -- meterstick, stopwatch, sonic ranger and
LabPro, protractor, etc -- to solve the problem. Students must decide
what principle they should use to solve the problem and what quantities
they should measure before they can successfully solve the problem.

I like to use Physlets for homework problems because they are more like
what I call "real-world" problems than neatly defined textbook
exercises. However, these kinds of problems are much harder because the
technique students rely on (look at what is given and find the right
equation) just doesn't work.

With that said, writing down important information given in the problem
statement is helpful because when you don't know what principle to use,
drawing a picture, redefining the problem in your own words, or
creating a table with known data sometimes helps you see what direction
to head in. I tell my students that when you're lost in the forest,
it's easier to find your way out if you are walking--maybe you'll see
something familiar.

See the Context-Rich Problems web site for more info about problem
solving. The UMINN research group has worked extensively on problem
solving.

http://groups.physics.umn.edu/physed/Research/CRP/crintro.html

AT


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