[Fhsst-maths] Maintaining problem solving chapter...

[Sanya Rajan]

Hi Sam,

I would be happy to work on the problem solving chapter. I have a couple
of questions about the chapter though; does this chapter deal with
strategies/methods to solve specific types of equations, like the
flowchart for solving quadratic equations or should it deal with solving
real world problems using the strategies learnt before?

Quadratic equations, trigonometric equations, etc. should already be
covered in the Functions and Trigonometry chapters. Therefore the
methods/tricks used to solve these problems should be covered in the
relevant chapters. If this chapter is to be about the philosophy of
problem solving then it should discuss how to model real world problems
in maths.

For example, students should be able to state the unknown, or the thing
they want to find to answer the question, the data the question gives
them to work with, and the condition, or limiting circumstances they
must work around. If they can identify all of these, and explain the
question to other people, then they have a good understanding of what
the problem is asking.

In order to solve the problem, students can start by trying to think of
a related problem they have solved before to help them. If the student
can think of a problem they have solved before that had a similar
unknown, it could also be helpful. Students can also try to restate the
problem in an easier or different way, and try to solve that. By looking
at these related problems, students may be able to use the same methods.
After students have decided which calculations, computations, or
constructions they need, and have made sure that all the data has been
used and all the conditions have been met, they can try out their
strategy. They must do all the calculations, and check them as they go
along. Then they should ask themselves, "Can I see it is right?" and
then, "Can I prove it is right?"

An example of the sort of problem in this chapter would be the rate
equation type problems, e.g. One pump fills a tank in 5 hours, another
pump fills up the same tank in 3 hours. How long will it take both
pumps, working together, to fill the tank? Then we can show how to
convert problems like these into algebraic equations, which they have
seen before, and know how to solve.

I believe that this chapter should also deal with problems that are open
ended and which might not have a single "perfect" solution.

I would welcome your comments on this.

Cheers,

Sanya Rajan
http://www.sanya.at.tt

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