Problem Solving

Problem Solving

Often the biggest barrier to solving problems is the students negative attitude toward problem solving in general. Un fortunately many students enter a class with one or more of the following common misconceptions about problem solving

The way to solve a problem should be obvious when you first read a problem
No trial and error or "playing around" with different approaches to a problem is allowed
There is only one "right" way to solve a problem
You can't change a problem to make it simpler
Problem solving always proceeds in a linear, logical manner
Guessing and hunches are not allowed

Most novices will focus on getting the "right" answer and not see similarities to problems they already know how to solve. Each problem is often looked upon as a completely new and unique situation.

The following general plan for attacking problems may help.

Verbalize the problem- state the problem out loud and believe that you can solve it.
Define the problem- analyze the information provided and determine what you know and what you need to know in order to solve the problem.
Explore- brainstorm strategies for organizing the given information and finding out what you need to know.
Plan- decide on a strategy or group of strategies and list steps and substeps to the strategies.
Carry out the plan.
Assess- decide what was done, determine if you are closer to solving the problem, and why or why not.

As you become more proficient at problem solving, some of these steps will blend together and you will use less than six steps.

Once you have a plan for solving your problem you will need a strategy to help you accomplish your task. A strategy is an organized approach to a problem that breaks down the task of obtaining and organizing information into stages.

Some sample strategies

Construct a table, graph, or figure.
Look for a pattern.
List all possible solutions.
Act out the problem.
Make a model.
Talk to an expert.
Make a drawing.
Guess and check.
Work backwards.
Solve a simpler or similar problem.

It is important to remember that attitude can bring success or failure. The old adage about self-fulfilling prophesies applies to Science as well as life. If you think you will fail, you will probably fail. Focus on the process of solving the problem, rather than attaining the correct outcome.

5 Steps to Better Problem Solving

I= Identify the problem

D= Define/Represent the problem

E= Explore possible strategies

A= Act on the strategies

L= Look back and evaluate your effects

Strategies (to try)

1) Recognizing Patterns.

2) Simplify, substitute, reduce, round off...make it manageable.

3) Experiment, model, visualize.

4) Estimate: guess and test.

5) Organized Listing.

6) Deduction.

7) Algebra, Geometry skills.

8) Working Backwards: when the outcome is known and the initial conditions are needed.

problem solving skills using these steps:

l) Read and re-read the problem, at least three times.

2) Restate (list) the "facts" given, and rephrase the question. What information is needed? Is there extra information included? What's missing? Would a diagram, drawing, chart, or graph help? Organize what is known and what is needed.

3) Predict, estimate the answer, within a reasonable range. How does the problem connect with concepts, facts, already acquired?

4) Select a strategy or combination of them.

5) Work the strategy to solve the problem.

6) Check the solution in terms of the question. Does it make sense? Can it be demonstrated, extended, or applied further?

MAKE SURE YOU UNDERSTAND THE PROBLEM.
This may seem obvious but it is easy to jump straight into solving a problem before you really understand it.
So, sure, have a bit of a play around with it at first, if you like, but then read the problem carefully two or three times if necessary.
If you are still not sure about the problem try :

Talking it over with someone else; or
Writing out the problem in your own words and hvaing someone else check that what you have written is the same as the original problem.

Another way of getting going with problem solving is MAKING A START. Don't be scared of having a go! Draw some sketches, try some possible answers, talk the problem over with a friend.

MAKING MISTAKES!!
It's true. good problem solvers make plenty of mistakes.
You may have heard the expression : learn from your mistakes.
Well this statement is true. Try things out, make mistakes, then try some other way of attacking the problem.

DO NOT GET FRUSTRATED.
I know that is easy to say, but problem solving is all about coming up against some thing you don't quite understand.
That is why it is a problem.
So accept that fact and take it easy. if you worry about it too much you might lose concentration. So stay cool.

Problem Solving resources

http://www2.hawaii.edu/suremath/lessonPlans/lpMenu.html

http://www.vta.spcomm.uiuc.edu/PSG/psgl3-ov.html

http://www.awesomelibrary.org/Classroom/Science/Problem_Solving/Problem_Solving.html

http://www.enc.org/topics/inquiry/

http://ai.eecs.umich.edu/cogarch0/atlantis/index.html

http://ai.eecs.umich.edu/cogarch0/

http://www.virtualsalt.com/crebook4.htm

.:VirtualSalt

Problem Solving Techniques AWESOME

http://www.bownet.org/gradetwomath/ 2^nd grade

http://www.une.edu.au/psychology/staff/malouff/problem.htm
VERY GOOD 50 STRATEGIES EXPLAINED