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Problem and problem solving

Problem is defined as a real life situation that satisfy two conditions which

are do not have solution and the problem solvers accept the challenge to solve it.

Besides, a problem exists when there is a situation you want to resolve but no

solution is readily apparent and it is decided by purposes.

When, considered the most complex of all intellectual functions, problem

solving can be defined as a higher-order cognitive process that requires the

modulation and control of more routine or fundamental skills. It occurs if an

intelligence system does not know how to proceed from a given state to adesired goal state. Not only that, a process that permeate the entire program and

provide the context in which concepts and skills can be learned. Problem solving

is part of the larger problem process that includes problem finding and problem

shaping.

There are many approaches to problem solving, depending on the nature

of the problem and the people involved in the problem. The more traditional,

rational approach is typically used and involves, such as clarifying description of

the problem, analyzing causes, identifying alternatives, assessing each

alternative, choosing one, implementing it, and evaluating whether the problem

was solved or not.

Another, more state-of-the-art approach is appreciative inquiry. That

approach asserts that problems are often the result of our own perspectives on a

phenomenon. For example, if we look at it as a problem, then it will become one

and we'll probably get very stuck on the problem. Appreciative inquiry includes

identification of our best times about the situation in the past, wishing and

thinking about what worked best then, visioning what we want in the future, and

building from our strengths to work toward our vision.

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Routine and non-routine problem

We can categorize problems into two basic types, routine and non-

routine problems. The purposes and the strategies used for solving problems

are different for each type.

Routine problem involves solving problems that are useful for daily living.

In a routine problem, the problem solver knows a solution method and only

needs to carry it out. For example, for most adults the problem 321 x 45 = ___ is

a routine problem if they know the procedure for multicolumn multiplication.

Routine problems are sometimes called exercises. It technically does not fit the

definition ofproblem stated above. When the goal of an educational activity is to

promote all the aspects of problem solving, then non-routine problems are

appropriate. Here is an example of a routine problem:

My mom gave me 35 cents. My father gave me 45 cents. My grandmothergave me 85 cents. How many cents do I have now?

In a non-routine problem, the problem solver does not initially know a

method for solving the problem. For example, the following problem (reported by

Robert Sternberg and Janet Davidson) is non-routine for most people: "Water

lilies double in area every twenty-four hours. At the beginning of the summer,

there is one water lily on the lake. It takes sixty days for the lake to be completely

covered with water lilies. On what day is the lake half covered?" In this problem,

the problem solver must invent a solution method based on working backwards

from the last day. Based on this method, the problem solver can ask what the

lake would look like on the day before the last day, and conclude that the lake is

half covered on the fifty-ninth day. Non-routine questions are always in the form

of indirect question. It is mostly concerned with developing students

mathematical reasoning power and fostering the understanding that mathematics

is a creative endeavour. From the point of view of students, non-routine problem

solving can be challenging and interesting and it can motivate students.

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From the point of view of planning classroom instruction, teachers can use

non-routine problem solving to introduce ideas extend understandings of

algorithms, skills, and concepts. This is an example of a non-routine problem:

Place the numbers 1 to 9, one in eachcircle so that the sum of the fournumbers along any of the three sidesof the triangle is 20. There are 9circles and 9 numbers to place in thecircles. Each circle must have adifferent number in it.

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Differences:

ROUTINE PROBLEMS NON-ROUTINE PROBLEMS

It has direct questions

Eg:

(x+1)(x+1)=+2+1

It has indirect questions and

has to take time to understand it

Eg:

How many squares are there ina 8 x 8 square?

Straight away get the answer by

using mathematic skills

Eg:

My mom gave me 35 cents. Myfather gave me 45 cents. Howmany cents do I have now?

Answer is getting from the

experience and then relate to

the mathematic skills

Eg:

Joe counts 48 heads and 134

legs among the chickens and

dogs on his farm. How many

dogs and how many chickens

does he have?

The problem solver knows a

solution method and only needs

to carry it out

Eg:

321 x 45 = ___

The problem solver does not

initially know a method for

solving the problem

Eg:

Find the sum of the 200 oddnumbers

Easily to understand the solvingprocess

Eg:

Differentiate 3x -x

Difficult to understand thesolving process

Eg:

Find the sum f the first 100natural numbers

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Do not has any type There are two types of problem

solving situations:

Eg:

(i) Static non-routine

(ii) Active non-routine

Involves at least one of four

arithmetic operations and it is

straight to the point.

Eg:

Find the sum of the first 25natural numbers

Not involved the arithmetical

symbols straightly but have to

follow the procedures of solving

the problem.

Sometimes, not involved

arithmetic operations

Eg:

If you have a square that is 50 x

50 with small squares inside it,

how many squares will there be

altogether?

Stresses the use of sets of

known or prescribed procedures

(algorithms)

Stresses the use of heuristics

which do not guarantee a

solution to a problem but provide

a more highly probable method

for discovering the solution to a

problem

Similarities:

The real life situations that do not have solutions

The problem solvers had accepted the challenge to solve it