This document discusses problem solving and different types of problems. It defines a problem as a purposeful activity aimed at removing difficulties through reasoning. Problems are classified as mental, symbolic, or real. Mental problems involve contemplation, while symbolic problems require diagrams or models. Real problems are physical. The document also outlines functions and values of problem solving, including giving training in reasoning, developing proper thought habits, and improving attitudes. It provides characteristics of good problems and lists the typical steps in problem solving: recognizing the problem, proposing hypotheses, evaluating solutions, and verifying the accepted solution.

2. What is a Problem?
Is a purposeful
activity that will
remove a difficulty
or perplexity
through a process
of reasoning.

3. Reflective Thinking
Is utilized in problem solving; it
consists of two (2) phases:
1) Statement of the perplexity
or difficulty which gives rise
to thinking.
2) The act of searching, or
inquiring, to find the
material, process that will
solve or dispose of the
perplexity.
Problem solving is both a learning
and teaching procedure.

4. Classifications of Problems
1. Mental – These are
problems that are
contemplative,
reflective, academic,
reconstructive, or
imaginative. Arithmetic
problems fall under this
category.

5. Example of a Mental Problem

6. Classifications of Problems
2. Symbolic – These are
problems that require
written language,
drawing, modeling, or
construction for solution.

7. Example of a Symbolic Problem
A car starts from rest and accelerates uniformly
over a time of 5.21 seconds for a distance of 110
m. Determine the acceleration of the car.

8. Classifications of Problems
3. Real – These are material, physical, or
practical problems.
What would fall faster?

9. Functions of the Problem Method
1. To give training in reasoning.
2. To give practical knowledge
and skills.
3. To develop proper thought
habits that will enable the
child to meet whatever
exigencies in life there are.
4. To escape the consequences
of some acts.
5. To learn how to act in a new
situation.

10. Functions of the Problem Method
6. To learn how to make
something.
7. To solve a puzzling mental
problem.
8. To get out of a difficult
situation.
9. To learn to suspend judgment.
10.To satisfy curiosity.

11. Functions of the Problem Method
11.To learn to define and limit
problems.
12.To learn how to find solutions.
13.To improve judgment.
14.To verify opinion.
15.To discover a new process.
16.To invent a new device.
17.To create a new idea.
18.To improve knowledge.

12. Functions of the Problem Method
19.To entertain others.
20.To help another solve a
problem.

13. Values
Because the problem method is based on
psychological drives, like curiosity, the child’s
attitude toward school work is improved. The
problem become sits stimulus and its solution;
the goal. The child is encouraged to work on his
own ability and the teacher ceases to be a
taskmaster. It builds proper attitudes, among
which the scientific attitude of considering all
data accurately and objectively and testing the
conclusion carefully.

14. Values
Not only does the pupil improve his ability to
solve his own problems, but he also learns to
evaluate the thoughts and solutions of others.
Too often, students can recite facts but cannot
apply them to situations. Experience is problem
solving will provide opportunities to utilize these
facts, to acquire new meanings, and to gain new
insights.

15. Characteristics of a Good Problem:
1. A difficulty exists which
demands solution. It is
thought provoking.
2. The problem is clear,
definite, suitable to the level
of the students and of
practical value.
3. It is real, interesting, and
worthwhile to the class.

16. Steps in Problem Solving:
1. Recognition and statement
of the problem, originating
in a difficulty or perplexing
situation.
2. Statement of hypothesis –
inspection and proposal of
solution or solutions.
3. Critical evaluation of
suggested solution.
4. Verification of accepted
solution.