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Khoerul Umam

Mathematics Education PostgraduateSurabaya State University


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Problem solving is a process and skill that

you develop over time to be used whenneeding to solve immediate problems inorder to achieve a goal.

Problem Solving


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Mathematical problem solving is theresolution of a situation in mathematics

which regarded as a problem by the personwho resolves it.

Bell, F. H..1978. Teaching and Learning Mathematics. New York : Wm.C. Brown Company.

Problem Solving mathematics


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Benefits IN MATH EDU

As Prof. R. Soejadi said in Matematika untuk Guru

dan Orang Tua murid development of mathematics

occured when people around the world required to

solved abundence of real life tasks. Naturally, the

main point of problem solving is to educate

students to be able to solve a lot of problem in the

real life spesifically mathematics.


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Problem Solving Process

Problem Solving Approach Problem Solving Strategies

Problem Solving
http://var/www/apps/conversion/current/tmp/scratch23137/slide7.xmlhttp://var/www/apps/conversion/current/tmp/scratch23137/slide27.xmlhttp://var/www/apps/conversion/current/tmp/scratch23137/slide27.xmlhttp://var/www/apps/conversion/current/tmp/scratch23137/slide7.xml


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Understand the problem

Plan how to solve it

Carry out the plan

Look back at your work.

Problem Solving


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Polyas problem solving steps

1. UNDERSTANDING THE PROBLEM

2. DEVISING A PLAN (To invent something new or a new wayof doing

something)

3. CARRYING OUT THE PLAN

4. LOOKING BACK


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OthersSteps


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7 procee of problem solving

1. Finding the right problem to solve

2. Defining the problem

3. Analysing the problem

4. Developing possibilities5. Selecting the best solution

6. Implementing

7. Evaluating and learning

Understanding

DevisingPlan

Carrying out

PlanLookingBack


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Defining the problem


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Analysing the problem


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Developing possibilities


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Selecting the best solution


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Selecting the best solution


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Implementing


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Evaluating and learning


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Problem Solving Plan in 4 Steps:Deb Russel :

1. Clues = Understanding

a fact or a piece of evidence that helps you discover theanswer to a problem

2. Game Plan = Devising Plan3. Solve = Carrying out the plan

4. Reflect = Looking Back


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Problem Solving process

1. Problem Definition.

2. Problem Analysis.

3. Generating possible Solutions.

4. Analyzing the Solutions.

5. Selecting the best Solution(s).

6. Planning the next course of action (Next Steps)

Understanding

DevisingPlanCarrying outPlan Looking

Back


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The Six-Step Problem-SolvingProcess

1. Recognize the problem

2. Gather data relative to the problem

3. List possible solutions to the problem

4. Test possible solutions to the problem

5. Select the best solution to the problem

6. Implement the problem-solution

Understanding

DevisingPlan

Carrying outPlanLookingBack


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7 steps problem solving

Understanding : 1, 2

Devising Plan :3, 4, 5

Carrying outPlan ; 6

Looking Back ;7


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Instruction Students Response Mathematics Word

Teacher tell a question forequality in two kinds ofvariabel

Students write a question 2x + 3y = 24

Teacher ask to find thevalue of x if value of y is

6.

Students try to analyseand guess the answer.

And write the requirmentfor equestion.

If y is 6. What is thevalue of x for 2x +

3y =24

Teacher encourage tostudents to put the valueof y into a equestion.

Students write 2x + 3(6) = 24

Students multiple 3 by 6.The product is 18. soAfterwards, subtracting24 with 18.

2x + 18 = 242x = 24 18

Finally students found thevalue of x is

2x = 6X =3

Equestion Sampel

O d d P bl


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Open ended Problem

SolvingA class is planning transportation for a field trip. Cars can take

4 passengers. Vans can take 6 passengers. There are 24students in the class. How many cars and vans are necessaryto take the whole class? Please explain your work, usingpicture, numbers, and words. Show as many solution as youcan.

Let all students to take some notes. Teacher encouragestudents to try to imagine that we are going to held thevocation in the next month. Thus try some of your friendshave been in a car. Then you can try to count the reminders. Iffour students have been in car. Is there anyone of you can

guess how many students are we now ? Try to subtract thetotal students by some others who has just in. Any body whowants to try. 20 students. Try to put some of you in van andsome others in cars. Afterwards, you can try to count the totalof vans and cars which is used to take the entire class for afield trip.


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Comparasion

Traditional Problem Solving

- The question has only possible

answer.

- Dying the creativity ability

- Students can creatively reply the

question by a lot of choices.

- Encourage the students to decide

their own


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4/19/12Problem Solving Strategies

Draw a diagram

Make a list

Gues and check

Divide and conquer

Strat the entert

Look for a pattern


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Problem Solving Strategiesfcat

1. Look for a pattern

2. Make an organized list

3. Guess and check

4. Make a table

5. Work backwards

6. Use logical reasoning

7. Draw a diagram

8. Solve a simpler problem

9. Read the problem carefully

10. Create problem solving journals


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Problem Solving Strategies

1. Find a pattern2. Make a table

3. Work Backwards

4. Guess and Check5. Draw a Picture

6. Make a list

7. Write a Number Sentence8. Use Logical Reasoning


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Problem solving strategiesGoerge Lenchers Problem Solving in Mathematics.

Draw a picture of a diagram

Find a pattern Make an organized list

Make a table

Solve a simpler problem

Trial and error Experimenting

Act out the problem

Work backwards

Write an equation

Use deducation.


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Creative ProblemSoling


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Definition

Creative problem solving is the mental processof creating a solution to a problem. It is a specialform of problem solving in which the solution isindependently created rather than learned with

assistance.Mental means connected with or happening in themind, involving the process of thinking. Page 960(Oxford Advance Learners Dictionary)From Wikipedia, the free encyclopedia

The Creative Problem Solving Process (CPS), also known as the Osborn-Parnes CPS process,was developed by Alex Osborn and Dr. Sidney J. Parnes in the 1950s.[1] CPS is a structuredmethod for generating novel and useful solutions to problems
http://en.wikipedia.org/wiki/Creative_Problem_Solving_Process#cite_note-0http://en.wikipedia.org/wiki/Creative_Problem_Solving_Process#cite_note-0


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Creative problem solving

Process Stage Steps

Explore the

Challenge

Objective Finding (identify the goal, wish or challenge)

Fact Finding (gather the relevant data)

Problem Finding (clarify the problems that need to be solved

in order to achieve the goal)

Generate Ideas Idea Finding (generate ideas to solve the identified problem)

Prepare for ActionSolution Finding (move from idea to implementable solution)

Acceptance Finding (plan for action)

Source : International , Creative Problem Solving Insitute,

CRAV Conference.


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You are the mastersof your own world

Khoerul Umam,CC, SPd

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