khoerul umam
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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
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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