Problem Solving Steps in Problem Solving Teaching to Enable Transfer Obstacles to Problem Solving
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Microsoft PowerPoint - 327_ErinLecture.ppt [Compatibility
Mode]Transfer
– First you need to recognize that you have a problem
– Well-defined problems versus open-ended problems
Steps in Problem Solving
• e.g. preparing a science project
– Algorithms and heuristics • e.g. elimination strategies for multiple choice exams
– Means-end analysis
Solution: use external representation
Problem #1
• Irving has begun a jogging program. He jogs 2 miles north, then turns right and jobs 3 miles, then heads left 1 mile, then turns and jogs 2 miles to the right, then he jogs 3 miles south, and finally 5 miles west. How far is he from his starting point?
Problem #2
There are three separate, equal-sized boxes. Inside each box are two separate, small boxes, and inside each of the small boxes are four even smaller boxes. How many boxes are there altogether?
Problem #2 Solution
Problem #3
A man had four chains, each three links long. He wanted to join the four chains into a single, closed chain. Having a link opened cost 2 cents and having a link closed cost 3 cents. The man had his chains joined into a closed chain for 15 cents. How did he do it?
Problem #3
– First you need a clear criterion for a successful solution
• e.g. just completing a project or receiving positive feedback
Steps in Problem Solving
Obstacles to Problem Solving
• Fixation
– Using a previously learned strategy and failing to look at a problem with a new perspective
– Functional Fixedness is a type of fixation- an individual fails to solve a problem because he or she views the elements in terms of their usual functions
An Example of Functional Fixedness Luchin’s Water Jug Problem
You have three jugs that hold different amounts. There are no marks on the jugs to allow you to fill the jugs partially and still know how much you have. Indicate how you can use your three jugs to obtain the amount listed under “goal.”
A B C Goal
5. 23 – 3 = 20
Solution: B – A – (2c) works for all problems A – C is easier and works for #5
Functional Fixedness: Inability to see solution due to previous experience or learning
An Example of Functional Fixedness
Candle Problem
You are given a candle, a small box of tacks, and some matches
Your goal: affix the candle to the wall so that it doesn’t drip onto to the floor.
Solution: you must overcome the common use of a box as a container and use it as a platform
What is Transfer?
• Transfer occurs when a person applies previous experiences and knowledge to a new situation – Schools are not effectively educating our children
if they do well on tests but cannot apply their knowledge flexibly and adaptively on problems outside the classroom
Types of Transfer
Far transfer Is different from initial learning situation.
Low-road Almost unconsciously transfers to new situation.
High-road Is conscious and effortful
Problem #1 The Parallelogram problem
The Rote Method: Area = H x B
The Meaningful Method: Let the student cut the parallelogram into parts and rearrange them in a rectangle.
H
• Give opportunities for real-world learning – Visit museums – Give real-world problem-solving and thinking
challenges • Root Concepts in Applications
– Challenge students to apply concepts to their own lives
Strategies for Helping Students Transfer Information
• Teach strategies that will generalize – 3 phases for improving transfer:
1. Initial acquisition phase- receive information about importance of a strategy and how to use it
2. Retention- students get more practice using strategy 3. Transfer- students are given a new problem to solve
• Motivation is also an important aspect of transfer
Strategies for Helping Students Transfer Information
• Teach for understanding meaning – e.g. parallelogram problem
• Encourage self-explanations when solving problems – e.g. Tower of Hanoi Problem
TOWER OF HANOI
Move the discs from the right side to the left side as shown in the 1st display Cannot place a larger disc on a smaller disc Move only one disc at a time
Transfer Study Using the Tower of Hanoi
Subjects solved several problems involving two, three, and four discs.
There were four instructions groups:
Group 1: (verbalize and think) instructed to state the reason for each move and to think of a general principle involved
Group 2: (verbalize only) instructed only to verbalize the reason for each move
Group 3: (think only) instructed only to think of a general principle
Group 4: (control) received none of these instructions
All subjects were given a transfer problem with six discs.
Transfer Study Using the Tower of Hanoi - Results
Verbalize & Think Verbalize Think
Time to Solution (min) 4.2 3.8 10.1 10.0
– First you need to recognize that you have a problem
– Well-defined problems versus open-ended problems
Steps in Problem Solving
• e.g. preparing a science project
– Algorithms and heuristics • e.g. elimination strategies for multiple choice exams
– Means-end analysis
Solution: use external representation
Problem #1
• Irving has begun a jogging program. He jogs 2 miles north, then turns right and jobs 3 miles, then heads left 1 mile, then turns and jogs 2 miles to the right, then he jogs 3 miles south, and finally 5 miles west. How far is he from his starting point?
Problem #2
There are three separate, equal-sized boxes. Inside each box are two separate, small boxes, and inside each of the small boxes are four even smaller boxes. How many boxes are there altogether?
Problem #2 Solution
Problem #3
A man had four chains, each three links long. He wanted to join the four chains into a single, closed chain. Having a link opened cost 2 cents and having a link closed cost 3 cents. The man had his chains joined into a closed chain for 15 cents. How did he do it?
Problem #3
– First you need a clear criterion for a successful solution
• e.g. just completing a project or receiving positive feedback
Steps in Problem Solving
Obstacles to Problem Solving
• Fixation
– Using a previously learned strategy and failing to look at a problem with a new perspective
– Functional Fixedness is a type of fixation- an individual fails to solve a problem because he or she views the elements in terms of their usual functions
An Example of Functional Fixedness Luchin’s Water Jug Problem
You have three jugs that hold different amounts. There are no marks on the jugs to allow you to fill the jugs partially and still know how much you have. Indicate how you can use your three jugs to obtain the amount listed under “goal.”
A B C Goal
5. 23 – 3 = 20
Solution: B – A – (2c) works for all problems A – C is easier and works for #5
Functional Fixedness: Inability to see solution due to previous experience or learning
An Example of Functional Fixedness
Candle Problem
You are given a candle, a small box of tacks, and some matches
Your goal: affix the candle to the wall so that it doesn’t drip onto to the floor.
Solution: you must overcome the common use of a box as a container and use it as a platform
What is Transfer?
• Transfer occurs when a person applies previous experiences and knowledge to a new situation – Schools are not effectively educating our children
if they do well on tests but cannot apply their knowledge flexibly and adaptively on problems outside the classroom
Types of Transfer
Far transfer Is different from initial learning situation.
Low-road Almost unconsciously transfers to new situation.
High-road Is conscious and effortful
Problem #1 The Parallelogram problem
The Rote Method: Area = H x B
The Meaningful Method: Let the student cut the parallelogram into parts and rearrange them in a rectangle.
H
• Give opportunities for real-world learning – Visit museums – Give real-world problem-solving and thinking
challenges • Root Concepts in Applications
– Challenge students to apply concepts to their own lives
Strategies for Helping Students Transfer Information
• Teach strategies that will generalize – 3 phases for improving transfer:
1. Initial acquisition phase- receive information about importance of a strategy and how to use it
2. Retention- students get more practice using strategy 3. Transfer- students are given a new problem to solve
• Motivation is also an important aspect of transfer
Strategies for Helping Students Transfer Information
• Teach for understanding meaning – e.g. parallelogram problem
• Encourage self-explanations when solving problems – e.g. Tower of Hanoi Problem
TOWER OF HANOI
Move the discs from the right side to the left side as shown in the 1st display Cannot place a larger disc on a smaller disc Move only one disc at a time
Transfer Study Using the Tower of Hanoi
Subjects solved several problems involving two, three, and four discs.
There were four instructions groups:
Group 1: (verbalize and think) instructed to state the reason for each move and to think of a general principle involved
Group 2: (verbalize only) instructed only to verbalize the reason for each move
Group 3: (think only) instructed only to think of a general principle
Group 4: (control) received none of these instructions
All subjects were given a transfer problem with six discs.
Transfer Study Using the Tower of Hanoi - Results
Verbalize & Think Verbalize Think
Time to Solution (min) 4.2 3.8 10.1 10.0
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