Problem Solving and Creative Thinking Problem Solving What

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Problem Solving and Creative Thinking

Problem Solving and Creative Thinking

Problem Solving What is a Problem? A problem arises when a living creature has

Problem Solving What is a Problem? A problem arises when a living creature has a goal but does not know how this goal is to be reached. [A problem exists] whenever one cannot go from the given situation to the desired situation simply by action. What is Problem Solving? Problem Solving is the process of working out or discovering how to reach such a goal.

Critical Thinking • Critical thinking means making clear, reasoned judgements. • During the process

Critical Thinking • Critical thinking means making clear, reasoned judgements. • During the process of critical thinking, ideas should be reasoned and well thought out/judged

Critical Thinking • Critical thinking is that mode of thinking — about any subject,

Critical Thinking • Critical thinking is that mode of thinking — about any subject, content, or problem — in which the thinker improves the quality of his or her thinking • This is done by analyzing, assessing, and reconstructing. • Critical thinking is self-directed, self-disciplined, self-monitored, and selfcorrective thinking. • It requires effective communication and problem-solving abilities

Critical Thinking • When using critical thinking to solve a problem, we need to:

Critical Thinking • When using critical thinking to solve a problem, we need to: – Identify its purpose – Identify information – Identify inferences(s) – Identify assumptions – Identify implications

Critical Thinking A well-cultivated critical thinker: • • • Raises vital questions and problems,

Critical Thinking A well-cultivated critical thinker: • • • Raises vital questions and problems, formulating them clearly and precisely Gathers and assesses relevant information, using abstract ideas to interpret it effectively Comes to well-reasoned conclusions and solutions, testing them against relevant criteria and standards Thinks open-mindedly within alternative systems of thought, recognizing and assessing, as needs be, their assumptions, implications, and practical consequences Communicates effectively with others in figuring out solutions to complex problems

Creative Thinking Creative thinking is the process of generating novel ideas and alternative courses

Creative Thinking Creative thinking is the process of generating novel ideas and alternative courses of action, no matter how good those ideas and alternatives might be. Creative thinking should not be seen as an alternative to critical thinking When you have recognised a problem, then you should employ creative thinking to produce some options for solving the problem, then you should employ critical thinking If you haven’t come up with enough options to begin with, then your critical thinking decision procedure might produce the wrong result… a dangerous result!

Creative Thinking, Critical Thinking, and Problem Solving Creative thinking supports critical thinking While critical

Creative Thinking, Critical Thinking, and Problem Solving Creative thinking supports critical thinking While critical thinking focuses on step-by-step, linear processes aimed at arriving at a correct answer, creative thinking begins with possibility, multiple ideas, and suspended judgement. Creative thinking supports the ideas with which critical thinking works. Thus, even though these two kinds of thinking work in different ways, they actually support one another and aim at the same ultimate goal, which is to solve a problem …

Creative Thinking, Critical Thinking, and Problem Solving At the beginning of the process, creative

Creative Thinking, Critical Thinking, and Problem Solving At the beginning of the process, creative methods are used to examine the problem environment, generate ideas, and make associations. Then the analysis and judgment faculties are brought into play, and the possibilities are analyzed for a possible solution.

Who is this man?

Who is this man?

Archimedes Great inventor, mathematician etc.

Archimedes Great inventor, mathematician etc.

Archimedes’ puzzle • Did the smithy replace some of the kings gold with silver?

Archimedes’ puzzle • Did the smithy replace some of the kings gold with silver? • How did Archimedes find out? • (Not Archimedes style to torture the smithy)

Solution to Archimedes’ puzzle. • The solution, which occurred when he stepped into a

Solution to Archimedes’ puzzle. • The solution, which occurred when he stepped into a public bath and caused it to overflow, was to put a weight of gold equal to the crown, and known to be pure, into a bowl which was filled with water to the brim. Then the gold would be removed and the king’s crown put in, in its place. An alloy of lighter silver would increase the bulk of the crown and cause the bowl to overflow. [Vitruvius, De Architectura] • And the wreath was impure!

Creative thinking! • It was very useful to Archimedes – He was well respected

Creative thinking! • It was very useful to Archimedes – He was well respected and treated in Syracuse – Marcellus, the Roman general, ordered his life to be spared when Syracuse finally fell – But his obsession with maths was ultimately his downfall! • Can we be like Archimedes? • Can we learn to be creative thinkers?

4 Methods for Generating Ideas 1. Associative Techniques 2. Analytic Techniques 3. Brainstorming 4.

4 Methods for Generating Ideas 1. Associative Techniques 2. Analytic Techniques 3. Brainstorming 4. Role Playing

Associative Techniques 1. Compare something familiar to something unfamiliar.

Associative Techniques 1. Compare something familiar to something unfamiliar.

Analytic Techniques 2. • Breaking a problem down into smaller parts E. g. How

Analytic Techniques 2. • Breaking a problem down into smaller parts E. g. How can I make the Blue win the Rugby World Cup? • • • Vital components of the problem: Ensuring the Blue’s perform to their capacity Hence the 4 Rs: – – Rest Rotation Relationships within team are friendly Really discreet signaling during matches

Analytic Techniques • Good analytic techniques will help to ensure that all of the

Analytic Techniques • Good analytic techniques will help to ensure that all of the important components of the problem are addressed

Brainstorming 3. Deliberately set about coming up with alternatives, and write them all down,

Brainstorming 3. Deliberately set about coming up with alternatives, and write them all down, no matter what. • No idea is a bad idea (at least just yet)

Brainstorming is when a group comes up with a list of ideas for solving

Brainstorming is when a group comes up with a list of ideas for solving a problem They would then use critical thinking to determine what the best solution to the problem would be

Brainstorming Quantity breeds quality: the more ideas you come up with when brainstorming, the

Brainstorming Quantity breeds quality: the more ideas you come up with when brainstorming, the more likely you are to stumble across ideas of good quality

Brainstorming Avoid criticism: During the brainstorming phase, criticism should be withheld. All ideas are

Brainstorming Avoid criticism: During the brainstorming phase, criticism should be withheld. All ideas are important at this time. Once in the critical thinking stage, it is time to narrow down the ideas

Brainstorming Combine and improve ideas: Good ideas may be combined into one great idea

Brainstorming Combine and improve ideas: Good ideas may be combined into one great idea

Roleplaying 4. Roleplaying. Attempt to simulate aspects of the problem and proposed solutions. Try

Roleplaying 4. Roleplaying. Attempt to simulate aspects of the problem and proposed solutions. Try to imagine details of the relevant outcomes after your choice has been made, and attempt to put yourself in the shoes of other people. • A good method for gathering information and gaining perspective

But Archimedes was not just a creative thinker. . . • He was also

But Archimedes was not just a creative thinker. . . • He was also a prolific problem solver • So, how can we harness these 4 idea creation techniques to help us solve problems?

Problem Solving • The first thing we need to do is understand the problem

Problem Solving • The first thing we need to do is understand the problem properly and know how to represent it

The Main Message Solving real problems is a two step process: Problem Model Solution

The Main Message Solving real problems is a two step process: Problem Model Solution In order to generate potentially fruitful ideas, and thereby make it more likely that you solve your problem, make sure you understand the problem and represent the problem in the right way.

The Lights Example x y z • You have a set of 3 light

The Lights Example x y z • You have a set of 3 light switches outside a closed door. One of them controls the light inside the room. With the door closed from outside the room, you can turn the light switches on or off as many times as you would like. You can go into the room - one time only - to see the light. You cannot see the whether the light is on or off from outside the room, nor can you change the light switches while inside the room. C B A No one else is in the room to help you. The room has no windows. Based on the information above, how would you determine which of the three light switches controls the light inside the room? HINT: Be sure to use all of your senses!!!

No, there is no melting ice cube as in other 'closed room' stories nor

No, there is no melting ice cube as in other 'closed room' stories nor any real trick other than thinking out of the box. Here's the answer. Turn two switches ON, and left one switch OFF. Wait 10 minutes. Then shut one of the ON switches OFF. One switch is ON and two are now OFF. Immediately go into the room. If the light is on, you know it's the switch that is still ON. If the light is off, feel the light bulb. If the bulb is cold, it's the light switch that you never turned ON. If the bulb is still warm but the light is off, it's the switch you turned ON but then turned OFF prior to entering the room. See it's more than visual. You have to use your sense of touch. . not intuitive with a light bulb riddle!

The Drop Block Problem What will happen to the block of wood when the

The Drop Block Problem What will happen to the block of wood when the person lets go of it?

The Drop Block Problem The block will drop down as it is drawn to

The Drop Block Problem The block will drop down as it is drawn to earth by gravity

The Drop Block Problem … so long as the person is on earth.

The Drop Block Problem … so long as the person is on earth.

The Drop Block Problem It will float up if the person is under water.

The Drop Block Problem It will float up if the person is under water.

The Drop Block Problem And it will go nowhere (or a little bit sideways?

The Drop Block Problem And it will go nowhere (or a little bit sideways? !) if the person is in space.

So, how can I best represent a problem? Suggestion 1: Drop presuppositions that aren’t

So, how can I best represent a problem? Suggestion 1: Drop presuppositions that aren’t explicit in the original statement of the problem. In other words, don’t ASSUME

How can I best represent a problem? Suggestion 1: Drop presuppositions that aren’t explicit

How can I best represent a problem? Suggestion 1: Drop presuppositions that aren’t explicit in the original statement of the problem.

A Terrible Accident • • There was a terrible accident on the motorway coming

A Terrible Accident • • There was a terrible accident on the motorway coming into Wellington A man was killed on impact and his son was rushed to hospital with life-threatening injuries At the hospital, the surgeon saw the boy and said: “I can’t operate, that’s my son” What is going on here?

 • Many of us assume that surgeons have to be male, making us

• Many of us assume that surgeons have to be male, making us come up with crazy answers for a simple question • The Surgeon was the boy’s mother!!!

How can I best represent a problem? Suggestion 1: Drop presuppositions that aren’t explicit

How can I best represent a problem? Suggestion 1: Drop presuppositions that aren’t explicit in the original statement of the problem. Suggestion 2: Make sure you represent everything explicit in the original statement of the problem.

2 old high school math club pals meet up after many years Ted: All

2 old high school math club pals meet up after many years Ted: All three of my sons celebrate their birthday today. Can you tell me how old each one is? Fred: Yes, but you have to tell me something about them… Ted: The product of their ages is 36. Fred: I need more info… Ted: The sum of their ages is equal to the number of windows in the building next to us… Fred: I need more info… Ted: My oldest son has blue eyes. Fred: That is sufficient! Can Fred really know how old Ted’s sons are? How?

2 old high school math club pals meet up after many years “The product

2 old high school math club pals meet up after many years “The product of their ages is 36”: x y z 36 1 1 18 2 1 12 3 1 9 4 1 9 2 2 6 6 1 6 3 2 4 3 3

2 old high school math club pals meet up after many years “The sum

2 old high school math club pals meet up after many years “The sum of their ages is equal to the number of windows in the building next to us…” x y z 36 + 1 = 38 18 + 2 + 1 = 21 12 + 3 + 1 = 16 9 + 4 + 1 = 14 9 + 2 = 13 6 + 1 = 13 6 + 3 + 2 = 11 4 + 3 = 10

There are five houses, each of a different color and inhabited by men of

There are five houses, each of a different color and inhabited by men of different nationalities, with one unique pet, drink, and car. Some facts are given: 1. The Englishman lives in the red house. 2. The Spaniard owns the dog. 3. The man in the green house drinks cocoa. 4. The Ukrainian drinks eggnog. 5. The green house is immediately to the right (your right) of the ivory house. 6. The owner of the Oldsmobile also owns snails. 7. The owner of the Ford lives in the yellow house. 8. The man in the middle house drinks milk. 9. The Norwegian lives in the first house on the left. 10. The man who owns the Chevrolet lives in the house next to the house where the man owns a fox. 11. The Ford owner's house is next to the house where the horse is kept. 12. The Mercedes-Benz owner drinks orange juice. 13. The Japanese drives a Volkswagen. 14. The Norwegian lives next to the blue house. Who owns the Zebra? Who drinks Water?

House Color Drink Country Car Pet 1 2 3 4 5

House Color Drink Country Car Pet 1 2 3 4 5

House 1 Color Car Pet 3 blue Drink Country 2 milk Norwegian 4 5

House 1 Color Car Pet 3 blue Drink Country 2 milk Norwegian 4 5

How can I best represent a problem? Suggestion 1: Drop presuppositions that aren’t explicit

How can I best represent a problem? Suggestion 1: Drop presuppositions that aren’t explicit in the original statement of the problem. Suggestion 2: Make sure you represent everything explicit in the original statement of the problem. Suggestion 3: When thinking about how you could represent a problem, look for structural similarities between this problem and one you know the answer to. .

Why should solving logic puzzles be relevant or important to me? An ability to

Why should solving logic puzzles be relevant or important to me? An ability to solve logic puzzles is thought to be positively correlated with an ability to think creatively and solve problems of any kind. Whether or not such a correlation really exist, it is commonly believed to exist. Employers care more about creative thinking and problem solving abilities in the workforce more than any other general skill. . Creative thinking and problem solving abilities are among the most important skills sought after by universities. . Hence, universities and employers will screen candidates on the basis of their ability to solve logic puzzles.

ACTUAL MICROSOFT INTERVIEW QUESTIONS Interview Questions with a Determinate Answer 1. You have twenty

ACTUAL MICROSOFT INTERVIEW QUESTIONS Interview Questions with a Determinate Answer 1. You have twenty blue socks, twenty brown socks, and two black sock in a drawer in your room. If it is night time, and the room is completely dark, how many would you have to take out to be sure you have 2 of the same colour?

ACTUAL MICROSOFT INTERVIEW QUESTIONS Interview Questions with a Determinate Answer 1. A mother sent

ACTUAL MICROSOFT INTERVIEW QUESTIONS Interview Questions with a Determinate Answer 1. A mother sent her child to the lake and told him to bring back exactly 7 litres of water. She gave him a 5 litre bucket and a 3 litre bucket. How can the child measure out exactly 7 litres of water using nothing but the two buckets.

Summary How to solve problems creatively: • Make sure you represent the problem in

Summary How to solve problems creatively: • Make sure you represent the problem in the right way! i. Don’t assume restrictions that aren’t stipulated ii. Do represent everything explicit in the question iii. Do compare the structure of the problem with similar ones • Then generate lots of creative ideas with: i. Associative techniques ii. Analytic techniques iii. Brainstorming iv. Roleplaying

Problem Solving in the Workplace

Problem Solving in the Workplace

 • Developing the skills to solve problems logically using mathematical examples can help

• Developing the skills to solve problems logically using mathematical examples can help us learn how to approach problems in the real world • We always want to take some time to think about how we are going to handle a situation so that we know we are making the right decisions • What are some effective steps we can take to help us problem solve in the workplace?

Seven Steps to Effective Problem Solving 1. 2. 3. 4. 5. 6. 7. Identify

Seven Steps to Effective Problem Solving 1. 2. 3. 4. 5. 6. 7. Identify the Issue Understand Everyone’s Interests List the Possible Solutions Evaluate the Options Select an Option Document the Decision Evaluate the Result

Identifying the Issue • Be clear about what the problem is. • Remember that

Identifying the Issue • Be clear about what the problem is. • Remember that different people might have different views of what the issues are. • Separate the listing of issues from the identification of interests (that's the next step!).

Understand Everyone’s Interests • Interests are the needs that you want satisfied by any

Understand Everyone’s Interests • Interests are the needs that you want satisfied by any given solution. We often ignore our true interests as we become attached to one particular solution. • The best solution is the one that satisfies everyone's interests. • This is the time for active listening. Put down your differences for awhile and listen to each other with the intention to understand. • Separate the naming of interests from the listing of solutions.

List Possible Solutions • This is the time to do some brainstorming. There may

List Possible Solutions • This is the time to do some brainstorming. There may be lots of room for creativity. • Separate the listing of options from the evaluation of the options.

Evaluate the Options • What are the pluses and minuses? Honestly! • Separate the

Evaluate the Options • What are the pluses and minuses? Honestly! • Separate the evaluation of options from the selection of options.

Make a Selection • What's the best option, in the balance? • Is there

Make a Selection • What's the best option, in the balance? • Is there a way to "bundle" a number of options together for a more satisfactory solution?

Document the Agreement • Don't rely on memory. • Writing it down will help

Document the Agreement • Don't rely on memory. • Writing it down will help you think through all the details and implications.

Evaluate • Conditions may change. Make contingency agreements about foreseeable future circumstances (If-then!). •

Evaluate • Conditions may change. Make contingency agreements about foreseeable future circumstances (If-then!). • How will you monitor compliance and followthrough? • Create opportunities to evaluate the agreements and their implementation. ("Let's try it this way for three months and then look at it. ")