Enrichment Seminar #3“Creative Thinking” –

Part B

Dr. Kelly CohenJuly 21, 2009

Getting Unstuck

Persevere! Keep tryingdifferent strategies andstay open to creative ideas.Try not to get frustrated.

Getting Unstuck

Be more active in the solution!! 1. Ask yourself questions about the problem.

Is this problem a routine one? What dataare missing? What equations can I use?Explore the problem.

2. Draw sketches of what you think that thesolution should look like.(e.g. temperature-time curve).

3. Write equations. 4. Keep track of your progress.

Getting Unstuck

• Re-focus on the fundamentals. • Review the textbook and lecture material. • Look for similar examples. • Study the examples given. • Change what is given in the example and what is

asked, then try to see how it might relate to the problem you are addressing.

Getting Unstuck

• Break the problem into parts. • Analyze the parts of the problem. • Concentrate on the parts of the problem you

understand and that can be solved.

Getting UnstuckVerbalize the problem to yourself and others

 Describe...

what the problem is what you have donewhere you are stuck

Getting Unstuck

Paraphrase. Re-describe the problem. Think of simpler ways to describe the problem. Ask other classmates to describe the problem to you in their own words.

Getting Unstuck

Use a heuristic or algorithm. The algorithm for closed-ended problems may be available to you.

Getting Unstuck

Look at extreme cases that couldgive insight and understanding.For instance: What happens if x = 0? x = infinity?

Getting Unstuck

Simplify the problem and solve alimiting case. Break up theproblem into simpler pieces andsolve each piece by itself. Finda related but simpler example andwork from there.

Getting Unstuck

Try substituting numbers to seeif a term can be neglected.

Getting Unstuck

Try solving for ratios to drop outparameters that are not given. You may find that you don't needto find some parameters becausethey cancel out!

Getting Unstuck

Look for hidden assumptions or forwhat information you have forgottento use. After reading each phraseor sentence of the problem statement,ask yourself if any assumptions canbe inferred from that phrase.

Getting Unstuck

Alternate working forward towards asolution and backwards from a solutionyou assumed. Working backwards may atleast give you clues as to how you shouldapproach the problem while working forward.

Getting Unstuck

Take a break. Incubate. Let your subconsciouswork on the problem while you do something else,like exercising, talking to friends, or justrelaxing! Sometimes all you need is a breakto achieve that final breakthrough!

Getting Unstuck

Brainstorm. Think of different approachesto the problem, no matter how strange.Guess the solution to the problem and thencheck the answer.

Getting Unstuck

Check again to make sure youare solving the right problem.Double-check all of your values,assumptions, and approaches. Makesure you haven't missed anything and that you are looking for the correct solution.

Getting Unstuck

Try using a different strategy.There is usually more than oneway to solve a problem, and youmay find a method that you haven'tconsidered is much easier than theone you're working on currently.

Getting Unstuck

Ask for help! There are manyresources you may go to for additional instruction or ideas.Instructors can usually steeryou in the right direction and clarify your understanding of theproblem. If allowed, your classmatesmay be the biggest source of help,since they usually utilize many different approaches and can relateto your approach.

R.W. Paul’s 9 Types of Socratic Questions

For a more complete and further description of Socratic Questioning, the reader is referred to “The Thinker’s Guide to The Art of Socratic Questioning”, 2006, by Richard Paul and Linda Elder. Details may be found at: www.criticalthinking.org/

R.W. Paul’s 9 Types of Socratic Questions

1. Questions for Clarification: • Why do you say that? • How does this relate to our discussion? • What do you mean? • What do we already know about...? • What is your main point? • Could you put that another way? • What do you think is the main issue? • Could you give me an example? • Could you explain that further? • Would you say more about that?

R.W. Paul’s 9 Types of Socratic Questions

2. Questions that Probe Assumptions: • What could we assume instead? • How can you verify or disprove that assumption? • Could you explain why you arrived at that conclusion? • What would happen if ...?

3. Questions that Probe Reasons and Evidence: • What would be an example? • What is... analogous to? • What do you think causes this to happen? Why? • What evidence is there to support your answer? • How do you know? • What are your reasons for saying that? • Why did you say that? • Are those reasons adequate?

R.W. Paul’s 9 Types of Socratic Questions

4. Questions about Viewpoints and Perspectives: • What would be an alternative? • What is another way to look at it? • Could you explain why it is necessary or beneficial, and to

who’s benefit? • What are the strengths and weaknesses of...? • How are... and... similar? • What is a counter argument for...?

5. Questions that Probe Implications and Consequences: • What generalizations can you make? • What are the consequences of that assumption? • What are you implying? • How does... affect...? • How does... tie in with what we learned before? • Why is… important? • What effect would that have?

R.W. Paul’s 9 Types of Socratic Questions

6. Questions about the Question: • How can we find out? • Can the question be broken down? • Is the question clear? • What does the question assume? • Why is this question important? • Is this the real question?

7. Questions that Probe Purpose: • What is the purpose of ... ? • Was this purpose justifiable? • What is the purpose of addressing this question at this

time? • What is the purpose of the main character in this story?

R.W. Paul’s 9 Types of Socratic Questions

8. Questions that Probe Concepts: • What is the main idea we are dealing with? • Why/How is this idea important? • Do these two ideas conflict? If so, how? • What main theories do we need to consider in

figuring out ... ?• 9. Questions that Probe Inferences and

Interpretations: • What conclusions are we coming to ... ? • What is the conclusion based on? • How did you reach that conclusion? • What do you think of ...? • How to interpret the data?

Critical Thinking ActionsApplying Standards: judging according to

established personal, professional, or social rules or criteria

• “I rank ordered the various…”“I grouped things together”

Analyzing: separating or breaking a whole into parts to discover their nature, function and relationships

• “I studied it piece by piece”“I sorted things out”

Information seeking: searching for evidence, facts, or knowledge by identifying relevant sources

• “I knew I needed to lookup/study…”“I kept searching for data.”

Critical Thinking ActionsLogical Reasoning: drawing inferences or

conclusions that are supported by evidence • “I deduced from the information that…,”

“My rationale for the conclusion was…”

Predicting: envisioning a plan and its consequences.

• “I envisioned the outcome would be…,”“I was prepared for…”

Transforming Knowledge: changing or converting the condition, nature, form, or function of concepts among contexts.

• “I improved on the basics by…,”“I wondered if that would fit the situation of …”

References• Strategies for Creative Problem Solving, Second Edition (ISBN: 0-

13-008279-1), by H. Scott Fogler and Steven E. LeBlanc. 2008, Pearson Education, Inc.

• http://www.boundless.org/2005/images/articles/1106_large.jpg