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Creative thinking involves calling into question the assumptions underlying our customary, habitual ways of thinking and acting and then being ready to think and act differently on the basis of the critical questioning.

Components of Critical Thinking

Identifying and challenging assumptions.

Recognizing the importance of context.

Imagining and exploring alternatives.

Developing reflective skepticism.

Creative Thinkers

Consider rejecting standardized formats for problem solving.

Have an interest in a wide range of related and divergent fields.

Take multiple perspectives on a problem.

Use trial-and-error methods in their experimentation.

Have a future orientation.

Have self-confidence and trust in their own judgment.

Critical Thinking Involves

Recognizing underlying assumptions.

Scrutinizing arguments.

Judging ideas.

Judging the rationality of these justifications by comparing them to a range of varying interpretations and prospective.

Providing positive as well as negative appraisal.


Due to the rapid addition of new information and the advancement of science and technology that occur almost daily, an engineer must constantly expand his or her horizons beyond simple gathering information and relying on the basic engineering principles.

A number of homework problems have been included that are designed to enhance critical thinking skills. Critical thinking is the process we use to reflect on, access and judge the assumptions underlying our own and others ideas and actions.

Socratic questioning is at the heart of critical thinking and a number of homework problems draw from R.W. Paul’s six types of Socratic questions:

1. Questions for clarification:· Why do you say that?· How does this relate to our discussion?· “Are you going to include diffusion in your mole balance equations?”
2. Questions that probe assumptions:· What could we assume instead?· How can you verify or disapprove that assumption?· “Why are neglecting radial diffusion and including only axial diffusion?”·
3. Questions that probe reasons and evidence:· What would be an example?· What is….analogous to?· What do you think causes to happen…? Why:?· “Do you think that diffusion is responsible for the lower conversion?”
4. Questions about Viewpoints and Perspectives:· What would be an alternative?· What is another way to look at it?· Would you explain why it is necessary or beneficial, and who benefits?· Why is the best?· What are the strengths and weaknesses of…?· How are…and …similar?· What is a counterargument for…?· “With all the bends in the pipe, from an industrial/practical standpoint, do you think diffusion will affect the conversion?”
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?· “How would our results be affected if neglected diffusion?”
6. Questions about the question:· What was the point of this question?· Why do you think I asked this question?· What does…mean?· How does…apply to everyday life?· “Why do you think diffusion is important?”
1. Trigger EventAn unexpected happening that prompts a sense of inter-discomfort and perplexity
2. AppraisalA period of self scrutinizing to identify and clarify the concern.
3. ExplorationSearch for ways to explain discrepancy of to live with them
4. Developing alternative perspectives.Select those assumptions and activities that seem the most satisfactory and congruent.
5. IntegrationBecoming comfortable with, and acting, on new ideas assumption and new ways of thinking
Critical Thinking Skills

Scheffer and Rubenfeld discuss critical thinking habits and critical thinking skills. For each of the critical thinking skills shown below, they give a number of activity statements.

1. AnalyzingSeparating or breaking a whole into parts to discover their nature, functional and relationships.“I studied it piece by piece”“I sorted things out”
2. Applying StandardsJudging according to established personal, professional, or social rules or criteria.“I judged it according to…”
3. DiscriminatingRecognizing differences and similarities among things or situations and distinguishing carefully as to category or rank.“I rank ordered the various…”“I grouped things together”
4. Information SeekingSearching for evidence, facts, or knowledge by identifying relevant sources and gathering objective, subjective, historical, and current data from those sources“I knew I needed to lookup/study…”“I kept searching for data.”
5. Logical ReasoningDrawing inferences or conclusions that are supported in or justified by evidence“I deduced from the information that…”“My rationale for the conclusion was…”
6. PredictingEnvisioning a plan and its consequences“I envisioned the outcome would be…”“I was prepared for…”
7. Transforming KnowledgeChanging 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 …”

Courtesy of B. K. Scheffer and M.G. Rubenfeld, “A Consensus Statement on Critical Thinking in Nursing,” Journal of Nursing Education, 39, 352-9 (2000). Courtesy of B. K. Scheffer and M.G. Rubenfeld, “Critical Thinking: What Is It and How Do We Teach It?,” Current Issues in Nursing, J.M. Grace, Rubl, H.K. (2001).

Critical Thinking Habits of the Mind

Scheffer and Rubenfeld state that critical thinking is an essential component of professional accountability. These also give critical thinking habits that ca apply to any discipline. These habits are show below.

ConfidenceAssurance of one’s reasoning abilities
Contextual PerspectiveConsideration of the whole situation, including relationships, background, and environment, relevant to some happening
CreativityIntellectual inventiveness used to generate, discover, or restructure ideas, imagining alternatives
FlexibilityCapacity to adapt, accommodate, modify, or change thoughts, ideas, and behaviors
InquisitivenessAn eagerness to know by seeking knowledge and understanding through observation and thoughtful questioning in order to explore possibilities and alternatives
Intellectual IntegrityProcess of seeking the truth through sincere, honest means, even if the results are contrary to one’s assumptions and beliefs
IntuitionInsightful sense of knowing without conscious use of reason
Open-mindednessA viewpoint characterized by being receptive to divergent views and sensitive to one’s biases
PerseverancePursuit of a course with determination to overcome obstacles
ReflectionContemplation of a subject, especially one’s assumptions and thinking, for the purposes of deeper understanding and self-evaluation

Adapted from R. W. Paul, Critical Thinking (Santa Rosa, Calif.: Foundation for Critical Thinking, 1992).

Critical Thinking Questions

One of the goals of the course is to have the readers further develop their critical thinking skills. One way to achieve this goal is through Socratic questioning. Throughout the course students will be asked to write questions on critical thinking drawing from information the Preface section B2. Below are some examples of critical thinking questions (CTQ) that are either superficial or don’t use R. W. Paul’s Six Types of Socratic Questioning.

(1) What specifically is the product?

While this question could be a CTQ from the clarification category, it is not a good critical thinking question because it is superficial and the information is about the product and is not relevant to solving for the conversion and reactor volumes as well as critiquing the answers.

(2) Is the reactor really tubular or does it have some bulges in it?

This is not a good critical thinking question because we know in Chapter 1 that even if the reactor varies in cross sectional area the conversion-volume relationship is the same.

(3) Other no so good critical thinking questions Will this be on the exam? What’s the correct answers? Why is there a “2” in this equation? What are the units of this symbol?

While the last two questions are not CTQs, they may be valid questions.

(4) Is the rate law expected to hold at a lower temperature?

This question is not a good CTQ because it is superficial and not sufficiently penetrating.

Better would be Under what conditions might the activation energy and reaction order change in temperature. This question is a good CTQ because it explores the assumptions under which the rat e law might change, such as in Langmuir Hinschelwood kinetics.

(5) What equations should I use to solve the problem?

This question is not a good CTQ.

A similar, but better question is,

What thought process led you to choose the CSTR equation for the case of constant volumetric flow rates?

This question asks to describe the assumptions needed to arrive at the CSTR equation.

(6) Do the experimental data taken to formulate the rate law justify the reaction order being in integer?

This is a good CTQ because it probes the reason of perhaps rounding a reaction order of 1.8 up to a second order reaction when the evidence from the data support an order of 1.8.

(7) What are the consequences of make the reaction order in integer?

This is a good CTQ because it probes implications and consequences.

(8) The liquid phase volumetric flow rate was et at 25 dm3/s giving as space time of 45 seconds. This flow rate is quite high. Do you feel this flow rate can be achieved in practice and that 90% conversion can be achieved?

This is a good CTQ because it challenges the questions perspective and view points from a practical standpoint (is









) reasonable, and probes implications as to whether 90% conversion can be achieved because of perhaps poor mixing resulting from the high flow rates. 

(9) Constant molar flow rates were assumed in the treatment of this question, how would your approach to this problem differ if this assumption were not valid? Assuming that the given reaction is highly exothermic, what is the advantage of using a semi-batch reactor for this process?

These questions are of the Socratic form because they probes implications and consequences of changing the conditions of the original problem.  The student is required to understand the problem in its entirety rather than just memorizing the approach used for specific conditions.


Creative Thinkers:

Consider rejecting standardized formats for problem solving.

Have an interest in a wide range of related and divergent fields.

Take multiple perspectives on a problem.

Use trial-and-error methods in their experimentation.

Have a future orientation.

Have self-confidence and trust in their own judgment.

Creative Thinking Questions

What would exist that does not exist now?

What would be happening that does not happen now?

What decisions would be made and executed?

What accomplishments would be in place that are not now?

What patterns of behavior that currently in place would be eliminated?

Sample Questions from Reaction Engineering

P4-1 Make up and solve an original problem based on the material in this chapter. In preparing your original problem, first list the principles you want to get across and why the problem is important. Also consider relevance, interest, impact of solution, time required to obtain a solution, degree of difficulty.

P8-5(e) Explore the problem. Vary the activation energy, E, the heat of reaction, , or some other parameter to learn their effect in the reaction. Write a paragraph describing your findings.

P8-5(h) Ask another question or suggest another calculation for this reaction.

Improving Your Creative Abilities
image2.png· Keep track of your ideas at all times. Many times ideas come at unexpected times. If an idea is not written down within 24 hours it will usually be forgotten
image3.png· Pose new questions to yourself every day. An inquiring mind is a creatively active one that enlarges its area of awareness.
image4.png· Keep abreast of your field. Read the magazines, trade journals, and other literature in your field to make sure you are not using yesterday’s technology to solve toady’s problems.
image5.png· Engage in creative hobbies. Hobbies can also help you relax. An active mind is necessary for creative growth.
image6.png· Have courage and self-confidence. Be a paradigm pioneer. Assume that you can and will indeed solve the problem Persist and have the tenacity to overcome obstacles that block the solution pathway.
image7.png· Learn to know and understand yourself. Deepen your self-knowledge by learning your real strengths, skills, weaknesses, dislike, biases, expectations, fears and prejudices.
image8.png· Learn about things outside your specialty. Use cross-fertilization to bring ideas and concepts from one field or specialty to another.
image9.png· Avoid rigid, set patterns of doing things. Overcome biases and preconceived notions by looking at the problem from a fresh view point, always developing at least two or more alternative solutions to your problem.
image10.png· Be open and receptive to ideas (yours and others). New ideas are fragile; keep them from breaking by seizing on the tentative, half formed concepts and possibilities and developing them.
image11.png· Be alert in your observations. Look for similarities, differences, as well as unique and distinguishing features in situations and problems.
image12.png· Adopt a risk taking attitude. Fear of failure is the major impediment to generating solutions which are risky (i.e., small chance of succeeding) but would have a major impact if they are successful. Outlining the ways you could fail and how you would deal with these failures will reduce this obstacle to creativity.
image13.png· Keep your sense of humor. You are more creative when you are relaxed. Humor aids in putting your problems (and yourself) in perspective. Many times it relieves tension and makes you more relaxed.

Brainstorming is one of the most important techniques to generate and develop new ideas

Lateral ThinkingVertical Thinking

Comments that Reduce Brainstorming to Braindrizzling

· That won’t work· That’s too radical· It’s not our job· We don’t have enough time· That’s too much hassle  
· It’s against our policy· We haven’t done it that way before· That’s too expensive· That’s not practical· We can’t solve this problem  

Suggested Uses of Old Cars as Equipment for a Children’s Playground


      Free Association

· Take the tires and roll them along the ground.

· Get on the roof and use the car as a slide.

· Take the seats out and use them as a bed to rest between activities

· Teenagers could take the engine apart and try to put it back together.

· Cut the body of the car up to make a 3-D puzzle.

· Make a garden by planting flowers inside.

· Use the tires to crawl through as an obstacle course.

· Make into sculpture.

· Take off the doors and use as a goal for hockey.

You will notice that in every free association phase of a brainstorming exercise the ideas are generated very rapidly at first but after a while very few additional ideas are generated.  To restart the flow of ideas one can use the techniques of Vertical Thinking (Osborn) and Lateral Thinking (DeBono).  In vertical thinking you build on the ideas already generated.  For example, choose one of the ideas and ask some of the questions from Osborn’s check list.  For example, how could I make it bigger or smaller? How could I rearrange the idea or substitute for part of the idea.  A complete checklist is shown below.


Osborn’s Checklist for Adding New Ideas

Adapt?….How can This (product, idea, plan, etc.) be used as is? What are other uses it could be adapted to?
Modify?….Change the meaning, material, color, shape, odor, etc.?
Magnify?….Add new ingredient? Make longer, stronger, thicker, higher, etc.?
Minify?….Split up? Take something out? Make lighter, lower, shorter, etc.?
Substitute?…..Who else, where else or what else? Other ingredient, amterial, or approacj?
Rearrange?….Interchange parts? Other patterns, layouts? Transpose cause and effect? Change positives to negatives? Reverse roles? Turn it backwards or upside down? Sort?
Combine?….Combine parts, units, ideas? Blend? Compromise? Combine from different categories?



Practicing Creative Thinking

Practice creative thinking by with the following techniques:

· Brainstorm ideas to ask another question or suggest another calculation that can be made for this homework assignment.

· Brainstorm ways you could work this homework problem incorrectly.

· Brainstorm ways to make this problem easier or more difficult.

· Brainstorm a list of things you learned from working this homework problem and what you think the point of the problem is.

· Brainstorm the reasons why your calcualtions overpredict the conversion that was measured when the reactor was put on stream. Assume you made no numerical errors in your calculations.

· “What if…” questions: The “What if…” questions are particularly effective when used with the Living Example Problems where one varies the parameters to explore the problem and to carry out sensitivity analysis. For example, what if someone suggested that you should double the catalyst particle diameter, what would you say?.

First Steps in Solving Open-Ended Problems From  Strategies for Creative Problem Solving  by H. Scott Fogler and Steven E. LeBlanc, 1995

Write an initial problem statement. Include information on what you are to solve, and consider why you need to solve the problem.image49.jpg
Make sure you are proceeding to solve the real problem as opposed to the perceived problem (chapter 3). Carry out one or more of the following:A. Find out where the problem came fromB. Explore the problemC. Apply the Duncker DiagramD. Use the statement-restatement techniqueE. Apply Problem Analysisimage20.jpg

2. Generate solutions (chapter 4)

Understand what conceptual blocks can occur so that you will be aware of them when they surface.1. Perceptual2. Emotional3. Cultural4. Environmental5. Intellectual6. Expressiveimage21.jpg
Brainstorm7. Free association8. Osborn�s Check List9. Lateral Thinkinga. Random Stimulationb. Other People’s Viewsimage22.jpg
Analogy10. State the problem11. Generate analogies12. Solve the analogy13. Transfer the analogy to the solutionimage23.jpg
Organize the ideas/solutions that have been generated.14. Fishbone Diagramimage24.jpg
Cross Fertilize15. Draw analogies from other disciplinesimage25.jpg
Futuring. Today’s constraints (e.g. computing speed, communications) may be limiting the  generation of creative solutions. Think to the future when these constraints may no longer exist. Remove all possible constraints from the problem statement and solution criteria.image26.jpg
Incubate. Take a break. Let your subconscious work on the problem while you do something else. Sometimes all you need is a breather to achieve that final breakthrough!image27.jpg

3. Choose best alternative from the ideas generated (chapter 5)

Decision Making1. Musts2. Wants3. Adverse Consequencesimage28.jpg
Planning4. Potential Problem5. Consequences6. Preventative Action7. Contingent Actionimage29.jpg
Follow Through (chapter 6)B. Gantt ChartC. Deployment ChartD. Evaluation – Is the problem you are solving still relevant?image30.jpg
Evaluate (chapter 7)E. Does the solution satisfy all the stated and implied criteria?F. Is the solution safe to people and property?G. Is the solution ethical?image31.jpg

image32.png See an example of the OEP Algorithm in action, as applied to the Cobra Problem from the Chemical Reaction Engineering Web Site.

image33.png  Bloom’s Taxonomy  can help you classify your problem and determine a method of attack.


Problem solving is an activity whereby a best value is determined for an unknown, which is subject to a set of constraints. To determine how to attack a problem, three problem classifications can be used to direct the investigation: by type of unknown, difficulty, and open-endedness.

The author�s preference in problem classification is that of Bloom, who classifies and identifies six problem-solving skills.


A. Level of Difficulty or Skill Level

Each successive skill level calls for more advanced intellectual ability.

1. Knowledge: The remembering of previously learned material. Can the problem be solved simply by defining terms and by recalling specific facts, trends, criteria, sequences, or procedures? This level solves the type of problems such as recallin g the type of continuous flow reactor normally used for liquid-phase reactions. This is the lowest intellectual skill level. Examples of knowledge level questions are the following: Write the equations for a batch reactor and list its chara cteristics. Define image36.pngWhich reactors operate at steady state? Other words used in posing knowledge questions: Who…, When…, Where…, Identify…, What formula ….

2. Comprehension: This is the first level of understanding. Given a familiar piece of information, such as a scientific principle, can the problem be solved by recalling the appropriate information and using it in conjunction with manipulation, tr anslation, interpretation, or extrapolation of the equation or scientific principle? For example, given the reactor volume [V=(v0/k)ln(CA0/CA)], can one manipulate the design equation formulas to find the effluent concentration to find the reactor volume if the inlet concentration were doubled? Compare and contrast the advantages and uses of a CSTR and a PFR. Construct a plot of NA as a function of tOther comprehension words: … Relate…, Show…, Distinguish…, Reconstruct…, Extrapolate… This is skill level 2.

A. Drilling the concepts

A1. Plug and chug


B. Extrapolate

What is the time at 400 K?


C. More difficult/Think Problems

C1.Intermediate calculation

Example: 80% conversion is achieved for a first order reaction in a 1000 gal PFR, what conversion could be achieved in a CSTR for the same conditions?

C2.More than one intermediate calculation

Example: 80% conversion is achieved for a first order reaction achieved 1000 gal PFR, what conversion could be achieved in a CSTR operated at a temperature 100C higher.

3. Application: The next higher level of understanding is recognizing which set of principles ideas, rules, equations, or methods should be applied, given all the pertinent data. Once the principle is identified, the necessary knowledge i s recalled and the problem is solved as if it were a comprehension problem (skill level 2). An application level question might be: Make use of the mole balance to solve for the concentration exiting a PFR. Other words: … Apply…, Demonstrate…, Determine…, Illustrate….

4. Analysis: This is the process of breaking the problem into parts such that a hierarchy of subproblems or ideas is made clear and the relationships between these ideas is made explicit. In analysis, one identities missing, redundant, and contradictory information. Once the analysis of a problem is completed, the various subproblems are then reduced to problems requiring the use of skill level 3 (application). An example of an analysis question is: What conclusions did you come to after reviewing the experimental data? Other words: … Organize…, Arrange…, What are the causes …, What are the components….

5. Synthesis: This is the putting together of parts to form a new whole. Synthesis enters problem solving in many ways. A synthesis problem would be one requiring the type, size, and arrangement of equipment necessary to make styrene from ethylben zene. Given a fuzzy situation, synthesis is the ability to formulate (synthesize) a problem statement and/or the ability to propose a method of testing hypotheses. Once the various parts are synthesized, each part (problem) now uses the intellectual skill described in level 4 (analysis) to continue toward the complete solution. Examples of synthesis level question are: Find a way to explain the unexpected results of your experiment. Propose a research program that will elucidate the reaction mechanism. Other words: … Speculate…, Devise…, Design…, Develop…, What alternative…, Suppose…, Create…, What would it be like…, Imagine…, What might you see….

6. Evaluation: Once the solution to the problem has been synthesized, the solution must be evaluated. Qualitative and quantitative judgments about the extent to which the materials and methods satisfy the external and internal criteria should be m ade. An example of an evaluation question is: Is the author justified in concluding that the reaction rate is the slowest step in the mechanism. Other Words: … Was it wrong…, Will it work…, Does it solve the  real  problem…, Argue both sides…, Which do you like best…, Judge…, Rate….

B. Classification as Closed- or Open-Ended

As an application of the strategy outlined in Figure PS1-1, we consider a thumbnail sketch of the design of a chemical plant. Specifically, we want to produce 200 million pounds of styrene per year from ethylbenzene. First we synthesize a sequence of processing operations as shown in the synthesis level (row 1) in Figure PS1-2. In synthesis level we develop the type and arrangement of operations and equipment to produce ethylbenzene. Next we evaluate this sequence to learn if additional operations are necessary, such as a heat-exchange system following the separation sys tem or a feed purification system before the first heat exchanger. Following this cursory evaluation of our sequence, we analyze (row 2) each system (i.e. break it down into a number of subproblems). For example, Figure PS1-2 shows an analysis of t he reaction system. Here, we determine the type of reactor and catalyst to be used, the best temperature at which to carry out the reaction, the type and arrangement of reactor peripherals (e.g., heating/cooling of the reactor), and the optimum feed condi tions. After breaking down the reaction system into a number of subsystems, we proceed to the application skill level (row 3) to decide which laws or principles are to be applied to each subsystem. For example, to calculate the catalyst weight, W, we make use of the design equation (Ch. 6) for a packed-bed reactor,


In using our comprehension (level 2) skills we recall or look up the equation that gives –image40.png as a function of concentration, express concentration as a function of conversion X (Ch. 2), carry out the integration, and finally determine the catalyst weight necessary to achieve a conversion X.

. Use a specific example to explain how one could work backward from Bloom�s levels 5 through 1 to solve ill-defined open-ended problems.

A. For each of Bloom�s skill levels, construct an example that illustrates the skill used in that level (e.g., for level 1, what assumptions are used to derive the CSTR equation?).


image42.png Try our cobra example (check-listweb module) or move on to Closed-Ended Problems.


Open-ended problems are those which have many solutions or no solutions for the problem as defined. The solutions to these problems usually involves the use of all the skills discussed in Bloom’s Taxonomy.

image45.png Examples of Previous OEPs

image46.png First Steps in Solving Open-Ended Problems

image47.png Bloom’s Taxonomy

image48.png Creative Thinking


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