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Creative-and-Critical Productive Thinking

I recommend first reading the summary` of this page
because it's shorter, and some ideas have been revised.
When you effectively combine creative thinking and critical thinking, plus knowledge-of-ideas, the result is productive thinking

Generation by Selection or Invention:  During a process of problem solving, you evaluate solution-Options that are “candidates” to be a solution for the problem.  You have generated each Option by selecting an old (already known) Option or inventing a new Option.    Generating Old Information and New Information

Here are four ways to generate ideas:


• Invention by Revision:  To invent, you can revise an old Option to improve it.


• Creative Uses of Analysis:  You may find it useful to analyze an old Option into its different features, and think about ways to revise each feature to get a closer match with your goals.  This is one of the techniques that let you creatively use Analysis.


• Guided Generation of Ideas by Using Evaluation:  A creative-and-critical process of Retroduction occurs when Creative Generation is stimulated-and-guided by Critical Evaluation.  How?  Guided by critical evaluation in Quality Checks` — so you understand how the properties of current options don't match the desired properties you have defined as Goals — you creatively imagine possibilities and ask “how can I generate options that more closely match my Goals?”    { Guided Generation, Part 2 }

• Free Generation of Ideas by Avoiding Evaluation, or Avoiding Assumptions or Stimulating Creativity:  One strategy for promoting creativity is trying to temporarily avoid critical evaluation, to allow uninhibited free generation.  A more general strategy is to minimize restrictive assumptions.  And you can try various techniques to stimulate creativity.    { Free Generation, Part 2 }

Guided Generation can be free, and Free Generation can be guided, so these two thinking strategies are compatible.


More — The rest of this page will examine Guided Generation and Free Generation, plus mixed strategies that combine them (and Creative Analysis) for generating ideas by Revision.  But first,


Here is a summary of ideas from

• logical organization of knowledge is useful for thinking;  and memory – which is not sufficient for productive thinking, but is necessary – makes ideas available for quick retrieval-and-application so you can actively process the ideas in creative-and-critical thinking;

• because you use theories about “the way things are” when you think, a theory's cognitive utility (for helping you think productively) is important:

   you want a theory to be accurate (so it corresponds to reality) and easy to convert into a mental model so you can “think with the theory” to understand and make predictions;

   you "construct theory-based models of a system's composition (what it is) and operation (what it does)";  different models of a system can be useful in different ways;

  "your external representations of a model, which help you think and communicate, can be verbal, visual, mathematical, and/or physical, expressed in words, diagrams, graphs, tables, equations;  you decide how to combine these representations (using some or all, emphasizing each in the way you want, to form a personally customized blend)" when you construct internal representations in your mental models.


• you should try to "view things from the perspectives of important stakeholders in a design project" with empathetic thinking (external metacognition?) to supplement the egocentric thinking you do from your own perspective.


The Overview of Productive Thinking also explains that "thinking is examined most deeply" in Creative-and-Critical Productive Thinking which is this page, the one you're now reading.



Guided Generation of Ideas — Part 2

a summary:   a creative Generation of Ideas, guided by critical Evaluation of Ideas, is Retroduction.

a summary with more detail:   Retroductive Logic is used during a process in which your creative generation of ideas is stimulated-and-guided by your critical evaluation of ideas during Quality Checks in which quality is defined by the goals you have defined;  this goals-directed critical evaluation provides an “aiming point” for creative generation, with your awareness of the goals “pulling your ideas” toward these goals.


A useful visual-and-verbal description of Creative-and-Critical Retroduction, showing the interactions between Generation-modes and Evaluation-modes, is in Using the 3 Evaluation-Comparisons`.


We’ll look at retroductive generation applied for three objectives, for designing a Theory, Product, and Experiment.  Historically, retroductive logic was first used for theories, and that’s where we'll begin.


• Generating Theories by Retroduction:  We can use Deductive Logic to make predictions with an if-then question: “If this is the theory, then what will be the observations?”   By contrast, Retroductive Logic asks a question that is past tense (thus the “retro” in retroduction) and is reversed: “These were the observations, so what could the theory be?”   In retroductive generation you do mental experiments, over and over, each time “trying out” a different Theory-Option (being generated by selecting an old theory, or inventing a new theory) with the goal of producing Predictions that match the known Observations.  Your goal is to find a theory that, if true, would explain what has been observed.    { Predictions can be made by using theory/model-based deduction or simulation, or experience-based inductive extrapolation. }

• Generating Products by Retroduction:  In a similar way, you can do mental experiments, over and over, each time “trying out” a different Product-Option (old or new) with the goal of finding an Option whose Properties match your desired Goal-Properties.     { The process of retroductive generation is similar, whether the objective is a product, activity, or strategy. }

• Generating Experiments by Retroduction:  And you can do mental experiments, over and over, each time “trying out” a different Experimental System (old or new) with the goal of finding “Experimental Systems that will produce new information (to supplement old information) that could be useful for your design project, or at least could be interesting.”    { quoting from Introductory Overview of Experimental Design }


Similarities and Differences in Applications 

Let's compare Guided Generation for Theories, Products (or Activities, Strategies), and Experiments.

Reality and Quality:  For a designing of theories, your creative generation is guided by critical evaluation in Reality Checks.  For products, strategies, activities, or experimental systems (which are a special type of activity), your creative generation is guided by critical evaluation in Quality Checks.

Mental versus Physical:  During retroduction there is a difference between the two kinds of Quality Checks, which use feedback that is either Mental or Physical, provided by Predictions or Observations.  This is indicated in two diagrams of Design Process`.  When you click Diagram 3 the term "retroductive logic" appears three times, but... why does one of these have a dotted line?  And in the lower part of Diagram 4b (to EVALUATE), why does purple text-and-arrows (for retroduction) appear on the left side and center, but not the right side?   It’s because in a Mental Quality Check you make PREDICTIONS, and also in a Mental-and-Physical Reality Check, but not in a Physical Quality Check;  mental predicting is required for retroductive generation, so each description above begins with “do mental experiments” because these let you make mental predictions.   A knowledge of Observed Properties (in a Physical Quality Check) can help guide retroduction by showing ways in which an Option's observed properties don't match the desired properties for a Solution, but (and thus its line is dotted, not solid) the actual retroductive generation must be done using predictions in Mental Quality Checks, or in Mental-and-Physical Reality Checks.


Differences in Divergence

Now we'll compare Divergence-of-Inventions for Theories, Products, and Experiments.

When you search for the best option, you'll find that a tough competition — because several options offer different benefits, with each better for achieving some goal-properties but not others — is more likely with products (or activities, strategies) or experiments, compared with theories.  Why?  When you design a theory the main goal is to match known observations, and this tight constraint — compared with the less restrictive goal of finding "useful... interesting" experiments — allows less divergence for theories.  And typically there are more ways for several product-options to "offer different benefits" than for several theories.*

This difference in divergence occurs whether you search for options by using Guided Generation (above) and/or Free Generation (below).


* Despite some claims of radical postmodernism — which takes a rational idea and “runs with it” to silly extremes — nature operates in a particular way, and if some scientists describe it in another way their science is wrong.    { But to avoid misinterpretation, this bold statement should be clarified — by explaining that temporary controversies often occur, and theories differ in cognitive utilities, and some questions (e.g., what causes cancer? what is the best strategy for nutrition?) require complex “answers” — which I've done in another page (along with thoughts about short-term and long-term divergences in science & design) so in this page it won't interrupt the main flow of ideas. }


A Divergent Search for New Objectives

In a design project, the objective (the problem to be solved) has been specified.  Therefore, even if many divergent solution-options are being generated, the objective-and-goals are fixed.

In a different type of divergence, we ask “what kinds of problems might the current options solve?”  This question will stimulate searches — which are retroductive because they are based on known options with known properties — whose purpose is to find new applications for these options (as-is, or revised to make them more effective for a different application), to find new objectives for new design projects.



• Free Generation  (Part 2)

This page begins by saying that Productive Thinking occurs “when we effectively combine Creative Thinking and Critical Thinking, plus Knowledge-of-Ideas.”  How can you effectively combine these three aspects of thinking?  Critical Thinking and accurate Ideas-Knowledge are mutually supportive, because critical evaluation helps you construct accurate ideas, and the more you truly know (when your ideas are accurate) the better you can evaluate.  But when Creative Thinking is combined with Critical Thinking or with Ideas-Knowledge, the result can be either productive or unproductive, as explained below.


Stimulating Free Generation by Reducing Harsh Attitudes

A productive invention of useful ideas requires combining creative invention with critical evaluation.  But being critical in the wrong way — with a harsh attitude, causing someone (yourself or another) to worry about feeling insulted later when they hear “your idea was dumb,” implying “you're not very smart if that was the best you could do” — can stifle creativity.

To avoid this, a technique of Brainstorm-and-Edit combines two strategies:

First, do what is necessary to minimize harsh attitudes, to produce a comfortable working atmosphere that encourages and nurtures creativity.  Then stimulate creativity by “playing games” with the balance of creative-and-critical, temporarily shifting this balance in favor of creativity.  How?  During a brainstorming phase, critical restraints are minimized to encourage a free creativity in generating lots of ideas.

Second, in a later editing phase these ideas will be critically checked for quality.

Because of this second step, during a brainstorming phase the inventors can feel comfortable in thinking freely (by consciously trying to see in new ways, to imagine new possibilities without critical restrictions) because they have the security of knowing that their wild ideas will not be used prematurely before these ideas have been logically evaluated in the editing phase that follows.*  The principle of this strategy is to allow an effective operation of both creative thinking and critical thinking.  Of course, the editing phase requires logical evaluation and saying “no” to some ideas;  but this should be done carefully, with sensitivity and caring, in a way that doesn't discourage creativity during future brainstorming sessions.

Brainstorming can stimulate individual creativity and collaborative creativity.

* We should not hinder the motion of a car by always driving with restrictive brakes, and we should not hinder the flow of creativity by always thinking with restrictive critical attitudes.  But a car needs brakes, and a productive thinker needs critical thinking.

You Decide:  In their Bootcamp Bootleg (which includes brainstorming and much more) the Stanford Design School says "the fundamental principle of ideation is to be cognizant of when you and your team are generating ideas and when you are evaluating ideas, and mix the two only intentionally."  Notice that they don't tell you to never mix generating with evaluating;  instead their principle is to be aware of your thinking, and control it.    /    Another useful summary of principles for brainstorming comes from EPICS Design Process. }

Some pros & cons of brainstorming, and ways to do it more effectively, are examined in my links-page for Creative Thinking.


Stimulating Free Generation by Reducing Restrictive Assumptions

In my model of Design Process a Generation of ideas includes both Selection (of old ideas) and Invention (of new ideas) because either might become a solution for a problem.  A productive interaction between old and new occurs when an old idea is revised to invent a new idea.  But a knowledge of old ideas can hinder creative invention of new ideas,* IF a knowledge of “the way things have been” becomes an assumed psychological certainty about “the way things must be” and this blocks creativity.

* Similarly, if some old ideas are viewed as “the way things must be” this can hinder a finding-and-selecting of other old ideas.  Thus, a full range of free generation will allow a free selection (of old ideas) and a free invention (of new ideas).

Although "knowledge... can hinder creative invention," for productive thinking you want the best of both.  You want a solid foundation of knowledge about what has been and now is, plus the ability to think creatively about what could be, with a flexible style of thinking that lets you expand the range of options you generate.  How?

When you're aiming for innovation, but you seem to be stuck in a rigid mental rut, ask “am I making any unwarranted assumptions that are reducing the flexibility of my thinking and restricting the scope of my inventions?”

If you’re worried about “making a mistake” you can try Brainstorm-and-Edit, as described above.
You can intentionally try to “think outside the box” by viewing situations from new perspectives, with conscious shifts of perspective.


Or just take a break:  If you work on a problem but don't solve it, and then stop for awhile to do something else (for work or play), when you return to the problem you may be able to solve it.  Why?  Your thinking may have escaped from an unproductive rut, or the break has reduced your fatigue and restored fresh thinking, or you have learned new information or discovered a key insight, or subconscious thought (during work or play, or while sleeping) has supplemented your conscious thinking in useful ways.    MORE – Incubation: the On-and-Off Process of Using “Vacations” to Solve Problems


Revision and Innovation:  These will clash IF an assumption that "the way things must be" is to begin invention with an old idea, which restricts the freedom of creative innovation.  But they should be compatible and supportive.

Old and New:  Productive thinking can arise from tradition and/or innovation.  You can generate useful ideas by seeing from a new perspective, or just seeing more clearly from a familiar perspective.  Sometimes new ideas are needed, but a skillful application of old ideas might be the easiest-and-best way to succeed, or (more often) using a combination of old and new.     { Perseverance and Flexibility }


Using Techniques to Stimulate Creativity

Tips for Enhancing Creativity:  You'll find web-resources with a variety of creativity-stimulating techniques (brainstorming, reducing restrictions, and more) in my links-page for Creative Thinking in Education and for Life which also briefly explains what creativity is, why you should want more of it, and how you can improve it.  One set of techniques for stimulating creativity is...

Creative-and-Critical Uses of Analysis is a partner-page, written to extend-and-supplement for this page by describing techniques that can be useful during a problem-solving project, and for helping students improve their productive thinking.



Combining Strategies-for-Invention

The page introduction` describes four strategies for generating ideas: Revision, Analysis, Guided Generation & Free Generation.  All of these can be mutually supportive.


I.O.U. — I think this concluding part of the page contains many interesting ideas, but (re-looking at it again in June 2013) parts of it could use some revising, and I'll try to do this sometime during late summer, maybe in late August.


Compatibility — for Innovation and Free Generation

In a Free Generation of Ideas, you have "the ability to think creatively about what could be, with a flexible style of thinking that lets you expand the range of options you generate."  This is compatible with all of the other strategies.


A Useful Combination — Revision using Analysis with Guided Generation

Thinking that is productive often arises from this combination of strategies, when you revise a known Option by using analysis — by thinking about the Option's features (and how these affect its properties) and imagining how you can change each feature to improve its properties — while you are being guided by an awareness (based on feedback from evaluative Quality Checks) of ways in which the Option's current properties don't match the desired properties you have defined as goals.  As in a children's game where “you're getting warmer” is a clue, being aware of goals can help you decide if your current revising is moving in a productive direction because it's moving you closer to the goals.


Left Side and Right Side:  If you have clicked any of the three links above (left side, properties, an awareness...), this page will be in the right frame.  Because every link below opens in the left frame, you'll be able to see the linked-to section (left side) and this section (right side), which makes it easier for you to mentally combine what both sides say about a topic.

Free Generation can use Guided Generation

The main requirement for Free Generation is freedom from the restrictive assumptions that occur when a knowledge of "the way things have been" becomes a freedom-restricting certainty about "the way things must be."  But these past-oriented assumptions are different than the future-oriented awareness of “what should be” in the goal-directed searching of Guided Generation that can stimulate a Free Generation of ideas about "what could be, with a flexible style of thinking that lets you expand the range of options you generate."

Another condition for Free Generation is freedom from worries about humiliation due to harsh attitudes that imply “your idea was dumb” so “you're not very smart.”  But this harsh attitude, which is different than the beneficial goal-directed awareness of Guided Generation, should be minimized.  When using a strategy of Brainstorm-and-Edit for the purpose of “feeling more free” in the brainstorming phase, the editing phase does require logical evaluation, but "this should be done carefully, with sensitivity."



When you generate options, sometimes you invent a new Option that is very different.  It's difficult (impossible?) to invent a new option that is totally different and also is useful.  But in a spectrum of innovation — ranging from no change through minor revision and major revision to very innovative — some new options are “more new” than others.

update:  Originally, I categorized Innovation as a "way to generate" (along with Revision, Analysis, Guided Generation, Free Generation) but...  Although aiming for innovation is a strategy for a process, the actual innovations — the ideas for options that are innovative, that seem “especially new” — are a result of thinking, and they can be produced by any of the other 4 strategies for thinking.  Because innovation is a result (not a "way"), I have revised the sections about innovation.   /   I.O.U. - This revision will be finished later.  Currently it isn't yet complete, as you can see in the following paragraph:


Innovation can arise from revision of old ideas or from invention of new ideas, although almost all “new” ideas have some connection with old ideas, as explained above.  But for simplicity, the sections below assume that innovations are “new enough” to be considered new.  { Revision can be guided (as in analysis-with-guidance) or relatively unguided. }


Using Revision for Innovative Invention

Here is a visually-logical way to think about interactions between selection-and-revision (of old options) to produce innovative new options:

Imagine a “landscape of solution-options” with many hills.  On each hill is a set of related options that are variations on the same basic theme, that could be generated by starting with one option (old or new) and revising it.  The altitude of an option represents its evaluation-status (based on all available information) so “higher is better.”

A Local Maximum:  Imagine that you first invented Option 1a, on Hill 1.  Then invention-by-revision led to Option 1b that you think is better than 1a, so 1b (with higher evaluation-status) is “higher on the hill” and is thus closer to the best possible option in this set of related options, which is the Local Maximum for Hill 1.  In this example, we'll imagine that 1b is also higher than later revisions, 1c and 1d.

Other Local Maximums:  You also may decide to revise an Option 2a (on Hill 2) that you have selected or invented, to invent Options 2b, 2c,... in an effort to find the Local Maximum of Evaluation-Status for Hill 2.  You also can try to select-or-invent Option 3a (on Hill 3) and then revise it into 3b,... to seek the Local Maximum on Hill 3, and so on.  Each new option (2a, 3a, 4a,...) is the “pioneer on a new hill” that can be a starting point for revisions.

The Global Maximum:  You compare the Local Maxima (on Hills 1, 2, 3, 4,...) and evaluate them to decide which is the best of all, the Global Maximum.

different ways to revise, like mountain climbers trying one pass or another??


Revision of an old option can be innovative because:

    different options (1, 2, 3, 4,...) might themselves be the result of revisions;  for example, Option 3 might be a revision of Option 1, or perhaps a combining of Options 1 and 2.  ( In terms of analogy with landscape-topology, sometimes a ridge connects two hills, making it difficult to know where one hill ends and the other begins. )
    degree of innovation varies, "ranging from no change through minor revision and major revision to very innovative," so it may be difficult to clearly distinguish between revision and innovation.
    revision can produce innovation, when revising part(s) of an old option generates a new option that is different enough to be truly innovative;  revision should not imply “small change” or “not creative”, because a revision-change can be small and creative, or large and creative.
Ideally, you can combine the best of Revision and Innovation, Old and New.



The theme of "combining" continues in these two brief sections:


Combining Cognition-and-Metacognition Effectively

This page begins by analyzing a process of productive thinking into three aspects (creative thinking, critical thinking, ideas-knowledge)* whose interactions are examined in Free Generation - Part 2.  Design Process promotes a synergistic blending of all three, with each supporting the others to make thinking more productive.

When a process of problem solving (or listening, reading, writing,...) is going well, these aspects of thinking spontaneously combine in ways that are effective and intuitive, so we can just “go with the flow” and let it happen.  At other times it can be useful to “think about thinking” which is called metacognition.  Deciding when to let it flow, and when to think about the process — making decisions that effectively regulate your metacognition by turning it off & on, and fine-tuning its characteristics by adjusting how it’s done — is a valuable metacognitive skill.

* In addition to my three-aspect analysis (which is a simplified model of complex thinking), other analyses are used in other models of productive thinking, described in the page-ending appendix.


Collaborative Productivity

Most of this page examines the thinking of an individual person.  But in groups, productive interactions can occur.  For example, I describe the benefits of "seeing from a new perspective" for free generation and this often occurs when two people contribute their differing perspectives.  A communication about perspectives (about “how it seems from my perspective”) occurs when ideas-for-options are shared, and in a sharing of feedback about the ideas of other people.

For more about collaboration in design, see the conclusion of Coordinating a Process of Design.



Competitive Options — Opportunities and Challenges

When you compare different local maximums (like 2c versus 3d) to search for a global maximum, you'll probably find "a tough competition because each option offers different benefits, with each better for achieving some goal-properties and not others."  But a tough competition also can occur between closely related options like 2c vs 2d.  In either case you can...

try to get the best of both:  Don't limit yourself to viewing this only as a competition of 2c-versus-3d, so it's 2c-OR-3d.  Instead, think “2c-AND-3d” by trying to find a creative solution that combines the best of both.  Ask “how can I revise 2c so it will gain some of the unique benefits of 3d, or revise 3d so it also has what 2c offers?”  Or, in a similar strategy (just described differently), try to invent an innovative new option that is a hybrid of 2-plus-3 (2+3) or 2c-plus-3d, combining the best of both while minimizing their weaknesses.

decide what is more important:  If these actions (revising or combining) don't seem possible, so you're forced to choose between the differing benefits of 2c and 3d, you'll have to think carefully about your goals to decide which goal-properties are more important, based on your values and priorities.


Creative Uses of Analysis (more about Competitive Options)
Cognitive Utility & Productive Thinking (a summary-with-links)



Here are a few of the many Models of Thinking:  my three-aspect analysis (Creativity, Critical Thinking, Conceptual Knowledge) used in this page;  my original model of Scientific Method described Productive Thinking as a combining of Creativity & Critical Thinking with the Memory (for Conceptual Knowledge & Procedural Knowledge) and Motivation that I still think are very important, even though they aren't heavily emphasized in this page;  in other models for ideas-and-skills, educational researchers at CRESST constructed a model of Problem Solving with Motivation, Metacognition, Conceptual Knowledge and Procedural Knowledge, plus Collaboration and Communication;  and Robert Marzano defines educational objectives in terms of three systems (Self-System, Metacognitive System, Cognitive System) and a Knowledge Domain that includes Information, Mental Procedures, and Physical Procedures.

These models, and others, are useful in different ways for different purposes, as explained in Functions of Models.