Be Creative-and-Critical
What, Why, and How
Principles and Strategies
Liberating Creativity
Creativity for Living
Creativity in Education
Research about Creativity
What is critical thinking?
Why teach critical thinking?
How to teach it effectively?
The Ethics of Critical Thinking


Problems and Problem Solving

Creative-and-Critical Thinking
Multiple Intelligences & Styles
Problems in Design & Science

Problem Solving in Education

You can explore other parts of our
website for Whole-Person Education
(using links at bottom of page) and
our community of science-and-faith.

Education for
Problem Solving

( in Schools, for Life )

The sections in this page are:


Problems and Problem Solving


Creative-and-Critical Problem Solving


         Multiple Intelligences & Learning Styles         


Problem Solving in Design and Science


Teaching Problem Solving in Schools


Problems and Problem Solving

What is a problem?  In common language, a problem is an unpleasant situation, a difficulty.  But in education the first definition in Webster's Dictionary — "a question raised for inquiry, consideration, or solution" — is a more common meaning.  More important, in life a problem is any situation, in any area of life, where you have an opportunity to make a difference, to make things better;  and problem solving is converting an actual current state into a desired future state.  Whenever you are thinking creatively-and-critically about ways to increase the quality of life (or to avoid a decrease in quality), you are actively involved in problem solving.     {Problem Solving in All Areas of Life by Craig Rusbult, editor of this links-page}  {more about



Problem-Solving Skills — Creative and Critical

An important goal of education is helping students learn how to think more productively while solving problems, by combining creative thinking (to generate ideas) and critical thinking (to evaluate ideas).  Both modes of thinking are essential for a well-rounded productive thinker, according to scholars in both fields:

Richard Paul (a prominent advocate of CRITICAL THINKING) says, "Alternative solutions are often not given, they must be generated or thought-up.  Critical thinkers must be creative thinkers as well, generating possible solutions in order to find the best one.  Very often a problem persists, not because we can't tell which available solution is best, but because the best solution has not yet been made available — no one has thought of it yet." {source}

Patrick Hillis & Gerard Puccio (who focus on CREATIVE THINKING) describe the combining of divergent generation and convergent evaluation in a strategy of Creative Problem Solving that "contains many tools which can be used interchangeably within any of the stages.  These tools are selected according to the needs of the task and are either divergent (i.e., used to generate options) or convergent (i.e., used to evaluate options)." {source}



Multiple Intelligences & Learning Styles

We solve problems (to "make it better") in all areas of life.   When we're solving a wide variety of problems, we can think productively in a variety of ways, as described in a theory of MULTIPLE INTELLIGENCES developed by Howard Gardner.  While we're trying to help students improve a wide variety of abilities, we can develop teaching strategies that will be effective for students with different LEARNING STYLES.  For example, we can help students understand-and-use...

Visual Logic:  We can think logically in a variety of ways;  useful tools for VISUAL THINKING include visually logical organizing techniques — concept maps, matrices and diagrams (cluster, hierarchical, webbing, Venn,...), flowcharts,... — that can encourage and facilitate creative-and-critical thinking.  [[== also art]]



Problem-Solving Process for Science and Design

We'll look at problem-solving process for Science (below) and Design, plus Science-and-Design.


Problem-Solving Process for Science

Is there a “scientific method”?  We have reasons to say...

    NO, because there is not a rigid sequence of steps that is used in the same way by all scientists, in all areas of science, at all times.
    and also YES, because expert scientists (and designers) tend to be more effective when they use flexible strategies — analogous to the flexible goal-directed improvising of a hockey player, but not the rigid choreography of a figure skater — to stimulate & coordinate their thinking-and-actions in productive ways, so they can solve problems more effectively.

Here are some models that can help students understand and do the process of science.  We'll begin with simplicity, before moving on to models that are more complex so they can describe the process more completely-and-accurately.

A simple model of science is PHEOC (Problem, Hypothesis, Experiment, Observe, Conclude).  When PHEOC, or a similar model, is presented — or is misinterpreted — as a rigid sequence of fixed steps, this can lead to misunderstandings of science, because the real-world process of science is flexible.  An assumption that “model = rigidity” is a common criticism of all models-for-process, but this unfortunate stereotype of "rigidity" is not logically justifiable because all models emphasize the flexibility of problem-solving process in real life, and (ideally) in the classroom.  If a “step by step” model (like PHEOC or its variations) is interpreted properly and is used wisely, the model can be reasonably accurate and educationally useful.  For example,...

A model that is even simpler — the 3-step POE (Predict, Observe, Learn) — has the essentials of scientific logic, and is useful for classroom instruction.

Science Buddies has Steps of the Scientific Method with a flowchart showing options for flexibility of timing.  They say, "Even though we show the scientific method as a series of steps, keep in mind that new information or thinking might cause a scientist to back up and repeat steps at any point during the process.  A process like the scientific method that involves such backing up and repeating is called an iterative process."   And they compare Scientific Method with Engineering Design Process.

Lynn Fancher explains - in The Great SM - that "while science can be done (and often is) following different kinds of protocols, the [typical simplified] description of the scientific method includes some very important features that should lead to understanding some very basic aspects of all scientific practice," including Induction & Deduction and more.

From, many thoughts to explore in a big website.


Other models for the problem solving process of science are more complex, so they can be more thorough — by including a wider range of factors that actually occur in real-life science, that influence the process of science when it's done by scientists who work as individuals and also as members of their research groups & larger communities — and thus more accurate.  For example,

Understanding Science (developed at U.C. Berkeley - about) describes a broad range of science-influencers,* beyond the core of science: relating evidence and ideas.  Because "the process of science is exciting" they want to "give users an inside look at the general principles, methods, and motivations that underlie all of science."  You can begin learning in their homepage (with US 101, For Teachers, Resource Library,...) and an interactive flowchart for "How Science Works" that lets you explore with mouse-overs and clicking.

* These factors affect the process of science, and occasionally (at least in the short run) the results of science.  To learn more about science-influencers,...
    Knowledge Building (developed by Bereiter & Scardamalia, links - history) describes a human process of socially constructing knowledge.
    The Ethics of Science by Henry Bauer — author of Scientific Literacy and the Myth of the Scientific Method (click "look inside") — examines The Knowledge Filter and a Puzzle and Filter Model of "how science really works."

Another model that includes a wide range of factors (empirical, social, conceptual) is Integrated Scientific Method by Craig Rusbult, editor of this links-page.  Part of my PhD work was developing this model of solving problems (answering questions) with science, in a unifying synthesis of ideas from scholars in many fields, from scientists, philosophers, historians, sociologists, psychologists, educators, and myself.  The model is described in two brief outlines (early & later), more thoroughly, in a Basic Overview (with introduction, two visual/verbal representations, and summaries for 9 aspects of Science Process) and a Detailed Overview (examining the 9 aspects more deeply, with illustrations from history & philosophy of science), and even more deeply in my PhD dissertation (with links to the full text, plus a “world record” Table of Contents, references, a visual history of my diagrams for Science Process & Design Process, and integrative analysis of instruction).   /   Later, I developed a model for the basic logic-and-actions of Science Process in the context of a more general Design Process.



Problem-Solving Process for Design

Because "designing" covers a wide range of activities, we'll look at three kinds of designing.

Engineering Design Process:  As with Scientific Method,

    a basic process of Engineering Design can be outlined in a brief models-with-steps  –  5  5 in cycle  7 in cycle  8  10  3 & 11.     {pages are produced by ==}
    and it can be examined in more depth:  here & there  and in some of the models-with-steps above, and later.

Problem-Solving Process:  similar thinking strategies, applied to a wider range of life — for all problem-solving situations, not just for engineering — also have models-with-steps  –  4  4  5  6  7.     {pages are produced by ==}

Design-Thinking Process:  similar thinking strategies, but with a strong emphasis on empathy, are examined later.



Problem-Solving Process for Science-and-Design

Science and Design:  Science Buddies has separate models for Scientific Method (with a flowchart showing options for flexibility-of-timing when using "Steps of the Scientific Method") and for Engineering Design Process.  They compare these models to show their similarities & differences.  And they explain how both models describe a flexible process even though each model-framework has steps.


Above and below, you'll see separation (into Science and Design, above) versus integration (for Science-and-Design, below):  Above, Science Buddies has separate models for Science, and for Design.  Below is one model that includes both together, with an integration of...

  3 Elements used in 3 Comparisons

Science-AND-Design:  While thinking about the problem-solving process we use for Science and for Engineering, I (Craig Rusbult, editor of this links-page) discovered functional connections between 3 Elements — PREDICTIONS (made by imagining in a Mental Experiment) and OBSERVATIONS (made by actualizing in a Physical Experiment) and GOALS (for a satisfactory Problem-Solution) — when they are used in 3 Comparisons:  one Comparison is an evaluative REALITY CHECK;  two Comparisons are evaluative QUALITY CHECKS.

This diagram distinguishes between Science-Design (usually it's called Science, is done mainly by using Reality Checks) and General Design (which includes Engineering & much more, and is done mainly by using Quality Checks) because this distinction is useful, because thinking about these two kinds of design helps us understand the problem-solving process we use for Science-Design and General Design and their overlaps.

MORE – Two Kinds of Design and Comparing Cousins - Engineering vs Science - to see their Similarities & Differences.


The Wide Scope of Design

By using science and design, people try to make things better by solving problems.   It can be educationally useful to define "design" broadly so it includes two kinds of design, with different problem-solving objectives:

    in Science-Design (commonly called Science) we want to answer a question (a problem-question about “what happens, how, and why?”) by designing an explanatory theory, to “make knowledge better” and help satisfy a human desire for understanding.
    in General Design (commonly called Design) we want to solve a problem by designing a solution that is a better product, activity, strategy, or relationship, to “make things better” by helping satisfy other human needs-and-desires.
* In both kinds of Design, the objective is to solve a problem by "making things better" with improved understanding (in Science-Design) and (in General Design) by improving other aspects of life.  Together, these objectives include almost everything we do in life.     { Examples of Design Objectives for "almost everything" in All Areas of Life }

One part of "almost everything" is... The Wide Scope of Science-Design:  In all of life, not just in science, we use our explanatory theories about “how the world works” to understand “what is happening, how, why” and to predict “what will happen” in the future.  When our theories about the world are more thorough and accurate, this improved understanding will increase the accuracy of our theory-based predictions that, along with good values & priorities, help us make wise decisions, personally and professionally, while pursuing our goals in life.  We use scientific thinking often in life, whenever we hear a claim, or make a claim, and ask “what is the evidence-and-logic supporting this claim?” and “how strong is the support for this claim?” and “should I (or we) accept this claim?”, or “how might we adjust this claim, to make a revised claim that is more strongly supported, is more likely to more accurately describe what is happening, how, and why?”

Another part of "almost everything" is... The Wide Scope of General Design:  General Design is used for “engineering” and much more.  The Next Generation Science Standards, for K-12 Education in the United States, use a broad definition of engineering (it's "any engagement in a systematic practice of design to achieve solutions to particular human problems") and technologies (which "result when engineers apply their understanding of the natural world and of human behavior to design ways to satisfy human needs and wants" and "include all types of human-made systems and processes") in order to "emphasize practices that all citizens should learn – such as defining problems in terms of criteria and constraints, generating and evaluating multiple solutions, building and testing prototypes, and optimizing – which have not been explicitly included in science standards until now." (from Appendix I, "Engineering Design in the NGSS")   /   When we also include other kinds of General Design, and Science-Design, the scope of Design Thinking expands to "include almost everything we do in life."


Problem-Solving Process

The basic process is simple:

    first, to Define a Problem you Define your Objective (for what you want to “make better”) and Define your Goals (for a satisfactory Problem-Solution);
    then, to Solve the Problem you creatively Generate Options (for a Problem-Solution) and critically Evaluate Options, and continue to Generate-and-Evaluate in creative-and-critical iterative Cycles of Design.

Later in this page you can see “more about process” in different models-for-process.  In all models, an important activity is...


Designing Experiments so you can Use Experiments

What is an experiment?   Basically, an experiment is experience that is mental or physical.  An experiment is the experience you get whenever you mentally imagine a situation (you think it) or physically actualize a situation (you do it).     {these experimental situations can be called an experimental systems}

How do you DESIGN experiments?  You can do a wide variety of experiments.  To stimulate your creative thinking — to reduce restrictive assumptions so you can more freely explore the wide variety of Options for Experiments — with a simple, broad, minimally restrictive definition:  an Experiment is any Situation/System that provides an opportunity to get Information by making Predictions (in a Mental Experiment) or making Observations (in a Physical Experiment), so an Experimental Situation is any Prediction-Situation or Observation-Situation.


How do you USE experiments?  During a process of problem solving, you often Design Experiments (they're “things happening” in Experimental Situations, in Experimental Systems) that you think might provide useful Information, that might help you solve the problem.  Then you USE Experiments in three ways: [[== also design/revise for next round of expmt/us? check my pages for wording]]

    1. USE an Experiment (Mental or Physical) to make Information (Predictions or Observations);
    2. USE this Experimental Information to do Evaluation of an Option;
    3. USE this Experiment-Based Evaluation to guide Generation of other Options.

These USES are described in more detail below, and you can see them in the diagram.  When you study it, 8 times you'll find "using" or "Use" or "use".  And when you move your mouse over the "1 2 3 3" boxes added to it, you can see four isolation diagrams that show only the problem-solving actions for USE #1 ("using" to make Information) and USE #2 ("Use" to do Evaluation) and USE #3 ("use" to guide Generation in one Science Cycle & two Design Cycles).

  3 Ways to Use Experiments

1. for Experiment → Information,  you USE an Experiment — by “running it” physically or mentally — to make two kinds of Experimental Information.  How?

    You imagine the Experimental System in a Mental Experiment so you can make PREDICTIONS,
    or you actualize the Experimental System in a Physical Experiment so you can make OBSERVATIONS.

2. for Information → Evaluation,  you USE this Experimental Information (from #1) to do two kinds of Experiment-Based Evaluation, with...

    • evaluative Reality Checks:  During a process of Science-Design or General Design, you can test your explanatory Theory(s) by comparing your Theory-based PREDICTIONS with Reality-based OBSERVATIONS.  This evaluative comparison is a Reality Check that will help you determine how closely “the way you think the world is” corresponds to “the way the world really is.”
    • evaluative Quality Checks:  Early in a process of General Design, you Define your GOALS for a Solution, for the properties you want in a problem-Solution that is ideal, or at least is satisfactory.  Later, you generate Options for a Solution.  You can test the Quality of an Option by comparing your GOALS (for your desired properties, which define Quality) with your PREDICTIONS (about expected properties of this Option) or with OBSERVATIONS (the observed properties of this Option).  These evaluative comparisons — when you ask “how closely do the properties of this Option match the properties I want?” — are Quality Checks.

3. for Evaluation → Generation,  you USE this Experiment-based critical Evaluation (of an old Option in #2) to stimulate-and-guide your creative Generation (of a new Option in #3).  How?

    • In Science-Design, if necessary — if you were “surprised” because (when you Evaluated in #2 using a Reality Check) your OBSERVATIONS didn't match your PREDICTIONS — you ask (when you're Generating in #3) “how can I revise my old Option {for a Theory} about how I think the world is, so it corresponds more closely to how the world really is.
   • In General Design, you ask (based on Evaluation in #2 using a Quality Check) “what aspects of the old Option {for a Solution} need to be improved?” and then (for Generation in #3) “how can I revise this old Option to improve it, to generate a better new Option?”


MORE – ==[later, here I will add a link - re: 8 ways & options for branching]



Problem Solving for Education — Teaching Skills in Schools

Educators should want to design instruction that will help students improve their thinking skills.  An effective strategy for doing this is...
Goal-Directed Designing of Curriculum & Instruction

When we are trying to solve a problem (to “make it better”) by improving education, a useful two-part process is to...

    • Define GOALS for desired outcomes, for the ideas & skills we want students to learn;
    • Design INSTRUCTION with Learning Activities that will provide opportunities for experience with these ideas & skills, and will help students learn more from their experiences.

Basically, the first • is about WHAT to Teach, and the second • is HOW to Teach.

But before looking at WHAT and HOW , here are some ways to combine them with...


Strategies for Goal-Directed Designing of WHAT-and-HOW.

Understanding by Design (UbD) is a team of experts in goal-directed designing,

    as described in an overview of Understanding by Design from Vanderbilt U.
    UbD has a resources-page from ASCD (the Association for Supervision and Curriculum Development) that includes pages about The UbD Framework* and Teaching for Meaning and Understanding: A Summary of Underlying Theory and Research.   /   UbD "offers a planning process and structure to guide curriculum, assessment, and instruction.  Its two key ideas are contained in the title:  1) focus on teaching and assessing for understanding and learning transfer, and   2) design curriculum “backward” from those ends."
    The Understanding by Design Institute of EduPlanet21 (about) says, "students succeed when educators start with the end goal in mind.  This backward design approach allows educators to create deliberate and focused unit design choice."
    ASCD (the Association for Supervision and Curriculum Development) offers resources that include online articles and books (by Grant Wiggins and Jay McTighe & others) and — when you explore using the Navigation Bar (Articles, Books, Webinars,...) or just scroll down the page — much more.
    Wikipedia describes two key features of UbD:  "In backward design, the teacher starts with classroom outcomes and then plans the curriculum, choosing activities and materials that help determine student ability and foster student learning," and  "The goal of Teaching for Understanding is to give students the tools to take what they know, and what they will eventually know, and make a mindful connection between the ideas. ...  Transferability of skills is at the heart of the technique. Jay McTighe and Grant Wiggin's technique.  If a student is able to transfer the skills they learn in the classroom to unfamiliar situations, whether academic or non-academic, they are said to truly understand."

Other techniques include Integrative Analysis of Instruction and Goal-Directed Aesop's Activities.


In two steps for a goal-directed designing of education, you:  1) Define GOALS (for WHAT you want students to improve);  2) Design INSTRUCTION (for HOW to achieve these Goals).  Although the sections below are labeled 1. WHAT to Teach and 2. HOW to Teach there is lots of overlapping, so you will find some "how" in the WHAT, and much "what" in the HOW.


1 — Define GOALS (decide WHAT to Teach)

What educational goals are most valuable for students?  Here are some options:

Ideas-and-Skills:  We define goals for ideas (what students know) that are conceptual knowledge, and for skills (what they can do) that are procedural knowledge.  Our goals for ideas-and-skills include ideas, and skills that are applied in skills-with-ideas when creative-and-critical thinking skills interact with ideas in productive thinking.

A Bigger Picture:  We want to help students improve their multiple intelligences and achieve a wide range of desirable outcomes that are COGNITIVE (for ideas-and-skills in many areas of school & life) and AFFECTIVE (for attitudes, motivations, emotions) and PHYSICAL (for nutrition, health & fitness, physical skills) and for CHARACTER (for empathy, kindness, compassion, ethics,...).

Because we have limited amounts of educational resources — of time, people, money,... — we must ask, “How much of these resources should we invest in each kind of goal?”


Although the discussion below recognizes the wide-context “big picture” of educational goals, it will focus mainly on Cognitive Goals for Ideas-and-Skills, but with some discussion of goals for Affective and Physical and Character.  Even within this restricted range (of goals that are mainly cognitive) we must make many decisions, including the following choices (re: ideas & skills, science & design, performing & learning) about priorities:


Ideas versus Skills?

Most educators want to teach ideas AND skills, but unfortunately a competitive tension often exists.  If we are not able to maximize a mastery of both, we should aim for an optimal combination of ideas and skills.  But what is optimal?  Many educators, including me, think the balance should shift toward more emphasis on skills and skills-with-ideas, aiming for an improvement in skills-ability that outweighs (in our value system) any decrease in ideas-ability.  This is possible because "ideas versus skills" is not a zero-sum game, especially for lifelong learning when we educate for life to help students cope with a wide range of challenges in their futures.

The Difficulty of Designing Exams to Evaluate Skills:  We want to generate accurate information about student achievements with both ideas and skills.  But measuring ideas-knowledge is easy compared with the difficulty & expense of accurately measuring skills-knowledge.  This is an important factor when educators (at the levels of classroom, school, district, state, and nation) develop strategies & make policy decisions for education, and there are Rational Reasons to Not Teach Thinking Skills.


Two Kinds of Inquiry Activities  (for Science and Design)

To more effectively help students improve their problem-solving skills, teachers can provide opportunities for students to be actively involved in solving problems, with inquiry activities.  What happens during inquiry?  Opportunities for inquiry occur whenever a gap in knowledge — in conceptual knowledge (so students don't understand) or procedural knowledge (so they don't know what to do, or how) — stimulates action (mental and/or physical) and students are allowed to think-do-learn.

Students can be challenged to solve two kinds of problems during two kinds of inquiry activity:

    during Science-Inquiry they try to improve their understanding, by asking problem-questions and seeking answers.  During their process of solving problems, they are using Science-Design, aka Science, to design a better explanatory theory.
    during Design-Inquiry they try to improve some other aspect(s) of life, by defining problem-projects and seeking solutions.  During their process of solving problems, they are using General Design (which includes Engineering and more) to design a better product, activity, or strategy.
    But... whether the main objective is for Science-Design or General Design, a skilled designer will be flexible, will do whatever will help them solve the problem(s).  Therefore a “scientist” sometimes does engineering, and an “engineer” sometimes does science.  A teacher can help students recognize how-and-why they also do these “crossover actions” during an activity for Science Inquiry or Design Inquiry.  Due to these connections, we can build transfer-bridges between the two kinds of inquiry,  and combine both to develop “hybrid activities” for Science-and-Design Inquiry.

Goal-Priorities:  There are two kinds of inquiry, so (re: Goals for What to Learn) what emphasis do we want to place on activities for Science-Inquiry and Design-Inquiry?  (in the limited amount of classroom time that teachers can use for Inquiry Activities)


Two Kinds of Improving  (for Performing and Learning)

Goal-Priorities:  There are two kinds of improving, so (re: Goals for What to Learn) what emphasis do we want to place on better Performing (now) and Learning (for later)?

When defining goals for education, we ask “How important is improving the quality of performing now, and (by learning now) of performing later ?”   For example, a basketball team (coach & players) will have a different emphasis in an early-season practice (when their main goal is learning well) and end-of-season championship game (when their main goal is performing well).     {we can try to optimize the “total value” of performing/learning/enjoying for short-term fun plus long-term satisfactions}



2 — Design INSTRUCTION (decide HOW to Teach)

Strategies for Designing  (of instruction)

One useful strategy for Goal-Directed Designing of Curriculum & Instruction is Understanding by Design.

Other educators also have developed strategies for goal-directed designing.  For example, integrative analysis of instruction can help guide our selection-and-sequencing of activities that include goal-directed Aesop's Activities to achieve specific learning outcomes for students.  With more detail,

    "An integrative analysis of instruction can improve our understanding of the functional relationships between activities, between goals, and between activities and goals.  This knowledge about the structure of instruction (as it is now, or could be later) can help us coordinate – with respect to types of experience, levels of difficulty, and contexts – the activities that help students achieve goals for learning.  The purpose of a carefully planned selection-and-sequencing of activities is to increase the mutually supportive synergism between activities in a coherent system for teaching all of the goals, to produce a more effective environment for learning."


Strategies for Teaching  (of skills)

There is a wide variety of views, and thus controversy, when educators ask important questions:

• What role should thinking skills play in education?     { As discussed earlier, if there are “competitions” — of ideas vs skills (and of cognitive vs affective vs physical vs character) — how much of our limited resources (our time, people, money,...) should we invest in improving problem-solving skills? }

• How can we most effectively teach thinking skills?   This question leads to many sub-questions, including these:

    What are useful strategies for teaching Problem-Solving Skills? 
    For classroom instruction,
    What are the benefits of using various teaching methods?   {e.g., What are the benefits of subject-area infusion versus separate programs?  and  What about “flipping” a classroom? }
    Should we explicitly teach principles for thinking skills and process skills?  and  Should we use a “model” for problem-solving process?

improving Educational Equity by increasing motivations & confidence and opportunities



Problem-Solving Skills

What are useful strategies for teaching Problem-Solving Skills (Thinking Skills + Process Skills) that are Metacognitive & General & Experimental and are used for Science & Engineering & Design Thinking & Problem-Based Learning?



METACOGNITIVE Problem-Solving Skills

What is metacognition?  Thinking is cognition.  When you observe your thinking and think about your thinking (maybe asking “how can I think more effectively?”) this is meta-cognition, which is cognition about cognition.  To learn more about metacognition — what it is, why it's valuable, and how to use it more effectively — some useful web-resources are:

a comprehensive introductory overview by Nancy Chick, for Vanderbilt U.

my links-section has descriptions of (and links to) pages by other authors: Jennifer Livingston, How People Learn, Marsha Lovett, Carleton College, Johan Lehrer, Rick Sheets, William Peirce, and Steven Shannon, plus links for Self-Efficacy with a Growth Mindset, and more about metacognition.

my summaries about the value of combining cognition-and-metacognition and regulating it for Thinking Strategies (of many kinds) to improve Performing and/or Learning by Learning More from Experience with a process that is similar to...

the Strategies for Self-Regulated Learning developed by other educators.

videos — search youtube for [metacognition] and [metacognitive strategies] and [metacognition in education].


And in other parts of this links-page,

As one part of guiding students during an inquiry activity a teacher can stimulate their metacognition by helping them reflect on their experiences.

While solving problems, almost always it's useful to think with empathy and also with metacognitive self-empathy by asking “what do they want?” and “what do I want?” and aiming for a win-win solution.



GENERAL Problem-Solving Skills

CREATIVE THINKING and CRITICAL THINKING are useful for solving all problems, in all areas of life.

Productive Thinking occurs "when you effectively combine Creative Thinking and Critical Thinking with relevant Knowledge-of-Ideas."

Thinking can be productive in a variety of ways.  For example, skillful argumentation "combines Evaluative Thinking with a Persuasion Strategy and Communication Skills."

Later in the page we'll look at Strategies for helping students improve their Productive Thinking.  The rest of this section describes some interesting ways to analyze General Thinking Skills that are useful for Problem Solving.


Bloom's Taxonomy:  The basic principles of Bloom's Taxonomy (Original 1956, and Revised 2001) are described by Patricia Armstrong (for Vanderbilt U) who links to a summary and a guide to Bloom’s Taxonomy (by Mary Forehand, U of Georgia) that "is particularly useful because [in addition to its valuable information] it contains links to dozens of other web sites."   Assessing Learning Objectives using Bloom's Taxonomy (from U of Illinois) includes Sample Test Questions — and Using Bloom's Taxonomy for [Goal-Directed] Course Design by Barbara Shadden.

Domains of Learning:  Benjamin Bloom led a committee that proposed a Taxonomy of Learning Domains (Cognitive, Affective, Psychomotor) along with Levels of Learning (e.g. for Cognitive, Bloom's levels are Knowledge, Comprehension, Application, Analysis, Synthesis, Evaluation);  introduction - elaboration - an overview (by Vernellia Randall, U of Dayton School of Law) describes the domain-categories, "Cognitive is for mental skills (Knowledge), affective is for growth in feelings or emotional areas (Attitude), while psychomotor is for manual or physical skills (Skills)."

Thinking Skills in Common Core:  In a framework similar to Bloom's, but going beyond it, Robin Fogarty – in 7 Thinking Skills of Common Core – analyzes 7 Thinking Skills (Critical, Creative, Complex, Comprehensive, Collaborative, Communicative, with Cognitive Transfer) plus The Three Story Intellect (Gather, Process, Apply), and outlines strategies for explicitly teaching these skills.



Problem-Solving Skills with EXPERIMENTS

Although experimental skills — by Designing Experiments and Doing Experiments and Using Experiments — are generally useful (playing key roles in all problem solving), experimenting is typically associated with Science.  For example,...

In an overview of Scientific Method by Kathleen Marrs (of IUPUI),  Section 2 — "Experimentation: The Key to the Scientific Method" — begins, "A key ingredient of the scientific process: the controlled experiment."  She describes principles of experimenting, and links to a page with experiments to test explanatory theories about Why are we sleepy in class?

Or, from U of Arizona, in an everyday situation you might wonder why doesn't the light work? and design/do/use experiments so you can find the cause and solve the problem.

Lester Miller's Introduction to Scientific Method uses a model with 7 steps and a flowchart showing Hypothetico-Deductive Logic.  To illustrate the scientific skill of designing useful experiments, they use the historical question of Spontaneous Generation, and explain how the hypothesis of Francesco Redi — proposing that, to produce maggots, flies (not meat by itself) are necessary — was supported by observations in the experiments he designed and ran.     {also: Katie Mayfield cleverly designed a slide show with more details about the history of "spontaneous generation" theories (pro & con) and the scientific resolution of this controversy due to the carefully designed experiments of Francesco Redi and (later) Louis Pasteur.}  {more about the scientific controversy and the experiments of Pasteur}

You can find many articles — when you explore by scrolling and clicking links — about designing controlled experiments by Anne Marie Helmenstine & others.

Some ideas about experiments, from my studies of Scientific Methods, are summarized in a brief overview and with details about goal-directed design, anomaly resolution, crucial experiments, heuristic experiments, vicarious experimentation, thought-experiments, and more.

And more generally — for Science and/or General Design — my 3 Ways to Use Experiments and Principles & Strategies for Experimental Design to Generate Useful Information that is Old or New.

Generally useful experimental skills (examined in ERIC Digests) are observation skills & measurement skills.

Mill's Methods:  These logical principles can help you Design Useful Experiments and Analyze Experimental Observations to Determine Causes.   Examples (in visual tables) & Explanations and Examples (more thorough) & Explanations



Problem-Solving Skills used for SCIENCE

This section supplements models for Scientific Method that "begin with simplicity, before moving on to models that are more complex so they can describe the process more completely-and-accurately."  On the spectrum of simplicity → complexity, one of the simplest models is...

POE (Predict, Observe, Learn) to give students practice with the basic scientific logic we use to evaluate an explanatory theory about “what happens, how, and why.”  POE is often used for classroom instruction — with interactive lectures & in other ways — and research has shown it to be effective.  A common goal of instruction-with-POE is to improve the conceptual knowledge of students, especially to promote conceptual change their alternative concepts to scientific concepts.  But students also improve their procedural knowledge for what the process of science is, and how to do the process.     { more – What's missing from POE (experimental skills) when students use it for evidence-based argumentation?   and Ecologies - Educational & Conceptual }

Dany Adams (at Smith College) explicitly teaches critical thinking skills – and thus experimental skillsin the context of scientific method.

Science Buddies has models for Scientific Method (and Engineering Design Process) and offers Detailed Help that is useful for “thinking skills” education.


Next Generation Science Standards (NGSS) emphasizes the importance of designing curriculum & instruction for Three Dimensional Learning with productive interactions between problem-solving Practices (for Science & Engineering) and Crosscutting Concepts and Disciplinary Core Ideas.

Science: A Process Approach (SAPA) was a curriculum program earlier, beginning in the 1960s.  Michael Padilla explains how SAPA defined The Science Process Skills as "a set of broadly transferable abilities, appropriate to many science disciplines and reflective of the behavior of scientists.  SAPA categorized process skills into two types, basic and integrated.  The basic (simpler) process skills provide a foundation for learning the integrated (more complex) skills."   Also, What the Research Says About Science Process Skills by Karen Ostlund;  and Students' Understanding of the Procedures of Scientific Enquiry by Robin Millar, who examines several approaches and concludes (re: SAPA) that "The process approach is not, therefore, a sound basis for curriculum planning, nor does the analysis on which it is based provide a productive framework for research."  But I think parts of it can be used creatively for effective instruction.     {more about SAPA}



Problem-Solving Skills used for ENGINEERING

Engineering is Elementary (E i E) develops activities for students in grades K-8.  To get a feeling for the excitement they want to share with teachers & students, watch a video and explore their website.  To develop its curriculum products, EiE uses educational research and works closely with teachers to get field-testing feedback, in a rigorous process of educational design.  During instruction, teachers use a simple 5-phase flexible model of engineering design process "to guide students through our engineering design challenges... using terms [Ask, Imagine, Plan, Create, Improve] children can understand."   {plus other websites about EiE}

Project Lead the Way (PLTW), another major developer of k-12 curriculum & instruction for engineering and other areas, has a website you can explore to learn about their approach & programs (at many schools) & resources and more.  And you can web-search for other websites about PLTW.

Science Buddies, at level of k-12, has tips for science & engineering.

EPICS (home - about), at college level, is an engineering program using EPICS Design Process with a framework supplemented by sophisticated strategies from real-world engineering.  EPICS began at Purdue University and is now used at 30 schools including Purdue, Princeton, Dartmouth, Notre Dame, Texas A&M, Arizona State, UC San Diego, and Butler.



I.O.U. - Soon, November 8-11, I'll continue revising everything in this "brown box" in simple ways (like checking-and-fixing links) and by developing the ideas in it more fully, expressing them more clearly, and organizing them better. 

(note: Places with "==" are notes-to-myself about things that need to be fixed.  And other "fixers" will be obvious.)



Problem-Solving Skills for DESIGN THINKING

DESIGN THINKING -- dschool, nueva, etc -- with strong emphasis on empathy!


WIDE SCOPE ==[here, I will describe differences between my broad definition of "design" and narrower definitions that emphasize problem solving that is human-centered, and the importance of empathy;  also, differences in models-for-process]

Problem-Solving Objectives:  An objective is a problem you want to solve, so you can "make things better."  People use creative-and-critical productive thinking to solve problems in a wide range of design fields — such as engineering, architecture, mathematics, music, art, fashion, literature, education, philosophy, history, science (physical, biological, social), law, business, athletics, and medicine — when the objective is to design (to find, invent, or improve) a better product, activity, strategy (in General Design) and/or (in Science-Design) an explanatory theory.  These objectives include almost everything we do in life.


Problem-Solving Skills for PROBLEM-BASED LEARNING

Problem-Based Learning

is a way to improve motivation, thinking, and learning:  you can read a ==brief overview of Problem-Based Learning and (in ERIC Digests) using Problem-Based Learning for science & math plus ==a longer introduction - ==ten requirements - challenges for students & teachers (we never said it would be easy!) — two websites to explore (Samford University -

the book-intro for Problems as Possibilities (use quotes==) - ==a search in ACSD for problem-based learning - and a comprehensive ==links-page for Problem-Based Learning.

PBL -- Problems as Possibilities by Linda Torp and Sara Sage

Table of Contents

Introduction --

plus samples from the first & last chapters, and PBL Resources (including WeSites in Part IV) from ACSD.

==background - ==process - and [click the links] evaluation & more)

(Illinois Math & Science Academy - about us [with links to mission,...] and

PBL Network [==sitemap includes ==external links]) —

[[get others]] [service learning] projects field trips -- Vanderbilt U has information & resource-links about


If you're wondering "What can I do in my classroom tomorrow?", eventually there will be a section for "thinking skills activities" in the area for TEACHING ACTIVITIES.




Should we teach principles for thinking?  and  Should we use a “model” for problem-solving process? 

What are the benefits of infusion and separate programs? 


An excellent overview is Teaching Thinking Skills by Kathleen Cotton. (the second half of her page is a comprehensive bibliography)

This article is part of The School Improvement Research Series (available from Education Northwest and ERIC) where you can find many useful articles about thinking skills & other topics, by Cotton & other authors.

* [== it still is excellent, even though it's fairly old, written in 1991 -- IOU - soon, I will search and find more-recent overviews ]]


Another useful page — What Is a Thinking Curriculum? (by Fennimore & Tinzmann) — begins with principles and then moves into applications in Language Arts, Mathematics, Sciences, and Social Sciences.

My links-page for Teaching Strategies to promote Active Learning == summarizes and explores a variety of ideas about effective teaching (based on principles of constructivism, meaningful reception,...) designed to stimulate active learning and improve thinking skills.  Later, a continuing exploration of the web will reveal more web-pages with useful "thinking skills & problem solving" ideas (especially for K-12 students & teachers) and we'll share these with you, here and in TEACHING ACTIVITIES. [==this duplicates a sentence above]

Of course, thinking skills are not just for scholars and schoolwork, as emphasized in an ERIC Digest, Higher Order Thinking Skills in Vocational Education.  And you can get information about 23 ==Programs that Work from the U.S. Dept of Education. 

affective & character == helping students learn how to develop/use non-violent solutions for social problems


Infusion and/or Separate Programs?

In education for problem solving, one unresolved question is "What are the benefits of infusion and separate programs?"  What is the difference?  With infusion, thinking skills are closely integrated with content instruction in a subject area.  In separate programs, independent from content-courses, the explicit focus is to help students improve their thinking skills.

In her overview of the field, Kathleen Cotton says,

    Of the demonstrably effective programs, about half are of the infused variety, and the other half are taught separately from the regular curriculum. ...  The strong support that exists for both approaches... indicates that either approach can be effective.  Freseman represents what is perhaps a means of reconciling these differences [between enthusiastic advocates of each approach] when he writes, at the conclusion of his 1990 study: “Thinking skills need to be taught directly before they are applied to the content areas. ...  I consider the concept of teaching thinking skills directly to be of value especially when there follows an immediate application to the content area.”

For principles and examples of infusion, check the National Center for Teaching Thinking which lets you see ==What is Infusion? (an introduction to the art of infusing thinking skills into content instruction), and ==sample lessons (for different subjects, grade levels, and thinking skills). [== lessons designed to infuse Critical and Creative Thinking into content instruction]

Infusing Teaching Thinking Into Subject-Area Instruction (by Robert Swarz & David Perkins) also


And we can help students improve their problem-solving skills with teaching strategies that provide structure for instruction and strategies for thinking. ==[use structure+strategies only in edu-section?]




During any thinking-and-learning activity == (like inquiry for science and/or design) a teacher's interactions with students produce mini-activities == that are opportunities for thinking-and-learning.  To “guide” students a teacher can ask questions, respond to questions, give tips (to adjust the level of difficulty), model thinking skills, provide formative feedback, and encourage reflection by directing attention to “what can be learned” at appropriate times during the activity.  The main objectives of skillful guiding — by wisely choosing the types, amounts, and timings of guidance — are to help students improve their current performing (so they can solve a problem now) and/or their current learning (so they can improve their future performing), to optimize the total value (in performing + learning + enjoying) of their educational experience.     {an overview by Craig Rusbult}== cm-ei.htm%23dai / ws.htm%23hwmini

Effective feedback-for-learning can come from a teacher, or in other ways.  For example,...

ThinkSpace is "an interactive online teaching resource developed at ISU [Iowa State U] that encourages students to think critically about the solutions to complex, real-world problems. ... By using real-world scenarios, it allows students to work through electronic platforms and permits faculty to see how the students arrive at their final solutions."  ThinkSpace "enables a case-study approach that simulates real-world problems and environments, thereby encouraging... innovative curriculum and instructional approaches to problem solving."  It "can be used to present complex problems to students, which are completed through a series of intermediate tasks.  By receiving automated feedback on their work, students will be able to track their progress as they work to solve the problems."

Some teachers are

(e.g.,  learning by discovery and/or with explanations;  with lecture or flipped classroom;  and so on)




The wide scope of problem-solving Design Thinking lets us build bridges == (from life into school, and from school into life) to improve transfers of learning & transitions of attitudes, and problem-solving skills.  This will help us improve diversity-and-equity in education by increasing confidence & motivations for a wider range of students, and providing a wider variety of opportunities for learning in school, and success in school. etalk.htm%23br1/ws.htm%23mo

Problem-Solving Activities and Educational Equity:  What are the connections?  One

These bridges — from life into school, and back into life — will improve transfers-of-learning and transitions-of-attitudes.  This will help more students, with a wider diversity, improve their confidence & motivations and problem-solving skills, for better educational equity.


A motivated student — perhaps inspired by an effective teacher — can adopt ==a problem-solving approach to personal education by imagining the benefits of improved personal knowledge-and-skill in the future. mo.htm#life / website#trlife ws.htm#trlife ?? [find others?]

overview - Educational Equity - What does it mean? How do we know when we reach it? by Patte Barth, director of the Center for Public Education.

Equity of Opportunity from U.S. Dept of Education.


Carol Dweck Revisits the Growth Mindset and (also by Dweck) a video, Increasing Educational Equity and Opportunity.

3 Ways Educators Can Promote A Growth Mindset by Dan LaSalle, for Teach for America.

Growth Mindset: A Driving Philosophy, Not Just a Tool by David Hochheiser, for Edutopia.

Growth Mindset, Educational Equity, and Inclusive Excellence by Kris Slowinski who links to 5 videos.

What’s Missing from the Conversation: The Growth Mindset in Cultural Competency by Rosetta Lee.

YouTube video search-pages for [growth mindset] & [mindset in education] & [educational equity mindset].


Teaching Problem Solving --

Strategies for Problem Solving (for word problems and beyond)

Effective Learning Skills (memory, concentration, reading & listening, exams, time use)

Skills and Strategies for Effective Learning (a links-page)


ERIC Digests give tips for parents helping their children with problem-solving homework and summarize research about problem solving in science courses.

You can read about "word problems" (like those typically found in textbooks and on exams) and general problem-solving strategies that are also useful outside school.  For problem solving in everyday life (including business,...) a series of pages by Robert Harris provides a thorough overview of ==practical problem solving if you scroll down to the section about "Tools for the Age of Knowledge" and you'll find An Introduction to Creative Thinking, Creative Thinking Techniques, Criteria for Evaluating a Creative Solution, Introduction to Problem Solving, Human-Factor Phenomena in Problem Solving, Problem Solving Techniques, Introduction to Decision Making, and (in other parts of his links-page) much more.




Teaching of "Thinking Skills" Principles?

research support/ing for explicit/direct teaching of principles? -- yes,

link to my #wy

link to Dany Adams, quote


explicit direct teaching of principles? -- yes,

zb, CER for all (+ POE for Science)

What's missing in POE? designing experiments by asking "what additional evidence would be useful? get more evidence with more experiments (old/new, website/ws/#dpmo2aoldnew/- gaps (check details.htm for quote-paraphrasing)


When asking “should we teach a model-for-process?” we want to know whether a well-designed combination of experience plus principles (along with reflection) will be more educationally effective than experience by itself, to help students improve their problem-solving abilities.


thinking skills and thinking process.  What is the difference?

Based on evidence and logic — using what we know about thinking (cognition-and-metacognition), learning, and performing — we should expect a well-designed combination of "experience plus principles" to be more educationally effective than experience by itself, to help students improve their creative-and-critical thinking skills and whole-process skills in solving problems (for design-inquiry) and answering questions (for science-inquiry).

Educational Value:  Teaching principles of Design Process can help students improve their Coordination Strategies (improve their Conditional Knowledge and — so they can skillfully coordinate their thinking skills into whole-process skills when they are solving problems (in design-inquiry) and answering questions (in science-inquiry).



#NSM - using models?

During inquiry activities, students can learn principles of inquiry-process by using a model and/or semi-model and/or no model. website#dpomnsm??/wsepp?


COMBINING MODELS -- combining two (or more) Models-for-Process

Structure + Function -- structure for instruction, strategies for thinking

combining models -- Short-Term plus Long-Term -- link to home.htm%234a4b / dp-om.htm#seq/ws.htm#dpmo4aseq ? -- also



link to section above, with models for Science, and Engineering Design, plus my Science-and-Design

simple -- zb, CER for all problem-solving activities (+ POE when focus on Science)

Also, for different kinds of models -- Robert Marzano's New Taxonomy of Educational Objectives has three systems (Self-System, Metacognitive System, Cognitive System) and a Knowledge Domain that includes Information, Mental Procedures, Physical Procedures; 

and Models of Problem Solving & Learning (from educational researchers at CRESST) provide a framework for thinking about an ideas-and-skills curriculum == that uses Design Process to improve the mutually supportive interactions between ideas and skills. 




When educators develop strategies to improve the problem solving abilities of students, usually their focus is on thinking skills.  But thinking process is also important.

Therefore, it's useful to define thinking skills broadly, to include thinking that leads to decisions-about-actions, and actions:

        thinking  →  action-decisions  →  actions

[[ == here are some ideas that will be in this section:

== actions can be mental and/or physical (e.g. actualizing Experimental Design to do a Physical Experiment, or actualizing an Option-for-Action into actually doing the Action

== educational goals:  to help students combine their thinking skills (creatively Generating Options and critically Generating Options, using their Knowledge-of-Ideas that includes content-area knowledge plus the Empathy that is emphasized in Design Thinking) into an effective thinking process.

== how?  with a skillful Coordination of Problem-Solving Actions (using their Conditional Knowledge) into an effective Problem-Solving Process.

== Strategies for Coordinating:  During a process of design, you coordinate your thinking-and-actions by making action decisions about “what to do next.”  How?  During skillful coordination you combine cognitive/metacognitive awareness (of your current problem-solving process) with Conditional Knowledge (by knowing, for each skill, what it lets you accomplish, and the conditions in which it will be useful).






A model for Integrated Scientific Method

includes 9 aspects of Science Process:

simplified diagram of Integrated Scientific Method (= Science Process)

1. use Empirical Factors for Theory Evaluation,

2. use Conceptual Factors for Theory Evaluation,

3. use Cultural-Personal Factors for Theory Evaluation,

4. Evaluate Theories (with critical thinking), and

5. Generate Theories (with creative thinking);


6. Design Experiments (by generating-and-evaluating);


7. do Science Projects (planning and coordinating);


8. be influenced by Thought Styles (cultural & personal),

9. use creative-and-critical Productive Thinking.


These two representations — verbal & verbal/visual, on the left & right sides — describe relationships within and between four sub-categories: 12345, 6, 7, 89.

Here is an Inquiry Activity:  In the diagram, do you see...

    symbolisms in the colors?   (yellow & green & yellow-greenred & blue)
    three kinds of meanings for the arrows?
A brief outline contains responses for these two inquiry-questions about colors & arrows. 


A DISCLAIMER:  The internet offers an abundance of resources, so our main challenge is selectivity, and we have tried to find high-quality pages for you to read.  But the pages above don't necessarily represent views of the American Scientific Affiliation.  As always, we encourage you to use your critical thinking skills to evaluate everything you read.
This website for Whole-Person Education has TWO KINDS OF LINKS:
an ITALICIZED LINK keeps you inside a page, moving you to another part of it, and
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The area of THINKING SKILLS has sub-areas for
CREATIVE THINKING in Education and Life    CRITICAL THINKING in Education and Life
PROBLEM SOLVING in Education and Life [it's this page]
This links-page for Thinking Skills & Problem-Solving Methods in Education and Life,
by Craig Rusbult, is
copyright © 2001 by Craig Rusbult, all rights reserved
All links are now being checked and fixed, in late-February 2017.
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