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}  {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.   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?]

Here are some models that can help students understand-and-do the process of science.  We'll begin with simplicity, before moving on to descriptions that are more thorough and accurate.

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 Craig Rusbult explains why 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,...

The 3-step model of POE (Predict, Observe, Learn) 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.


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.  My model is described in two brief outlines (A  B) and, 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 the 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 history of my diagrams for Science Process & Design Process, and integrative analysis of instruction).



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
    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, also have models-with-steps  –  4  4  5  6  7.

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

Later we'll look at more models, and how they can be used for education. ==[add links]



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.


separation (into Science and Design) versus integration (for Science-and-Design):  Science Buddies has separate models for Science, and for Design.  Below is one model for both together, for 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, used for Science;  two Comparisons are evaluative Quality Checks, used for Engineering.


Science and Engineering are related, but are not the same, of course.  Therefore it's useful to distinguish between Science-Design (usually called Science) and General Design (which includes Engineering & much more).  This helps us think about problem-solving process for Science-Design and General Design and their overlaps.

MORE – Two Kinds of Design & Comparing Cousins - Engineering vs Science


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 your 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, or strategy, 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?”

Another part of "almost everything" is... The Wide Scope of General Design:  General Design is used for “engineering” and much more.  In the Next Generation Science Standards for K-12 Education, there is 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, in 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?   While you are Designing Experiments, you can stimulate your creative thinking — by reducing 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 Observations (in a Physical Experiment) or making Predictions (in a Mental Experiment), so an Experimental System is any Observation-Situation or Prediction-Situation.


How do you use experiments?  During a process of problem solving, you often Design Experiments (they're “things happening” in Experimental Systems) that you think might provide useful Information, that might help you solve the problem.  Then you USE Experiments in three ways:

    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 when you move your mouse over the "1 2 3 3" boxes added to this diagram you can see four isolation diagrams that show only the problem-solving actions for Use #1 (to make Information) and Use #2 (to do Evaluation) and Uses #3 (to guide Generation for Science-Design & General Design).

  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, add links - ws#2cde for 8 ways, etc / branching?]



Problem Solving for Education — Teaching Skills in Schools


I.O.U. - Soon, February 22-25, this section will be revised in simple ways (like checking-and-fixing links, both inside & outside this page) and by developing the ideas in it more fully, and expressing them more clearly.   (note:  places with "==" are notes-to-myself about things that need to be fixed, but other places [without ==] also need fixing.)


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.


Strategies for Goal-Directed Designing

Understanding by Design is a team of experts in goal-directed designing:

    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 designing goal-directed Aesop's Activities.



1 — WHAT to Teach?  (in a Goal-Directed Designing of Curriculum & Instruction)

In the two steps of goal-directed designing of education, you:  1) Define GOALS (for WHAT you want the Desired Outcomes to be);  2) Design INSTRUCTION (for HOW to achieve these Goals).


1 — DEFINE GOALS for 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 achieve a wide range of desirable outcomes that are COGNITIVE (for ideas-and-skills in many areas of school and life, using multiple intelligences) and AFFECTIVE (for motivation & attitudes) and PHYSICAL (for nutrition, health & fitness, physical skills), plus other worthy goals (for compassion, ethics, character,...).  Therefore we must ask, “How much of our educational resources (time, people, money,...) should be invested in each goal?”

The discussion below recognizes this wider context, but will focus on cognitive goals for ideas-and-skills.   {Educational Goals for Many Types of Knowledge}cm-kn.htm

There also is a time-dimension, with goals to improve students' current performing and future performing, for satisfactions now and later.  We want to optimize the total value of their performing and/or enjoying and/or learning. ==[ws#mcpal,


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-knowledge that outweighs (in our value system) any decrease in ideas-knowledge.  This is possible because "ideas versus skills" is not a zero-sum game, especially for lifelong learning when we educate for life [etalk/ws#trlife] to help students cope with a wide range of challenges in their futures. exam scores [for students, at competitive levels of teacher, school, district, state, country]   

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 measuring skills-knowledge.  This challenge in assessing skills is an important factor when educators (at the levels of classroom, school, district, state, and nation) develop strategies & policies for education, making it difficult to place more emphasis on teaching skills-knowledge, because usually there are...

5 Rational Reasons for Teachers to Not Teach Thinking Skills==website.htm#cm5/ws#cme] also, 4 levels


Two Kinds of Inquiry Activities

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.


I.O.U. - As explained above, soon (February 22-25) the rest of this section will be revised and improved.


Ideas plus Skills:  The importance of teaching ideas-and-skills (i.e. ideas, skills, skills-with-ideas) is emphasized by prominent educators, including NGSS, Marzano, CRESST. [==find more links, + NGSS, Common Core]


==[the next 4 paragraphs - and more - need fixing] Due to overlaps in what people do — because an engineer sometimes does science, and a scientist sometimes does engineering — students often will combine both types of inquiry in a Learning Experience, which thus becomes Science-and-Design Inquiry.  By using these overlaps we can build transfer-bridges from design-inquiry to science-inquiry, and vice versa.   {Relationships between Science Process and Design Process}ws.htm%23dpmomix2/ws.htm%23dsmix  {Transfers of Learning between Science & Engineering} etalk.htm%23br3/ws.htm%23br2

Building Educational Bridges (for Transfers of Learning & Transitions of Attitudes) between School and Life}

Building Educational Bridges between School and Life, for Transfers of Learning & Transitions of Attitudes}


==[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.

In some ways, science process (aka scientific method) is similar to design process but there is a new focus for action.  In science the main goal is to understand nature, to construct a theory and test its accuracy with reality checks that help us decide if "the way we think the world is" corresponds to "the way the way the world really is."  It can be useful to think of science as the designing of theories, and conventional design as the designing of products or strategies.  [== the Science Question - Were you surprised? (why?)]

Models for Process:  Short-Term plus Long-Term -- link to dp-om.htm#seq/ws.htm#dpmo4aseq ? -- also Structure + Function


Learning in Bloom's Taxonomy can be described in terms of domains (cognitive, affective, psycho-motor) and levels, as you can see in this ==overview (of the original & revised versions) & ==introduction & elaboration.   And here are tips for using Bloom's Taxonomy — ==sample questions & assessing learning objectives (with examples) & ==course design.

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.

Two related questions are:  How can we effectively teach thinking skills?  and  What role should thinking skills play in education?  For each question, there is a range of views.  Among the unresolved issues are the amount of time to invest in developing thinking skills, and the advantages of two general teaching approachesinfusion (in which thinking skills are closely integrated with content instruction) and separate programs (independent from content-courses, with the explicit goal of helping students improve their thinking skills).

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

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.” "

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.

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]

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. 

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

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.

Dany Adams (Smith College) helps students learn how to think more effectively by combining critical thinking skill with scientific method: "Because the scientific method is a formalization of critical thinking, it can be used as a simple model that... puts critical thinking at the center of a straightforward, easily implemented, teaching strategy. ...  Explicitly discussing the logic and the thought processes that inform experimental methods works better than hoping students will ‘get it’ if they hear enough experiments described."

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 - PBL ==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]) — 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 Iowa State University's ==ThinkSpace is "an instructional and collaborative website designed to provide real-world problems and environments to students."

Problem-solving methods (like Design Method and Scientific Method) are just strategies for effectively combining familiar thinking skills in order to achieve a goal, to solve a problem.  Thinking Skills and Problem-Solving Methods are closely related, as shown in an Overview of Thinking Skills that compares four perspectives: Design Process (Rusbult), Dimensions of Thinking (Marzano, et al), Infusion of Thinking Skills (Swartz), Four Frames of Knowledge (Perkins);  ==[more generally, Problem Solving & Thinking Skills in Education is a sitemap for pages by Craig Rusbult.

Productive Thinking -- we can help students improve their creative-and-critical thinking skills by using Design Process for Problem Solving.

Skills in Life -- ==[ use mo#life/ws#dtlife etalk(#eq?)/?

==[in the Next Generation Science Standards for K-12 Education, there is (in Appendix I, Engineering Design in the NGSS).....]


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.




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. 


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This website for Whole-Person Education has TWO KINDS OF LINKS:
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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
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This links-page for Thinking Skills & Problem-Solving Methods in Education and Life,
by Craig Rusbult, is
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All links are now being checked and fixed, in late-February 2017.
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