THINKING SKILLS:

 

PROBLEM SOLVING

Problems & Problem Solving

Basic Problem-Solving Skills

Education for Problem Solving

Problems in Design & Science

Problem Solving in Schools

 
CREATIVE THINKING
Be Creative-and-Critical
Creativity for Living
(Part 1)
What, Why, and How
Principles and Strategies
Liberating Creativity
Creativity for Living
(Part 2)
Education for Creativity
Research about Creativity
 
CRITICAL THINKING
What is critical thinking?
Why teach critical thinking?
How to teach it effectively?
Effects of Motivated Reasoning
Ethics of Critical Thinking
 
 
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 )

 

 

In this page the sections are:

 

Problems and Problem Solving

 

Problem-Solving Skills

(creative and critical)

 

    Education for Problem Solving    

 

Problem-Solving Process

(in Design and Science)

 

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 common meaning.

More generally in education, it's useful to define problem broadly — as any situation, in any area of life, where you have an opportunity to make a difference, to make things better — so problem solving is converting an actual current state into a desired future state that is better, so you have "made things better."  Whenever you are thinking creatively-and-critically about ways to increase the quality of life (or to avoid a decrease in quality) for yourself and/or for others, you are actively involved in problem solving.  Defined in this way, problem solving includes almost everything you do in life.

 


 
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) with accurate knowledge (about the truth of reality).  Both modes of thinking (creative & critical) are essential for a well-rounded productive thinker, according to experts 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."

Patrick Hillis & Gerard Puccio (who focus on CREATIVE THINKING) describe the combining of creative generation with critical evaluation in a strategy of creative-and-critical 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)."

 

Creative Thinking + Critical Thinking in Cycles of DesignSolving Problems by using Creative Skills plus Critical Skills:  Many times throughout every day – whenever you make a decision so you can do an action – you're trying to "make things better" by solving a problem.  When you make a conscious decision, you combine creative thinking (to get ideas, to generate options for “what to do”) with critical thinking (to evaluate your options and decide “what to do”), as shown in the diagram.  During this process — when you creatively Generate Options and critically Evaluate Options — you are using cycles of creative-and-critical thinking, when you Generate-and-Evaluate-and-Generate-and-Evaluate-..... until you make a decision, and do an action.

 

Creative Thinking can be motivated and guided by Creative Thinking:  One of the interactions between creative thinking and critical thinking occurs when we use critical Evaluation to motivate and guide creative Generation in a critical-and-creative process of Guided Generation that is Guided Creativity.  In my links-page for CREATIVITY you can explore this process in three stages, to better understand how a process of Guided Creativity — explored & recognized by you in Part 1 and then described by me in Part 2 — could be used (as illustrated in Part 3) to improve “the party atmosphere” during a dinner you'll be hosting, by improving a relationship.

 


 
Education for Problem Solving

 
By using broad definitions for problem solving and education, we can show students how they already are using productive thinking to solve problems many times every day, whenever they try to “make things better” in some way.
 

Problem Solving:  a problem is an opportunity, in any area of life, to make things better.  Whenever a decision-and-action helps you “make it better — when you convert an actual state (in the past) into a more desirable actual state (in the present and/or future) — you are problem solving, and this includes almost everything you do in life, in all areas of life.     { You can make things better if you increase quality for any aspect of life, or you maintain quality by reducing a potential decrease of quality. }     /     design thinking (when it's broadly defined) is the productive problem-solving thinking we use to solve problems.  We can design (i.e. find, invent, or improve) a better product, activity, relationship, and/or strategy (in General Design) and/or (in Science-Design) explanatory theory.     { The editor of this links-page (Craig Rusbult) describes problem solving in all areas of life.}

note:  To help you decide whether to click a link or avoid it, links highlighted with green or purple go to pages I've written, in my website about Education for Problem Solving or in this website for THINKING SKILLS (CREATIVE and CRITICAL) we use to SOLVE PROBLEMS.

 

Education:  In another broad definition, education is learning from life-experiences, learning how to improve, to become more effective in making things better.  For example, Maya Angelou – describing an essential difference between past and present – says "I did then what I knew how to do. Now that I know better, I do better," where improved problem solving skills (when "do better" leads to being able to more effectively "make things better") has been a beneficial result of education, of "knowing better" due to learning from life-experiences.

 

Growth:  One of the best ways to learn more effectively is by developing-and-using a better growth mindset so — when you ask yourself “how well am I doing in this area of life?” and honestly self-answer “not well enough” — instead of thinking “not ever” you are thinking “not yet” because you know that your past performance isn't your future performance;  and you are confident that in this area of life (and in other areas) you can “grow” by improving your understandings-and-skills, when you invest intelligent effort in your self-education and self-improving.  And you can "be an educator" by supporting the self-improving of other people by helping them improve their own growth mindsets.    {resources for Growth Mindset}

 

Growth in Problem-Solving Skills:  A main goal of this page is to help educators help students improve their skill in solving problems — by improving their ability to think productively (to more effectively combine creative thinking with critical thinking and accurate knowledge) — in all areas of their everyday living.    {resources: growth mindset for problem solving that is creative-and-critical}

 

How?  You can improve your Education for Problem Solving by creatively-and-critically using general principles & strategies (like those described above & below, and elsewhere) and adapting them to specific situations, customizing them for your students (for their ages, abilities, experiences,...) and teachers, for your community and educational goals.

 
Promote Productive Thinking:

classroom (with Students & Teachers) actively doing Design ThinkingWith an effective general strategy, teachers can promote productive thinking by letting their students do activities that provide opportunities to solve problems and stimulate productive thinking, while supporting them psychologically so they are expecting to “do it better” because they are developing-and-using a growth mindset (so they're confident that they can improve all of their everyday skills, including practical creativity, by investing intelligent effort in their self-improving) and they are learning useful principles for increasing their creativity.

 
Build Educational Bridges:

When we show students how they use a similar problem-solving process (with design thinking) for almost everything they do in life, we can design a wide range of activities that let us build two-way educational bridges:

• from Life into School, building on the experiences of students, to improve confidence:  When we help students recognize how they have been using a problem-solving process of design thinking in a wide range of problem-solving situations,... then during a classroom design activity they can think “I have done this before (during design-in-life) so I can do it again (for design-in-school)” to increase their confidence about learning.  They will become more confident that they can (and will) improve the design-thinking skills they have been using (and will be using) to solve problems in life and in school.

• from School into Life, appealing to the hopes of students, to improve motivation:  We can show each student how they will be using design thinking for "almost everything they do" in their future life (in their future whole-life, inside & outside school) so the design-thinking skills they are improving in school will transfer from school into life and will help them achieve their personal goals for life.  When students want to learn in school because they are learning for life, this will increase their motivations to learn.

 
Improve Educational Equity:

When we build these bridges (past-to-present from Life into School, and present-to-future from School into Life) we can improve transfers of learning in time (past-to-present & present-to-future) and between areas (in school-life & whole-life) for whole-person education — and transitions in attitudes to improve a student's confidence & motivations.  This will promote diversity and equity in education by increasing confidence & motivation for a wider range of students, and providing a wider variety of opportunities for learning in school, and for success in school.  We want to “open up the options” for all students, so they will say “yes, I can do this” for a wider variety of career-and-life options, in areas of STEM (Science, Technology, Engineering, Math) and non-STEM.

 

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.

 
Design Curriculum & Instruction:
 

teachers doing DEEPdt Design ThinkingAn effective strategy for a Goal-Directed Designing of Curriculum & Instruction is to...

DEFINE GOALS for desired outcomes, for ideas-and-skills we want students to learn,

DESIGN INSTRUCTION with learning activities (and associated teaching activities) that will provide opportunities for experience with these ideas & skills, and help students learn more from their experiences.    {more about Defining Goals and Designing Instruction}   {one valuable activity is using a process-of-inquiry to learn principles-for-inquiry}

 


 
Problem-Solving Process for Science and Design

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

 

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,  but 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 coordinate their thinking-and-actions in productive ways, so they can solve problems more effectively.
 

Below 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 thoughtco.com, 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."
 

[[ i.o.u. - soon, in mid-June 2021, I'll fix the links in this paragraph.]] 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 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 using my integrative model for [[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.     {these pages are produced by ==[later, I'll list their names]}

    and it can be examined in more depth:  here & here and in some of the models-with-steps (5... 3 & 11), and later.

 

Problem-Solving Process:  also has models-with-steps ( 4  4  5  6  7 )* and models-without-steps (like the editor's model for Design-Thinking Process) to describe creative-and-critical thinking strategies that are similar to Engineering Design Process, and are used in a wider range of life — for all problem-solving situations (and these include almost everything we do in life) — not just for engineering.     {these pages are produced by ==}

 

Design-Thinking Process:  uses a similar creative-and-critical process,* but with a focus on human-centered problems & solutions & solving-process and a stronger emphasis on using empathy.  (and creativity)

* how similar?  This depends on whether we define Design Thinking in ways that are narrow or broad.   {the wide scope of problem-solving design thinking}  {why do I think broad definitions (for objectives & process) are educationally useful?}

Education for Design Thinking (at Stanford's Design School and beyond)

 


 

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.

 

Two Useful Perspectives:  We can think about separation (into Science and Design, above) AND 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 ComparisonsScience-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.

Two Kinds of Design:  This diagram distinguishes between Science-Design (usually it's just called Science, and 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 (and design thinking) very broadly so it includes two kinds of design, with different kinds of 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 knowledge about the world (produced when we design/do/use experiments) and 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 look beyond engineering, we see a much wider range of objectives for General Design, which therefore includes a MUCH wider range of human activities.

Combining these "wide scopes" (for Science-Design & General Design) shows that people are solving problems with creative-and-critical design thinking in a wide range of design fields that include engineering, architecture, mathematics, music, art, fashion, literature, education, philosophy, history, science (physical, biological, social), law, business, athletics, and medicine.  People also use Design Thinking throughout their everyday lives in activities that are not defined by a "field", whenever their objective is to solve a problem by "making things better," whenever they want to design (to find, invent, or improve) a better product, activity, strategy, relationship (in General Design) and/or (in Science-Design) an explanatory theory.  These objectives 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 (in Science-Design and General Design) 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:

    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.
    4. USE this Experiment-Based Evaluation to guide Design of New Experiments.
 

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?”
 

4. for Evaluation → Generation,  analogous to #3, you USE the Experiment-Based Evaluation (from #2) to stimulate-and-guide your creative Generation of more Information, with more Experiments.   Why?  in Science-Design or General Design, you will want more Information if you think it will help you do better Evaluation.   How?  you ask “what additional Information (Predictions or Obervations) would be useful for Evaluation, and what Experiments will help me get this Information?” to guide you in Designing More Experiments that you can Use-Use-Use-Use in the four ways (1 2 3 4) outlined above.

 

MORE – [i.o.u. - later, maybe in late-2022, here I will add a link to explain 9 ways to use experiments]

 


 
Problem Solving in Our Schools:

Improving Education for Problem Solving

 
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 things better”) by improving our education for problem solving, a useful two-part process is to...

    1.  Define GOALS for desired outcomes, for the ideas-and-skills we want students to learn;
    2.  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 part (Define Goals) is deciding WHAT to Teach, and the second part (Design Instruction) is deciding 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.

Wikipedia describes two key features of UbD:  "In backward design, the teacher starts with classroom outcomes [#1 in Goal-Directed Designing above] and then [#2] 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."

* 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."

ASCD – the Association for Supervision and Curriculum Development (specializing in educational leadership) – has a resources-page for Understanding by Design that includes links to The UbD Framework and Teaching for Meaning and Understanding: A Summary of Underlying Theory and Research plus sections for online articles and books — like Understanding by Design (by Grant Wiggins & Jay McTighe with free intro & U U) and Upgrade Your Teaching: Understanding by Design Meets Neuroscience (about How the Brain Learns Best by Jay McTighe & Judy Willis who did a fascinating ASCD Webinar) and other books — plus DVDs and videos (e.g. overview-summary) & more.

 

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 mainly about 1. WHAT to Teach (by defining Goals) and 2. HOW to Teach (by designing Instruction) there is lots of overlapping, so you will find some "how" in the WHAT, and lots of "what" in the HOW.

 
Step 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, their conceptual knowledge), and for skills (what they can do, their procedural knowledge).     { Our goals for ideas-and-skills include ideas, and skills that usually are skills-with-ideas when 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 [iou - later, these links will work] and Physical and Character.  Even within this restricted range, with 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.

* For example, in Education for Thinking (ToC), Deanna Kuhn explains why "schools... should teach students to use their minds well, in school and beyond."  In her website (educationforthinking.org), she asks What should education accomplish? and answers "the most important mission of schools should be to teach children how to use their minds – how to think and learn – so that as adults they will be able and disposed to acquire whatever new knowledge and skills they may need."

 

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.

 


 
PROBLEM-SOLVING Skills

We can define goals for helping students use a variety of Problem-Solving Skills, including General & Experiment-Using & Metacognitive & Process-Coordinating.

 

GENERAL Skills  (for Problem-Solving)

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

Most problem solving (to "make it better") involves people, and Design Thinking emphasizes the essential skill of empathy.

Productive Thinking occurs "when you effectively combine Creative Thinking and Critical Thinking with accurate 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 Teaching Strategies for helping students improve their Productive Thinking.  The rest of this section describes some interesting ways to analyze General Thinking Skills.F8E2FF

 

Bloom's Taxonomy

Using Bloom's Taxonomy for [Goal-Directed] Course Design by Barbara Shadden.

What is it?  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 to a guide to Bloom’s Taxonomy & Bloom's Taxonomy: Original and Revised by Mary Forehand.   Assessing Learning Objectives using Bloom's Taxonomy (from U of Illinois) includes Sample Test Questions.   {a brief summary and in-depth analysis}

more about Domains-with-Levels:  Between 1948 and 1956, 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, 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.

 

 

EXPERIMENT-USING Skills  (for Solving Problems)

During life, we naturally “do EXPERIMENTS” that give us EXPERIENCES.  Sometimes we consciously decide to Design Experiments.  Why?  You will want more experiences (so you can get more information about “what is happening”) if you think this will help you do better Evaluation.   How?  You ask “what additional Information (Predictions or Obervations) would be useful for Evaluation, and what Experiments will help me get this Information?” to guide you in Designing More Experiments that you Use-Use-Use-Use in four ways.

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.

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

 

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 4 Ways to Use Experiments and Principles & Strategies for Experimental Design to Generate Useful Information that is Old or New.

 

When it was still online — before it unfortunately disappeared between early-2017 and mid-2018 [[check Wayback Machine]] Lester Miller's Introduction to Scientific Method used a model with 7 steps and a flowchart showing Hypothetico-Deductive Logic.  To illustrate the scientific skill of designing useful experiments, they used the historical question of Spontaneous Generation, and explained 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.

 

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

 

 

I.O.U.This section is in a "brown box" because it needs to be developed-and-revised, with a better introduction to describe its "big picture" context in education and in life;  and fixing the links.  I'll continue working on it during mid-June 2021.

 

INTERPERSONAL Skills  (for Thinking about Self-and-Others)

Empathy in Education:  In my page about empathy in education & life a paragraph for empathy in teamwork — which is useful because "when you're co-designing as part of a group, you'll want to develop empathy for the other solution-designers in your team, to make your process of cooperative problem-solving more enjoyable and productive" — leads into a section about empathy in relationships that begins with educational goals:  "our most important problems (our opportunities to make things better) usually involve people, so improving relationships is a worthy goal.  When we're designing whole-person education to help students improve personally useful ideas & skills in their whole lives as whole people, our goals should include the important life-skill of building better relationships, with empathy & kindness and in other ways. 

An effective general strategy — for educating students (and teachers & everyone else)* in all of the multiple intelligences, including social-emotional intelligences (empathy & self-empathy, and much more) — is to develop & consistently use a growth mindset" by thinking (re: an ability they want to improve) “not yet” instead of “not ever.”   /   * developing-and-using a growth mindset is useful for "everyone" because education (as broadly defined in the home-page for my website about Education for Problem Solving) is the lifelong “learning from experience” that everyone does.}

{more - If you want to learn more about these ideas (that are not discussed later in this page) you can read my page about empathy in education and in life.}

[[ A very useful personal skill is developing-and-using a... growth mindset.....]]

 

iou - the remainder of this brown box is idea-scraps about one strategy for societal problem solving more generally (not just in relationships) so it probably will be moved out of this section.

often the weighting of outcomes, deciding what is most important (based on their values & priorities) how to weigh the importance of each outcome, and will depend on their life-experiences & life-situation.

worldview-based values & priorities

{e.g. try to imagine how your evaluations would be affected if you didn't know “who you are” regarding your intelligence, looks, race, health, wealth, status, location,... so, due to your imagining, your actual current knowledge of “who you are” has less influence on your evaluative weighting of different outcome-factors.}    /    But many people aren't skilled in “coping with complexity” and they don't enjoy trying to cope with it, especially when the actual complexity challenges the oversimplistic reasoning they have been using to defend their own views, so it decreases their over-confidence in their views, and the policies they advocate.

[[ obviously we cannot do this "veil of ignorance" now, instead the best we can do is use empathy-and-kindness so we'll want (with kindness) to make things better for more people, and (with empathy) we'll understand what life is like for others, to help us problem-solve ways to make things better for them.

 

 

 

PERSONAL Skills  (for Thinking about Self)

A very useful personal skill is developing-and-using a...

Growth Mindset:  If self-education is broadly defined as learning from your experiences,   better self-education is learning more effectively by learning more from experience, and getting more experiences.   One of the best ways to learn more effectively is by developing a better growth mindset so — when you ask yourself “how well am I doing in this area of life?” and honestly answer “not well enough” — you are thinking “not yet” (instead of “not ever”) because you are confident that in this area of life (as in most areas, including those that are most important) you can “grow” by improving your skills, when you invest intelligent effort in your self-education.  And you can support the self-education of other people by helping them improve their own growth mindsets.
    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].

also:  Growth Mindset for Creativity

Self-Perception -- [[a note to myself: accurate understanding/evaluation of self + confidence in ability to improve/grow ]]

 

METACOGNITIVE Skills  (for Solving Problems)

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.

 

 

PROCESS-COORDINATING Skills  (for Solving Problems)

THINKING SKILLS and THINKING PROCESS:  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

[[ I.O.U. -- later, in mid-June 2021, the ideas below will be developed -- and i'll connect it with Metacognitive Skills because we use Metacognition to Coordinate Process.

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

Collaborative Problem Solving [[ this major new section will link to creative.htm#collaborative-creativity (with a brief summary of ideas from there) and expand these ideas to include general principles and "coordinating the collaboration" by deciding who will do what, when, with some individual "doing" and some together "doing" ]]

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

[[a note to myself: educational goals:  we should help students improve their ability to combine their thinking skills — their creative Generating of Options and critical Generating of Options, plus using their Knowledge-of-Ideas that includes content-area knowledge plus the Empathy that is emphasized in Design Thinking — into an effective thinking process.

[[ Strategies for Coordinating:  students can do this by skillfully Coordinating their Problem-Solving Actions (by using their Conditional Knowledge) into an effective Problem-Solving Process.

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

[[ a little more about problem-solving process

[[ here are more ideas that might be used here:

Sometimes tenacious hard work is needed, and perseverance is rewarded.  Or it may be wise to be flexible – to recognize that what you've been doing may not be the best approach, so it's time to try something new – and when you dig in a new location your flexibility pays off.

blank no-content spacer gif
Sometimes PERSEVERANCE
is needed, so DIG DEEPER.
  
Sometimes FLEXIBILITY
is needed, so DIG ELSEWHERE.
treasure is beneath hole where man is digging
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treasure is to the side of hole where man is digging

Perseverance and flexibility are contrasting virtues.  When you aim for an optimal balancing of this complementary pair, self-awareness by “knowing yourself” is useful.  Have you noticed a personal tendency to err on the side of either too much perseverance or not enough?  Do you tend to be overly rigid, or too flexible?

Making a wise decision about perseverance — when you ask, “Do I want to continue in the same direction, or change course?” * — is more likely when you have an aware understanding of your situation, your actions, the results, and your goals.  Comparing results with goals is a Quality Check, providing valuable feedback that you can use as a “compass” to help you move in a useful direction.  When you look for signs of progress toward your goals in the direction you're moving, you may have a feeling, based on logic and experience, that your strategy for coordinating the process of problem solving isn't working well, and it probably never will.  Or you may feel that the goal is almost in sight and you'll soon reach it.

- How I didn't Learn to Ski (and then did) with Persevering plus Flexible Insight -

 


 

PRINCIPLES for PROBLEM SOLVING

Should we explicitly teach principles for thinking?
Can we use a process of inquiry to teach principles for inquiry?
Should we use a “model” for problem-solving process?

combining models?

What are the benefits of infusion and separate programs? 

Principles & Strategies & Models ?

 

Should we explicitly teach “principles” for thinking?

Using evidence and logic — based on what we know about the ways people think and learn — we should expect a well-designed combination of “experience + reflection + 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).

 

Can we use a process-of-inquiry to teach principles-for-inquiry?

classroom (with Students & Teachers) actively doing Design ThinkingYes.  Students can use inquiry Process to recognize inquiry Principles.  How?  A teacher can combine Experience + Reflection + Principles into sequences (of E+R→P, ERP)* while guiding students with questions that will help them use a process-of-inquiry to learn principles-of-inquiry.

* In a typical sequence of ERP, students first get Experiences by doing a design activity.  During an activity and afterward, they can do Reflections (by thinking about their experiences) and this will help them recognize Principles for doing Design-Thinking Process that is Problem-Solving Process.    {design thinking is problem-solving thinking}

During reflections & discussions, typically students are not discovering new thoughts & actions.  Instead they are recognizing that during a process of design they are using skills they already know because they already have been using Design Thinking to do almost everything in their life.  A teacher can facilitate these recognitions by guiding students with questions about what they are doing now, and what they have done in the past, and how these experiences are similar, but also are different in some ways.  When students remember (their prior experience) and recognize (the process they did use, and are using), they can formulate principles for their process of design thinking.  But when they formulate principles for their process of problem solving, they are just making their own experience-based prior knowledge — of how they have been solving problems, and are now solving problems — more explicit and organized.

 

Should we use a “model” for problem-solving process?

If we help students "make their own experience-based prior knowledge... more explicit and organized" by showing them how their knowledge can be organized into a model for problem-solving process, will this help them improve their problem-solving abilities?

I.O.U. — in mid-June 2021, I'll continue deciding what to do with ideas & resources in this BROWN BOX. 
note: here and elsewhere, places with "==" or [[ are notes-to-myself about things that need to be fixed.

 

Should we teach principles for problem solving, to help students improve their thinking skills and problem-solving process?

SHOULD WE USE 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?

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

simple -- e.g. CER for all problem-solving activities (+ POE when focus is 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. 

 

SHOULD WE COMBINE MODELS ?

what are some benefits of 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 ?

 

IOU - This mega-section will continue being developed in mid-June 2021.

[[a note to myself: thinking skills and thinking process — What is the difference? - Experience + Reflection + Principles - coordination-decisions

 

[[are the following links specifically for this section about "experience + principles"? maybe not because these seem to be about principles, not whether to teach principles.]]

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.  [[a note to myself: it still is excellent, even though it's fairly old, written in 1991 -- soon, I will search to 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 that promote Active Learning explores a variety of ideas about strategies for teaching (based on principles of constructivism, meaningful reception,...) in ways that are intended 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 I'll share these with you, here and in TEACHING ACTIVITIES.

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. 

goals can include improving affective factors & character == e.g. helping students learn how to develop & use 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, or separate programs?"  What is the difference?

With infusion, thinking skills are closely integrated with content instruction in a subject area, in a "regular" course.

In separate programs, independent from content-courses, the explicit focus of a course 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). -- resources from teach-think-org -- [also, lessons designed to infuse Critical and Creative Thinking into content instruction]

Infusing Teaching Thinking Into Subject-Area Instruction (by Robert Swarz & David Perkins) - and more about the book

 

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?

Adobe [in creative]

 

MORE about Teaching Principles for Problem Solving

 
 
 
 
Step 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?

 

I.O.U. — in mid-June 2021, I'll continue deciding how to revise the ideas & resources in this BROWN BOX. 
note: here and elsewhere, places with "==" or [[ are notes-to-myself about things that need to be fixed.

 

STRATEGIES FOR TEACHING

GUIDING — using MINI-ACTIVITIES, FLIPPING A CLASSROOM, ETC

 

[[a note to myself: begin with intro-overview, goals -- link ws#hw ]]

Mini-Activities:  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}

 

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."

 

OPTIONS FOR TEACHING -- (e.g.,  learning by discovery and/or with explanations;  with lecture or flipped classroom;  and so on) - from Vanderbilt U, flipping a classroom & using clickers & just-in-time teaching.   /   and some ideas for creative teaching

A summary of key ideas from How People Learn is one of many high-quality CFT Teaching Guides offered by The Center for Teaching at Vanderbilt University in Nashville. - also, Active Learning by Cynthia Brame

 

miscellaneous possibilities: ==

Teaching Problem Solving -- https://cft.vanderbilt.edu/guides-sub-pages/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)

Five Steps to Better Skills (in Critical Thinking, Problem Solving, Decision Making) by Mary Ellen Guffey

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.

 

Probably it will be useful for teachers to consider that among students there is a variety of different "ways to think" with different kinds of "intelligences" as in the concept of...

Multiple Intelligences

People 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.  For example,

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.

 

AND certainly it will be useful to consider the widely-varying backgrounds of students, and — by Building Educational Bridges to Improve Educational Equity — try to design Teaching Strategies that will be more helpful for more students, across a wider diversity of backgrounds.

MOTIVATIONS and EQUITY

Motivating Students (an overview from Vanderbilt U)

[[ Problem-Solving Activities (and associated Teaching Activities) – Can they promote Educational Equity?  [[What are the connections? @ etalk.htm#eq ]]

[[ we can improve Educational Equity by increasing motivations & confidence (by building bridges to promote transitions of attitudes) and opportunities.

A motivated student — perhaps [[affectivel]] 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. [[ or link to mo.htm#life or ws.htm#mo ]]

Diversity & Equity:  overviews from Vanderbilt and by Patte Barth (director of the Center for Public Education), Educational Equity - What does it mean? How do we know when we reach it? and Equity of Opportunity from U.S. Dept of Education.

 

 


[[ i.o.u. -- this section is an "overlap" between #1 (Goals) and #2 (Methods) so... maybe i'll put it in-between them? -- i'll decide soon, maybe during mid-June 2021 ]]

 

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}

 


 

SCIENCE  (to use-learn-teach Skills for Problem Solving)

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 [iou - their website is temporarily being "restored"] & 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 experiment-using skillsin the context of scientific method.

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

 

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}

 

 

ENGINEERING  (to use-learn-teach Skills for Problem Solving)

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 an "about EiE" video and explore their website.  To develop its curriculum products, EiE uses research-based Design Principles 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 educational philosophy & 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 (29 schools) (and more with IUCCE) including Purdue, Princeton, Notre Dame, Texas A&M, Arizona State, UC San Diego, Drexel, and Butler.

 

 

DESIGN THINKING  (to use-learn-teach Skills for Problem Solving)

Design Thinking emphasizes the importance of using empathy to solve human-centered problems.

Stanford Institute of Design (d.school) is an innovative pioneer in teaching a process of human-centered design thinking that is creative-and-critical with empathy.  In their Design Thinking Bootleg – that's an updated version of their Bootcamp Bootleg – they share a wide variety of attitudes & techniques — about brainstorming and much more — to stimulate productive design thinking with the objective of solving real-world problems.   {their first pioneer was David Kelley}

The d.school wants to "help prepare a generation of students to rise with the challenges of our times."  This goal is shared by many other educators, in k-12 and colleges, who are excited about design thinking.  Although d.school operates at college level, they (d.school + IDEO) are active in K-12 education as in their website about Design Thinking in Schools (FAQ - resources) that "is a directory [with brief descriptions] of schools and programs that use design thinking in the curriculum for K12 students...  design thinking is a powerful way for today’s students to learn, and it’s being implemented by educators all around the world."     {more about Education for Design Thinking in California & Atlanta & Pittsburgh & elsewhere} [[a note to myself: @ ws and maybe my broad-definition page]]

 

On twitter, #DTk12chat is an online community of enthusiastic educators who are excited about Design Thinking (DT) for K-12 Education, so they host a weekly twitter chat (W 9-10 ET) and are twitter-active informally 24/7.

 

 

PROBLEM-BASED LEARNING  (to use-learn-teach Skills for Problem Solving)

Problem-Based Learning (PBL?) is a way to improve motivation, thinking, and learning.  You can learn more from:

overviews of PBL from U of WA & Learning-Theories.com ;

and (in ERIC Digests) using PBL for science & math plus a longer introduction - challenges for students & teachers (we never said it would be easy!) ;

a deeper examination by John Savery (in PDF & [without abstract] web-page);

Most Popular Papers from The Interdisciplinary Journal of Problem-based Learning (about IJPBL).

videos about PBL by Edutopia (9:26) and others ;

a search in ACSD for [problem-based learning] → a comprehensive links-page for Problem-Based Learning and an ACSD-book about...

Problems as Possibilities by Linda Torp and Sara Sage:  Table of Contents - Introduction (for 2nd Edition) - samples from the first & last chapters - PBL Resources (including WeSites in Part IV).

 

PBL in Schools:

Samford University uses PBL (and other activities) for Transformational Learning that "emphasizes the whole person, ... helps students grow physically, mentally, and spiritually, and encourages them to value public service as well as personal gain."

In high school education, Problem-Based Learning Design Institute from Illinois Math & Science Academy (about);  they used to have an impressive PBL Network (sitemap & web-resources from 2013, and 9-23-2013 story about Kent, WA) that has mysteriously disappeared. https://www.imsa.edu/academics/inquiry/resources/research_ethics

Vanderbilt U has Service Learning thru Community Engagement with Challenges and Opportunities and tips for Teaching Step by Step & Best Practices and Resource-Links for many programs, organizations, articles, and more.

 

What is PBL?  The answer is "Problem-Based Learning and/or Project-Based Learning" because both meanings are commonly used.  Here are 3 pages (+ Wikipedia) that compare PBL with PBL, examine similarities & differences, consider definitions:

    John Larmer says "we [at Buck Institute for Education which uses Project Based Learning] decided to call problem-based learning a subset of project-based learning [with these definitions, ProblemBL is a narrower category, so all ProblemBL is ProjectBL, but not vice versa] – that is, one of the ways a teacher could frame a project is to solve a problem," and concludes that "the semantics aren't worth worrying about, at least not for very long.  The two PBLs are really two sides of the same coin. ...  The bottom line is the same:  both PBLs can powerfully engage and effectively teach your students!"
    Chris Campbell concludes, "it is probably the importance of conducting active learning with students that is worthy and not the actual name of the task.  Both problem-based and project-based learning have their place in today’s classroom and can promote 21st Century learning."
    Jan Schwartz says "there is admittedly a blurring of lines between these two approaches to education, but there are differences."
    Wikipedia has Problem-Based Learning (with "both" in P5BL) and Project-Based Learning.

 


i.o.u. - If you're wondering "What can I do in my classroom today?", eventually (maybe in June 2021) there will be a section for "thinking skills activities" in this page, and in the area for TEACHING ACTIVITIES.


 


 

APPENDIX:

 

My model for Integrated Scientific Method

includes these 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, an opportunity to think-and-discover:  In the diagram, do you see...

    symbolisms in the colors?   (in the yellow & green & yellow-green?   in red & blue?)
    three kinds of meanings for the arrows?
A brief outline contains responses for these three inquiry-questions about colors & 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
 a NON-ITALICIZED LINK opens another page.  Both keep everything inside this window, 
so your browser's BACK-button will always take you back to where you were.
 
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
 
This links-page – Education to improve Problem Solving, in Schools for Life
(being written by Craig Rusbult, PhD, during life on a road less traveled) is
http://asa3.org/ASA/education/think/methods.htm
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( continuing to be updated/revised in June 2021 )
 
Most links were checked-and-fixed July 17-19, 2018.
 
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