Learning by Discovery
what ? When you explore the three diagrams in this page, you will “discover” the principles-for-process in my model for Design Process (i.e. for Problem-Solving Process) by solving a problem when you make something better. { more about Design Process is in the HomePage of my website about Education for Problem Solving }
how? In each diagram, observe (and think about) the words & colors, and spatial relationships. Use “what you learn from each diagram” to help you understand the other diagrams.
why? Using this page will make your process of learning easier than you would expect IF you began by seeing Diagram 3, so you justifiably were thinking “this is too much, it's too complex, and understanding it will be difficult, maybe impossible.” Why will it be easier? Because instead of the "IF" you will begin with the simpler Diagrams 1 & 2 so you will learn the model in easy-to-do steps. And because the problem-solving actions are logically organized. For these two reasons, your learning will be easier and better.
What is Problem Solving?
With a broad definition of problem – it's any opportunity to make something better – problem solving (when we're “making things better”) includes almost everything we do in life. Your problem-solving objective – for what you want to make better – can be a better product, activity, relationship, or strategy (in General Design) or (in Science) explanatory theory.
If you think about the actions you use while you are solving problems, you will recognize that Your Actions are the Problem-Solving Actions you see in the diagrams of Design Process, and your Discovery Learning will become Recognition Learning. Why? It's because Design Process describes Your Process, because people (including you) use a similar process – that is accurately described in Design Process – for almost everything we do.
two wide scopes: Design Process has wide scopes for Problem-Solving Activities (that include almost everything people do) and for Problem-Solving Process (it's similar for almost everything we do, as described below). { more - why the wide scopes occur & how they're useful for education }
Diagram 1 - Define and Solve:
While you're studying this diagram, think about a Mystery Question by asking “why is there an arrow on the right side of the Cycle to Generate-and-Evaluate?” and maybe asking two related questions. Diagram 2 - Evaluate an Option:
to be useful for Evaluation, the Situation-for-Experience (whether the Experience is mainly Mental or Physical) must involve the Option, so it's relevant Experience. It will be easier to understand Diagram 3 after you first see all three diagrams simultaneously, so you can get a “big picture overview” that shows you how they all fit together. Below is most of Diagram 1 (its bottom part has been removed) and all of Diagram 2 and most of Diagram 3 (the same bottom part has been removed). Where is Diagram 2 in Diagram 1 ? Where is Diagram 1 in Diagram 3 ? Where is Diagram 2 in Diagram 3 ? How do the “extra parts” of Diagram 3 (its left & right sides) answer the Mystery Question? (by explaining why 1 has a right-side arrow)
Diagram 3 - a model for Design Process:
In Diagrams 1 & 3, the word "Cycle" shows that you can choose the option of using an iterative Cycle to let you improve an Option with Guided Generation when critical Evaluation motivates-and-guides creative Generation by revising the Old Option so it's a closer match with GOALS. { using a Cycle is optional, as explained in Action-Sequences } re: the questions "Where is Diagram X in Diagram Y ?", most of Diagram 2 is inside “the gray box” of Diagram 1 , and 3 is basically a combination of 1-plus-2 or in the language of mathematics, 1 + 2 = 3. But it's only "basically" (not exactly) because 3 contains many new ideas. You can search for them (and use hints for finding 22 new ideas) in another page that lets you simultaneously see the 3 full-diagrams, including "bottoms" of 1 & 3. the flexibility of Design Process options for actions: The next section describes common "Action Sequences" that people use while they are solving a problem. Each different Sequence-of-Actions is an option for “what to do” that a person can choose. The different options illustrate how we can “use a problem-solving process that is similar for almost everything we do, but is not identical,” because our Problem-Solving Actions can be combined in many different ways by different people to solve different problems. your process is flexible: When you coordinate your Problem-Solving Process by making Action-Decisions about “what to do next” your flexible improvising IS analogous to the flexible goal-directed improvising of a hockey skater, but IS NOT like the rigid choreography of a figure skater. more – You can read a little more about the flexibility of our “similar but not identical” process, and much more with analogies about using roadmaps (for guided exploring) or music theory (for guided improvising of semi-harmonious melodies), plus the choosing of tools by a carpenter (or mechanic, electrician, plumber,...), and using simple Lego bricks (to build complex structures) or simple atoms (to build complex molecules & materials). Action Sequences in Design Process These occur because people intuitively use Actions in a logical sequence. Below you see the middle part of Diagram 3, without its top & bottom. The shadings convert it into an “isolation diagram” that calls attention to some of the Actions. The unshaded parts show a sequence that is common because when people finish one Action often the logical “next step” is to USE the results from this Action in their next Action.
Then after this “use, use” maybe — in the area that is lightly shaded (to show that it's optional) — you will continue onward to “use, use, use” if you choose to use the Quality Check (in a Design Cycle) by asking "revise Option?" to decide if you want to Generate an improved New Option that has higher Quality because there is a closer match between its Actual Properties (in your Predictions) and the Desired Properties (that you're defining as GOALS for a satisfactory Solution). During this process of Guided Generation you are using critical Evaluation to Motivate-and-Guide your creative Generation. * In a comparative Quality Check you're asking “how close is the match?” (i.e. “how high is the Quality?” with Quality defined by your GOALS), and this is The Design Question during General Design. And during Science-Design {shown in center diagram below} in a Reality Check you're asking “am I surprised?” with The Science Question. two other options for Action-Sequences: When people coordinate their process of problem solving by making Action-Decisions about “what to do next” we often use these three Action-Sequences: • As described above {and shown in the unshaded parts of left-side diagram below}, you can decide to "Evaluate this Option" with a Mental Experiment and a Predictions-Based Quality Check; and maybe (it's optional) you "use QC" by asking "revise Option?" in a Design Cycle. • Or to "Evaluate this Option" you can Use a Physical Experiment (as in right-side diagram) to make Observations that you use in an Observations-Based Quality Check; and maybe you use QC and ask "revise Option?" in a similar kind of Design Cycle. • And if you are “surprised” due to a failed Reality Check {in center diagram} when Predictions are not matched by Observations, maybe you will decide to "revise Model" in a Science Cycle.
These three common Action-Sequences — when you Evaluate in a Predictions-Based Quality Check, Evaluate in a Reality Check, Evaluate in an Observations-Based Quality Check — are highlighted (in areas that are unshaded or lightly shaded) in these isolation diagrams. In each Action-Sequence, the result of one Action is used in the next Action: first you use an Experiment to make INFORMATION (to make Predictions, or make Observations, or make Predictions & Observations); then you use THIS INFORMATION in a comparison to do EVALUATION; then maybe you use THIS EVALUATION to "revise" and do Generation of a New Option. Then you could (as an option) decide to begin a new Action-Sequence if – as before – "first you use an Experiment to make INFORMATION" and then you continue by doing one of the three Sequences. other options: Of course you also can do other kinds of Action-Sequences. For example, instead of deciding to Evaluate An Option (as in the sequences above for use-use or use-use-use) you might want to Generate Multiple Options (as in a creativity-stimulating strategy of Brainstorm-then-Edit) and delay Evaluations until later. This would involve a simple decision that “I will Generate Many Options” instead of deciding “I will Evaluate this Option.” / This is just one additional example. Many other kinds of Action-Sequences are possible, and each can be useful in some problem-solving situations. |
the Two Wide Scopes of Design Process:
what? Design Process has a wide scope for Problem-Solving Activities because problem solving includes almost everything we do. It also has a wide scope for Problem-Solving Process because people use a Problem-Solving Process that is similar (but is not identical) for almost everything we do, and this intuitively natural Problem-Solving Process is accurately described by my model for Design Process.
why? Brief “explanations for why” are in the Page Introduction, and detailed explanations are below, for Activities and for Process.
so what? The two wide scopes are educationally useful because they – along with the logical organization of Design Process – promote transfers-of-learning that we can use to motivate students so they will want to pursue their own personal education when we build bridges from school into life so they get direct benefits by improving their abilities (to learn & perform) plus indirect benefits by improving important attitudes, in their motivations (for wanting to learn) and their confidence (in being able to learn, with a growth mindset). And the wide scope of Activities gives teachers the option of choosing to use Design Process (or not use it) for most of what they do in the classroom, with options ranging from improving basic skills-for-learning to creatively designing a wide variety of fun-and-useful activities.
the wide scope of our Problem-Solving Activities:
what? With educationally-useful broad definitions, a problem is an opportunity to make things better in any area of life, and problem solving happens when we do make something better. / Yes, this differs from a common perception that a problem always begins with “a bad situation” because with my definition your feelings about the current now-situation could range from dismal thru lukewarm and wonderful to awesome. If your actions produce a “move toward a better place” anywhere within the wide range — whether it's a change from dismal to lukewarm, or from wonderful to awesomely spectacular — it's “problem solving” because the situation has become better.
why? People solve problems because we want to make things better. Or we want to avoid letting things get worse. { We can make things better by increasing quality or maintaining quality, by promoting a helpful change or resisting a harmful change. }
what? We begin a design project (it's a problem-solving project) by asking “what do we want to make better?” When making this decision, we Define an Objective by choosing to design (to invent or modify or find, or find-and-modify) a better product, activity, relationship, and/or strategy (in General Design) and/or (in Science-Design) a better explanatory theory. These objectives – extending far beyond traditional “design fields” – include almost everything we do in life. { iou – during August 16-23, I'll link to a section that describes the wide variety of objectives for design projects. }
why? The main reason that it's "almost everything we do" is because we design-and-use a strategy many times every day, in many ways. In fact, you do this every time you make a decision, most commonly by asking “what is the best use of my time now? and later?” in a strategy for effectively using your time and – because “time is the stuff life is made of” (Ben Franklin) – using your life.
the wide scope of our Problem-Solving Process
and the descriptive accuracy of Design Process:
how? [[ iou – I'll develop this intro-paragraph tonight, August 14. ]] You will recognize the similarity-in-process when you compare The Actions of Design Process (in Diagrams 1-3) with Your Actions (while you solve problems) and you think “These Problem-Solving Actions are My Problem-Solving Actions” so your Discovery Learning becomes Recognition Learning. This recognition will happen for most people, because Design Process accurately describes the practical problem-solving process that is intuitively used by most people, for almost everything we do.
Design Process describes Your Process: A model for problem solving should accurately describe the process that people actually do use (intuitively & naturally) while we are solving problems. Design Process does this, because while you're solving problems you actually do the Actions that you see in Design Process, whenever...
⊡ you do creative-and-critical thinking (as shown in Diagram 1) by creatively Generating Options and critically Evaluating Options in iterative Cycles of Design.
⊡ you use logical comparisons (as in Diagram 2) because...
you want to Evaluate an Option during General Design so you do a Quality Check by comparing Predictions with Goals, or by comparing Observations with Goals; or
you want to Evaluate a Theory during Science-Design so you do a Reality Check by comparing Predictions with Observations.
These three Action-Sequences (Quality Check, Quality Check, Reality Check) are common because they are useful, so people naturally-intuitively-logically combine Actions into sequences that occur when the result of one Action is used in the next Action.
⊡ you do guided generation (as in Diagram 3)...
when during General Design you ask “how close is the match?” (it's The Design Question, aka The Engineering Question) about your Quality Check and then you choose to ask "revise Option?" and to revise this Old Option in an attempt to creatively Generate a New Option that is a better match with your Goals; or...
when during Science-Design you ask “am I surprised?” (it's The Science Question) about your Reality Check and then you choose to ask "revise Theory?" and to revise this Old Option in an attempt to creatively Generate a New Theory that produces a better match between Predictions and Observations.
With either Action-Sequence, you do Guided Generation by using your critical Evaluation to motivate-and-guide your creative Generation during a Cycle of Design.
iou – tonight, August 14, I'll finish writing this section, and all of the gray text below – until the next section, "other options for Action-Sequences" – will be used or deleted.
an educational benefit: Due to this descriptive accuracy, when students get Problem-Solving Experiences and then Reflect on their Experiences, they will observe themselves doing the Actions of Design Process, and this recognition lets them use a Process-of-Inquiry to discover Principles-of-Inquiry, with Experiences + Reflections ➞ Principles. / in home.htm I'll describe challenges (convergent aiming for a specific problem-solving framework, for Design Process, but... if a teacher wants to modify it that's fine with me, and doing this might be empowering for students; but even if a teacher stays with Design Process as-is there are plenty of details (e.g. the detailed descriptions in the HomePage, or the "22 new ideas" in Diagram 3 (that are not in Diagrams 1 or 2) with elaborations of the basic framework, and most of these Principles (probably all) can be "discovered" by students during their Reflections on their problem-solving Experiences, with E + R ➞ P.
you actually do the functional actions, i.e. actions that are done in order to perform a function during your problem-solving process -- Design Process is a logical framework that shows how we Make Information & Use Information. / one way is by integrating General Design with Science-Design.
Design Process also seems accurate for describing our subconscious processing-thinking
these actually ARE the Actions you do while you're solving problems.
for "so what?" -- well-designed uses of Design Process can help students learn more from their problem-solving experiences by developing-and-using metacognitive thinking strategies. }
learning Design Process
will be easier than you expect:
Initially you could justifiably think “Diagram 3 is complex and will be difficult to understand,” but learning will be easier-and-better than you think because...
you will learn the model in easy-to-do steps: Learning is easier because you begin by understanding the simpler Diagrams 1 & 2, then seeing how these “logically fit together” to form Diagram 3.
the problem-solving process is logically organized: Learning is better because, reinforcing our intuitive common sense, scientific research shows the benefits of organizing knowledge. / The apparent “initial complexity” of Design Process becomes actual “eventual simplicity” when students understand how the actions combine to form a logically organized problem-solving process. And when they recognize their own problem-solving process in Design Process. Both of these factors – organization and familiarity – help their model-understanding and their model-using become psychologically intuitive for them.
two questions will help you
answer the Mystery Question:
What? In the 1st Diagram ("Define and Solve"), why does The Cycle have arrows on both sides? It's easy to understand its left-side arrow (from Generate to Evaluate) because you must Generate An Option before you can Evaluate This Option, and you should Evaluate any Option before you actualize it with Actions. But there is...
• a mystery question: Why does the cycle have a right-side arrow, from Evaluate to Generate? Think about this, and then ask...
• a related question: The right side-side arrow points from Evaluate to Generate. Therefore, ask “after I critically EVALUATE an Old Option, how can this help me creatively GENERATE a New Option?” And continue by asking...
• a similar question: While you're exploring the 2nd Diagram ("Evaluate An Option"), ask yourself “after I Compare Predictions with Goals in a Quality Check and decide that the quality-of-matching isn't fully satisfactory, what is a useful next action?”
All of these are basically the same question. You can answer it with your own thinking, then confirm what you have discovered in the 3rd Diagram that is followed by my brief explanation.
a strategy for instruction: A teacher can use these three questions to “guide the discoveries” of their students, to produce an optimal level of challenge that lets them have more fun and get more satisfaction during their process of learning-by-discovering.
my favorite verbal-and-visual representation...
is the 2nd Diagram (to "Evaluate An Option") due to its combination of art-and-logic, with spatial relationships & elegant symmetries in the 3 Comparisons of 3 Elements (using Predictions-Observations-Goals in two Quality Checks and a Reality Check), with color-codings for the Elements (yellow, green, gold) and Comparisons (yellow-green, blue), plus blue & black text. This diagram is my favorite – 🙂 – and I hope you also will like it, will appreciate its logical beauty and what can be learned from it. / More generally, I'm fascinated by (and have creatively designed) a wide variety of verbal-and-visual representations.
The logical integrating of Design-with-Science in the diagram can help students understand how they can improve the logical integrating of Design-with-Science in their thinking when they internalize this logic with experience in problem solving, when they practice using the diagram's comparative Evaluations for General Design (aka Design) and for Science-Design (aka Science) by using comparative Quality Checks and comparative Reality Checks to ask The Design Question and The Science Question. { more about logical integrations in The Comparisons and The Questions }
iou – during August 16-23, I'll finish developing “the extras” in this section, by briefly describing and linking-to sections where you can learn about...
strategies a teacher can use to help their students learn by discovery; plus improving their understanding-and-using of Design Process with digital flashcards and other evidence-based principles for effective learning.
my overall model for Design Process is a family of individual models (e.g. with Diagrams 1,2,3, plus the “isolation diagram” and DP-for-SRL diagram. why? I'll describe the benefits-for-instruction of having “a family of models” in Design Process; e.g. in another page you can see 19 diagrams (the 5 in this page plus 14 others), including a Clicker Map but I think the only one that will be commonly used in classrooms is the SRL-for-DP that is designed for teaching SRL-with-DP.