Learning by Discovery:
What? In my website about Education for Problem Solving, the HomePage encourages you to learn about my model for Design Process — i.e. for Problem-Solving Process, for trying to make something better — by thoroughly exploring the four verbal-and-visual diagrams in this page.
How? In each diagram, observe (and think about) the words & colors, and spatial relationships. And compare the diagrams, using the principles you learn in each one to help you understand the others.
Why? Your studying may stimulate you to think about the process in new ways, or maybe it will show what you already have been thinking. While you're studying each diagram, think about the actions you use while you are solving problems, and these self-reflections will convert your Discovery Learning into Recognition Learning.
a tip: To make the diagrams more concrete, you can imagine that your design objective is to design a better product by improving an old product.
options – You probably will want to temporarily ignore this gray box and thoroughly explore the four diagrams. But if you're curious you can read the box-ideas now (instead of later) and maybe click a link. { 14 additional diagrams for more variety }
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• 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. Our main problem-solving objective can be a better product, activity, relationship, or strategy (in Design) or (in Science) a better explanatory theory. {more} • What IS shown (and IS NOT shown) in each the four Action-Diagrams you see below? (it isn't a snapshot, instead it's a time-lapse superimposing) And why is my model for Design Process analogous to one kind of olympic skater, but not another? {more} • Why does my “overall model” for Design Process include many semi-similar “individual models”? And how is this “family of models” useful when a teacher is designing instruction? {more} • You can learn from your discoveries (as when you're studying the diagrams in this page) and learn from my explanations. In the classroom, a teacher can design a process of “Experience + Reflection ➞ Principles” that will help students use a process-of-inquiry to learn principles-for-inquiry, to learn principles for problem solving. {more} • You can choose to view this page in a full-width window (to see larger diagrams & for simplicity in using links) or in a half-width right frame (so links will open in the left frame and you can simultaneously see the ideas in both frames). {more} |
1 – a simple description-of-process:
What? In the 2nd 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) — STOP READING and “think about why” if you want to self-discover the reasons for this arrow — because you must Generate An Option before you can Evaluate This Option. But why does the cycle have a right-side arrow, from Evaluate to Generate?
another question – While you're exploring the 3rd Diagram ("Evaluate An Option by Using Comparisons"), ask yourself “after I Compare Predictions with Goals and decide that the quality-of-matching isn't satisfactory, what can I do next?”
and another question – While you're thinking about this question, a related question is... “When I critically EVALUATE an Old Option, how can this help me creatively GENERATE a New Option?”
All of these questions are essentially the same question. You can answer it with your own thinking, then confirm what you already know (and see things from a different perspective) by studying the 4th Diagram. And you can understand the process more thoroughly by reading my explanations of Guided Generation, when you use critical Evaluation to motivate-and-guide your creative Generation.
is the 3rd Diagram ("Evaluate An Option by Using Comparisons") 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 red & 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 }
What? When educators choose to use broad definitions, a problem is an opportunity (in any area of life) to make things better, and problem solving happens whenever we do make something better. / We can try to solve a problem and “make things better” by trying to increase quality for some aspect of life, or maintain quality by minimizing a potential decrease of quality.
Why? People solve problems because we want to make things better.
What? We begin a design project (it's a problem-solving project) by asking “what do we want to make better?” When we make 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. The main reason that it's basically "everything we do" is because we design-and-use a strategy MANY TIMES every day, most often by asking-and-deciding “what should I do?” or (with more details) “what is the best use of my time now? and later?”
Each of my diagrams (the four you see in this page are the most important) is an Actions Diagram showing the multiple Actions that occur at different times – not simultaneously – during a process of problem solving. Therefore an Actions-Diagram IS NOT a snapshot photo of what is happening at any specific time. Instead you can imagine how each multi-action diagram IS like a photo that shows the superimposition of all Actions that have occurred in a time-lapse video of “the Action being done now” (at many different now-times) during an entire process of problem solving, so it shows a superimposing of all time-lapse Actions, by making all of the Actions visible in a single photo. / For each process-of-solving the sequence of Actions can be different, because making Action-Decisions about “what to do next” is analogous to the goal-directed flexible improvising of a hockey player, but not the rigid choreography of a figure skater.
A process of problem solving can be described in many different ways. One way is to use...
a family of models: My “overall model” for Design Process contains many semi-similar “individual models” that in this page I'll call models. Each model has an Actions-Diagram that is accurate in different ways — because each model selects different Actions to include & exclude — and is educationally useful in different ways. All models are similar because each describes the same overall Design Process; but each is different (so they are semi-similar) because each model includes – and thus encourages a student to think about – different aspects of the overall process.
using models for instruction: Having a variety of models gives a teacher flexibility in their instruction, so they can use a progression – beginning with simplicity and gradually building complexity – to help students understand the individual models and the overall model. And it's practical for students, encouraging them to “think in different ways” for different problems, because their problem-solving process varies from one life-situation to another. In the four diagrams you can see a progression from simplicity to complexity, and this complexification can be used to design a progression of instruction, to help students gradually develop understandings that are more accurate-and-thorough. { And a teacher has more options, can choose from 14 additional diagrams to add variety. }
You can improve your understanding by learning from your discoveries – as when you're studying the four diagrams above – and also learning from my explanations. { e.g. when I describe the 3rd & 4th Diagrams}
Students are learning from their discoveries when you ask them to carefully study the four diagrams — (Now-Situation ➞ Goal-Situation), (Define and Solve), (3 Comparisons of 3 Elements, to Evaluate an Option), (completing a Cycle of Generation-and-Evaluation with Guided Generation) — by examining each diagram and...
• asking “what is the meaning?” for every word & phrase, and for the colors;
• asking “how are these two things connected?” for every arrow;
• thinking about “why the spatial relationships are logically meaningful” ...
and also (during each • ) to think about how all of this describes the actions they use when they are solving problems, with reflections on their own experiences, so their Process of Discovery is also a Process of Recognition.
A classroom teacher can help students learn Principles for Problem Solving in both ways – from discoveries & explanations – with classroom activities they have designed for the purpose of guiding students in a process of Experience + Reflection ➞ Principles that uses a process-of-inquiry to help them understand principles-for-inquiry, i.e. to understand principles for problem solving.
[[ iou – sometime during July 4-6, I'll finish this section and will make the page that's intended to be used in a half-width right frame. Until then the basic ideas are described in a brief summary. ]]
In another page you can see 18 diagrams (these 4 plus 14 others), including a Clicker Map and 2 isolation diagrams.