At the top is the analysis process, the management of the investigation into the structure of the situation.

We gather in information, and look for significant stable elements. These might be People, Things, Ideas or Events (P.T.I.E.).

We classify or categorise them by looking at their similarities and differences.

We look at the way these things behave and interact, their capacity to affect each other, the range and circumstantial limitations of their capabilities, patterns of activity, trends, sequences, relationships of cause and effect, etc.

Ever mindful that we live in a sea of false assumptions, we repeatedly test our latest understanding, taking measurements and setting up experiments to test out ideas.

We know from experience that a single viewpoint can produce a flawed and incomplete perception, so we try to look at the situation from many different points of view, deliberately looking for what we may have missed, particularly when we have assumed something was obvious.

The analysed information is generalised and abstracted, and built into a GT model (centre right) that contains all our knowledge about the nature and behaviour of all the participating elements, and the subtle nuances and limitations of the relationships between them.

Winding the handle, and exploring the emergent properties of the model will suggest ways in which the situation can be controlled, adjusted and transformed.

Upper centre left - we have the problem and goal framing process. What do we know about the problems we are trying to overcome and the goals we are trying to achieve? Whose viewpoints are we looking at it from? What is the boundary, how far are we prepared to go to get a solution? What filters are we imposing? What aspects of the situation are we interested in (economic, mental, spiritual, cultural, ecological, environmental, political, marketing, PR, etc.) and what are we excluding? What methods and practices will we accept and reject en route?

The framing of the problem can be dynamic and iterative, as it may be influenced by the information that comes to light in the analysis, or in the exploration of the consequences of possible actions.

Changes in the problem definition may mean we need to adjust the scope and focus of the analysis.

Now we are into the problem-solving phase, winding the handle to generate a range of options that will hopefully have the effect of getting us to our goals without creating any more problems.

The options are evaluated: what are their consequences, are they worth the effort, do they change our understanding of the problem or the framing of our goals?

The answers may be intuitively obvious. If not, we may need to employ some mathematical decision support tools to help us decide which of the model's predictions give the best solution.

Then we try the best solution in the real world. Hopefully it works just as the model predicted. If it doesn't, we have potentially got some useful information to be added to our model of reality.

The final problem is to decide when to stop. If we have worked hard but have not found a satisfactory solution, then at some point it may be sensible to stop trying. Even if we have found a satisfactory solution, we might find an even better one if we keep trying. It is not an easy judgement because it is impossible to know how much effort it would take and how much better the improved solution would be, if we find one.

Most of this activity takes place in our heads, with occasional experiments out there in reality to see if the predictions are accurate, and to test if the mental model is still an accurate representation of reality. The balance between the mental and practical depends on the nature of the problem. If you are a rocket scientist trying to get a space probe to Mars, you do most of it in your head (with the aid of computer simulations). If you are a sculptor trying to beat a piece of metal into an interesting shape you do most of it out there in reality.

There is a story that the Americans designed their space rocket motors with a lot of expensive computer simulations and the Russians built theirs using a lot of cheap trial and error, (build it, fly it, see what happens, learn). The Russian rocket motors were much better, more efficient and cheaper to build. After the Soviet system collapsed the Americans bought a job lot of surplus Russian rocket motors. I don't know if it's true.

How Does This Dynamic Approach Contrast With The Usual Critical Thinking Model?
Figure 4.16 A typical critical thinking model with isolated components.

This is a mind map style diagram that represents a fairly typical 'Critical Thinking' style approach to thinking and problem solving. As you can see, it chops thinking into a number of separate isolated skills. This particular map represents the ideas in a document advising teachers to plan lessons that focus on the development of each specific thinking skill, in isolation, such as 'analysing' or 'information gathering'.
Figure 4.17 Connecting the isolated parts.

This amended version of the diagram seeks to demolish the idea of the separateness of these skills, by identifying just some of the interconnectivity that is involved in real-world problem solving. For example, in order to be able to analyse something into its attributes and components, we must surely get involved in classifying, comparing, ordering, and integration, before we can assemble the elements into a model that shows the relationships and patterns.

If I put all the obvious interconnections onto the diagram it would become a blur.