# How to solve problems

Key message: It is not enough to just name the steps of the problem-solving process, each step must be explained and understood.

I have a problem when I am dissatisfied with a current situation, but at the moment I am not able to achieve a desired target situation (the goal). It may be that I do not know what the goal looks like or the means to achieve the goal are unknown or an obstacle must be overcome on the way to the goal (e.g. the required means may be known but not available). So a problem has four main elements: the initial situation, the obstacle, the goal (the target situation) and the method to achieve the goal.

"A problem occurs when a problem solver has a goal but initially does not know how to achieve the goal. This definition has three parts: (1) the current state - the problems begins in a given state; (2) the goal state - the problem solver wants the problem to be in a different state, and problem solving is required to transform the problem from the current (or given) state into the goal state, and (3) obstacles - the problem solver does not know the correct solution and an effective solution method is not obvious to the problem solver." (https://education.stateuniversity.com/pages/2168/Learning-PROBLEM-SOLVING.html, 24.01.20)

In order to solve a problem, three main steps must always be carried out:

1. analyze the problem
2. generate several alternative solutions (find existing ideas or create new ones)
3. make a decision.

(Lindemann, U. (2009). Methodische Entwicklung technischer Produkte. Heidelberg: Springer, p. 46)

### How to understand problems? How to understand situations / systems?

A situation describes the relations between several elements (persons or things) at a point in time. (I cannot imagine a situation that consists of only one element.) So a situation is a system at a certain point in time. When I analyze a situation, it means that I am analyzing a system.

A system is a set of interrelated elements. The viewer can decide where to place the system boundary, but the boundary should make sense.

When we say: “I want to analyze this system (situation)” then we really mean: “I want to understand this system.” Why is it not possible to understand a system just by analyzing it? Because “A whole is greater than the sum of its parts.” Not only the individual elements of a system must be examined, but also their relationships to one another. Analysis breaks a system down into its constituent elements (into its parts). Synthesis combines the relations between the elements to come to an understanding of the whole.

Watch this video: www.youtube.com/watch?v=Miy9uQcwo3U&list=PLsJWgOB5mIMBinjH9ZAbiWiVxsizC5mU_&index=2 (15.02.20). In contrast to the video I believe that analysis and synthesis belong together and that it is impossible to understand a system without doing both.

"Analysis and synthesis, as scientific methods, always go hand in hand; they complement one another. Every synthesis is built upon the results of a preceding analysis, and every analysis requires a subsequent synthesis in order to verify and correct its results." (www.swemorph.com/pdf/anaeng-r.pdf , 26.02.20, page 1)

In another video the authors say that 3 cups on a table are not a system because they exist independently from each other. I also don't agree. I analyze: there are three cups on the table. Their function is to take up liquid. I synthesize: I can invite two friends to drink a coffee with me (or I can do somthing else with the cups). (www.youtube.com/watch?v=GARpWOLqP6E&list=PLsJWgOB5mIMBinjH9ZAbiWiVxsizC5mU_&index=3, 15.02.20)

"In very general terms, a system is any (circumscribed) object which consists of a number of "parts" or "components" which, in some way or another, work together in order to produce an overall effect or behavior. ... We can only concede to the obvious: that just about everything in the world would seem to be some sort of "system". (www.swemorph.com/pdf/anaeng-r.pdf , 26.02.20, page 6)

Three cups on a table are a simple system. Complex systems have many elements and many relations exist between them (high interconnectivity). In addition complex systems may be intransparent (some information about the system is missing) and they may be dynamic (the system changes over time). Complex systems are much harder to understand than simple systems.

A complex system is "made up of a large number of parts that interact in a non-simple way. In such systems, the whole is more than the sum of the parts ... in the important pragmatic sense that, given the properties of the parts and the laws of their interaction, it is not a trivial matter to infer the properties of the whole." (Simon, H. A. (1962) The architecture of complexity. Proc. Amer. Philos. Soc. 106(6) 467–482)

Therefore it makes sense to arrange the elements in groups. The groups can be seen as subsystems of the whole system. The continuation of this approach results in a hierarchical representation showing the structure of the system. Only if all elements are equal, they cannot be categorized.

The figure above shows the hierarchical structure of a complex system (the structure of a system is the arrangement of its elements). The figure gives us an overview of the system elements and also a first indication of their relationship to each other, because we can see which elements belong together. Non-fiction books are systems of statements and their table of contents shows the hierarchical arrangement of these statements. Therefore the table of contents of a book is an example for the figure above.

"Only the knowledge of the elements and their structural arrangement enables understanding of systems and explains the statement that the whole is more than the sum of the parts." (Daenzer, W. F. (1976) Systems Engineering: Leitfaden zur methodischen Durchführung umfangreicher Planungsvorhaben. Peter Hanstein Verlag, Köln, page 12, my translation)

Some psychologists do situation research because they want to predict the behavior of a person in a special situation:

"... considering the situation the person is currently in can enhance behavioral prediction. ... [To assess situational information, we need to measure the physical cues of the situation and the perceiver’s interpretation of the situation’s characteristics.]

Elements that are physically present and constitute the situation are referred to as situation cues ... Cues give the answer to five simple W-questions. Who is with you? Which objects are around you? What is happening? Where are you? When is this happening? ... Listing and quantifying all cues ... in a situation would take a tremendous amount of time and effort, if it could even be achieved.

... assessing situations via their perceived characteristics requires that perceivers rate situations on these characteristics. ... For example, most people would agree that sitting in a café and enjoying a drink with friends is more pleasant than cleaning one’s house. Of course, some people may hold a different view on this, which needs to be explicitly considered when seeking to assess the situation in its completeness." (Horstmann, K. T., Rauthmann, J. F., & Sherman, R. A. (2017). The measurement of situational influences. In V. Zeigler-Hill and T. K. Shackelford (eds.), The SAGE Handbook of Personality and Individual Differences, page 2-9)

This means: To understand a situation, we first need to identify the main elements the cues (see above the figure "Situation Analysis"). Between the main elements exist relations. These relations are governed by rules and have characteristics. Therefore in a second step we must examine these rules and characteristics.

We need imagination to understand the relations between the elements of a situation because we need to put ourselves in the position of the elements. In the position of an element we can ask ourselves:

What are my characteristics?  How do I influence the other elements of the situation? Which rules apply to me? How have I developed over time? How will I develop in the future?

Often the information about a system is not complete, so we need imagination and creativity to predict unknown characteristics of the elements and to synthesize "the whole". The study of a system can start with an investigation of "the whole" as a functioning unit or with an investigation of its parts (its elements).

"We regard a system as a primary unit [a functioning unit] when we treat it as a black box and ask about its overall behavior - i.e. what it does or accomplishes. For example, we may submit our black box to various inputs and observe the resulting outputs.
As a set of parts or components (which somehow work together to produce the system's overall behavior) we can examine the system's construction - i.e. its internal structure and processes. ... and the specific relationships between its parts ...

... the choice of a suitable method for the study of a given system depends, to a large extent, on the type of knowledge that is empirically accessicble to us ..." (www.swemorph.com/pdf/anaeng-r.pdf , 26.02.20, page 6-7)

Sometimes it is useful to start an analysis and a synthesis at the same time. For example, when the police are looking for a serial killer, they investigate all the crime evidence (the elements) and hire a profiler to describe the killer's criminal profile ("the whole").

"The whole is more than the sum of its parts." So what is "the whole"?

There are many different types of systems and you can look at each system from different angles. "The whole" of a system is the most useful for the viewer of the system. It is the answer to the main question the viewer poses to the system. Therefore "the whole" of a system depends on the observer.

If we put all the parts of a car in a box, then we have the sum of its parts. If we assemble all of these parts, we have a functional unit (the car) as "the whole".
The main question to the system is here: "Can I use it as means of transport?" As means of transport the parts in the box are useless.

Here are some examples for "the whole":

"The whole" as knowledge/conclusion: The "whole" is the conclusion which is drawn from the examination of a system. The police analyze a crime because they want to know the offender. Another police department analyses the same crime from a different angle because they want to know how such crimes can be prevented.

"The Whole" as a function: A customer says to a product developer: "Please develop me a product with these main functions."

"The whole" as a key message: Every text has a key message (Literature often has a moral.)

"The whole" as the main characteristic: Two people talk about a car. The first says, "This is a nice car." The other says, "This car uses a lot of gas." They look at the car from different angles.

"The wole" as the main rule: You organize a meeting. The last meeting was very controversial. For the coming meeting you set the rule: everyone respects the other's point of view. (In this text here I synthesize the main rules for solving problems.)

"The whole" as an idea: A scientist sees that many people have the same problem. He has an idea to solve this problem and starts a research project.

We understand a system when we can explain how all of its elements work together to make the whole.

Conclusion:

People who don't distinguish between analyzing and synthesizing don't understand the importance of synthesis. They draw conclusions, but they don't take into account that "the whole is more than the sum of its parts". They do not consider the multiple relationships between the elements of a complex system. Therefore they draw simple conclusions that are often wrong.

### How to set goals and requirements?

"A goal is the object or aim of an action ... usually within a specified time limit." (Locke, E.A. & Latham, G.P. (2002). Building a Practically Useful Theory of Goal Setting and Task Motivation: A 35-Year Odyssey, American Psychologist, 57, page 705)

Definition:  A goal is a desired future result toward which effort is directed. (For the sake of simplicity, I do not distinguish between goal, objective, aim and target.)

A desired future result toward which no effort is directed is a whish, not a goal. A goal (the desired future result) can be broadly determined or specific. If someone has the goal to become rich, he can make a great effort to reach that goal although it is not precisely defined. When several people work together to achieve a goal, it is advisable to define that goal precisely.

A goal is not an isolated goal value, but it is a situation. A situation is a system at a point in time. Just as there are simple and complex systems, there are simple and complex goals. "I want to go to the kitchen and drink a glas of water." This is a simple goal and the answer to the question "Have you achieved your goal?" can normally be yes or no. For a complex goal, the question cannot be answered with a simple yes or no, because in a complex goal situation there are always several elements that are related to the goal. Here is an example:

A student sets himself the goal to get a very good grade in an exam. He prepares day and night for the exam for 7 weeks. He reaches his goal and gets a very good grade in the exam. Unfortunately, his girlfriend is annoyed with him because he hasn't spent any time with her and she separates from him. In addition, he learned too hard and he is sick for 4 weeks after the exam. He should have considered his goal as a goal situation. A complex goal should be set in a comprehensive way: a very good grade without annoying the girlfriend and damaging the health.

The prerequisite to anticipate the goal situation is that we understand the current unsatisfactory situation. The main question is: Why is this situation unsatisfactory? A superficial answer to this question would not be sufficient to set a goal for the solution of a complex problem. An unsatisfactory situation has deficiencies. Deficiencies represent opportunities for improvement. For example, if the growth of a business is 3% and 5% would be possible, then 3% growth is a deficiency.

To understand an unsatisfactory situation, we first need to identify the main elements responsible for the deficiencies. In a second step we must examine the rules and characteristics causing these deficiencies. Then we understand what is positive and negative about the current situation. It is important to understand both because when we improve the negative, we must not damage the positive.

"In the ﬁeld of user experience understanding negative experiences and the conditions in which they arise may prove very important in order to further develop products iteratively based on the user experience evaluations."

(Timo Partala, Aleksi Kallinen, Understanding the most satisfying and unsatisfying user experiences: Emotions, psychological needs, and context, Interacting with Computers, Volume 24, Issue 1, January 2012, page 26)

"It is good engineering practice to state the problem in terms of the top-level function that the system must perform. However, it is better to state the problem in terms of the deficiency that must be ameliorated. This stimulates consideration of more alternative designs." (http://prod.sandia.gov/techlib/access-control.cgi/1996/961620.pdf, 22.08.20, page 3)

The whole process of goal setting looks like this:

"Typically, the current system under consideration is analyzed in its organizational, operational and technical setting; problems [deficiencies] are pointed out and opportunities are identified; highlevel goals are then identified and refined to address such problems and meet the opportunities; requirements are then elaborated to meet those goals. ... Goals may be formulated at different levels of abstraction, ranging from high-level, strategic concerns ... to low-level [specific concerns]" (A. van Lamsweerde, Goal-Oriented Requirements Engineering: A Guided Tour, Proceedings of the 5th IEEE International Symposium on Requirements Engineering, IEEE Computer Society, 2001, page 249, 250)

Specific goals can be called requirements (in software and systems engineering) or SMART goals (specific, measurable, achievable, relevant and time-bound). A goal is a desired future result toward which effort is directed. A requirement is a capability, a function or a property of a desired result.

"I think in terms of three levels of requirements ... At the top are the business requirements, representing the high-level objectives ... The second level addresses the user requirements, which describe the tasks that users must be able to perform using the new product. [The third level are specific functional requirements.]" (K. E.Wiegers. Karl Wiegers describes 10 requirements traps to avoid. Software Testing and Quality Engineering, 2(1), 2000, page 1-2)

There is another aspect that plays a role in setting a goal. We normally want to achieve our goals at a certain point in time with as little effort as possible. So what would be the perfect goal? A goal would be perfect if it satisfies all aspects of the goal situation as well as possible and if it can be achieved at a certain point in time with as little effort as possible. The following figure shows the dependence of the quality of the result on the effort. It shows that it is impossible to achieve a perfect result. So setting a perfect goal is pointless. Goals and requirements must match the available budget and schedule.

The optimal goal for a complex problem always lies within an optimal range.

"... there is no single optimal solution to complex systems problems. Most system designs have several performance and cost criteria. Systems Engineering creates a set of alternative designs that satisfies these performance and cost criteria to varying degrees. Moving from one alternative to another will usually improve at least one criterion and worsen at least one criterion (i.e., there will be trade-offs). None of the feasible alternatives is likely to optimize all the criteria (Szidarovszky, Gershon, and Duckstein, 1986)." (http://prod.sandia.gov/techlib/access-control.cgi/1996/961620.pdf, 22.08.20, page 3)

So far we do not know the solution of the problem. We do not know which method to apply to reach the goal. Different methods result in different goal situations (goal systems). Therefore all goals and requirements are still uncertain.

"... if a project applies a rigid development approach and fails to recognise uncertainty and the need for evolution, it can actually drive additional costs into a project. A common reason for project problems is insufficient management of changing requirements during all stages of the project life." (Nolan, A., Abrahao, S., Clements, P. and Pickard, A. 2011. Managing Requirements Uncertainty in Engine Control Systems Development. Proceedings of the 19th International Requirements Engineering Conference. IEEE, page 259)

Nevertheless, at this stage we are making a list of possible goals and requirements and we prioritize them. This list will help us to decide what is the right method to solve the problem.

"One characteristic of excellent requirements is that they are explicitly prioritized. When customer expectations are high, timelines are short, and resources are limited, you want to make sure the product contains the most essential functions. ... A common approach to prioritization is to group requirements into three priority categories. Essential [must have] ... Conditional [should have] ... Optional [nice to have] ... Keep the prioritization as simple as possible to help you make the necessary development choices." (K. Wiegers, “First things first: prioritizing requirements,” Software Development, vol. 7, no. 9, pp. 48–53, 1999.)

Even if the goals and requirements are still uncertain, we need them to be able to assess the result quality. The figure above can be interpreted in two ways:

1. We compare two possible goal systems and find that System 2 gives us a better result quality.
2. We compare the current system 1 with the goal system 2 and see that the desired result quality is significantly higher than the current one.

Example: A pizzeria buys a new oven. With this new oven (system 2) more and better pizzas can be baked than with the old oven (system 1).

### How to find or have new (alternative) ideas for the solution of a problem?

It is always good to ask the basic questions first and answer them precisely: What is a solution? A solution is the way to solve a problem and thereby achieve a desired goal. The way to a goal is a method. To develop a method, we first need an idea. An idea arises from knowledge. Knowlege consists of facts and rules.

"... hard problems are those for which a solver (human or computer) has insufficient knowledge and resources ..." (Wang, P. (2007). The logic of intelligence. In Artificial General Intelligence eds. B. Goertzel and C. Pennachin. New York, NY: Springer, page 31/39)

If we had sufficient knowledge, we could easily find or have ideas for the solution to our problem or we would know that it is unsolvable. How can we come to the necessary knowledge? There are two possibilities:

We find ideas someone else has used to solve our problem

Nowadays we can find almost everything on the internet. In order to search with the right keywords, it is always good to ask a basic question or to look at the definition of the term we are interested in. I did a search with the sentence "How to find ideas someone else has used to solve our problem" and I found this article:

"Find Someone Else Who Has Solved Your Problem Before ... Before any project, we need to stop and ask ourselves, has somebody already solved this problem. Then we need to genuinely ask ourselves, is there a good reason why our solution needs to be different." (www.producttalk.org/2013/08/find-someone-else-who-has-solved-your-problem-before, 03.10.2020)

We want to find an optimal solution for our problem. If someone else has already used an idea to solve our problem, we should still try to improve that idea. If we want to choose an optimal solution for our problem from several alternatives, we need to have several ideas.

We need to be creative and have new ideas to solve our problem

So what is creativity?

"I define creativity more specifically as the process of having original ideas that have value. ... Creativity is about producing something new. ... It does have to be new to the maker at least and not just a copy or a repetition." (www.interaliamag.org/interviews/ken-robinson, 21.09.20)

"Too often ... “creativity” means having great, original ideas. ... the ideas are often judged more by their novelty than by their potential usefulness ..." (https://hbr.org/2002/08/creativity-is-not-enough, 26.09.20)

Creativity is when someone produces "something new" that is useful. "Something new" is useful when it improves our lives or helps to solve a problem.

Definition: Creativity is the ability to have new and useful ideas to solve problems.

To produce "something new" a person needs to have a new idea. An idea is a brief mental image of something. An idea is only useful if it can be implemented. If an idea is concretized, a plan or a method emerges (a method is the way to a goal, see figure below).

We have a problem when we want to achieve a goal, but our knowledge is insufficient to find the way to it. We need ideas to fill our knowledge gaps ("blanks") and thus achieve our goal.

"... in Leo Tolstoy’s novel “War and Peace”, Prince Andrei Bolkonsky explains the concept of war ʹ... in war, a battalion is sometimes stronger than a division and sometimes weaker than a company; it all depends on circumstances that can never be known. In war, you do not know the position of your enemy; some things you might be able to observe, some things you have to divine (but that depends on your ability to do so!) and many things cannot even be guessed at. ... If you decide to attack, you cannot know whether the necessary conditions are met for you to succeed.ʹ In essence, war is characterized by a high degree of uncertainty. A good commander ... can add to that what he or she sees, tentatively fill in the blanks ... A bad commander extrapolates from what he sees and thus arrives at improper conclusions." (Dörner, D., & Funke, J. (2017). Complex problem solving: What it is and what it is not. Frontiers in Psychology, 8,1153, page 7)

"Ideally, we would like Artificial intelligence (AI) agents to interact with an arbitrary environment where only partial information is available with uncertainty. ... AI agents are much better at quantitative computation than humans but are less capable of perceiving concepts qualitatively. This is the reason why AI agents can beat human experts in deterministic games such as chess and go but are struggling to complete an everyday task ..." (https://openresearch-repository.anu.edu.au/handle/1885/154259, 11.10.20)

The method "trial and error" is the simplest method to fill a knowledge gap with an idea and thus to find a solution for the problem. The search for solutions consists of trials to reach the goal. Nobody wants to rely on his luck and choose the ideas for the trials randomly.

"If trials are chosen randomly, the probability of arriving at a valuable solution
to a complex, high-interaction problem is very low. More efficient orderings utilize knowledge to direct this search process." (Nickerson, J. a. and Zenger, T.R. (2004) A Knowledge-Based Theory of the Firm—The Problem-Solving Perspective. Organization Science, Vol. 15 No. 6, page 620)

What knowledge is needed to have new ideas to solve a problem?

1. Domain specific knowledge

Become an expert in the domain the problem belongs to. Read the domain literature, do experiments and ask other expert about the problem.

"... experts do not possess better general cognitive skills than novices – such as better memory capacity – but rather experts have better domain knowledge based on their experience ..." (Pisa 2012 Field Trial Problem Solving Framework, www.oecd.org/pisa/pisaproducts/46962005.pdf, 01.11.20)

The knowledge gap of experts concerning the problem is smaller than that of other individuals. Because they know all the facts and rules in their field, they can use them

to create ideas that overcome obstacles and solve the problem.

"Gaps in knowledge must be filled by observation and exploration of the problem situation. This often involves interaction with a new system to discover rules that in turn must be applied to solve the problem." (Pisa 2012 Field Trial Problem Solving Framework, www.oecd.org/pisa/pisaproducts/46962005.pdf, 01.11.20)

Example: If I want to fly I can use the rule that hot air has a lower density than cold air and I can build myself a hot air balloon.

"In the broadest sense, a rule could be any statement which says that a certain conclusion must be valid whenever a certain premise is satisfied, i.e. any statement that could be read as a sentence of the form “if ... then ...” ... it should be noted that there are a number of rather different interpretations of the term “rule” outside of first-order logic." (Hitzler P., Krötzsch M., Rudolph, S. (2009). Foundations of Semantic Web Technologies. Chapman & Hall/CRC, page 213 - 216)

Logic is important for creativity: If I want to reach a goal, then what do I have to do? I have to look for facts and rules that I can use to fill my knowledge gaps. In order to do that, it is helpful to know or imagine what knowledge I am missing.

If I want to fly I should study all things that go up: hot air, some gases, birds, leaves in the wind, etc. When I understand the rules why these things go up, then maybe I can use these rules to fly myself. Birds can fly. It is possible that they can fly because their wings have a special shape. So I should examine the shape of their wings.

"A sense of possibility ... imagines something that might be possible but has not been considered possible or even potentially possible so far. (... sense of
possibility is often used synonymously with imagination even though imagination is not the same as sense of possibility, for imagination also encapsulates the impossible)." (Dörner, D., & Funke, J. (2017). Complex problem solving: What it is and what it is not. Frontiers in Psychology, 8,1153, page 7)

The difficulty lies in imagining the unknown unknows as well.

"In February 2002, Donald Rumsfeld ... stated at a Defence Department
briefing: ‘There are known unknowns. That is to say, there are things that we now know we don’t know. But there are also unknown unknowns. There are things we do not know we don’t know.’ ... Much scientific research is based on investigating known unknowns. In other words, scientists develop a hypothesis to be tested, and then in an ideal situation experiments are best designed to test the null hypothesis. ... it is common for the researcher to believe that the result that will be obtained will be within a range of known possibilities. Occasionally, however, the result is completely unexpected—it was an unknown unknown." (
Logan, D. C. (2009). Known knowns, known unknowns, unknown unknowns and the propagation of scientific enquiry. Journal of Experimental Botany, 60(3), p. 712)

Another difficulty is to find the knowledge that is relevant to the problem at hand.

"... chess masters described above considered only a subset of possible chess moves, but those moves were generally superior to the ones considered by the lesser ranked players. Experts have not only acquired knowledge, but are also good at retrieving the knowledge that is relevant to a particular task. In the language of cognitive scientists, experts’ knowledge is “conditionalized”—it includes a specification of the contexts in which it is useful (Simon, 1980; Glaser, 1992). Knowledge that is not conditionalized is often “inert” because it is not activated, even though it is relevant (Whitehead, 1929). ... “Textbooks are much more explicit in enunciating the laws of mathematics or of nature than in saying anything about when these laws may be useful in solving problems” (Simon, 1980:92)." (National Research Council. (2000) How people learn: Brain, mind, experience, and school. Washington, DC: National Academy Press, p. 43)

"An expert system is a modular program consisting of a knowledge base, an inference engine and a user interface ... The knowledge base contains human expertise, which is often expressed in terms of rules and facts. Rules are conditional statements that state what action occurs if a specific condition is satisfied. ... An "inference engine" applies a reasoning strategy and generates solutions based on the rules in the knowledge base and data collected by the expert system." (Taylor, T. and Lubkeman, D. (1989). Applications of Knowledge-Based Programming to Power Engineering Problems. IEEE Transactions on Power Systems, Vol. 4, No. 1, p. 345)

If I want to calculate the area of a rectangle, I can use the formula A = L x W (rule). But that is only possible if I know the values for L and W (facts).

2. General knowledge

Become an "expert" in general knowledge. We need general knowledge to be able to find analogies that inspire us to have new ideas.

“The ability to perceive similarities and analogies is one of the most fundamental aspects of human cognition. It is crucial for recognition, classification, and learning and it plays an important role in scientific discovery and creativity. ... analogical reasoning involves the identification and transfer of structural information from a known system (the source) to a new and relatively unknown system (the target).” (Vosniadou, S. and Ortony, A. (1989). Similarity and analogical reasoning, Cambridge: Cambridge University Press, p. 1)

"An analogy is said to exist when the pattern of relations amongst one set of elements ... is shared with that of another set." (Nathaniel Barr (2014). Reasoned connections: Complex creativity and dual-process theories of cognition. UWSpace., p. 12)

The relations between the elements of a system are determined by rules (patterns). When two systems have analogies, it may be possible to apply the rules of the known system to the unknown system.

"... expertise in a domain helps people develop a sensitivity to patterns of meaningful information that are not available to novices. ... experts and competent beginners (college students) were asked to describe verbally the approach they would use to solve physics problems. Experts usually mentioned the major principle(s) or law(s) that were applicable to the problem, together with a rationale for why those laws applied to the problem and how one could apply them (Chi et al., 1981). ... Differences in how physics experts and novices approach problems can also be seen when they are asked to sort problems, written on index cards, according to the approach that could be used to solve them (Chi et al., 1981). Experts’ problem piles are arranged on the basis of the principles that can be applied to solve the problems; novices’ piles are arranged on the basis of the problems’ surface attributes." (National Research Council. (2000) How people learn: Brain, mind, experience, and school. Washington, DC: National Academy Press, p. 34, 37, 38)

So it is not important to accumulate a large amount of general knowledge, but rather to try to recognize the rules behind the information.

"Many ways of teaching science ... overemphasize facts (American Association for the Advancement of Science, 1989; National Research Council, 1996). The Third International Mathematics and Science Survey (TIMSS) (Schmidt et al., 1997) criticized curricula that were “a mile wide and an inch deep”... (National Research Council. (2000) How people learn: Brain, mind, experience, and school. Washington, DC: National Academy Press, p. 42)

3. Problem-solving knowledge

Become an expert in problem solving. Problem solving is a skill. So what is a skill?

Knowledge has two meanings: We use the word knowledge for things we know and for things we understand. We know all the things that we have memorized in our brain and can recall. Understanding means something different.

"Making matters worse is our tendency to use the terms know, know how, and understand interchangeably in everyday speech. ... Understanding is about transfer ... The ability to transfer our knowledge ... effectively involves the capacity to take what we know and use it creatively, flexibly, fluently, in different settings or problems, on our own." (Wiggins, G. P., & McTighe, J. (2005). Understanding by design (Expanded 2nd ed.). Alexandia, VA: Association for Supervision and Curriculum Development)

"... ‘skills’ means the ability to apply knowledge and use know-how to complete tasks and solve problems. ... ‘competence’ means the proven ability to use knowledge, skills and personal, social and/or methodological abilities, in work or study situations and in professional and personal development" (https://eur-lex.europa.eu/legal-content/EN/TXT/HTML/?uri=CELEX:32017H0615(01)&from=DE#d1e32-20-1, 14.11.20)

For me understanding and skill/competence are the same. Understanding/skills/competence can only be acquired through practice. Problem-solving knowledge is only helpful for someone who practices problem solving.

"The reason the executive so often rejects new ideas is that he is a busy man whose chief day-in, day-out task is to handle an ongoing stream of problems. He receives an unending flow of questions on which decisions must be made. Constantly he is forced to deal with problems to which solutions are more or less urgent and the answers to which are far from clear-cut. It may seem splendid to a subordinate to supply his boss with a lot of brilliant new ideas to help him in his job. But advocates of creativity must once and for all understand the pressing facts of the executive’s life: Every time an idea is submitted to him, it creates more problems for him—and he already has enough." (https://hbr.org/2002/08/creativity-is-not-enough, 26.09.20)

Many people think problem-solving knowledge and creativity is only for big problems. They think they don't have time to optimise the solutions of their daily live problems. They see that they have to invest a little time, but they do not understand that they can also save a lot of time by solving problems optimally. Learning starts with small steps. First solve many small problems optimally, then you can try to solve a larger problem optimally.

"Harrington (1995) described that, for any organization to keep pace with the
fast-changing environment, it needs to take full advantage of both CI
[continuous improvement] and breakthrough improvement. Organizations which are just starting their improvement process activities should first direct their efforts to CI, establishing a working base. Then they should expand their improvement effort to include breakthrough improvement." (Singh, J., and Singh, H. (2015), “Continuous improvement philosophy–literature review and directions”, Benchmarking: An International Journal, Vol. 22 No. 1, p. 95)

### How to check the ideas and turn ideas into methods?

"Creative ideas take time to mature. ... Many well-known theories of creativity, ... involve two stages: generation of possibilities, followed by exploration and ultimately selective retention of the most promising of them. However, the generation stage of creative thinking may be divergent ... in the sense that it produces a raw idea that is vague or unfocused, that requires further processing to become viable." (Gabora, L., and Saab, A. (2011). “Creative inference and states of potentiality in analogy problem solving,” in Proceedings of the Annual Meeting of the Cognitive Science Society, Boston, MA, p. 3506)

Example: A friend calls me and tells me that he wants to visit me in an hour. I want to offer him something to eat. Since he is vegetarian, I have the idea to cook a vegetable soup. It is too late for shopping. So I have to think of a recipe (a method) how to make a delicious soup with the ingredients I have available.

A recipe is a set of instructions that describes how to prepare or make something, especially a dish. A process is a series of actions to achieve a result. A method is a way of doing something to achieve a goal. So a recipe, a process and a method are the same.

"Methods are well-planned, well-founded procedures for achieving defined goals ... A method is a systematic instruction for action (a procedure) to solve tasks of a certain class. It is based on one or more principles. The instruction describes how, starting from given conditions, a goal can be achieved with a defined sequence of steps." (http://www.informatikbegriffsnetz.de/arbeitskreise/vorgehensmodelle/themenbereiche/prinzipMethodeWerkzeug.html, 12.02.14, my translation)

to be continued ...

### How to solve the climate change problem?

LEARN-STUDY-WORK is not a political website. Therefore this is just an example how to apply the first and the second step of the problems solving process shown in the image above.

First step: Understand the unsatisfactory situation, the obstacle and the goal.

The climate of our world changes. This is an unsatisfactory situation because as a result glaciers and sea ice melt, the sea level rises, more flooding and droughts occur, hurricanes and other storms become stronger, species become extinct and some diseases can spread due to migration.

The goal is to stop the climate change by reducing the amount of CO2 and other greenhouse gases in the atmosphere.

Unfortunately this is not easy to do because there are two obstacles:

1. To stop the climate change, many people would have to change their lifestyles considerably but not enough people agree.

2. To stop the climate change without changing the lifestyle would cost a huge amount of money but not enough countries are able or agree to invest this amount of money.

Second step: After understanding the situation, the obstacles and the goal I think of several solutions to overcome the obstacles and to achieve the goal. I list all conceivable strategies (a strategie is a long-term plan):

*) "Use economic power" means buying green products and services and investing in "green" business.

Everyone must decide for himself which of these alternative strategies is effective and is in line with his values. Maybe you are creative and can find further strategies.