Problems can be broadly categorised as well-defined and ill-defined. 

• Well-defined problems have a clear initial state, a clear goal state, a definite set of operators, and clear rules for solving. Examples include mathematical equations and jigsaw puzzles.
• Ill-defined problems lack clarity in one or more of these aspects. An example given is the creation of a painting.

Problems can also be classified as:

• Problems of inducing structure: These require identifying relationships among presented elements and creating new relationships to solve the problem.
• Transformation problems: These involve changing an initial state into a goal state using a series of steps. The Tower of Hanoi is given as an example.
• Problems of arrangement also exist.

4. What is meant by difficult problems?

Difficult problems are characterised by several factors including:

• Intransparency (lack of clarity about the situation)
• Commencement opacity (confusion about how to start)
• Continuation opacity (ongoing confusion)
• Polytely (multiple goals)
• Inexpressiveness (inability to clearly express the problem)
• Temporal sensitivity (influenced by time)
• Phase effects (changes that affect the problem)
• Dynamic unpredictability (complexity and unpredictability)

5. What are the characteristics of difficult problems?

Difficult problems are characterised by: lack of clarity, confusion, multiple goals, inexpressibility, time sensitivity, phase changes, and high unpredictability.

6. Describe the nature of problem-solving.

Problem-solving is a cognitive process that involves moving from an initial state to a desired goal state when there are obstacles. It's a higher-order cognitive process requiring modulation and control of fundamental skills. It also involves mental representation of information, which is then manipulated to solve the problem. Problem solving is a dynamic and complex process involving different types of thinking depending on the problem.

7. What are the two processes in human problem-solving?

Human problem-solving consists of two related processes:

• Problem orientation: This involves the motivational, attitudinal, and affective approach to problematic situations.
• Problem-solving skills: This involves the actual cognitive and behavioural steps used to resolve the problem.

8. Describe the stages of problem-solving.

The problem-solving process can be broken down into stages:

• Initial State: This is the starting condition of the problem.
• Operators: These are the moves or operations used to move from one state to another.
• Intermediate Problem States: These are the states generated by applying an operator on the way to the final goal.
• Goal State: This is how the final state or goal conditions are described.

The internal representation of these four stages is called the "Problem Space".

9. What are the four molar components of any problem-solving activity?

The four molar components of problem-solving are the initial state, the operators, intermediate problem states, and the goal state.

10. What types of thinking are involved in problem-solving?

• Problem-solving involves productive thinking and the ability to be sensitive to structural requirements, which is the ability to go beyond learned information.
• The kinds of thinking processes are:
  • Analytical thinking: Where the solution is directly derived from the premises.
  • Synthetic thinking: Where the solution combines premises to create something new.

11. What is an insight problem?

Insight problems are solved suddenly, when a new understanding of the problem occurs. These problems are different from non-insight problems, which are solved step-by-step.

12. What are the various categorisations of problems? Can you categorise your day-to-day problems into these categories?

• Problems can be categorised as well-defined or ill-defined. They can also be categorised as problems of inducing structure, transformation problems, or arrangement problems.
• One could categorise day-to-day problems like:
  • Planning a route to work (well-defined transformation problem).
  • Choosing what to eat for dinner (ill-defined problem).
  • Organising a party (a problem with elements of arrangement and transformation).

13. What is the role of various types of thinking involved in solving different kinds of problems?

• Analytical thinking is useful in problems where the solution is directly derived from the given information, such as counting or calculations.
• Synthetic thinking is required when the problem requires combining information in a new way, which is useful in creative or complex problems.
• Productive thinking is required for problems that require a restructuring of the problem itself.

14. Compare and contrast the role of productive thinking and structurally blind thinking in problem-solving.

1. Productive thinking involves restructuring a problem and creating new solutions with insight, going beyond previously learned steps.
2. Structurally blind thinking is the opposite; it relies on previously known steps or solutions without insight. It may not lead to effective solutions.

15. Emotional states can affect many cognitive processes. What can be the affect of these various emotional states on problem-solving?

While the source material doesn't explicitly detail the effects of specific emotional states, it does state that poor emotional control can disrupt focus on the task and impede problem resolution. Emotions can influence problem orientation.

16. Critically discuss the concept of insight problems and insightful solutions.

• Insight problems are solved with a sudden understanding of a problem, rather than a step-by-step procedure. The process by which insight comes is not well understood.
• Insightful solutions come suddenly and involve the restructuring of the problem.

17. Solutions involving insight and solutions without involving insight – Differentiate.

• Solutions with insight occur suddenly, often after a period of impasse, and involve restructuring the problem or a new way of understanding it.
• Solutions without insight are reached step-by-step, and one feels progress with each step. These do not involve any restructuring of the problem or a new understanding.

18. What are real-world problems? Give suitable examples.

• Real-world problems are complex, often lack clear-cut solutions, and have emotional and practical implications. They differ from simple, laboratory-based problems, which have clearly defined optimal solutions solvable within a short timeframe.
• Real-world problems can be more difficult because they involve multiple factors, may have multiple goals, and can change over time. They also often evoke emotional responses that can impact the ability to solve them.
• Examples of real-world problems include:
  • Career-related issues, such as deciding how to get promoted or how to study for a test.
  • Personal dilemmas, such as who to marry or whether to have a child.
  • Social issues, such as how to bring peace.
  • Scientific challenges, like finding a cure for cancer.
  • Everyday issues, like how to prepare a meal or develop a psychological test.

19. What is meant by "Problem Space"?

• A "problem space" is the internal representation or mental model of a problem. It encompasses the initial state, the goal state, and all the possible intermediate states that can be reached by applying operators.
• The problem space is unique to each individual and depends on the nature of the problem. It's the environment in which problem-solving occurs.
• It includes all the elements required to be organised in a particular manner to solve a problem. A successful understanding of the problem space would require coherence, correspondence, and a relationship to background knowledge.

20. What are the kinds of thinking processes?

The kinds of thinking processes involved in problem-solving are:

• Analytical thinking: In this kind of thinking, the solution is already present in the premise and does not involve generating anything new. It involves breaking down a problem into smaller parts to understand them better. An example would be counting the number of doors in your house.
• Synthetic thinking: This involves synthesising available information and facts to derive new solutions, and is also termed as developing insight. It entails constructing a mental model to see new relationships that were not evident before, leading to problem-solving.

21. Describe Newell’s Mental Model.

• Newell suggests that problem-solving involves constructing a mental model. This model is a representation of the problem that one can inspect to find solutions.
• The solver mentally "writes" parts of the problem onto the model. Once the model is constructed, the solver "reads" the results of what has been written, using the "mind's eye".
• Newell argues that a problem solver constructs a mental model and from this model, one finds answers to the problem by inspecting that model.
• The concept of the "mind's eye" is controversial in cognitive psychology as it is sometimes considered to be nonscientific as it is based on theories of behaviour that are largely based on the soul.
• Newell and Simon used the idea of a "problem space" to characterize human problem-solving behaviour, suggesting that the objective structure of a problem can be characterised as:
  • A set of states, beginning from an initial state,
  • Many intermediate states,
  • A set of operators that move one from one state to another.