Have you prepared the most important questions from Block 4 Unit 3 for IGNOU MAPC MPC001 Exam? Don't miss this chance to score good marks - start now!

Block 4 Unit 3 Theoretical Approaches to Problem Solving

1. Describe traditional approaches to problem-solving.

• Traditional approaches explain problem solving through associative learning principles derived from classical and instrumental conditioning.
• These approaches suggest that an individual enters a problem situation with pre-existing stimulus-response associations based on prior experiences.
• The problem elicits certain associations more than others, and problem difficulty depends on the strength of correct associations compared to incorrect ones.
• During problem-solving, the associative complex is rearranged: some tendencies weaken through failure (extinction), and others strengthen through success (reinforcement).
• This viewpoint emphasises the transfer of past learning to the current problem and the learning that occurs during problem-solving.

2. Describe Gestalt approaches to problem-solving.

• Gestalt psychology distinguishes between reproductive and productive thinking.
• Reproductive thinking involves applying tried and tested methods to a problem, using rote memory to repeat known steps.
• Productive thinking requires insight and creativity, leading to a new way of organising the problem.
• Gestaltists believe that a problem must be restructured so that the thinker can see a new way of organising the problem.
• An example is the nine-dot problem, which requires restructuring the problem and the removal of the assumption that the lines must lie within the visual boundaries to solve it.

3. Compare and contrast the traditional and Gestalt approaches.

• Traditional approaches focus on past learning and associations and how they influence the response, emphasising a more trial and error method.
• Gestalt approaches, in contrast, emphasise insight, restructuring of the problem and productive thinking over mere association, as a necessary element in finding a solution.
• Traditional approaches are based on behavioural principles whereas Gestalt psychology focuses on perception and problem restructuring.
• While traditional approaches are based on strengthening existing responses, Gestalt psychology focuses on finding a novel approach that provides insight.

4. Describe and delineate the characteristic features of the information processing and computer simulation approach to problem-solving.

• This approach emphasizes how humans process, modify and transform information to reach a solution, as well as the retrieval of both factual and procedural knowledge from long-term memory.
• It proposes that reaching a solution requires a series of organised and executed activities.
• Computer simulation attempts to recreate human problem solving on computers, comparing computer performance to humans.
• Key concepts include the General Problem Solver (GPS) developed by Newell, Shaw and Simon, which introduced a way of looking at problem solving that has influenced subsequent theories.
• The information processing approach focuses on using computer programs to simulate the methods humans use to solve problems.

5. Put forward in detail the general problem-solving strategies of Wickelgren.

Wickelgren's view of problem-solving is based on information processing theories and proposes the following strategies:

• State action tree: A solution is defined as a sequence of states or actions that can be represented in a diagram called the State Action Tree.
• Classification of action sequences: Organising possible action sequences that are equivalent as far as the problem is concerned, called equivalence classes.
• State evaluation and hill climbing: Defining a quantitative function for all possible problem states and choosing the next action that is closer to the goal.
• Subgoals: Breaking down a problem into simpler sub goals.
• Contradiction: Deriving inferences from given information that are inconsistent with the goal, to eliminate possibilities.
• Working backwards: Beginning from the goal state and working backward to the initial state.
• Finding relations between problems: Identifying connections between new problems and previous ones.

6. What are the traditional approaches to understanding problem-solving? Think of some problems that you can explain based on these approaches.

• Traditional approaches explain problem-solving through principles of associative learning, based on classical and instrumental conditioning. These approaches suggest that we enter problem-solving situations with existing stimulus-response associations, which determine our actions.
• Problem difficulty is explained by the strength of correct associations compared to the incorrect ones, and learning occurs via strengthening correct associations and weakening incorrect ones.
• An example of how this applies to a problem: Suppose you are learning to play a new sport and, initially, you rely on your understanding of similar sports you have played. Your initial responses may be based on pre-existing associations from previous experiences, and with practice, your associations that are successful are strengthened, and unsuccessful ones are weakened.

7. Explain Wickelgren's approach to general problem-solving strategies.

• Wickelgren's approach is based on information processing and includes several strategies for solving problems including: a) creating a state action tree, b) classifying action sequences, c) state evaluation and hill climbing, d) the creation of subgoals, e) applying contradiction, f) working backwards and g) finding relations between problems.
• These strategies can be used to create a path towards a goal state from an initial state and to approach a solution from different perspectives.

8. Compare the Gestalt approach to problem-solving with the information processing approach to problem-solving.

• The Gestalt approach emphasises insight and restructuring of a problem as essential elements of problem solving, focusing on the whole rather than the individual parts. Gestalt psychology proposes productive thinking, not just a reproduction of past steps.
• The information processing approach focuses on the step-by-step processes of how the problem is encoded, stored, and retrieved from memory, and on how it is transformed to reach a solution. It uses computer simulations to model these processes.
• Gestalt focuses on how we perceive and structure a problem, while information processing is more concerned with the processes involved in problem solving.

9. Newell's problem-solving approach rests on a famous hypothesis in the literature of problem-solving. Name and explain this hypothesis.

• Newell's approach rests on the Problem Space Hypothesis.
• The Problem Space Hypothesis proposes that for any given problem, there exists a large number of alternative paths from the initial state to a goal state. The entire set of states, generated by legal operators, is the basic problem space.
• People’s problem-solving behavior involves producing knowledge states by applying mental operators, moving from an initial state to a goal state. Mental operators are the rules of the problem space and encode the possible moves that can be made.
• The problem space is the abstract structure of a problem.

10. Critically discuss Newell's approach to problem-solving.

• Newell's approach provides a clear and precise framework for understanding problem-solving, using the concept of the problem space.
• It highlights how mental operators and knowledge states are crucial in problem-solving, providing an abstract structure to analyse problem-solving.
• However, some limitations of this model include its emphasis on structured problems and its inability to explain insight and creativity in problem solving.
• Newell's approach focuses on a logical process that might not fully capture the less conscious cognitive processes that are also often involved in problem solving.

11. What do you understand by the term "General Problem Solver"? Explain with examples.

• The General Problem Solver (GPS) is a computer program developed by Newell, Shaw, and Simon. It is designed to solve a variety of problems using the same core procedures, and it attempts to simulate human problem-solving behaviour.
• GPS uses techniques like means-ends analysis, breaking problems down into sub-goals, and searching for operations to reduce differences between the current and goal states.
• For example, GPS could be used to solve a mathematical problem by breaking the problem into sub-goals and identifying the methods to reduce differences between the current state of the problem and the desired goal state.
• Another example could be solving the Tower of Hanoi puzzle by defining the current state and the goal state and finding the methods to transform the current state into the goal state.

12. Do you think that a single approach amongst the approaches discussed in this chapter is sufficient to explain all kinds of problems and problem-solving that we face?

• No single approach discussed in this chapter is sufficient to explain all types of problem-solving because the nature of problem solving is complex.
• Traditional approaches explain only one aspect of problem-solving through associative learning.
• Gestalt theories provide an insight into the importance of restructuring, but do not explain the step-by-step processes involved.
• Information processing approaches including GPS can explain certain steps in problem solving but do not adequately cover the role of creativity in problem solving.
• Therefore, an integrated approach is more likely to be necessary to account for the complexities of human problem-solving.

13. What do you understand by the term General Problem Solver?

• The General Problem Solver (GPS) is a computer program developed by Newell, Shaw, and Simon. It was designed to simulate human problem-solving processes.
• The GPS is not specific to one type of problem; it aims to solve a variety of problems using the same core procedures.
• GPS uses heuristics, like means-end analysis, rather than algorithms, which would require a large amount of high-speed calculation. It relies on setting sub-goals to achieve a final goal.
• The GPS works by representing a problem as a problem space, consisting of nodes representing states of knowledge about the problem. It moves from an initial knowledge state to a goal state using operators (actions that are permitted).

14. Describe the means-end analysis with examples.

• Means-end analysis is a problem-solving heuristic used in GPS. It involves identifying the difference between the current state and the desired goal state, and then using methods to reduce this difference.
• The steps involved in means-end analysis are:
  • Setting up a goal.
  • Identifying a difference between the current state and the goal state.
  • Finding a method to reduce this difference.
  • Setting up a sub-goal to apply that method.
  • Applying means-end analysis to any sub-goals, if needed.
• For example, consider the problem of proving that in a rectangle ABCD, the sides AD and BC are equal. One might reason that if the triangles ACD and BDC are congruent, their sides must be equal. To prove the triangles are congruent, one might try to show that two sides and the included angles are equal. This is an example of working backwards from a goal to a sub-goal.
• Another example of using the means-end analysis is solving an algebraic equation such as 2s – 10 + 5 = s + 5 + 8. Here the goal is to have the s variable alone on one side of the equation. To reach the goal, you can add and subtract the same values on both sides of the equation, thereby getting closer to a state in which the s variable is isolated.

15. Describe Newell's approach to problem-solving.

• Newell and Simon’s approach characterises human problem-solving using the concept of problem space.
• The objective structure of a problem consists of:
  • A set of states, starting from an initial state.
  • Many intermediate states.
  • A set of operators that can move you from one state to another.
• In any given state, many different operators may apply, generating many different alternative states. This creates the problem space, which is the abstract structure of the problem.
• Newell's approach uses parallels to basic ideas, like the exploration of a maze, to demonstrate how people move through different paths to a solution. Strategies are the systematic methods people use to navigate the different paths and select a solution.
• This approach suggests that people use their knowledge and heuristic methods (like means-end analysis) to search through the problem space to find a path from the initial state to the goal state.
• This approach focuses on the knowledge level, using it to explain behaviour by exploring the reasons an individual believes that actions lead to certain goals.

16. What do you understand by the term problem space hypothesis?

• The problem space hypothesis suggests that for any given problem there are numerous alternative paths from the initial state to the goal state.
• The entire set of these possible states, generated by applying legal operators, is called the basic problem space.
• People’s problem-solving can be seen as the production of knowledge states through the application of mental operators, moving from an initial knowledge state to a goal state.
• Mental operators are the legal moves that are possible, and these may be restricted if certain conditions hold.
• This approach considers problem solving behaviour to be a search process through the space of all possible states.

17. Summarise the Problem Space Hypothesis.

• The problem space hypothesis states that a large number of paths exist from the initial state to the goal state. The complete set of all these possible states, as generated by the rules of the problem, makes up the problem space.
• Human problem-solving behavior involves generating knowledge states using mental operators.
• Mental operators are the actions (moves) one is allowed to make within the problem space and they are governed by rules.
• People use their knowledge and heuristics to search through the problem space to find a path from initial to goal state.
• This entire process operates under the constraints of the person’s cognitive system such as working memory limitations.
• The approach rationalises behaviour in terms of the reasons a person has for believing that certain actions will lead to certain goals.

18. What is problem-solving as modelling?

• Problem-solving as modelling is a newer approach that suggests that problem-solving involves constructing a situation-specific model or case model.
• From a knowledge perspective, a person's perception of the world is through their knowledge. A goal corresponds to the desired state of one’s knowledge about the world.
• The case model summarises the person’s understanding of the problem and allows the person to conclude that a goal has been reached. Actions are the means by which the person interacts with the world to gain knowledge about reality.
• Problem-solving is not just about selecting actions, but also about constructing a model that can lead to achieving the goal.
• Modelling a task is to make more precise what one assumes that the goal is intended to mean.

19. Discuss successful problem-solving.

• Successful problem-solving involves the construction of a situation-specific model or case model that encompasses the understanding of the problem.
• It requires both domain-specific and general strategies, as well as the ability to use these strategies.
• Successful problem solving requires the proper implementation of cognitive skills and this will lead to effective problem resolution.
• A key component of successful problem solving is the capacity for metacognition which allows a problem solver to be aware of the overall goal, current activity, and the effectiveness of chosen strategies.
• It involves productive thinking, being sensitive to the structure of the problem, and moving beyond the knowledge learned from previous problem-solving tasks.
• Successful problem solving will depend on the creation of a clear plan and monitoring the progress of this plan, as well as consulting with others during the problem solving process.
• Successful problem solving is a dynamic and complex process that depends on the nature of the problem.
• Successful problem-solving also depends on a clear description of the problem, as well as describing all the negative or limiting factors, the scope of the problem, and the consequences if the problem is not solved. Brainstorming possible solutions is also key in effective problem solving.