Chapter 10 – Problem Solving and Reasoning

•Thinking is the process of mentally representing the aspects of the world and then

transforming those representations to new representations that can prove useful to our goals.

•Thinking is often a conscious process and we are aware of the process of transforming mental

representations and we get a chance to reflect on the thoughts.

•Thinking involves problem solving and reasoning

•Problem Solving is that goal-directed activity; involving the application of cognitive

processes to overcome the obstacles and achieve a goal

•Reasoning involves the cognitive processes that we use to make inferences from knowledge

and draw conclusions.

The Nature of Problem Solving

•Problem is a situation where there is no apparent, standard or routine way of reaching a goal.

Often there is difficulty in the pathway to the goal that has to be overcome.

•Problem solving requires surmounting obstacles to achieve a goal

•Routine situations with routine answers are not considered problems. There must be novel or

non-standard solution that the problem solver must discover.

•The research on problem solving works to identify the strategies used when confronted with a

novel situation and we must decide on a course of action.

•Problem solver:

i.Identifies the problem

ii.Finds a way to represent it

iii.Choose a course of action that will make it possible to achieve the goal

•Problem solving makes use of memory, attention and perception

The Structure of a Problem

•At a basic level, problem comprises of 3 parts:

i.Initial state/start state; where you face the problem that has to be solved

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ii.Set of operations; that need to be carried out to the destination/goal

iii.Goal state; where the solution has been attained and problem has been solved

•Problems can be well-defined where the initial state, goal state and the set of possible moves

are clearly defined e.g. chess

•Often problems can be ill-defined where the initial state, operations or even the goal of the

problem is not known for sure.

•To solve an ill-defined problem, it is important to first find the constraints i.e. restrictions on

solutions. By removing the constraints, we can make the pathway to the goal easier

•A type of ill-defined problem is called insight problem where despite all the unknowns, the

answer seems to come to mind in a flash second of understanding. E.g. when solving riddles

Problem Space Theory

•Problem space theory involves searching for a solution within a problem space

•Problem space refers to a set of possible choices that the problem solver comes across at

each step in moving from the initial state to the goal state. It includes the initial state, the goal

state and all the possible intermediate states. The problem solver moves from state to state by

various operations.

•This theory clearly applies to highly constrained situations where there are specific rules and

clearly defined initial and goal states.

•For more complex and less constrained problems, the problem space theory includes multiple

spaces e.g. in a scientific situation, hypothesis space to theory, experiment space to design

experiments and data space to interpret results

•Our real life problems are more similar to such less constrained problems

Strategies and Heuristics

•Algorithm is a set of procedures for solving a problem that will always produce the correct

answer. E.g. calculating a square root or following a recipe where there are clear steps that

have to be followed, and following those steps will lead to the desired outcome.

•Algorithms are often time-consuming and make greater demands on both working memory

and long-term memory

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•Heuristic is a ‘rule of thumb’ way of solving the problem. Such rule gives the correct answer

but not always. It involves the idea of always moving towards the goal state but often to arrive

at the correct solution, it is important to move back e.g. Rubik’s cube where it is necessary to

move away from the goal state before finally achieving it.

•Random search (Generate and test) is the simplest, cognitively least demanding problem-

solving heuristic – it involves the process of trial and error where the problem solver

randomly picks a move and tests to see if the goal state is achieved or not. It may appear

inefficient but we often turn to it when nothing else seems to work – and at times it may even

provide the solution. Therefore, it is fall back heuristic to use when other heuristics do not

work or are cognitively too demanding

•Hill climbing is the problem solving heuristic where the problem solver looks one move

ahead and choose the move that most closely resembles the goal state. It is relatively more

reliable heuristic but it can also lead the problem solver astray since problem solving requires

the person to move down the hill at times e.g. 3 jugs example

•Means-end analysis is more cognitively demanding but a successful strategy where a

problem is broken down into sub-problems. If the sub-problem is not solvable at the first

stage then it is further broken down into other sub-problems until a soluble sub-problem is

found. E.g. Tower of Hanoi

•Researchers by brain imaging can record every move that a problem solver makes to get to

the goal state. They can also determine how long it takes to solve a problem and different

types of moves that problem solvers take

•Verbal protocol analysis is a behavioural approach where the problem solver describes the

process outloud in the course of working through the problem. The problem solver is

recorded in audio and video. Researchers then transcribe the protocol and analyze the

transcript to determine the ways in which the problem was represented, the sequence of steps

that were used to solve the problem and the problem space is inferred.

•Another strategy used focuses on computers where building programs are used by a

computer, such building programs embody the strategy people use to solve problems, we then

compare the computer output to the moves made by a person.

•Computer models make it necessary for us to explicitly describe every step of problem

solving and makes uses of all problem solving heuristics; random search, hill climbing, and

means-end analysis

The Role of Working Memory and Executive Processes

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