Problem Solving Lecture 5

Arrangement problems involve presentations of .....

-all the necessary elements to solve the problem. But...the solver must figure out how the elements are to be arranged. e.g., Anagrams Rearrange the letters to form another word: "KIGVIN"

There have been three general approaches to problem-solving in psychology:

1) Behaviourism 2) Gestalt psychology 3) Cognitive psychology

GPS Problem-solving techniques applied at two levels:

1) Microlevel: minimise 'distance' between current state and sub-goal state. 2)Macrolevel: minimise 'distance' between the initial state and goal state.

There are at least five types of problems

>Transformational problems. >Arrangement problems. >Induction problems. >Deduction problems. >Divergent problems.

There are two general approaches to problem-solving:

Algorithms Heuristics

Behaviourism: Problem Solving as...

Associative learning ! -Thorndike was interested in learning and used "puzzle boxes" to examine problem solving. Specifically, cats placed in puzzle boxes, which posed a problem for cats because they do not like confinement.

Generate-and-test...

Consists of generating possible solutions and then testing them to determine whether they met all the criteria Akin to a trial-and-error approach to problem solving

Everyday mechanisms....

Creative insight stems from ordinary cognitive processes. An incremental process of getting closer and closer to the solution. On this view, the answer does not just appear "out of the blue". Directed remembering= The ability to channel your memory in order to make conscious some knowledge that meets the constraints of the problem at hand. Noticing= An important part of creative insight involves revising drafts. In revising, one must notice where the problems are. Contrary recognition= The ability to recognise objects not for what they are but as something else (cf. Functional fixedness).

THE GPS APPROACH: 'DISTANCE' MINIMIZATION.

First, recall the distinction made earlier between the basic components of problems: an initial state (the situation at the beginning of a problem) . a goal state (the solution to the problem). a set of obstacles that must be overcome. a set of rules (or constraints) that must be followed. The GPS approach to problem solving minimises the "distance" between the initial state and the goal state by breaking the problem down into a series of sub-goals. Sub-goals are depicted as 'nodes' in problem space.

Backtracking....

In solving a problem, problem solvers often need to make certain provisional assumptions Sometimes they turn out to be wrong and need to be "unmade" In those instances, it is useful to have some means of keeping track of when and which assumptions were made so that you can back up to certain points of choice and start over

Gestalt psychology, Problem Solving as...

Insight! Problem-solving involves a restructuring of the problem elements, which results in the sudden realization of the solution This sudden realization is insight Köhler conducted experiments with chimpanzees to study problem-solving. Eg- they had to work out how to get the bananas with crates.

Blocks to problem solving..,..

Mental set Functional fixedness Using incomplete or inaccurate representations Lack of problem-specific knowledge/expertise

Insight problems are...

Problems in which a solution appears suddenly Key assumptions: It involves a mistaken assumption that, once removed, will clear the way to a successful solution of the problem. The solver is hit with the solution suddenly, "out of the blue," and has what might be described as an "Aha!" experience.

Non-routine problems are...

Problems that Cannot be solved by applying well-practiced procedures

Non-Insight problems are:

Problems that are likely to be solved through incremental or "grind out the solution" processes. Non-insight problems require analytical, step-by-step processing. Exemplified by logic, arithmetic and chess problems. I Hate these problems!

Routine problems are

Problems that can be solved by applying well-practiced procedures.

Knowledge-rich problems are...

Problems that require domain specific knowledge (i.e., expertise). Such problems may have many and/or complex constraints and procedure for their resolution may not be known or available. Such problems may require specialist procedures for their resolution.

Knowledge-lean problems are...

Problems that require little or no specific knowledge. Such problems have few constraints and procedures for their resolution are known and available. Informal, intuitive, strategies such as heuristics—natural reasoning strategies—are often used.

Unconscious processing (incubation) ...

Refers to the sort of cognitive processing that occurs while other, conscious processes are occurring. The idea here is that unconscious processing of a problem 'churns away' in the background while a person is sleeping or working on something else and the answer is announced all at once. On this view, creative insight is due to unconscious processing of the problem space.

We have a problem when....

Something that can't be solved in a single, obvious step We have a problem when we have a goal for which no direct means of achieving it is immediately available

Transformation problems present the solver with a ...

Specific goal state that must be achieved. The solver must find the proper strategies or "moves" that will initially transform the initial state into the goal state. e.g., the Tower of Hanoi problem

Lack of problem-specific knowledge/expertise

The assumption is that most of these problems are about equally unfamiliar to everyone and that people go about solving them in basically the same way This assumption is fine for knowledge-lean problems but not knowledge-rich problems knowledge-rich problems require domain specific knowledge, may have many and/or complex constraints, and may require specialist procedures for their resolution

Means-ends analysis & Working backwards

The means-ends approach to problem solving involves Comparing your goal state with your initial state Thinking of the possible ways of overcoming the "distance" between the initial state and the goal state Choosing the best one This working backwards approach analyses the goal state to determine the last step needed to achieve it, then the next-to-last step, and so on

THE GPS APPROACH: THE 'PROBLEM SPACE' is defined by...

The problem solver's mental representations of the initial state. The final goal state. All possible intermediate (subgoal) states The operators that can be applied to reach each subgoal and the final goal.

Using incorrect or incomplete representations...

The process of problem representation may seem automatic or trivial, but it is a critical component of successful problem solving If the problem is misunderstood, or if the wrong interpretation or representation is focused on, the problem solver is at a disadvantage . eg. First, consider this arithmetic problem: 3 + 4 X 2 = BODMAS

Reasoning by analogy

The reasoning by analogy approach to problem-solving involves the identifying common (i.e., analogous) features of problems and using the same logic strategy to solve a problem This approach to problem-solving involves attending to the "deep structure" of the problem rather than the "surface structure" Example: The story of the general and the tumour problem

Creativity & insight...

The resolution of some problems seems to require insight. i.e., sudden changes in the way in which the elements of a problem are interpreted and organised. But...the issue of whether insight problem solving involves special, unconscious processes (like the sudden restructuring of a problem or removal of mistaken assumptions) remains controversial. Competing explanations for insight problem solving: Special unconscious processes (i.e., incubation) Ordinary conscious processes.

Mental set...

The tendency to rely on habits or procedures used in the past Mental sets are essentially mindless strategies or routines. A mental set can interfere with an individual's ability to see things in a certain way instead of in other, equally plausible ways Mental set causes people to make unwarranted assumptions without being aware of making them A mental set can be induced by even small amounts of practice Luchins' Water Jar Problem

Reasoning by analogy....

This working backwards approach analyses the goal state to determine the last step needed to achieve it, then the next-to-last step, and so on

A problem consists of several basic components:

an initial state - the situation at the beginning of a problem. a goal state - the solution to the problem. a set of obstacles that must be overcome. a set of rules or constraints that must be followed.

Divergent problems require the solver to generate ...

as many solutions as possible to a given problem. "Think of as many uses for a brick as you can" 1).................. 2)................. 3).................. 4) .................. 5)..................

Well-defined problems are:

clear and structured The initial state, goal state, the constraints and the rules to find the solution are all understood Once you reach a solution, it is easily assessed e.g., solving an anagram: R M O P L B E

In deduction problems, premises or conditions are given and the solver must ...

determine whether a conclusion fits the premises. e.g., Categorical syllogisms: All professors are caring people. All caring people are good. All professors are good. Is this correct?

Ill-defined problems is...

fuzzy and abstract the goal state, constraints and rules may all be unclear e.g., writing a lab report

Cognitive Psychology: Problem-solving as

information processing ! Early cognitive psychologists like Newell & Simon thought that computer programs might serve as useful tools to model human thinking and problem-solving. On this view, humans solve problems by applying mental processes to representations in memory. Newell & Simon created a program called the General Problem Solver (GPS), which they proposed as a general model of human problem-solving.

In induction problems, the solver is given a ...

series of examples and must figure out the pattern or rule that relates them e.g., Take a look at the following number sequence: 8, 5, 4, 1, 7, 6, 10, ... What is the next number in the sequence?

Heuristics are general

strategies, or rules of thumb, that can be applied to various problems Heuristics serve as "shortcuts" through problem space There are a number of general purpose heuristics that can be applied to a wide range of problems Generate-and-test Means-ends analysis Working backwards Backtracking Reasoning by analogy

An algorithm is a set of ....

that can be applied systematically to solve certain types of problems A mathematical formula is a good example of an algorithm. Algorithms are very powerful problem-solving techniques; applied correctly, an algorithm will always lead to the correct solution, if one exists