Lecture 18 Flashcards
Why is it important to study problem solving?
Because almost all cognitive activities are goal directed, involve controlled processes and involve the removal of obstacles in your goal directed path. This ability isn’t just present in humans.
What are the three features of problem solving?
Goal directedness
Subgoal decomposition (splitting the process into smaller checkpoints)
Operator application (an action that transforms the problem to state into another state).
The solution cannot be immediately available either.
What is the process of problem solving?
Firstly, you’re presented with the initial state which you then transform into a goal state. Once you have done this, you can start thinking about the intermediate steps required, e.g. the operators, they can be counter-intuitive moves. This forms a hierarchy for your problem solving. However, operators have legal rules that need to be followed; cannot exceed the weight limit when transporting the people across the river.
Cognitive operations also come into play and they help get from one step to another but the steps are discrete. People tend to focus on the whole (Gestalt processing) as they don’t look at the individual pieces but look at the relationship between them. Finding out the relationship is the key to solving a problem and it’s sometimes referred to as insight.
What are the two types of goal?
A well defined goal: this has a specific and explicit outcome.
An ill defined goal: this has many different outcomes that can fulfil the goal, e.g. buying someone a ‘good’ gift.
What mental calculations are involved with problem solving?
Speed/accuracy measures, intermediate products, verbal protocols (verbalising your steps, this can change how you tackle the problem) and computer simulations.
What are the difficulties with problem solving?
Persistence of set; using old strategies even if they’re less efficient.
Incorrect problem representations; focusing on the wrong information, perhaps because of how the problem is presented.
Functional fixedness; using objects in a standard way instead of thinking about them in an alternative manner. For example, nailing a candle to the wall scenario. This is because of semantic knowledge leading to the recall of the object’s normal properties and its alternative use isn’t obvious.
Negative set; solving problems in a set way when a different approach would be more successful. This is also known as Einstellung, e.g. if you have a hammer everything looks like a nail. You can form uneccesary boundaries due to your inappropriate state of mind.
Individual differences
Lack of expertise; novices solve problems differently to experts.
Discuss incubation is relation to problem solving
This supports the idea of the representational change theory; the idea that certain factors can help you overcome a block in problem solving. Incubation is a type of this, it’s when you take a break from solving the problem and you come back to it. This happen more if the problem is creative with multiple solutions.
What’s an algorithm?
A systematic procedure that guarantees a solution, however, it might not always be the quickest method as counter intuitive actions are sometimes necessary. However, a heuristic is a rule of thumb mental shortcut using previous knowledge to solve the problem.
What are the methods of problem solving?
Brute force search; exploring the entire problem space, so you test all states which can be impractical with large spaces. This is used a lot with super computers (like online chess) but rarely with humans.
Hill climbing; moving towards a better state, this is a good strategy as you’re constantly moving closer to the goal but sometimes you need to take a step backwards.
Work backwards; start with a goal and work to the starting point. This is good when there are a lot operators at the initial state and is efficient when there’s only one solution. For example, finding the optimal route when there are a lot of uneccesary routes that don’t reach the goal or when you’re given the solution and are told to find the starting point.
Means ends analysis; A combination of hill climbing and working backwards. This involves you finding the distance between the goal state and your current state and finding operators/sub-goals to reduce this distance. It’s a general method and is extremely powerful. This works with the Tower of Hanoi.
Mental imagery
During problem solving, why is there only a modest amount of planning involved?
Because we have a limited short term memory capacity, there are costs involved when using time and effort and simple heuristics often work well enough.
Discuss previous knowledge in relation to problem solving
Positive transfer; this is when previous experience aids us with the problem
Negative transfer; this is the opposite, previous knowledge disrupts solving the problem
Sometimes we form analogies to help understand the problem and it allows us to see the relationship between two similar things, this can be the difficulty in solving problems (thinking things are dissimilar). For example, people can use an analogy to see how case study is similar to another, allowing the issue to be resolved. Also, the cases that are presented can lead to different solutions (sometimes incorrect) as the wrong analogies are formed or the analogies are less obvious.
Discuss the multiconstraint theory
This theory predicts how people use analogies and what factors decide what analogies are formed. It explores 3 factors; problem similarity, problem structure and the purpose of the analogy. The similarity allows the recognition of the analogy to be clear. The structure of the situation must be the same as well so you can substitute each thing for another. The goals of the analogy must match and the procedure, e.g. operators must match.
Discuss the properties that someone has when they have expertise in certain problem solving
They have domain-specific knowledge, superior memory in this domain, highly procedural knowledge and representations of underlying principles. Experts are more flexible and have better judgement. For example, chess experts remember previous experiences, arranged positions, have larger memory chunks in this field and know about the strength of their position. However, when the positions are random, their knowledge isn’t more elite. The same number of moves are considered and the depth of search is the same but experts fixate on tactically relevant moves. They’re fast and have strong self monitoring skills.
Discuss the differences between puzzles and real world problems
Puzzles are unfamiliar, involve no previous knowledge, have all necessary information available but the requirements are unambiguous.
Real world problems are the opposite of all of these and are a lot less well defined.
How can you improve your problem solving skills?
Increase domain knowledge, have a systematic plan, develop subgoals, work backwards and practise. To attain an international level, you need 10 years of deliberate practise. However, some studies support the idea of a natural talent as it takes them less time to master the skill.
