Lecture 15: Problem Solving Flashcards
1
Q
Problem solving definitions
A
- A multi-step process to shift your current problem state to a goal state (trying to move from a current problem state to a goal state)
- Math problems
- Social problems
- And everything in between
- How do we engage in this process of problem solving efficiently?
- Involves a lot of processes: memory, attention, perception, decision making
2
Q
Engaging in problem solving is …
A
- Cyclical
- Enact steps that occur in a loop (series of steps that we go through to reach a solution).
- Step 1: know the problem/define the problem. Represent it mentally
- Step 2: Think about how you could solve it (defining strategies to attack your problem)
- Step 3: decide on the best solution
- Step 4: implement best solution.
- Step 5: evaluate what you did to see if you used the best strategy and reached a solution.
- Store this cycle in memory and apply it to new problem.
- Recursive
- Repeat this cycle as many times a necessary to find a solution
- Applicable
- Apply successful cycles (solutions) to hew problems
3
Q
Types of problems
A
Well defined problems: Unambigious, straight path from problem to solution. Can apply existing rules or algorithms to reach a solution.
Ill defined problem: problem is ambiguious. Could be many solution paths or it can have many types of goals. Have to determine the context and the solution and bring more info to formulate the solution plan – need to take into account more information.
4
Q
Well-defined problems
A
- Goal directedness
- Problems with a defined goal state and set task constraints such that there are clear steps
- Ex: soduku
5
Q
Ill defined problems
A
- Ambiguous situations that:
- Have few limitations (rules) for how to solve the problem
- Must create your own path
- Multiple solutions
- Need to take into account a lot of other information
- Social problem solving is a form of ill defined problem solving:
“I need to figure out how to make new friends.”
“I want to learn a new musical instrument”
6
Q
Ill-defined problems carry a load
A
- This study controlled for content to look at differencess in how people solved well-defined and ill defined problems.
- They had to solve anagrams. Create a word from jumbled letters.
- They made one anagram more well-defined task (easier to solve the problem).
- To measure Ill defined - they just showed a jumble of words and said to make a word out of it.
- Greater activity in the right lateral prefrontal cortex for ill-defined anagrams (this region is important for organizing cognitive processes) .
- Solving ill-defined problems carries a greater ‘cognitive load’. With ill-defined problems there is more organization, more maintaining that you have to do with information (greater cognitive load).
- Cognitive load: the amount of information held in mind at one time
7
Q
Moravec’s paradox
A
- Artificial intelligence (AI) can solve well-defined problems (chess, go) well, but not ill-defined problems and simple skills
- “Everything that’s easy is hard, and everything that’s hard is easy”
- AI is often defined by the use of algorithms, deep neural networks, that work well with certainty but not with un- certainty
- AI is not very good at predicting future events, navigating unnfamiliar environments, riding a bike (skill based tasks).
8
Q
Problem solving algorithms
A
- Strategies to move through a “problem space”
- Often used to solve well-defined problems
- A problem space is a representation of a problem and algorithms that can take you to a solution. Within a problem space we have 4 main features:
- Initial and goals states
- Intermediate paths and operators (transformations that occur as you move from state to state): actions to change between states
- Task constraints (allowable moves that can be made).
9
Q
The Tower of Hanoi
A
- Well defined problem
- Move 3 discs from peg A to C so they are in the same initial order
- Task constraints :No disc can lie on top of a smaller one & only one
disc can be moved at a time (i.e., the top disc of a pile)
10
Q
The Tower of Hanoi problem space
A
- Initial and goals states
- Intermediate states and operators
- Task constraints
You have to figure out how to move from the initial state to the goal sstate that you want by implementing the operators and moving between those intermediate stages. The operators that are going to get you to the desired goal are constrained by those rules you have.
11
Q
A brute force approach
A
- Brute force approach means that you consider all the entire problem space and every possible move to get to a solution. Consider everything
- Systematic algorithm that represents all the possible steps from the problem to goal state
- Guaranteed to find a solution, but inefficient (takes a lot of time)
- Combinatorial explosion: computing too many alternatives. System will shut down and not reach a solution.
12
Q
Narrowing down search: Heuristics
A
- Good problem solving often comes when we use heuristics or strategies to select the best operators to move effectively to a goal.
- Menal shortcuts that you take so that you dont have to consider all the information out there.
- Strategies to select moves in a problem space
- Helps avoid combinatorial explosion
- Hill climbing strategy
- Means end analysis
13
Q
Hill climbing strategy
A
- Hill climbing strategy is the difference reduction strategy.
- In hill climbing, you are going to move in any direction hthat is going to take you closer to that goal.
- Select the operation that brings you closer to the goal without examining the whole problem space.
- This strategy can lead to a false outcome, a ‘local maxima’ (subgoal) is mistaken as the final goal
- Does not always work because some problems require you to move away from the goal in order to solve it
14
Q
The hobbits and orcs problem
(Cannot be solved with hill climbing)
A
- Three Hobbits and Three Orcs are on one side of a river, and they all want to cross to the other side
- There is one boat that holds 1 or 2 creatures
- If there are ever MORE Orcs than Hobbits in one place, the Orcs eat the Hobbits.
- At least one creature must bring the boat back each time.
- How can you get everyone safely to the other side
- You must move away from the goal to get there
- IF you look at the soution on how you get these hobbits and orcs to the other ssidde with all these task constrainsts is that theres’s a lot of intermediate steps that you have to take. And in these steps a lot of the time you have to move away from the goal state.
- shows that
15
Q
Means ends strategy
A
- What “means” do I have to make the current state look like the goal state I want to be in? We want to reduce the difference between our current state and our gaol, butt we are going to consider the means that we have to do to get to that goal state (consider all the possible routes).
- Identifying sub-problems to complete the goal
- Includes forward and backward movements and constantly evaluating the difference between current and goal states
- More flexible approach than hill-climbing
- Takes into account the full problem space.
17
Q
Expertise (familiarity) and problem solving
A
- Experts are more familiar with certain information and so they represent a problem differently than non-experts
- Experts will spend much more time defining a problem and a problem space then novices or non experts/ novices that will just try to run towards a solution.
- Experts will take a more holistic or globabl view of a problem space rather than getting drowned by the detail.
- Expert radiologists use ‘global’ visual processes when viewing scans (study used eye tracking to examine how expert and novice radiologist would view chest X-rays).
- novices used a lot of eye fixation and saccades. Experts had fewer sort of eye fixations so they weren’t sort of stoping and looking at details. Shows that as we become more familiar, we can implement more search strategies.
18
Q
Analogical problem solving
A
- Making comparisons between two situations; applying the solution from one of the situations to the other situation
- ** Target**: the situations the person is currently in (The Tumor Problem). The one you are trying to solve.
- Source: the situation that shares similarity with the target (the Fortress Story)
- Consider or remember another problem that you solved that is similar in some way to a current one. It can have similarities in the underlying structure or general meaing of the past experience that you are applying to a current one.
- Analogical problem solving is very effective for illdefined scenarios.
21
Q
Functional fixedness
A
- The inability to see beyond the most common use of a particular object
- “Fixed” on the function of an object that you know.
- HArd time recognizing that you can use something in your environment a different way to get you to a solution.
23
Q
The candle problem
A
- Researchers give the participantss a candle , a thumbtack and a box of matches.
- They are asked to use these objects to attach the candle onto the wall so it didnt drip wax onto the table.
- BEst way is to tack the matchbox onto the wall to use it as a platform.
- Few people realized to do this because they were fixated on the funnctions they knew od the objects. The matchbox was used to light the cadle.
24
Q
The development of functional fixedness
A
- Children of different ages solved the ‘candle’ problem
- Difference with respect to pre- utilization: experience with the objects
- No fixedness in children without pre-utilization. Faster reaction time for children without pre-utilization. Children are more resistant to functional fixedness because they have less experience with those objects.
- Too much experience may lead to fixedness and the Einstellung effect.
26
Q
Mental sets: The water jug problem
Example of mental fixedness
A
- In the water jug task, you are told how much water 3 jugs can hold.
- You are given a desired amount of watter and you have to use the capacity of the three jugs to get that specific solution amount.
- You can use that formula to get to all of these desired amounts across the 8 problems.
27
Q
Mental sets: The water jug problem
A
- Once you get to the later solutions, problems 7 and 8, there’s a much simpler way to reach the solution.
- If people are given the water drug problems in order (from 1-8) , you find that a lot of people will implement that less effective solution for problem 7 and 8.
- But an experimental group, if you give them just problem 7 and 8 then they will use the simpler task.
30
Q
Insight: The triangle problem
A
The triangle shown below points to the top of the page. How can you move three circles to get the triangle to point to the bottom of the page?
* Problems that are thought to be best solved with insight (you have to restructure the problem).
31
Q
Insight problems: The necklace
A
- You are given four separate chains that are each three links in length
- It costs 2 cents to open a link and 3 cents to close a link.
- All links are closed at the start.
- Join all links of chain into a single circle at a cost of no more than 15 cents.
- Open each link of one of the chains (2 cents * 3 = 6 cents)
- Attach the other chains together by closing
these links (3 cents *3 = 9) - You are restructuring the problem, a key characteristic of insight
- You have to realize that you dont need to use each chain as a whole - see this problem and pieces in a new way.
34
Q
Insight and the subjective experience
A
- Participants solved ten problems:
- Five verbal insight problems
- Five non-insight algebra problems
- Made ‘warmth ratings’ (how close they felt they were getting to a silution) every 15 seconds
- A person’s feeling that they are approaching solution
- Warmth ratings predicted performance on algebra by not insight problems
- Steady increase for warmth problems but for the insight problemss they weren’t associated with how peiople were to the actual solution. People arent able to judge how close they are.
