Module 12 Problem Solving (213)

problem solving

A multistep process to shift current problem state to a goal state ie. math problems, social issues

insight

A productive thinking process of forming new patterns of ways to view a problem Restructuring a problem in a new way leads to a sudden solution The Aha moment Gestalt switches: experience of having a sudden switch in how you see something

Moravec's paradox

AI can solve well defined problems well, but not ill defined problems and simple skills Everything that's easy is hard, and everything hard is easy AI often defined by use of algorithms, deep neural networks, that work well with certainty but not uncertainty

Zirhlioglu analyzed relationship between problem solving and creativity

Administered two scales: Problem Solving Inventory by Heppner andd Peterson and How Creative Are You Scale by Raudsepp Found that there is a positive directional relationship between problem solving and creativity Functional fixedness created a barrier to successfully solve candle problem When Dunker supplied them with an empty matchbox, participants were twice as likely to solve the problem Nine dot problem related to the origin of the statement "think outside the box" Maier nine dot problem requires you to connect nine dots, in a 3x3 matrix, with four straight lines drawn without lifting pen or retracing straight line Participants fixate on idea that dots create a square which does not extend outside themselves Only drew ouside square when also told cues that gave away part of the solution

What are the mental processes that go into problem solving

After recognizing there is a problem, you need to understand it by considering all relevant information Includes info available in the environment (bottom up) and info from previous knowledge and experiences (top down) As you actively solve problems, you search memory for relationships between past and current problem Info influences processing Next step is to figure out what steps to take to solve the problem To do that, you must think about the problem and generate possible solutions Thinking requires taking all relevant information into account and manipulation to come up with possible solutions After choosing a solution, must take the steps to solve the problem and reflect on effectiveness of decision

humans use heuristics while computers use algorithms

Algorithms are sequences of operations for how to solve problems that should produce the correct solution Solutions derived from heuristics are not predictable like those from algorithms Because solutions from heuristics are educated guesses and intuitive judgements not always guaranteeing a correct answer Directed by executive control processes which direct, monitor, select, manipulate and interpret information Computers able to use an unbelievable amount of high speed processing power to work out many possible solutions to a problem and choose the best quickly Humans have limited processing power, constraining steps of a problem and how many solutions can be considered at a time

Ill defined problems

Ambiguous situations that Have few limitations (rules) for how to solve problems Must create own path Multiple solutions Social problem solving is a form of ill-defined problem solving ie. need to figure out how to make new friends Computers not very good at solving these Part of the difficulty comes from fact that problems do not have one correct answer; can be solved in many ways Sometimes have unclear solutions Ill defined problems carry a load Greater activity in the right lateral PFC for ill-defined anagrams Solving ill-definedd problems carries a greater cognitive load Cognitive load: amount of information held in mind at one time

trial and error process of problem solving

As we work towards solving a problem, we gain information with each trial attempted Info used on subsequent trials and problems Behaviorists like Thorndike did not see fundamental difference between human and animal behavior Carried problem solving research out on cats Came up with Law of Effect after placing cats in puzzle boxes and recording how they learned to escape by trial and error

all cognitive activities are problem solving in nature

Basic argument is that human cognition is always purposeful, directed to achieving goals and removing obstacles to those goals Can use findings from problem solving research to further understanding of brains and their processes

Two main theories describing how we approach problem solving

Behaviourists posit that problems are solved using knowledge, trial and error Gestalt psychologists suggest that problems are solved by considering them more deeply

Barriers to Solving Problems

Being unable to ignore irrelevant information Ignoring irrelevant info is a skill developing in young children wwhich declines in old age Acquire the behavior with development Irrelevant info often misguides people and leads them down dead end paths Successful problem solving includes deciding what is relevant to the task at hand More difficult with ill defined problems

Einstellung effect

Bias to use familiar methods to solve a problem Can result in inability to seek and use a better method to solve a given problem Leads to rigid thinking and blocks in problem solving Functional and mental fixedness

Development of functional fixedness

Children of different ages solved the candle problem Difference with respect to preutilization: experience with objects No fixedness in children without preutilization Too much experience may lead to fixeddness andd Einstellung effect

Maier's two string problem

Classic test of functional fixedness Only 39% of people can find solution within 10mins The candle problem

Problem Solving with AI

Computers can be compared to humans using info processing approach Both combine new, incoming info with what is stored in memory, and both have central processor with limited capacity Because of limits to processing power of working memory, we are only able to consider a few possible steps toward goal at once Computers can calculate all possible moves at once and are very fast at solving well defined problems

Novices benefit from creative thinking while experts are stuck with conventional thinking

Could be that experts have such a strong mental set that they are unable to be flexible in problem solving techniques Novice has not created a mental set and has advantage of being able to think outside the box Or expert programmed automatic response could hold them back from coming up with novel solutions

Means End example: Meet the cog dog at the park

Current state: home alone Goal: being with dog at the park Evaluate: two major differences (subproblems), location an company Pick most relevant difference (location) Engage operators (walk to the park)

Engaging in problem solving is

Cyclical Enact steps that occur in a loop Recursive Repeat cycle as many times as necessary to find solution Applicable Apply successful cycles (solutions) to new problems

Information Processing Approach

Describes what happens between stimulus and response Sees people as processors of information Info about a problem enters your system; then to manipulate information, you draw related info from LTM into working memory Ideally, related info helps you arrive at solution because it comes from experience with similar problems

Can also use well defined problems and computer simulations to study how humans solve problems

Developing instructions for algorithms help us better understand how our brains could solve similar problems Goal is to program it to complete tasks as humans would Then can infer the actual mechanisms used Includes making mistakes and considering irrelevant information Challenge is to write the problem imitating the same steps and missteps of a human

models describing process of problem solving

Each model has an initial state that describes and defines the problem at hand, and a path for reaching a solution/goal state One model, problem space theory, states that problem-solving is a search within problem space Move through problem space from state to state through actions called operators Good for solving well defined problems, but not all problems are so easily modeled

Expertise and problem solving

Experts are more familiar with certain information and so they represent a problem differently than nonexperts Expert radiologists use global visual processes when viewing scans

Metcalfe and Wiebe studied if there is a difference between solving types of problems

Gave participants insight and non-insight problems to solve While participants were working on problems, they were asked every 15s how close they felt to a solution by indicating "warmth" When solving non-insight problems, participants could predict with some accuracy their closeness Those solving insight problems were very poor at estimating how close they were to the solution Two classes of problems relying on different cognitive processes

Insight problems: the necklace

Given four separate chains three links in length Costs 2c to open a link andd 3c to close a link All links closed at the start Join all links of chain into a singe circle at a cost of no more than 15c Restructure the problem Open each link of one chain Attach other chains by closing these links

Gestalt psychologists thought that how people approach a problem is based on their knowledge and experience of what has worked in the past

In Luchins water-jug problem, we can see how using what has worked in the past can solve a problem or pose a barrier to success Used water jug problem to investigate problem solvers who create mental sets to find quick solutions to problems Another example of a heuristic that can speed up problem solving or act as a barrier

Funcitonal fixedness

Inability to see beyond most common use of a particular object Fixed on the function of an object you know

insight problem

Insight occurs when a solution suddenly pops into mind or occurs in consciousness Is there an environmental cue or one in thoughts that triggeredd solution to pop into your head People usually unaware of what caused them to solve the problem

Insight and subjective experience

Insight problem solving feels like it happens suddenly People cannot accurately predict performance (finding solution) Noninsight problem solving comes with awareness Step by step algorithms help predict performance Participants solved ten problems Five verbal insight problems Five noninsight algebra problems Made warmth ratings every 15s A person's feeling that they are approaching a solution Warmth ratings predicted performance on algebra by not insight problems

Analogical problem solving

Making comparisons between two situations; applying the solution from one situation to another Target: situation the person is currently in (tumor problem) Source: situation sharing similarity with the target (fortress story) People aren't very good at using analogies unless they are reminded Without the hint, a person must look beyond surface details and consider general structure (the gist) Most success when a source and target share surface and structure ie. using a past school-related problem to solve a current school-related problem vs a current relationship-related problem

Insight results from impasse

Mental impasse being stuck in solution path Leads to sudden insight from restructuring problem to see a new solution

Experts know a great deal about a particular topic or skill

Organize knowledge differently than novices; notice features and patterns that others may not, and expertise affects how they perceive and represent info Novices do not understand how info is organized Expert's ability to remember, reason and solve problems are affected by the extent of their knowledge Chase and Simon demonstrated that expert chess players are far superior to novices in their memory for chess arrangements However, when pieces are randomly arranged, experts performed no better than novices Experts able to store LTM patterns of arrangements they could remember in terms of chunks Have larger and better organized store of knowledge than novices do

Insight defined by experience

Participants shown problems and asked to rate feeling of knowing Completed algebra and insight problems Feeling of knowing ratings predicted algebra but not insight problem solving ability Metacognitive assessments (what you know about what you know) is not accurate for insight problems

fixation

People tend to focus on a specific characteristic of a problem, a fixation, which inhibits them from arriving at a solution

Verbal insight problems

Prisoner escaping from a tower Found a rope in his cell half as long enough to permit him to reach the ground safely Divided rope in half, tied two parts together, and escaped How?

Gestalt psychologists began studying problem solving and theorized it as a productive process

Problem solving occurs when you are thinking about a problem andd it is characterized by manipulating and restructuring information in your mind Productive thinking is your ability to reconsider, reframe, rethink or consider a problem from multiple perspectives

Well defined problems

Problems with a defined goal state and set task constraints that make them possible to be effectively solved by humans and computers Initial state, goal state and operators are clearly specified Because well defined problems have solutions that can be broken down step by step, they are easily solved by algorithms

Thorndike was a behaviorist theorizing that problem solving was a reproductive process

Reproductive process involves solcing a problem by using knowledge from previous experiences, like remembered examples and rules A conscious and deliberate search through possible solutions to a problem

Mental fixedness: overusing mental states

Responding with previously learnedd rule sequences even when they are inappropriate or less productive Tendency to responded inflexibly to a particular type of problem and not alter response

Maier was interested in solving problems that demonstrate insight when hints to correct solution are provided

Roughly 40% of 61 participants solved the two string problem without hints or help While remainder of participants were trying to figure out solution, experimenter would run into the ropes, causing them to swing back and forth Prompts the answer to the problem Helped 38% of the rest of participants solve the problem Some needed an additional hint; were provided a hammer and told the problem could be solved using it 23% of those participants were unable to find the solution even with both hints Participants who got an aha moment were unaware that Maier swung rope as a cue or hint Would even offer creative stores of how they solved the problem Maier then presented more cues that would not help solve the problem, along with original cue of walking into the rope If participants solved problem in these conditions, they were just as likely to mention useless cue as useful cue Demonstrates lack of consciousness in nature of insight

Heuristics

Rules of thumb, educated guesses, common sense, intuitive judgements Mental problem solving shortcuts based on simple properties like experience with similar problems or ideas like simplest answer is best Relying on heuristics often makes sense because they get us to goals without taking processing power By using heuristics, we use less cognitive processing power and focus attention on the goal state and perhaps even the next problem Using heuristics does lessen cognitive load, but not always the best method available

Wertheimer described difference between reproductive and productive thinking

Saw that reproductive process uses previous knowledge and trial and error strategy, but does not explain phenomena like insight, where a solution occurs Gestaltists criticizedd behaviorists for rigid approach to problem solving Previously thought of as a reproductive process characterized by previous experience and info already stored in memory

Hill climbing strategy

Select operation that brings you closer to goal without examining whole problem space 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 moving away from goal to solve it

Problem solving algorithms

Strategies to move through a problem space Problem space is a representation that includes Initial and goal states Intermediate paths and operators Actions to change between states Task constraints

Narrowing down search: Heuristics

Strategies to select moves in a problem space Helps avoid combinatorial explosion Hill climbing strategy Means end analysis

Four features of insight

Suddenness: solution pops into mindd with surprise Ease: solution comes quickly and fluently Positive: pleasant experience, even before assessing if solution is effective Confidence: solution believed to be the right one

A Brute force approach

Systematic algorithm that represents all possible steps from problem to goal state Guaranteed to find a solution but inefficient

Hobbits and orcs problem

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 Atleastonecreaturemustbringtheboatbackeachtime. Howcanyougeteveryonesafelytotheotherside?

triangle problem

Triangle points to the top of the page; must move three circles to point to the bottom

Types of problems

Well defined Requirements unambiguous All info needed to solve problem is present Applying algorithms ie. Puzzles Ill defined How to overcome problem / goal is ambiguous Requires additional information Situational ie. laptop is broken

Means ends strategy

What means do I have to make the current state look like the goal state Identifying sub-problems to completer the goal Includes forward and backward movements and constantly evaluating difference between current and goal states More flexible approach than hill climbing

Likelihood of using heuristics increases when one of following conditions is met

When one is faced with too much info When time to make a decision is limited When decision is to be made is unimportant When there is access to very little information to use in making decision When an appropriate heuristic happens to come to mind in the same moment

How people solve problems depends on how they understand or represent the problems in their mind

Whole is greater than the sum of its parts Interested in not just the steps of a problem-solving task, but all the parts that make up problem solving as a whole Learned by studying barriers to problem solving

Problem solving

a cognitive process that involves recognizing there is a problem, analyzing and solving it, and verifying the effectiveness of the solution Goal is to overcome barriers and finding a solution that best resolves the problem Problems can range from small to large Both small and large problems involve a mental process directed as achieving a goal when you do not immediately know the solution

Working backwards

a useful heuristic when you begin solving a problem by focusing on the final result Use the working backwardsd heuristic to plan events without realizing itt Newall suggested working backwards is superior to working forwards

operators

actions transforming current problem state into another problem state Problem solving is a search for the appropriate steps through the problem space

Means-end analysis

also a readily used heuristic in which you begin by focusing on the goal state Achieve by choosing a subgoal at each step as you move closer to that goal state Break down a larger goal into smaller subgoals which each bring you closer to the goal state Used to make corrections or decisions along the way Means end analysis often used in AI Analyze progress toward goal state More flexible than other strategies

Sternberg's Triarchic Theory of Intelligence

analytical intelligence, creative intelligence, practical intelligence Analytical intelligence is academic problem solving skills like solving analogies and puzzles Similar to what IQ scores measure Practical intelligence is the ability to understand and deal with everyday tasks Creative intelligence focuses on developing ideas, applying new ideas and creating solutions

Creativity

being able to produce novel ideas which are appropriate and relevant to the situation No agreed upon definition of creativity Most definitions have a common focus on divergent thinking Guilford was the first to connect divergent thinking and creativity Characterized as thought process that could generate many solutions to a problem to determine one that works well enough to solve Convergent thinking often leads to conventional solutions rather than many creative options

initial state

describes and defines the problem at hand, and a path for reaching a solution/goal state

non-insight problem

distinguished by the process of consciously working through each step of a problem to arrive at a solution

Key mechanism of problem solving is

restructuring of information in the mind Must think flexibly about representations and solutions to a problem, and actively manipulate information in your mind Gestaltists theorized that insight comes from the process of restructuring Insight relies on reorganization of mental representations of a problem Occurs during the productive process, when info is restructured and solutions come into consciousness

Experts problem solving

spend more time analyzing problems and less time thinking about what steps to take than novices Novices conscious of task performance process, causing additional load on cognitive processing Process then becomes automatic in experts Experts initially spend more time matching a problem to those they have previously encountered Categorize problems based on principles current problem has in common with others they have faced Use their expertise to plan steps to solve a problem Quickly carry out plan using automatic processing

Law of effect

states that of several responses made to the same situation, those of which are accompanied or followed by satisfaction are more firmly connected with the situation Those which are accompanied by or followed closely by discomfort have connections weakened

problem space theory

states that problem-solving is a search within problem space Problem space includes an initial state, a goal state, and intermediate states Intermediate states are all the possible states between each step moving from an initial state to a goal state

Ideational fluency

the number of ideas a person can generate about a particular topic or item, often used to assess a person's creativity Fluency could be number of designs created in marketing, or number of room arrangements for a space in interior design ie. as many uses for a pencil as you can think of Can quantify creativity by adding up all ideas created which are useful More ideas one creates, the more creative they are thought to be Question remains as to whether we can correlate measure with success in problem solving tasks

Combinatorial explosion

the rapid expansion of resources required to encode configurations as the number of component features increases

functional fixedness

the tendency to perceive item in terms of its most common use Inability to discover new ways to use an object because we experience using the object in another way so many times Must engage in creative thinking People tend to focus on a specific characteristic of a problem, a fixation, which inhibits them from arriving at a solution

mental set

the tendency to use solutions that have worked in the past, or the tendency to respond to something in a given or set way Can make problem solvers blind to alternative solutions or simpler methods When creating a mental set, people usually pay attention to similarities or relationships between past and current problems Once relationship is established, people will keep trying same solution to a problem that has worked in the past In jug problem, participants made a mental set and continued to use it even when it was less convenient Leads to inflexible thinking Luchins' participants demonstrated inflexibility in thinking and continued to use the old pattern to solve problems rather than new simpler patterns

two types of problems

well defined problems ill defined problems