Psych 351A: Final Review (Problem Solving)

Problem

A situation with a current and goal state which is blocked by an obstacle that is not immediately obvious how to get around

Representation

How a problem is represented in the mind, most problems have multiple representations that are critical to determining how easy it is to solve

Restructuring

Changing/reorganized a problems representation

Kohler’s Circle

One is shown a circle with a right angle triangle in it and ask what x (hypotenuse) is the the circle radius is r

Answer relies on insight, recognizing that since it is a right angle, the hypotenuses just half the radius

Insight

Sudden realization of a problems solution, often due to restructuring

Insight Experiment (Metcalf and Wiebe)

Had participants engage in 4 different tasks and ask them to make warmth judgments every 15 s (ranging from 1 to 7, 1 being cold)

Triangle task

Chain task

Algebra task

Factor task

Findings of the insight experiment

Found that algebra and factor problems are solved gradually and insight problems solved suddenly

Fixation

Tendency to focus on specific characteristics of a problem that blocks arrival at solution

Functional fixedness

Restricting use of an object to its familiar functions

Dunker’s Candle Problem

Participant is asked to put 3 small candles at eye level side by side on a door, given matches, tacks and candles either in or with 3 small boxes

Found that people solved the problem much better if items were not in the boxes

Mental Set

Preconceived notion of how to approach a problem based on past experiences with the problem

Lunchin’s Water Jug Problem

Participants were either in the mental set or non mental set group and asked to obtain a required volume of water using only 3 empty jugs (A, B, C) over 8 trials. First 6 trials had same solution combination and the last two had easier solutions

Mental Set - demonstrated problem 1, performed others, only 23% used simpler solutions

No Mental Set  - performed problems 7 and 8, all used simpler solutions

Why is it important how a problem is stated

It can influence its representation, this is critical on how easy a problem is to solve

Mutilated Checkerboard Problem (Kaplan and Simon)

Participants told a checkerboard has 64 squares that can be filled by 32 dominos, if the corners are removed can one fill the board with 31 dominos

Had 4 conditions - (1) blank board, (2) coloured board, (3) pink/black word board, (4) bread/butter word board

What were the findings of the mutilated checkerboard experiment

Easier to solve the puzzle (say its impossible) when information provided points towards correct representation of the problem

Participants did best in the bread/butter board and moved down in success through numbers

What would happen if one is to read the russian marriage problem and then asked the checkerboard problem

They would do better than one who had not read the story, demonstrates how powerful analogies are

Analogical problem solving

Using a solution to a similar problem to guide solution to a new problem

Analogical transfer

Process of transferring the source problem to the target problem

What were the 3 key steps required for analogical problem solving according to Gick and Holyoak

Noticing the relationship between source and target

Mapping the correspondence between source and target

Applying mapping to generate problem solution

Note - any mistake in one of these steps will lead to failure

How did Gick and Holyoak test analogical problem solving

Had participants listen to Duncker’s radiation problem and fortress story

Participants who were only given the radiation problem solved 10% time

Participants who were given both stories solved 30% of time

Participants who were given both and a hint that they were correlated solved 75% of the time

What are the two elements that allow for better noticing of analogies

Surface - specific elements of a given problem

Structural - underlying principles and relationships that determine the solution

Does surface similarity help analogical transfer

Hint: radiation problem

Yes

Participants who were shown the lightbulb and radiation problem (very similar on the surface) solved 81% of the time, those told just the lightbulb only solved 10% of time

Does structural similarity helps with analogical transfer

Hint: lightbulb and radiation problem

Yes

Participants were shown v1 or v2 of the lightbulb problem, where v1 was more structurally similar to the radiation problem and v2 was similar to previous study of theirs

Found that those who saw v1 solved 69% of the time, and v2 only 33%

Information-Processing Approach (IPA)

Proposed by Newell and Simon, argued that problem solving acts as a search through problem space, has 5 characteristics

5 characteristics of the information-processing approach

State - a particular set of circumstances that can occur

Initial state - starting circumstances

Goal state - desired final circumstances

Operators - actions that move problem from one state to another

Problems/state space - all possible states of problem

How did Newell and Simon demonstrate IPA

Used the tower of hanoi (moving different sized discs between posts to stack them in pyramid shape) and used a means-end analysis

Means-ends analysis

Way to solve the problem by incrementally reducing the difference between the initial and goal states, accomplished by subgoaling

What is the major problem with the IPA

When the problem is too large the state-space will be gigantic and it will be difficult to trace a path

T or F: Modern AI uses theories based on IPA

F, typically uses reinforcement learning and personalized training

How was the AI used to master Go accomplished (Silver et al 2016)

Reinforcement learning - gave the model a policy (what moves to make) and a value network (how good a position is)

Training - let the model view millions of positions and had the game play against itself

Expert

Someone who has devoted a large amount of time to learning about a field such that they solve problems in their field faster and with a higher success rate than beginners

Chess Experiment (Chase and Simon)

Showed masters and beginners a chess board that was either set up in actual positions or randomly placed

Found chess masters did much better, but only when there was meaningful placements allowing them to chunk

Physics Experiment (Chi et al)

Asked experts and novices to sort physics problems into groups

Found that novices sorted based on surface similarity and experts sorted based on structural similarity

Concluded that experts are better at seeing the structural similarity between problems

X-Ray experiment (Lesgold et al)

Had experts and novices diagnose patients based on their x rays, experts spent proportionally more time generating an intial representation

What are the 3 major conclusions we can draw about cognition in experts

1. Experts solve problems in their field faster and with a higher success rate than beginners

2. Experts have more knowledge that is organized differently and spend more time on analysis

3. Experts are not better than novices outside their field, less likely to look at novel ways to solve problems

New lifeforms study (Smith et al)

Had groups come up with new toys that were new lifeforms, participants either shown 3 examples before doing so or no examples

Found that those who were shown examples ideas typically resembled examples and those with no examples had more novel/creative ideas

Cognitive Control hinderace test (Chi and Snyder)

Used TMS to deactivate participants ATL while solving 9 dot problem (requires thinking outside of the box to solve)

Found that 0% solved in given time with ATL intact and 40% solved problem with ATL disabled

What can be concluded from the cognitive hinderance test regarding inhibition

Inhibition keeps one focused on standard interpretation and disinhibition can open up new ways of thinking (may increase creativity)