PSY3051 Introduction: Problem Solving & Cognition

• The lecture introduces PSY3051, focusing on problem-solving strategies by Nathan, a lecturing psychologist.
• A tutorial on Wednesday will cover big-picture questions about the syllabus, including assessment.
• The course is split into two parts: Cognition (weeks 1-6) and Perception (weeks 7-12).
• Cognition topics include problem-solving, decision-making, judgment, reasoning, memory, associative learning, and attention.
• Perception covers motor skills, learning, visual and auditory cognition, and language.
• Lectures are broken into shorter mini-lectures to increase engagement.
• Students should focus on the conceptual logic of lectures and pick out major points, revisiting them later.
• Readings are meant to stimulate thinking and extend understanding.

Applied Introduction: St Michel Metro Station

• In the early 20th century, Paris built an extensive underground train system
• The geology of Paris presented engineers with difficult problems
• At St Michel station, the problem was how to build an underground structure in unstable soil. Standard excavation would have caused cave-ins and flooding
• The solution was to build the station above ground and gradually excavate beneath it

Overview of Mini-Lectures

• Mini-lecture 1 introduces problem-solving concepts.
• Mini-lecture 2 is on problem representation and functional fixedness.
• Mini-lecture 3 covers devising and executing problem-solving strategies.

Learning Outcomes

• You will define Wessell's four stages of problem solving.
• You will explain the role of insight and problem definition.
• You will define the role of mental representations in problem solving.
• You will give examples of strategies for reducing the effects of functional fixedness
• You will differentiate between heuristic and algorithmic strategies.
• You will define generate-test, difference-reduction, and subgoal generation strategies

Defining a Problem

• Jonassen & Hung (2011) define problem solving as the process of constructing and applying mental representations.
• Colloquially, a problem is anything not how we want it.
• Rigorously, a problem is a discrepancy between the current and goal states.
• A solution transforms the current state into the goal state.
• Examples of problems include caffeine withdrawal, anagrams (STBOUTOHRH), ending inequality, and side effects of anti-depressants

Wessels' (1982) Four Stages of Problem Solving

• Define the problem by identifying goal and current states, and available actions.
• Devise a strategy by selecting actions to move closer to the goal state.
• Execute the strategy by carrying out chosen actions.
• Evaluate progress by measuring the distance between goal and current states.

Problem Difficulty

• Greater distance between goal and current states increases problem difficulty.
• More difficult problems need require number of actions to be taken.
• Fewer possible actions make problems easier to solve.
• Expertise in a domain makes problem-solving easier.

Problem Solvability

• Solvable problems have a sequence of transformative actions.
• Examples of solvable problems include caffeine withdrawal, anagrams (STBOUTOHRH), and answering what has fingers and a thumb, but is not alive.
• Solving the anagram 'POLLASVFGE' and The inevitability of death' are example of unsolvable problems

Problem Definition: Well-defined problems

• Well-defined problems clearly specify current state, goal state, and available actions.
• Examples include solving anagrams like TSETMRAS or baking from a recipe.
• Well-defined problems are not always easy, like in chess with vast possible moves or the anagram POLLASVFGE, which is unsolvable.

Problem Definition: ill-defined problems

• Ill-defined situations have missing information on the current state, the goal state, or the actions to take to solve it.
• Examples include managing the economy or living a good life.
• Well-defined and ill-defined problems are on a continuum, with real-world problems in the middle.
• Well-defined problems have a specified goal state, such as following a recipe to bake a familiar cake.
• ill-defined (goal state is unspecified) problems are like following a recipe to bake an unfamiliar cake.
• ill-defined (available actions unspecified) problems are like baking a cake without a recipe.
• ill-defined {current state unspecified} bake a cake in an unfamiliar kitchen.

Insight

• In many problems, solutions appear suddenly as insight versus conscious progression.
• Insight examples include the anagrams and crosswords.
• The moment of insight is known as the "aha" moment. If a man is escaping from a 60m tower and has 30m of rope, cut the rope in half, tie the ends together and use that to escape
• Even without conscious steps, unconscious processes are still in involved.
• Non-human animals also engage in behaviours, that we night call problems solving

Role of Mental Representations

• Mental representation includes beliefs, knowledge, and memories stored in our minds.
• It is a representation of something and stands in for corresponding information.
• A problem's representation includes knowledge of components like starting/goal states, available actions

Role of Mental Representation in Problem Solving

• According to Jonassen & Hung (2011), problem-solving involves constructing and applying mental representations
• This can include mental representation of the initial state, the goal state or available actions

Accuracy of Mental Representations.

• Mental representations may be wrong, inaccurate, or incomplete and finding the correct one can lead to successful problem solving

Solving 9 dots problem.

• People assume lines must stay inside the grid, limiting representation of available actions.
• Requires relaxing this constraint.

Bookwork Problem

• Solving a common mistake assumes that it will take the bookworm 52 months (26 books x 2 months per book)
• The solution instead takes only 48 months
• Because the bookworm has to chew through 24 books, not 26
• If represented visually rather than with words, people get it correct more often

Two-pills riddle

• Mental representations help solve this, for the blind man, taking half of each pill is the only option

Dominoes and checkerboard

• You have a checkerboard, there are 32 dominoes that can cover 64 squares
• If you cut squares at both ends, is it possible to fit 31 dominoes on the board, impossible as they must be adjacent squares

Functional Fixedness (Drucker, 1945)

• Defined as a mental block against using an object in a new way.
• Reduced functional fixedness is marker of creative thinking
• Increased functional fixedness is useful for standard action problems

The candle problem

• Attach a candle to the wall, using items like a book of matches, and a box of tacks
• People don't do the problem if tacks are presented in a box

Reducing Functional Fixedness

• Training using objects differently to reduce functional fixedness
• Unusual labels encourage alternative thinking
• Listing alternative uses of objects can reduce functional fixedness

Mini-Lecture 3: Devising and executing a strategy

• A good problem representation is not enough: one needs to be able to reduce the distance between the current and goal state
• You will differentiate heuristic and algorithmic strategies

Heuristics vs Algorithms

• Algorithms are procedures guaranteed to find a solution.
• Algorithms exist for some problems, are often described as steps.
• Heuristics are easy, fast 'rules of thumb', without a solution guarantee.
• Developed by human in problem solving

Sort algorithm

• The insertion sort algorithm
• Compare the digit to the digit on its left. If there is no digit on the left, move to step 2
• If the digit is smaller than the digit on the left, swap them and compare the digit to the new digit on its left
• Repeat (b) until the digit is not smaller than the digit on its left
• Move one digit to the right and repeat steps (a) through (c)
• Stop once you reach the end of the list

Generate-Test Heuristic

• It repeatedly generates a simple solution and tests if it is correct
• For example, the solving letters by using a certain strategy NADL DNLA DLAN NALD LADN DALN LAND
• If the search space in small, this heuristic is helpful
• IF there is no way of measuring the current state, then generating testing might be helpful

Generate Test Heuristic Dependence

• Depends upon the solution
• IF we cannot test it, it is not effective

Difference Reduction Heuristic

• When a person takes what action to produce the reduction in difference between the goal and current state
• "Hill Climibing"
• WAM - below threshold
• Raise WAM by not studying or partying less

"Difference Reduction" Fail

• when it requires people to backtrack or move to the side
• Example: pay reduction with promotion opportunities
• It can take advantage of common puzzles of this

Creating Subgoals

• To solve the big problem, create smaller subgoals.
• Problems to be solved - you can only solve small pieces of the puzzle

Effectiveness of Subgoals

• effective is effective, the subgoals can be hard to solve

Subgoals effect

• can stop your orignal plan
• For example, chess

TakeCare

• independent subgoals
• Do not let this be a thing

Means-End Analysis

• Is to also create subgoals, solve feature analysis
• A theory about the problem

Invcubation

• Take time away
• It might work if sleeping
• It will help you with a solutino

INC effect

• INsight
• For example neckalce
• Silveiram - 71 - 1971
• Incubation might allow participation

RElating INC

• Is important