Problem Solving: Understanding the Process, Heuristics, and Role of Memory, Schemes and Mind Maps of Cognitive Development

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Problem Solving^ Overview. ^ The Process of Problem Solving. ^ The Role of Memory in Problem Solving. ^ Problems in Problem Solving. ^ Creativity.

The processes involved in transforming one  Always involves three components:

situation into another to obtain a goal.

Problem Solving

1. Initial State.^ •^

The^ problem; a given set of information.

2. Goal State.^ •^

The solution (or a general description thereof).- Subgoals - smaller problems; useful 'stepping stones'.

3. Operators.^ •^

The specific actions that allow one to go frominitial state to goal state.

^ Always come in one of two forms:

Problems

1. Well-defined (structured) - initial state, goal state,and operators are all clearly defined.^ •^

Chess; Crossword puzzles; Math problems

2. Ill-defined (open-ended) - states and operators are^ not

clearly defined. • Getting dinner; impressing boss; choosing career

^ Most interesting real-world problems are ill-defined.Scientists have thus spent most of their timestudying well-defined problems....

^ Well-defined problems are of three types:

Problems

1. Arrangement - reorganizing parts so as to obtainsome pre-defined criteria.^ •^ Anagrams; setting-up furniture in a new house

2. Inducing Structure - here, the arrangement is fixedand problem is to discover the underlying structure.^ •^ Series completion: 1, 2, 3, 5, 7, 11, 13,?

-^ Analogies: Gangs are to Cops as Terrorists are to? •^ Discovering the structure of DNA. 3. Transformation - reaching a specific goal in aproblem space using pre-specified operators. •^ Learning to drive; Solving the Tower of Hanoi…

Three steps: (1) Framing The Problem; (2)Generating Solutions; (3) Evaluating Solutions.  Framing / Understanding. •

The Process of Problem SolvingThe most important step! This is "the box"!^ •^ Identifying the critical aspects of the problem,as well as the non-critical aspects.^ •^ How a problem is defined will determine if yousolve it, and how you'll solve it.- Getting rid of a fly in your room.- The nine-dot problem....- The monk problem....

Connect all nine dots with 4 straight lines,

The Nine-Dot Problem without lifting your pencil.

Generating Solutions Two general ways to generate solutions.

^ Heuristics - Short-cuts that are fast and easy,

but^ don't

guarantee a solution.

^ Algorithms - Specific rules or procedures that

guarantee

a solution.

-^ Hill Climbing. •^ Generate-and-Test (Trial and Error). •^ Means/end analysis. •^ Working backwards. •^ Using Imagery & Analogies.

Heuristics

-^ Hill Climbing: Choosing any available optionthat moves you closer to your goal.^  •^ Generate-and-Test (trial-and-error): Generatea possible solution and test it. •^ Means/end analysis: Identify (1) your currentstate, (2) where you want to be (your goalstate), and (3) the means that will get you there.

Finding a bad smell in your house.  Arranging the furniture in your den.  Getting a particular job, writing a class paper.

Working Backwards

The Pennies Problem ^ Ten pennies are placed on a table. Two playerspick up one, two, or three pennies on each turn.The goal is to make the other player pick up thelast penny. Is there a strategy that will guaranteethat you will win if you go first?

^ Using a familiar problem to understand a novel problem.Requires one to ignore the surface structure of the twoproblems and instead map the deep structure of thefamiliar problem onto the novel problem.

Human Brain ~ Computer

Atom ~ Solar System

Using Analogies in Problem Solving

^ Masters show better memory for realboard configurations, but not non-meaningful configurations. ^ Masters don't always consider more moves thannovices, but do usually consider

better

moves.

^ Situations (and thus solutions) are beststored in memory as

condition-action pairs

The Role of Memory in Problem Solving ^ Lessons from the study of chess:^ •^ Masters create larger, more meaningfulchunks than novices.^ •^ Chunks free up mental resources that can be used toconsider relevant moves.

^ The problem of

inert knowledge

The Role of Memory in Problem Solving^ ^ A General wants to attack a fortress that has manyroads leading to it.^ ^ The Enemy has plantedmines on the roads that willbe triggered by large groups. ^ However, large numbers ofsoldiers are necessary tocapture the fortress.People often have appropriatesolutions in memory (either directly orvia analogies) yet fail to access thatinfo when confronted with a problem.

Problems in Problem Solving ^ Problem Presentation. ^ Conceptual Blocks.^ 

Persistence of set.  Functional fixedness.

^ Inert Knowledge

(the answer is in memory but

it's not retrieved when the problem is presented).

Problems in Problem Solving

^ Problem presentation:

The way a problem is

presented often has a large influence on whether,or how quickly, it's solved.  Problem solving is difficult when irrelevant information( surface structure

) is emphasized and relevant

information (

deep structure

) is difficult to identify.

E.g., Anagrams are more difficult to solve whenpresented as separate words:

A psychological condition

txaneyi

vs.

taxi yen

a rich zone ship

vs.

aishiezhrcpn