Problem Solving and Situated Cognition - PowerPoint Presentation

Slide1

Problem Solving and Situated Cognition

Murat

Perit

Cakir

COGS 503Slide2

Outline

Classical Theory of Problem Solving

Critiques to the Classical Theory

Situated Cognition Perspective

A case study of collaborative problem solving

DiscussionSlide3

Problem Solving

We solve problems daily

Not necessarily limited to math or science

Usually motivated by our needs/desires

Directed towards attaining a goal

Problem solving research

a

ims to develop a scientific theory to describe the main elements and dynamics of problem solving activitiesSlide4

Problem Solving

Current State

GoalSlide5

Classical Information Processing Theory of Problem Solving

Newell, A. & Simon, H. (1972). Human Problem Solving. Englewood Cliffs, NJ: Prentice-Hall.

Very influential on AI, Decision Science

Based on well-defined, knowledge-lean problems

e

.g.

g

ames and puzzles like chess, towers of

hanoi

Assumption

A theory for well-defined problems may be augmented to cover ill-defined onesSlide6

Classical Theory

Important concepts

Task Environment

Problem Space

States

Operators

Goals,

subgoals

HeuristicsSlide7

Task Environment

Abstract structure that corresponds to a problem

Specifies the fundamental structure of the problem

Capacities of agents for action may bring different task environments to them

Task environment includes only those actions that either bring agents closer or farther from the the goal condition

Abstract-> Same task environment can be instantiated in different ways

Chess with physical pieces

vs

computer-based

Scratching your head,

self-talk, simulating moves with gestures are all deemed irrelevant to task performance

Provides an interpretive frameworkWhat counts as a relevant pb solving moveSlide8

Task EnvironmentSlide9

Elements of Problem Solving

Goal directedness

– behavior is organized toward a goal.

Subgoal

decomposition

– the original goal can be broken into subtasks or

subgoals

.

Operator application

– the solution to the overall problem is a sequence of known operators (actions to change the situation).Slide10

Problem Space

Problem space

– the various states of the problem.

State

– a representation of the problem in some degree of solution.

Initial state

– the initial (starting) situation.

Goal state

– the desired ending situation.

Intermediate states

– states on the way to the goal.Slide11

Search

Operator

– an action that will transform the current problem state into another problem state.

The problem space is a maze of states.

Operators provide paths through the maze

ways of moving through states.

Problem solving is a

search

for the appropriate path through the maze.

Search trees – describe possible paths.Slide12
Slide13

Production Systems

Production rules

– rules for solving a problem.

A production rule consists of:

Goal

Application tests

An action

Typically written as if-then statements.

Condition – the “if” part, goal and tests.

Action – the “then” part, actions to do.Slide14

Features of Production Rules

Conditionality

–a condition describes when a rule applies and specifies action.

Modularity

– overall problem-solving is broken down into one production rule per operator.

Goal factoring

– each production rule is relevant to a particular goal (or subgoal).

Abstractness

– rules apply to a defined class of situations.Slide15

Sample Production RulesSlide16

Operator Selection

How do we know what action to take to solve a problem?

Possible criteria

for operator selection:

Backup avoidance

– don’t do anything that would undo the existing state.

Difference reduction

– do whatever helps most to reduce the distance to the goal.

Means-end analysis

– figure out what is needed to reach

the goal

and make that a goalSlide17

Backup Avoidance

To solve each of these problems one must backup but most people will not do this and so have difficulty.

Tower of Hanoi

Missionaries and Cannibals

Move 3 missionaries & cannibals across river. Cannibals cannot outnumber missionaries or else they will eat missionaries

Slide18

Difference Reduction

Select the operator that will produce a state that is closer to the goal state.

Or the one that produces a state that looks more similar to the goal state.

Also called “

hill climbing

”.

Only considers whether next step is an improvement, not overall plan.

Sometimes the solution requires going against similarity – hobbits & orcs.Slide19

Means-End Analysis

Newell & Simon –

General Problem Solver (GPS).

A more sophisticated version of difference reduction.

What do you need, what have you got, how can you get what you need?

Focus is on enabling blocked operators, not abandoning them.

Larger goals broken into

subgoals

.Slide20

General Problem SolverSlide21

Summary of Information Processing Framework

According to Newell & Simon PB Solving

The ability to reduce difference between current state & goal state

Constrained by information processing system

limited processing resources provide constraints on the degree to which multiple moves can be considered

Assumptions underlying GPS’s design

Serial processing

: execute one thing at a time

Limited working memory

Propositions are the basic unit of LTM

Heuristically or strategically driven processSlide22

GPS vs

Human Problem Solvers

Think aloud protocols conducted with human problem solvers show that humans approach puzzles in similar ways (

Greeno

, 1974)

GPS sometimes deviate from human problem solving since humans tend to employ heuristics that will take them closer to a solution (hill climbing)

GPS is resilient to cases when hill-climbing performs poorly (e.g. cannibals missionaries problem)

GPS sometimes fail to find a solution since it applies means-ends analysis very rigidlySlide23

GPS vs

Human Problem SolversSlide24

Well vs

Ill-

D

efined Problems

Puzzles

unfamiliar

involve no prior knowledge

all necessary info. is present in the problem statement

requirements are unambiguous

Real-world problems

familiar

require prior knowledge

necessary information often absent

solver must ask ‘what is the goal’?Slide25

Case study of group problem solvingSlide26

An Excerpt from VMT Spring Fest

A team of 3 upper-middle school students (14-16 years old)

Students were recruited via their teachers, who are Math Forum users

5 teams completed 4 online sessions in 2 weeks

A VMT project member was present in the room in case of technical difficulties

The members of the most collaborative team were awarded with

iPods

The excerpt is taken from the first session of the teamSlide27

Explicit

reference

from chat

to white

board

Activity awareness messages

Whiteboard

history

scrollbar

Message

to message

referencing

Drawing

activity

markers

embedded

in chat

Extra tabs (summary, math topic, wiki, browser, help manual)

Whiteboard

drawing

controls

List of active

users in the

chat room

VMT Chat

137

Who is active

on which tabSlide28

Task Description

1 1 4

2 3 10

3 6 18

4 10 28

N Squares Sticks

Here are the first few examples of a particular pattern,

which is made using sticks to form connected squares:

How many squares will be in the Nth example of the pattern?

How many sticks will be required to make the Nth example? Slide29

Task Description (cont.)

Mathematicians do not just solve other people's problems,

they also explore little worlds of patterns that they define and

find interesting. Think about other mathematical problems

related to the problem with the sticks.

Go to the

VMT Wiki

and share the most interesting math

problems that your group chose to work on.

N=1

N=2

N=3Slide30

Excerpt 1

Co-construction of a new stick pattern Slide31

Excerpt 2

Constituting a shared problemSlide32

Excerpt 2 (cont.)

Developing a systematic counting approachSlide33

Questions

How would you characterize the

Task environment?

Problem space?

Where is the problem space located?

Were the group members primarily engaged in search?

What is the role of representations in the group’s work?

Do you think they understand each other?Slide34

Critique to Classical Theory from a

Situated Cognition Perspective

Framing & Registration

Interactivity & Epistemic Activity

Interactions with others and cultural artifacts

Role of external representations

Adding structure to the environment

Socio-cultural context

Resources and Scaffolds

Knowledge richSlide35

Framing

Process of posing the problem in well-defined terms

i.e. constructing the graph structure, identifying initial and goal states,

subgoals

etc.

Inappropriate abstraction filters away important cognitive processes relevant to problem solving

e

.g. tic

tac

toe and the game of 15 are isomorphic mathematically but we rely on different practices of reasoning when we play each

Street math

vs school mathCoconut sellers in Brasil, milk men in the US, grocery shoppers optimize their

pb solving performance by recognizing common patterns and using cultural resourcesHow agents frame a problem, how they project meaning into a situation, determines the resources they see as relevant to its solution

A psychological theory of pb solving needs to explain many phases and dynamicshow one sees a problem, why one sees it that way, how one exploits resources, interacts with them, and solve the problems in acceptable timeSlide36

Registration

The activity of selecting environmental anchors to tie mental/physical representations to the world

In ecologically realistic problem solving settings registration is non-trivial

e

.g.

driving around

in a new city with a navigator

You need to constantly anchor your physical location to the dynamic representation presented in the navigator

Registration is less of a problem in classical theory

Puzzles constrain

pb

solving interactions to occur in a spatially bounded locatione.g. chess board, hanoi towers/pegsSlide37

Framing and Registration

Framing and Registration mutually inform each other

Cooking example

Back and forth between the recipe and materials in the kitchen

Recipe frames the problem in terms of things that are relevant to the cooking process

Ingredients, flame size, pots and pans, measurement cups

Not in terms of chemical reactions that took place during cooking

Framing constrains actions

Our understanding of problems is usually tied to the resources and tools at hand

Problem solving involves moves back and forth between the abstract and the concrete Slide38

Role of External Representations

Problem solving is a process located partly in the mind, partly in the world

External representations have a key mediating role in problem solving

They bring affordances (cues and constraints on actions) that shape our understanding of the problem

Later work of Simon and

Larken

(1987) attempted to incorporate external representations in their classical model

But the focus remained on problem space and search heuristics, external representations (diagrams, alternative symbolisms) were treated as secondary aids Slide39

Role of External Representations

Is an external representation same as its internal counterpart?

Experiments on mental imagery of ambiguous objects indicate that how people visually explore an external and mental image may differ

What if some of the mental constructs we use during problem solving have a similar property?Slide40

Further Criticism

Interactivity and epistemic activity

Real world details of problem solving is not adequately captured by the notion of task space

Some of the ignored actions may be important in understanding human problem solving (e.g. use of gestures, artifacts used to aid reasoning)

Interactions with artifacts and other people can be used to explore the structure of a problem and to manage its complexity

Scaffolds, practices, resources available as aids for problem solving

Problem solvers rarely work in isolation

Knowledge-rich problem solving

Most problems are ill defined, understanding a problem requires background knowledge

Even mundane tasks like shopping or cooking require background knowledgeSlide41

But…

Situated cognition does not offer an alternative theory of problem solving

It offers a conceptual framework

Focuses on practices of problem solving, what makes symbols, operators etc. meaningful to humansSlide42

Further Analysis of VMT Excerpts

Recurrent

practical concerns for VMT participants

w.r.t

. math artifacts and media affordances

Identify and produce relevant mathematical artifacts to constitute a shared problem

Refer to those artifacts and their relevant features

Manipulate and observe the manipulation of those artifacts based on math practices known to participantsSlide43

Representational Practices

Group members display their reasoning by enacting representational affordances of VMT

The

drawing

actions performed by 137 and

Qwertyuiop

The organization of the lines revealed in 137’s first attempt led

Qwertyuiop

to

project what is needed

Jason’s

question with the explicit referenceDisplays his understanding of the hexagonal pattern being developed

Availability of the production processWhiteboard affords an animated evolution of its contents that makes the reasoning embodied in drawing actions visible Slide44

Referential Practices

Group members establish relevancies across semiotic modalities by enacting referential uses of the available system features

Verbal and explicit references

The indexical

“

hexagonal array

”

refers to shared drawing co-constructed on the whiteboard.

Jason’s

use of the referencing tool to highlight a particular stage

Temporal organization of actions

The addition of 3 red lines were interpreted as a proposal to split the hexagon into 6 parts,

because it was made relevant in chat Slide45

Referential Practices (cont.)

Through referential practices group members

Isolate objects in the shared visual field and associate them with local terminology stated in chat

Establish sequential organization among actions performed in chat and whiteboard spaces

so it has at least

6 triangles? in

this, for instanceSlide46

Shared Mathematical Understanding

In short, mathematical understanding at the group level is achieved through the organization of representational and referential practices

Persistent whiteboard objects and prior chat messages form a shared

indexical ground

for the group

A new contribution…

is shaped by the indexical ground

i.e., interpreted in relation to relevant features of the shared visual field and in response to prior actions

reflexively shape the indexical ground

i.e., give further specificity to prior contents

set up relevant courses of action to be pursued nextSlide47

Summary

Shared mathematical understanding is a process, a temporal course of work in the actual indexical detail of its practical actions, rather than a process hidden in the minds of the group members

M

athematical

understanding can be located in the practices of collective multimodal reasoning displayed by teams of students through the sequential and spatial organization of their actions