hansjörg neth stephen j. payne school of psychology, cardiff university digital calculations 1 0011...

Hansjörg NethHansjörg Neth Stephen J. PayneStephen J. Payne

School of Psychology,School of Psychology,CCardiff Universityardiff University

Digital Digital CCalculationsalculations1 1 00110011 22

DigitDigit

Addition as Interactive Problem Addition as Interactive Problem SolvingSolving

Interactive Addition, CogSci 2001 2/17

Introduction: Feedback LoopsIntroduction: Feedback Loops

- Evolution of the genotype

- Development and learning of the individual

- Interactive problem solving

Cognitive Agent

Perception

Environment

Action


Interaction: internal Interaction: internal <<——>> external external

• External representations provide constraints on problem solving (e.g. Larkin & Simon, 1987; Zhang and Norman, 1994)

• Cost of operator application affects planning and learning (e.g. O’Hara & Payne, 1998)

• Information displays as a resource in human-computer interaction (e.g. Payne, 1991; Gray & Fu, 2001)


‘‘ComplementaryComplementary’ actions’ actions

Kirsh (1995): Counting coins with or w/o hands

- spontaneous ‘organizing activities’- increased speed and accuracy

But:- hands can serve multiple functions- coins ‘afford’ to be manipulated


Experiment: Interaction in AdditionExperiment: Interaction in Addition

Please add these numbers:

(a) Linear: Sum: 2 5 6 13 17

(b) Pairs: Sum: 2 1212 13 17 (c) Complements: Sum: 2 5 66 1010 17

2 3 1 7 42 3 1 7 4 2 2 33 1 1 77 4 4 2 3 1 7 2 3 1 7 44 Three strategies:

Task: Environmental Arithmetic


P4 3 9 7 8 6 5 4 2 1 5 9

N9 4 5 8 9 6 3 2 1 5 7 2

Materials: Lists of single digit numbers

•Same ingredients, e.g. R1 {1 2 3 4 5 5 6 7 8 9}1 2 3 4 5 5 6 7 8 9} R2

•Different structures:Pair lists:4 3 9 7 8 6 5 4 2 1 5 9 Σ=63

C 3 1 8 6 5 3 9 4 5 7 2 9 Complement list: 3 1 8 6 5 3 9 4 5 7 2 9 =623 4 10 18 23 26 30 39 44 51 60 62 Neutral list:9 4 5 8 9 6 3 2 1 5 7 2 =61 9 13 18 26 35 41 44 46 47 52 59 61

Structuring the Structuring the EnvironmentEnvironment


Design & ProcedureDesign & Procedure

Experimental factors:1. List type: linear (P, C, N) vs. spatial (S)2. List length: 4, 8, 12 single-digit numbers3. Interactive mode:

look only, point, mark, move

Mixed design: within/between-subjects; 44 undergraduates, each participant correctly added 36 lists in ~25 min.


Questions & HypothesesQuestions & Hypotheses

• What do people do when they think?• Spontaneous complementary actions? • If so, why and how?• Other factors?

Predictions• move > look only• mark > point• interactive features enable ‘smart’

strategies


0

5

10

15

20

25

look

only

point mark move

Mea

n la

tenc

y (s

ec.) .

Performance: Performance: AccuracyAccuracyandand Latency Latency

0

2

4

6

8

10

12

look

only

point mark move

Mea

n nu

mbe

r of

err

ors


Moderating factors?Moderating factors?Moderating factor 1:Moderating factor 1: List List lengthlength

0

5

10

15

20

25

30

look only point mark move

Mea

n la

tenc

y on

cor

rect

tri

als

(sec

.) 4 8 12


Moderating factor Moderating factor 2:2:

0

2

4

6

8

10

12

14

16

18

20

look only point mark move

Mea

n La

tenc

ies

(sec

.)

P

C

N

S

List typeList type


Strategies? Strategies?

Assessing ‘moves’ between two addends

→ Distance? Type?

Sum of move distances per trial:

• More activity on longer lists

• Group differences only for short lists: move < [mark = point]

Strategies:Strategies: Mouse moves Mouse moves


Move Move typestypes: Choice of next : Choice of next addendaddend

1629

1

8270

3

0%

20%

40%

60%

80%

100%

point mark

Mea

n pe

rcen

tage

(ou

t of

252 m

oves

):

Neutral moves

Complements

Pairs and triples


Move Move distance x typedistance x type

Selection of nearest neighbours:

- point group: 71% of all moves,- mark group: 61%

‘Attractiveness’ of move types?

- neutral move: 0.53 nearest neighbours skipped- complement: 1.12 - pair: 2.20


How did the movers move?How did the movers move?

•Economy: No movements for short lists

•Strategies:- move to mark added numbers- move to group (e.g. pairs, triples…)


ConclusionsConclusions

• Spontaneous exploitation of interactive resources

• reliable differences in performance

• modulated by task characteristics

• explained by strategy differences

Problems solving depends on the interactions between agent, task, and task environment.


ImplicationsImplications

• Methodological: studying problem solving at a higher resolution

• Practical: costs and benefits of minimal interactions

• Conceptual:‘action’ ~ ‘cognition’ ~ ‘perception’

What do we do when we think?What do we do when we think?

hansjörg neth stephen j. payne school of psychology, cardiff university digital calculations 1 0011...

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