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Digit. 1 0011 2. Digital C alculations. Addition as Interactive Problem Solving. Cognitive Agent. Action. Perception. Environment. Introduction: Feedback Loops. Evolution of the genotype Development and learning of the individual Interactive problem solving.

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Digital c alculations

Digit

1 00112

Digital Calculations

Addition as Interactive Problem Solving


Introduction feedback loops

Cognitive Agent

Action

Perception

Environment

Introduction: Feedback Loops

  • Evolution of the genotype

  • Development and learning of the individual

  • Interactive problem solving

Interactive Addition, CogSci 2001


Interaction internal external
Interaction: internal <—> 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)

Interactive Addition, CogSci 2001


Complementary actions
Complementary’ 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

Interactive Addition, CogSci 2001


Experiment interaction in addition

Please add these numbers:

Experiment: Interaction in Addition

Task: Environmental Arithmetic

2 3 1 7 4

2 3 1 7 4

2 3 1 7 4

Three strategies:

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

(b)Pairs: Sum:2 12 13 17

(c)Complements: Sum:2 5 610 17

Interactive Addition, CogSci 2001


Structuring the environment
Structuring the Environment

  • Materials: Lists of single digit numbers

  • Same ingredients, e.g. R1 {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

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

Complement list:3 1 8 6 5 3 9 4 5 7 2 9 =623 4 1018 23 26 3039 44 51 60 62

C3 1 8 6 5 3 9 4 5 7 2 9

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

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

Interactive Addition, CogSci 2001


Design procedure

Experimental factors:

List type: linear (P, C, N) vs. spatial (S)

List length: 4, 8, 12 single-digit numbers

Interactive mode: look only, point, mark, move

Design & Procedure

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

Interactive Addition, CogSci 2001


Questions hypotheses

What do people do when they think?

Spontaneous complementary actions?

If so, why and how?

Other factors?

Questions & Hypotheses

  • Predictions

  • move > look only

  • mark > point

  • interactive features enable ‘smart’ strategies

Interactive Addition, CogSci 2001


Performance accuracy
Performance: Accuracy

and Latency

Interactive Addition, CogSci 2001


Moderating factors
Moderating factors?

Moderating factor 1: List length

Interactive Addition, CogSci 2001


Moderating factor 2
Moderating factor 2:

List type

Interactive Addition, CogSci 2001


Strategies

Assessing ‘moves’ between two addends

→ Distance? Type?

Strategies?

Strategies: Mouse moves

  • Sum of move distances per trial:

  • More activity on longer lists

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

Interactive Addition, CogSci 2001


Move types choice of next addend
Move types: Choice of next addend

Interactive Addition, CogSci 2001


Move distance x type
Move distance 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

Interactive Addition, CogSci 2001


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…)

Interactive Addition, CogSci 2001


Conclusions
Conclusions

  • 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.

Interactive Addition, CogSci 2001


Implications
Implications

  • 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?

Interactive Addition, CogSci 2001


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