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Digital C alculations

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

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  1. Digit 1 00112 Digital Calculations Addition as Interactive Problem Solving

  2. 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

  3. 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

  4. ‘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

  5. 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

  6. 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

  7. 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

  8. 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

  9. Performance: Accuracy and Latency Interactive Addition, CogSci 2001

  10. Moderating factors? Moderating factor 1: List length Interactive Addition, CogSci 2001

  11. Moderating factor 2: List type Interactive Addition, CogSci 2001

  12. 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

  13. Move types: Choice of next addend Interactive Addition, CogSci 2001

  14. 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

  15. 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

  16. 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

  17. 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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