1. Hansjörg Neth Stephen J. Payne School of Psychology, Cardiff University Digital Calculations 1 0011 2 Digit Addition as Interactive Problem Solving

2. Interactive Addition, CogSci 2001 2/17 Introduction: Feedback Loops - Evolution of the genotype - Development and learning of the individual - Interactive problem solving Cognitive Agent Perception Environment Action

3. Interactive Addition, CogSci 2001 3/17 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)

4. Interactive Addition, CogSci 2001 4/17 ‘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

5. Interactive Addition, CogSci 2001 5/17 Experiment: Interaction in Addition Please add these numbers: (a) Linear: Sum: 2 5 6 13 17 12 (b) Pairs: Sum: 2 12 13 17 610 (c) Complements: Sum: 2 5 6 10 17 2 3 1 7 4 Three strategies: Task: Environmental Arithmetic

6. Interactive Addition, CogSci 2001 6/17 P 4 3 9 7 8 6 5 4 2 1 5 9 N 9 4 5 8 9 6 3 2 1 5 7 2 Materials: Lists of single digit numbers 1 2 3 4 5 5 6 7 8 9}Same ingredients, e.g. R 1 {1 2 3 4 5 5 6 7 8 9} R 2 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=62 3 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 Environment

7. Interactive Addition, CogSci 2001 7/17 Design & Procedure Experimental factors: 1.List type: linear (P, C, N) vs. spatial (S) 2.List length: 4, 8, 12 single-digit numbers 3.Interactive mode: look only, point, mark, move Mixed design: within/between-subjects; 44 undergraduates, each participant correctly added 36 lists in ~25 min.

8. Interactive Addition, CogSci 2001 8/17 Questions & 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

9. Interactive Addition, CogSci 2001 9/17 Performance: Accuracy and Latency

10. Interactive Addition, CogSci 2001 10/17 Moderating factors? Moderating factor 1: List length

11. Interactive Addition, CogSci 2001 11/17 Moderating factor 2: List type

12. Interactive Addition, CogSci 2001 12/17 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: Mouse moves

13. Interactive Addition, CogSci 2001 13/17 Move types: Choice of next addend

14. Interactive Addition, CogSci 2001 14/17 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

15. Interactive Addition, CogSci 2001 15/17 How did the movers move? Economy: No movements for short lists Strategies: - move to mark added numbers - move to group (e.g. pairs, triples…)

16. Interactive Addition, CogSci 2001 16/17 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.

17. Interactive Addition, CogSci 2001 17/17 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?