Interactive coin addition : how hands can help us think
2011, Neth, Hansjörg, Payne, Stephen J.
Does using our hands help us to add the value of a set of coins? We test the benefits and costs of direct interaction with a men- tal arithmetic task in a computerized yoked design in which groups of participants vary in their interactive mode (move vs. look) and the initial configuration of coins (pseudo-random vs. another mover’s final layout). By assessing performance and conducting a microgenetic analysis of the strategies employed we argue that the purpose of movement is the result, rather than the process of moving. Participants move coins in order to sort, rather than to mark, and select them by value, rather than by location. They spontaneously create remarkably smart solutions, thereby incidentally creating physical configurations that can help other problem solvers.
Modeling ancient and modern arithmetic practices : addition and multiplication with Arabic and Roman numerals
2008, Schlimm, Dirk, Neth, Hansjörg
To analyze the task of mental arithmetic with external representations in different number systems we model algorithms for addition and multiplication with Arabic and Roman numerals. This demonstrates that Roman numerals are not only informationally equivalent to Arabic ones but also computationally similar - a claim that is widely disputed. An analysis of our models' elementary processing steps reveals intricate trade-offs between problem representation, algorithm, and interactive resources. Our simulations allow for a more nuanced view of the received wisdom on Roman numerals. While symbolic computation with Roman numerals requires fewer internal resources than with Arabic ones, the large number of needed symbols inflates the number of external processing steps.