Instruction to support mental computation development in young children of diverse ability

Fostering young children's mental computation capacity is essential to support their numeracy development. Debate continues as to whether young children should be explicitly taught strategies for mental computation, or be afforded the freedom to develop their own. This paper reports on teaching experiments with two groups of students in their first year of schooling: those considered 'at-risk', and those deemed mathematically advanced. Both groups made considerable learning gains as a result of instruction. Importantly, the gains of the at-risk group are likely to renew both their own, and their teacher's confidence in their ability to learn. In this paper, the instructional programs are documented, highlighting the influence of instruction upon the children's development.

Learning to play Pac-Man: An evolutionary, rule-based approach

Pac-Man is a well-known, real-time computer game that provides an interesting platform for research. We describe an initial approach to developing an artificial agent that replaces the human to play a simplified version of Pac-Man. The agent is specified as a simple finite state machine and ruleset. with parameters that control the probability of movement by the agent given the constraints of the maze at some instant of time. In contrast to previous approaches, the agent represents a dynamic strategy for playing Pac-Man, rather than a pre-programmed maze-solving method. The agent adaptively "learns" through the application of population-based incremental learning (PBIL) to adjust the agents' parameters. Experimental results are presented that give insight into some of the complexities of the game, as well as highlighting the limitations and difficulties of the representation of the agent.

Incremental derivation of abstraction relations for data refinements

Data refinements are refinement steps in which a program’s local data structures are changed. Data refinement proof obligations require the software designer to find an abstraction relation that relates the states of the original and new program. In this paper we describe an algorithm that helps a designer find an abstraction relation for a proposed refinement. Given sufficient time and space, the algorithm can find a minimal abstraction relation, and thus show that the refinement holds. As it executes, the algorithm displays mappings that cannot be in any abstraction relation. When the algorithm is not given sufficient resources to terminate, these mappings can help the designer find a suitable abstraction relation. The same algorithm can be used to test an abstraction relation supplied by the designer.