Developing formal mathematical assessment for 4-to-8-year-olds

The assessment of children in their years before school and their first years of school has been, traditionally, informal. Further, assessment of children's mathematical skills at this level has been infrequent compared to social, emotional and physical assessments. However, there are contexts where reliable, valid, standardised data from assessment in mathematics are required. This paper outlines the development of two assessment tools for mathematics that were originally developed for such contexts. Item Response Theory (IRT) analyses enabled the construction of assessment forms that address the range of abilities of 4- to 8-year-old children, and provided the scales used for constructing formative and summative reports of achievement. A description of the development of the assessment tools and the IRT analysis that provides the reporting formats are presented together with some research uses of the tools.

A comprehensive formal ranking of the popularity of financial ratios in multivariate modeling of corporate collapse

This paper provides a fonnal ranking of the popularity of financial ratios in modeling corporate collapse. The analysis identified 48 financial ratios and ranked them according to their usefulness as portrayed in 53 studies that have utilized such ratios in modeling corporate collapse. The methodologies adopted in those studies are predominantly of the "multivariate" type. The 53 studies extend from 1966 to 2002, inclusive.

Protocols between programs and proofs

In this paper we describe a new protocol that we call the Curry-Howard protocol between a theory and the programs extracted from it. This protocol leads to the expansion of the theory and the production of more powerful programs. The methodology we use for automatically extracting “correct” programs from proofs is a development of the well-known Curry-Howard process. Program extraction has been developed by many authors, but our presentation is ultimately aimed at a practical, usable system and has a number of novel features. These include 1. a very simple and natural mimicking of ordinary mathematical practice and likewise the use of established computer programs when we obtain programs from formal proofs, and 2. a conceptual distinction between programs on the one hand, and proofs of theorems that yield programs on the other. An implementation of our methodology is the Fred system. As an example of our protocol we describe a constructive proof of the well-known theorem that every graph of even parity can be decomposed into a list of disjoint cycles. Given such a graph as input, the extracted program produces a list of the (non-trivial) disjoint cycles as promised.

A Compositional Semantics of UML-RSDS

This paper provides a semantics for the UML-RSDS (Reactive System Development Support) subset of UML, using the real-time action logic (RAL) formalism. We show how this semantics can be used to resolve some ambiguities and omissions in UML semantics, and to support reasoning about specifications using the B formal method and tools. We use `semantic profiles' to provide precise semantics for different semantic variation points of UML. We also show how RAL can be used to give a semantics to notations for real-time specification in UML. Unlike other approaches to UML semantics, which concentrate on the class diagram notation, our semantic representation has behaviour as a central element, and can be used to define semantics for use cases, state machines and interactions, in addition to class diagrams.

Fuzzy logic based metric in software testing

How to provide cost-effective strategies for Software Testing has been one of the research focuses in Software Engineering for a long time. Many researchers in Software Engineering have addressed the effectiveness and quality metric of Software Testing, and many interesting results have been obtained. However, one issue of paramount importance in software testing – the intrinsic imprecise and uncertain relationships within testing metrics – is left unaddressed. To this end, a new quality and effectiveness measurement based on fuzzy logic is proposed. The software quality features and analogy-based reasoning are discussed, which can deal with quality and effectiveness consistency between different test projects. Experimental results are also provided to verify the proposed measurement.