From research to practice: The case of mathematical reasoning

Mathematical proficiency is a key goal of the Australian Mathematics curriculum. However, international assessments of mathematical literacy suggest that mathematical reasoning and problem solving are areas of difficulty for Australian students. Given the efficacy of teaching informed by quality assessment data, a recent study focused on the development of evidence-based Learning Progressions for Algebraic, Spatial and Statistical Reasoning that can be used to identify where students are in their learning and where they need to go to next. Importantly, they can also be used to generate targeted teaching advice and activities to help teachers progress student learning. This paper explores the processes involved in taking the research to practice

Functional units for natural numbers

Interaction with services provided by an execution environment forms part of the behaviours exhibited by instruction sequences under execution. Mechanisms related to the kind of interaction in question have been proposed in the setting of thread algebra. Like thread, service is an abstract behavioural concept. The concept of a functional unit is similar to the concept of a service, but more concrete. A state space is inherent in the concept of a functional unit, whereas it is not inherent in the concept of a service. In this paper, we establish the existence of a universal computable functional unit for natural numbers and related results.Comment: 17 pages; notational mistakes in tables 5 and 6 corrected; erroneous definition at bottom of page 9 correcte

Troublesome youth groups, gangs and knife carrying in Scotland

"... the research reported here set out to: Provide an overview of what is known about the nature and extent of youth gang activity and knife carrying in a set of case study locations; Provide an in-depth account of the structures and activities of youth gangs in these settings; Provide an in-depth account of the knife carrying in these settings; Offer a series of recommendations for interventions in these behaviours based on this evidence." - exec. summary

The relative power of geodemographics vis a vis person and household level demographic variables as discriminators of consumer behaviour

Geodemographics is a field of study which involves the classification of consumersaccording to the type of neighbourhood in which they live. As a method of segmentingconsumers it has long been of value to direct marketers who, being often unable toidentify the age, marital status or occupational status of people in mailing lists, found it auseful means of applying selectivity to their mail shots. By analysing the behaviouralcharacteristics of consumers in different types of neighbourhoods they found they couldimprove business performance by targeting promotional activities to names and addressesfalling within specific types of postcode. From direct marketing the application ofgeodemographics spread to the targeting of door to door distribution and customercommunications and to the retail industry where it was found to be useful input into theprocess of deciding where to site new outlets. Government is increasingly using suchmethods to improve the targeting of its own communications to tailor local servicedelivery to the particular needs of local communities.During the 25 years since geodemographics was first introduced few users have had aclear understanding of precisely neighbourhood differences come about. Are differencesin consumption patterns at neighbourhoods level simply the predictable result ofdifferences in the age, household composition, educational status or occupational profileof their residents? Or do additional, incremental neighbourhood effects operate? Whendeciding neighbourhoods to live in do people select ones whose values and consumerpreferences are broadly similar to their own? Or is it only after they have moved thattheir behaviours change, as they become subject, consciously or not, to the prevailingethos of the new community in which they find themselves?To set these alternative explanations this study analyses a random set of consumerbehaviours covered by the Target Group Index, one of a number of market researchsurveys whose respondents have been coded by the type of neighbourhood in which theylive; it uses a statistic to measure the extent to which the Mosaic geodemographic systemis effective in discriminating on these behaviours; it then measures the relativeeffectiveness of other frequently used household and person level demographics inpredicting of these behaviours; finally it compares the predictive efficiency of differentdiscriminators.The conclusion that can be drawn from the exercise is that, across these behaviours aswhole, the type of neighbourhood in which a consumer lives is a significantly morepredictive piece of information that any person or household level discriminator (such asage or social grade). By implication therefore it is almost certain that significantneighbourhood effects must operate for many of the behaviours tested. However therelative discriminatory power of geodemographics and person and household leveldiscriminators varies considerably from behaviour to behaviour. Even when takingmeasures of status which one might have expected to be highly correlated, such as socialgrade, terminal education age or household income, there are considerable differences intheir relative predictiveness across most consumer behaviours

Interaction of agents and environments

A new abstract model of interaction between agents and environments considered as objects of different types is introduced. Agents are represented by means of labelled transition systems considered up to bisimilarity. The equivalence of agents is characterised in terms of an algebra of behaviours which is a continuous algebra with approximation and two operations: nondeterministic choice and prefixing. Environments are introduced as agents supplied with an insertion function which takes the behaviour of an agent and the behaviour of an environment as arguments and returns the new behaviour of an environment. Arbitrary continuous functions can be used as insertion functions, and we use functions defined by means of rewriting logic as computable ones. The transformation of environment behaviours defined by the insertion function also defines a new type of agent equivalence--- insertion equivalence. Two behaviours are insertion equivalent if they define the same transformation of an environment. The properties of this equivalence are studied. Three main types of insertion functions are used to develop interesting applications: one-step insertion, head insertion, and look-ahead insertion functions