What is rate? Does context or representation matter?

Rate is an important, but difficult, mathematical concept. Despite more than 20 years of research, especially with calculus students, difficulties are reported with this concept. This paper reports the results from analysis of data from 20 Australian Grade 10 students. Interviews targeted students’ conceptions of rate, focussing on the influence of representation and context on their expression of their understanding of rate. This analysis shows that different representations of functions provide varying levels of rate-related information for individual students. Understandings of rate in one representation or context are not necessarily transferred to another representation or context. Rate is an important, but commonly misunderstood, mathematical concept with many everyday applications (Swedosh, Dowsey, Caruso, Flynn, & Tynan, 2007). It is a complicated concept comprising many interwoven ideas such as the ratio of two numeric, measurable quantities but in a context where both quantities are changing. In mathematics classes, this is commonly expressed as change in the dependent variable resulting from a unit change in the independent variable, and variously described as constant or variable rate; average or instantaneous rate. In addition, rate may be seen as a purely abstract mathematical notion or embedded in the understanding of real-world applications. This paper explores the research question: Are students’ expressions of their conceptions of rate affected by either context or mathematical representation? This question was part of a larger study (Herbert, 2010) conducted with Grade 10 students from the Australian state of Victoria.

The capacity of criminal sanctions to shape the behaviour of offenders : specific deterrence doesn’t work, rehabilitation might and the implications for sentencing

There is a considerable gap between the law and knowledge regarding the efficacy of state-imposed sanctions to achieve several key sentencing objectives. Two sentencing objectives which often carry considerable weight in the sentencing calculus are rehabilitation and specific deterrence, despite the fact that neither has been proven to be attainable. This article examines the empirical data on whether specific deterrence and rehabilitation are attainable, and consequently whether they should be retained or abolished as sentencing objectives.

The paradox of parity in sentencing in Australia: the pursuit of equal justice that highlights the futility of consistency in sentencing

Parity in sentencing is the principle that offenders who are parties to a crime should, all things being equal, receive the same penalty. While it is a well-established principle, the reality is that its scope is greatly limited by the largely unfettered nature of the sentencing calculus. Things are rarely equal between offenders due to the large number of variables that current orthodoxy maintains are relevant to sentencing. This makes application of the parity principle unpredictable, resulting in the paradox that parity highlights the unfairness that it is meant to mitigate: inconsistency in sentencing. This article contends that parity will remain an aspiration, as opposed to a concrete principle, until the instinctive synthesis approach to sentencing yields to a more transparent and precise decision-making process. The article focuses on Australian jurisprudence, but the analysis applies to all jurisdictions where sentencing has a considerable discretionary component (including the UK and the USA--apart from the limited circumstances where mandatory sentences apply).

A Rational Approach To Sentencing White- Collar Offenders in Australia

There are no overarching (and few settled) principles governing the sentencing of white-collar offenders. This is especially the situation in relation to the relevance of public opprobrium to the sentencing calculus and the manner in which employment deprivations stemming from the penalty impact on the sentence. To the extent that there is general convergence in the approach to sentencing white-collar offenders, the approach is often not sound. This is the case in relation to the minor sentencing discount accorded for previous good character, and the prevailing orthodoxy which assumes that offences targeted at major institutions, such as banks, meaningfully impair community confidence in such institutions. Fundamental reform of the manner in which white-collar offenders are sentenced is necessary in order to make this area of law more coherent and doctrinally sound. These reforms include providing a significant and pre-determined discount for restitution, reducing the weight given to general deterrence in the sentencing calculus, and providing a greater discount for previous good character and employment deprivations suffered as a direct result of the sentence. Further, crimes against individuals should be regarded as being more serious than those committed against large corporations or the public revenue. The article focuses on the existing law in Australia, however, the reform proposals and doctrinal analysis could be applied to all jurisdictions.

Subject matters of science, technology, mathematics and engineering

This chapter offers a critical review of curriculum in the STEM disciplines, overviewing contemporary context and issues around the STEM acronym as a contested space, issues of inquiry, social justice, current concerns with student engagement and their history, theoretical perspectives on teaching and learning in these disciplines, and key forms and foci of inquiry into STEM curriculum.

In the heat of the moment: audience real time response to live music and dance performance

Coughing and Clapping: Investigating Audience Experience explores the processes and experiences of attending live music events from the initial decision to attend through to audience responses and memories of a performance after it has happened. The book brings together international researchers who consider the experience of being an audience member from a range of theoretical and empirical perspectives. Whether enjoying a drink at a jazz gig, tweeting at a pop concert or suppressing a cough at a classical recital, audience experience is affected by motivation, performance quality, social atmosphere and group and personal identity. Drawing on the implications of these experiences and attitudes, the authors consider the question of what makes an audience, and argue convincingly for the practical and academic value of that question.

Progressive adaptation in physical activity and neuromuscular performance during 520d confinement

To understand whether prolonged confinement results in reductions in physical activity and adaptation in the musculoskeletal system, six subjects were measured during 520 d isolation in the Mars500 study. We tested the hypothesis that physical activity reduces in prolonged confinement and that this would be associated with decrements of neuromuscular performance. Physical activity, as measured by average acceleration of the body's center of mass ("activity temperature") using the actibelt® device, decreased progressively over the course of isolation (p<0.00001). Concurrently, countermovement jump power and single-leg hop force decreased during isolation (p<0.001) whilst grip force did not change (p≥0.14). Similar to other models of inactivity, greater decrements of neuromuscular performance occurred in the lower-limb than in the upper-limb. Subject motivational state increased non-significantly (p = 0.20) during isolation, suggesting reductions in lower-limb neuromuscular performance were unrelated to motivation. Overall, we conclude that prolonged confinement is a form of physical inactivity and is associated with adaptation in the neuromuscular system.