Challenging the traditional sequence of teaching introductory calculus

Despite considerable research with students of calculus, rate, and hence derivative, remain difficult concepts to teach and learn. The demonstrated lack of conceptual understanding of introductory calculus limits its usefulness in related areas. Since rate is such a troublesome concept, this study piloted reversing the usual presentation of introductory calculus to begin with area and integration, rather than rate and derivative. Two classes of first-year university students taking introductory calculus were selected to pilot the effect of changing the sequence; one class was a control group and the other class followed the reversed sequence. Advances in technology, especially computer algebra systems (CASs) may facilitate new ways of studying mathematics. In this study, handheld CASs were used to support students’ thinking as they grappled with the concepts of introductory calculus. The use of CASs enabled consideration of symbolic patterns and numerical integration leading to a deeper conceptual understanding of integration. The easy access to the multiple representations of functions provided by CASs facilitated an exploration of rate where each representation highlighted different aspects of rate resulting in deeper conceptual understanding of differentiation.

A cross-national study of calculus

The results from a cross-national study comparing calculus performance of students at East China Normal University (ECNU) in Shanghai and students at the University of Michigan before and after their first university calculus course are presented. Overall, ECNU significantly outperformed Michigan on both the pre- and post-tests, but the Michigan students showed a larger gain and normalized gain, and hence narrowed the gap. ECNU's superior performance was especially striking on the subset of problems requiring only a pre-calculus background. On those, Michigan's post-test scores were below ECNU's pre-test scores and, indeed, ECNU's higher performance on both the overall pre-test and overall post-test is attributable to its success on these problems.

Sober assessment of the link between substance abuse and crime-eliminating drug and alcohol use from the sentencing calculus

The relevance of drug and alcohol involvement to sentencing law and practice is one of the most perplexing and unsettled areas of sentencing law and practice.1 It is also one of the most important issues in the criminal justice system. Most crimes are committed by offenders who are substance involved, and nearly half of all crimes that are committed are done so by offenders who are intoxicated at the time of the offense. Substance involved individuals are grossly over-represented in the criminal courts. Addiction and intoxication impair sound judgment, and hence, it intuitively appears that intoxicated offenders are less culpable for their crimes. Moreover, there is often a sense that addiction and intoxication causes aberrant behavior and that curing the substance involvement will lead to more prudent (law-abiding) conduct.

After three strikes-the continued discriminatory impact of the sentencing system against indigenous Australians: suggested reform

Three strikes laws are discriminatory but not for previously advanced reasons. The three strikes laws are merely an acute example of a fundamentally flawed sentencing system that discriminates against economically and socially disadvantaged people, particularly the group that is the focus of this article – Indigenous Australians. The repeal of the Northern Territory's mandatory sentencing laws has not remedied the unfair manner in which sentencing law and practice operate against Aboriginals; either in the Northern Territory or generally. Criminal punishment systems around the world punish a disproportionate number of socially deprived people. In Australia, Indigenous Australians were grossly over-represented in Australian jails prior to the three strikes laws and will remain so unless steps are taken to address their disadvantage. The obvious solution to redress the over-representation by Indigenous Australians is to provide them with the same social opportunities and resources as the rest of the community. This is overly ambitious – at least in the short term. This article suggests a more attainable change in sentencing law to remedy some of the disadvantages experienced by Aboriginals. It suggests that far less weight should be accorded to prior convictions in the sentencing calculus.

What's instinct got to do with it? A blueprint for a coherent approach to punishing criminals

As a result of the instinctive synthesis approach to sentencing, decisions are often based on the intuitive inclinations and sentiments of sentencers, as opposed to binding rules and principles. In particular, insufficient regard is paid to the purposes and objectives that can be achieved through a state-imposed system of punishment. Momentum is gathering for the High Court to revisit the manner in which the sentencing inquiry is undertaken. We believe that the court should use the opportunity to implement fundamental reform in sentencing and direct the sentencing process down a more transparent and forensic path. We suggest that there are seven basic steps that need to be undertaken to achieve enlightened sentencing reform. Ideally this is a role for the legislature. However, given the populist climate in which we live we have little confidence that the legislature will undertake such an exacting task – one which would almost certainly lead to a less severe sentencing regime. The judiciary offers the strongest hope that at least some of these steps will be taken. This article offers a blueprint for how such reform can be implemented. The first step is simply to assume that the institution of state-imposed punishment is justified – this has already been undertaken. The second is to select the theory which best justifies punishing wrongdoers. Thirdly, public opinion must be ignored in developing sentencing principle. Next it must be determined which objectives (such as deterrence and rehabilitation) can be achieved through sentencing. The fifth step involves matching the punishment to the crime. Step six is to critically analyse the foundation, and reassess the relevance, of the hundreds of aggravating and mitigating considerations that presently affect the sentencing calculus. Finally, sentencing law and practice should be subject to ongoing reform to take into account emerging empirical evidence concerning the positive benefits that can be achieved through sentencing.

Algebra skills and traps and diagnostic teaching for the future

Explores on some research about teaching and learning algebra and related classroom issues. Diagnostic instruments that may be used by senior secondary teachers in teaching algebra to senior classes; Strategies for remediating algebraic difficulties and misconceptions; Impact of technology on the algebra curriculum; Usefulness of copying algebraic expressions while using Computer Algebra Systems or mathematics processing software in a calculus class.

Scientific proof that humans enjoy punishing wrongdoers: The implications for punishment and sentencing

Recent developments in brain science confirm that as a race we are in fact a punitive lot. Human beings actually derive pleasure from inflicting punishment on wrongdoers. We are wired in such a way that the part of our brain that reports pleasure is activated when we punish norm violators. This is even when punishment has no tangible or demonstrable benefits. However, we are not slaves lo our emotions. Another region of our brain 'kicks-in' if punishment becomes self-defeating, in that it conflicts with our other interests. The implications of this research for punishment theory and the practice of sentencing are discussed in this paper. The findings give qualified support to the theory known as intrinsic retributivism, but do not suggest it is the soundest theory of punishment. This is because we stop punishing when it comes at a cost to us. The good feeling that punishment invokes in punishers is another consequential consideration in favour of the utilitarian theory of punishment. However, it is not clear that the utilitarian calculus is necessarily affected by the findings. The main implication of the research findings relates to the relevance of public opinion to sentencing practice. The findings support the view that public sentiment, which seems to support increasingly tougher sanctions, can be curtailed of the public are informed that punishment comes of a cost to community.

Precoder design for multi-antenna systems with temporally and spatially correlated fading channels

This paper addresses the problem of the design of a precoder for multiple transmit antenna communication systems with spatially and temporally correlated fading channels. Using the theories of matrix differential calculus, the paper derives a precoder for unitary space-time codes that can exploit the spatio-temporal correlation in the time-varying fading channels. The design criterion is based on minimizing the mean square error of the channel estimates. Computer simulation results show that a significant performance gain can be achieved by using the designed precoder.

Estimating intergenerational distribution preferences

Resource management decisions influence not only the output of the economy but also the distribution of utility between groups within the community. The theory of cost benefit analysis provides a means of incorporating distributional changes into the decision making calculus through the application of distributional or welfare weights. However, this practice has not been widely adopted in part due to difficulties in the estimation of distributional weights. This paper addresses this problem by using the stated preference method of choice modelling to estimate distributional weights suitable for inclusion in a cost benefit analysis framework. The findings of a choice modelling experiment designed to estimate community preferences with respect to intergenerational utility distribution illustrate the potential of this method in addressing distributional issues.