Calculus Students' Use and Interpretation of Variables: Algebraic vs. Arithmetic Thinking

Abstract

The ability to use and interpret algebraic variables as generalized numbers and changing quantities is fundamental to the learning of calculus. This study considers the use of variables in these advanced ways as a component of algebraic thinking. College introductory calculus students' (n = 174) written responses to algebra problems requiring the use and interpretation of variables as changing quantities were examined for evidence of algebraic and arithmetic thinking. A framework was developed to describe and categorize examples of algebraic, transitional, and arithmetic thinking reflected in these students' uses of variables. The extent to which students' responses showed evidence of algebraic or arithmetic thinking was quantified and related to their course grades. Only one third of the responses of these entering calculus students were identified as representative of algebraic thinking. This study extends previous research by showing that evidence of algebraic thinking in students' work was positively related to successful performance in calculus.     

Discrete-Time Expectation Maximization Algorithms for Markov-Modulated Poisson Processes

In this paper, we consider parameter estimation Markov-modulated Poisson processes via robust filtering and smoothing techniques. Using the expectation maximization algorithm framework, our filters and smoothers can be applied to estimate the parameters of our model in either an online configuration or an offline configuration. Further, our estimator dynamics do not involve stochastic integrals and our new formulas, in terms of time integrals, are easily discretized, and are written in numerically stable forms in W. P. Malcolm, R. J. Elliott, and J. van der Hoek, “On the numerical stability of time-discretized state estimation via clark transformations,” presented at the IEEE Conf. Decision Control, Mauii, HI, Dec. 2003.      

Inventive Tool Use to Comprehend Big Code

Software developers often need to understand a large body of unfamiliar code with little or no documentation, no experts to consult, and little time to do it. A post appeared in January 2008 on Slashdot, a technology news Web site, asking for tools and techniques that could help. This article analyzes 301 often passionate and sometimes articulate responses to this query, including the themes and the associated tool recommendations. The most common suggestions were to use a code navigation tool, use a design recovery tool, use a debugger to step through the code, create a runtime trace, use problem-based learning, ask people for help, study the code from top down, and print out all the code. This analysis presents an intriguing snapshot of how software developers in industry go about comprehending big code.     

Using electric actuation and detection of oscillations in microcantilevers for pressure measurements

Response characteristics of a microcantilever, such as resonant frequency, amplitude, phase and quality factor, can be used for absolute pressure measurements in the range of 10⁻⁴ to 10³ Torr. To this end, it would be very convenient to have the resonance of the microcantilever actuated and detected electrostatically. Herein, we report the nonlinear dynamics of microcantilevers under varying pressure and different gases using the harmonic detection of resonance (HDR) technique [J. Gaillard, M.J. Skove, R. Ciocan, A.M. Rao, Electrical detection of oscillations in 340 microcantilevers and nanocantilevers, Rev. Sci. Instrum. 77 (2006) 073907]. The HDR technique exploits nonlinearities in the cantilever-counter electrode system to allow electrostatic actuation and detection of the responses of the microcantilever to the pressure and gas composition. In particular, the 2nd and 3rd harmonics of the measured charge on the cantilever are investigated. The microcantilever demonstrates a quality factor of 10,000 at 10⁻³ Torr, and a usable response in the range from 10⁻³ to 10³ Torr. The use of different harmonics can enable us to adjust the range of pressures over which the sensor has an efficacious response, enhancing its sensitivity to a particular environment. The experimental results are in reasonable agreement with theoretical calculations, despite the nonlinearities involved.     

Asimov’s “three laws of robotics” and machine metaethics

Using Asimov’s “Bicentennial Man” as a springboard, a number of metaethical issues concerning the emerging field of machine ethics are discussed. Although the ultimate goal of machine ethics is to create autonomous ethical machines, this presents a number of challenges. A good way to begin the task of making ethics computable is to create a program that enables a machine to act an ethical advisor to human beings. This project, unlike creating an autonomous ethical machine, will not require that we make a judgment about the ethical status of the machine itself, a judgment that will be particularly difficult to make. Finally, it is argued that Asimov’s “three laws of robotics” are an unsatisfactory basis for machine ethics, regardless of the status of the machine.

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Triangulation in practice

Triangulation is the means by which an alternate perspective is used to validate, challenge or extend existing findings. It is frequently used when the field of study is difficult, demanding or contentious and presence research meets all of these criteria. We distinguish between the use of hard and soft triangulation—the former emphasising the challenging of findings, the latter being more confirmatory in character. Having reviewed a substantial number of presence papers, we conclude that strong triangulation is not widely used while soft triangulation is routinely employed. We demonstrate the usefulness of hard triangulation by contrasting an ontological analysis of in-ness with an empirical study of (computer) game playing. We conclude that presence research would be well served by the wider use of hard triangulation and for the reporting of anomalous and ill-fitting results.

Toward the Proteome of the Human Peripheral Blood Eosinophil

Eosinophils (EOSs) are granular leukocytes that have significant roles in many inflammatory and immunoregulatory responses, especially asthma and allergic diseases. We have undertaken a fairly comprehensive proteomic analysis of purified peripheral blood EOSs from normal human donors primarily employing 2‐DE with protein spot identification by MALDI‐MS. Protein subfractionation methods employed included IEF (Zoom^® Fractionator) and subcellular fractionation using differential protein solubilization. We have identified 3141 proteins, which had Mascot expectation scores of 10^?3 or less. Of these 426 were unique and non‐redundant of which 231 were novel proteins not previously reported to occur in EOSs. Ingenuity Pathway Analysis showed that some 70% of the non‐redundant proteins could be subdivided into categories that are clearly related to currently known EOS biological activities. Cytoskeletal and associated proteins predominated among the proteins identified. Extensive protein posttranslational modifications were evident, many of which have not been previously reported that reflected the dynamic character of the EOS. This data set of eosinophilic proteins will prove valuable in comparative studies of disease versus normal states and for studies of gender differences and polymorphic variation among individuals.     

Characterisation of flucloxacillin and 5-hydroxymethyl flucloxacillin haptenated HSA in vitro and in vivo

Flucloxacillin is a synthetic penicillin used in the treatment of Staphylococcal infections. Adverse reactions to the drug are believed to arise through covalent modification of proteins, with tissue damage occurring secondary to an immune reaction. Serum proteins have been shown by adduct-specific antibodies to be modified by flucloxacillin, but the nature and sites of modification have not been characterised. Here, in vitro studies on HSA have shown by MS that the modification of protein lysine residues occurs in a dose-, time- and site-dependent manner. Affinity, cation exchange and reversed phase chromatography prior to MS revealed in vivo modification of HSA with flucloxacillin in tolerant patients, with up to nine modified lysine residues being detected in each patient, and with modification of Lys190 and Lys212 being detected in 8/8 patients. It was also revealed for the first time that plasma proteins could be modified with the 5-hydroxymethyl metabolite of flucloxacillin, and that essentially the same Lys residues were targeted by both the parent drug and its metabolite. This study provides a detailed characterisation of sites of chemical modification of an endogenous target and reveals candidate peptides for T-cell and antibody assays of flucloxacillin hypersensitivity.     

Postural support strategies of disabled drivers and the effectiveness of postural support aids

The paper discusses a series of driving trials that were conducted to investigate postural stability of disabled drivers and to assess the effectiveness of a representative sample of support aids. Twenty-three disabled drivers with varying levels of physical disability and seven non disabled drivers participated in the study. The test car was equipped with transducers to measure vehicle velocity and acceleration (longitudinal and lateral), steering wheel movement and torque, and the bracing forces exerted by the driver on the steering wheel. Video cameras were installed to record postural support strategies and displacement of the driver and to record deviation of the car from the specified path. Subjective data regarding driver attitudes and acceptance were also collected through the administration of questionnaires. Findings from the study showed that support aids significantly improved driving performance and reduced physical exertion to maintain an upright driving position for disabled drivers. However, ergonomics design aspects regarding the ease of use and acceptance of the support aids by the end users were identified as obstacles to their sustained use in everyday driving.