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.     

Development of a Weather Forecasting Code: A Case Study

Computational science is increasingly supporting advances in scientific and engineering knowledge. The unique constraints of these types of projects result in a development process that differs from the process more traditional information technology projects use. This article reports the results of the sixth case study conducted under the support of the Darpa High Productivity Computing Systems Program. The case study aimed to investigate the technical challenges of code development in this environment, understand the use of development tools, and document the findings as concrete lessons learned for other developers' benefit. The project studied here is a major component of a weather forecasting system of systems. It includes complex behavior and interaction of several individual physical systems (such as the atmosphere and the ocean). This article describes the development of the code and presents important lessons learned.     

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.     

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.     

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.     

Exploring Privacy Management on Facebook: Motivations and Perceived Consequences of Voluntary Disclosure

This study examined the perceived motivations and consequences of voluntary disclosure of Facebook active users using a survey administered to college students in a public‐speaking course. College‐age students who took the survey were motivated to use Facebook because they perceived their relationships improved with friends and family, although using Facebook could become negatively habit forming. The research suggests that users of Facebook use it more for disclosing to distant friends rather than to close friends, which is divergent from most early disclosure research that equates disclosure with intimacy. This research utilizes Communication Privacy Management Theory for the theoretical framework.     

Extending the two‐stage information systems continuance model: incorporating UTAUT predictors and the role of context

This study presents two extensions to the two‐stage expectation‐confirmation theory of information systems (IS) continuance. First, we expand the belief set from perceived usefulness in the original IS continuance model to include three additional predictors identified in the unified theory of acceptance and use of technology, namely effort expectancy, social influence and facilitating conditions. Second, we ground the IS continuance model in the context of transactional systems that involve transmission of personal and sensitive information and include trust as a key contextual belief in the model. To test the expanded IS continuance model, we conducted a longitudinal field study of 3159 Hong Kong citizens across two electronic government (e‐government) technologies that enable citizens' access to government services. In general, the results support the expanded model that provides a rich understanding of the changes in the pre‐usage beliefs and attitudes through the emergent constructs of disconfirmation and satisfaction, ultimately influencing IS continuance intention. Finally, we discuss the theoretical and practical implications of the expanded model.