Aspects of elementary number theory illustrated in the spreadsheet environment

Number theory has in recent decades assumed a great practical importance, due primarily to its application to cryptography. This chapter discusses how elementary concepts of number theory may be illuminated and made accessible to upper secondary school students via appropriate spreadsheet models. In such environments, students can observe patterns, gain structural insight, form and test conjectures, and solve problems. The chapter begins by reviewing literature on the use of spreadsheets in general and the use of spreadsheets in number theory in particular. Two sample applications are then discussed. The first, factoring factorials, is presented and instructions are given to construct a model in Excel 2007. The second application, the RSA cryptosystem, is included because of its importance to Science, Technology, Engineering, and Mathematics (STEM) students. Number theoretic concepts relevant to RSA are discussed, and an outline of RSA. is given, with example. The chapter ends with instructions on how to construct a simple spreadsheet illustrating RSA.

Time, space, and text in the elementary school digital writing classroom

Theorists of multiliteracies, social semiotics, and the New Literacy Studies have drawn attention to the potential changing nature of writing and literacy in the context of networked communications. This article reports findings from a design-based research project in Year 4 classrooms (students aged 8.5-10 years) in a low socioeconomic status school. A new writing program taught students how to design multimodal and digital texts across a range of genres and text types, such as web pages, online comics, video documentaries, and blogs. The authors use Bernstein’s theory of the pedagogic device to theorize the pedagogic struggles and resolutions in remaking English through the specialization of time, space, and text. The changes created an ideological struggle as new writing practices were adapted from broader societal fields to meet the instructional and regulative discourses of a conventional writing curriculum.

Effectiveness of a puppet show on iodine knowledge, attitudes and behaviour of elementary students and the indirect effects on their parents and households in Ho Chi Minh City : a pilot study

Deficiencies in iodine levels have been shown to seriously affect a child’s intellectual development and learning capacity.1 In South-East Asia, iodine deficiency remains a major public health concern. Approximately 30% of the region’s population of 503.6 million have insufficient iodine intake, and only 61% of households have access to iodized salt.1 For this reason, it is necessary to initiate effective, community-based health promotion activities that are targeted toward populations of various ages. A puppet show is one imaginative and entertaining method of health education that has been advocated for use in communicating positive health behaviours to children.2e5 The authors undertook a literature review and found no studies assessing the effectiveness of a puppet show to teach an iodine education programme...

Exploring variation in measurement as a foundation for statistical thinking in the elementary school

This study was based on the premise that variation is the foundation of statistics and statistical investigations. The study followed the development of fourth-grade students' understanding of variation through participation in a sequence of two lessons based on measurement. In the first lesson all students measured the arm span of one student, revealing pathways students follow in developing understanding of variation and linear measurement (related to research question 1). In the second lesson each student's arm span was measured once, introducing a different aspect of variation for students to observe and contrast. From this second lesson, students' development of the ability to compare their representations for the two scenarios and explain differences in terms of variation was explored (research question 2). Students' documentation, in both workbook and software formats, enabled us to monitor their engagement and identify their increasing appreciation of the need to observe, represent, and contrast the variation in the data. Following the lessons, a written student assessment was used for judging retention of understanding of variation developed through the lessons and the degree of transfer of understanding to a different scenario (research question 3).

The effect of autonomy transparency in human-robot interactions : a preliminary study on operator cognitive workload and situation awareness in multiple heterogeneous UAV management

The autonomous capabilities in collaborative unmanned aircraft systems are growing rapidly. Without appropriate transparency, the effectiveness of the future multiple Unmanned Aerial Vehicle (UAV) management paradigm will be significantly limited by the human agent’s cognitive abilities; where the operator’s CognitiveWorkload (CW) and Situation Awareness (SA) will present as disproportionate. This proposes a challenge in evaluating the impact of robot autonomous capability feedback, allowing the human agent greater transparency into the robot’s autonomous status - in a supervisory role. This paper presents; the motivation, aim, related works, experiment theory, methodology, results and discussions, and the future work succeeding this preliminary study. The results in this paper illustrates that, with a greater transparency of a UAV’s autonomous capability, an overall improvement in the subjects’ cognitive abilities was evident, that is, with a confidence of 95%, the test subjects’ mean CW was demonstrated to have a statistically significant reduction, while their mean SA was demonstrated to have a significant increase.

Understanding children’s epistemic beliefs in elementary education

Research shows that the beliefs individuals hold about knowledge and knowing (epistemic beliefs) influence learning approaches and outcomes. However, little is known about the nature of children’s epistemic beliefs and how best to measure these. In this pilot study, 11 Australian children (in Grade 4 or Grade 6) were asked to ‘draw, write and tell’ about their epistemic beliefs using drawings, written responses and interviews respectively. Drawings were analysed, with the majority of children depicting external, one-way sources of knowledge. The written statements and interviews were analysed using inductive thematic analysis, showing that children predominantly described knowledge acquisition as processes of task-based learning. Interviews also enabled children to describe a wider range of views. These results indicate that the methodological combination of ‘draw, write and tell’ allowed for a deeper understanding of the children’s epistemic beliefs which holds implications for future research.

Statistical literacy in the elementary school: Opportunities for problem posing

This chapter addresses opportunities for problem posing in developing young children’s statistical literacy, with a focus on student-directed investigations. Although the notion of problem posing has broadened in recent years, there nevertheless remains limited research on how problem posing can be integrated within the regular mathematics curriculum, especially in the areas of statistics and probability. The chapter first reviews briefly aspects of problem posing that have featured in the literature over the years. Consideration is next given to the importance of developing children’s statistical literacy in which problem posing is an inherent feature. Some findings from a school playground investigation conducted in four, fourth-grade classes illustrate the different ways in which children posed investigative questions, how they made predictions about their outcomes and compared these with their findings, and the ways in which they chose to represent their findings.

A Chlamydia trachomatis strain with a chemically generated amino acid substitution (P370L) in the cthtrA gene shows reduced elementary body production

Background Chlamydia (C.) trachomatis is the most prevalent bacterial sexually transmitted infection worldwide and the leading cause of preventable blindness. Genetic approaches to investigate C. trachomatis have been only recently developed due to the organism’s intracellular developmental cycle. HtrA is a critical stress response serine protease and chaperone for many bacteria and in C. trachomatis has been previously shown to be important for heat stress and the replicative phase of development using a chemical inhibitor of the CtHtrA activity. In this study, chemically-induced SNVs in the cthtrA gene that resulted in amino acid substitutions (A240V, G475E, and P370L) were identified and characterized. Methods SNVs were initially biochemically characterized in vitro using recombinant protein techniques to confirm a functional impact on proteolysis. The C. trachomatis strains containing the SNVs with marked reductions in proteolysis were investigated in cell culture to identify phenotypes that could be linked to CtHtrA function. Results The strain harboring the SNV with the most marked impact on proteolysis (cthtrAP370L) was detected to have a significant reduction in the production of infectious elementary bodies. Conclusions This provides genetic evidence that CtHtrA is critical for the C. trachomatis developmental cycle.

Engaging elementary students in learning science: An analysis of classroom dialogue

Research over a long period of time has continued to demonstrate problems in the teaching of science in school. In addition, declining levels of participation and interest in science and related fields have been reported from many particularly western countries. Among the strategies suggested is the recruitment of professional scientists and technologists either at the graduate level or advanced career level to change career and teach. In this study, we analysed how one beginning middle primary teacher engaged with students to support their science learning by establishing rich classroom discussions. We followed his evolving teaching expertise over three years focussing on his communicative practices informed by socio-cultural theory. His practices exemplified a non-interactive dialogical communicative approach where ideas were readily discussed but were concentrated on the class acquiring acceptable scientific understandings. His focus on the language of science was a significant aspect of his practice and one that emerged from his professional background. The study affirms the theoretical frameworks proposed by Mortimer and Scott (2003) highlighting how dialogue contributes to heightened student interest in science.

Pole placement in multi-input systems via elementary transformations

This paper is concerned with the development of an algorithm for pole placement in multi-input dynamic systems. The algorithm which uses a series of elementary transformations is believed to be simpler, computationally more efficient and numerically stable when compared with earlier methods. In this paper two methods have been presented.

A Novel Operator-Splitting Technique for One-Dimensional Laminar Premixed Flames

This paper is concerned the calculation of flame structure of one-dimensional laminar premixed flames using the technique of operator-splitting. The technique utilizes an explicit method of solution with one step Euler for chemistry and a novel probabilistic scheme for diffusion. The relationship between diffusion phenomenon and Gauss-Markoff process is exploited to obtain an unconditionally stable explicit difference scheme for diffusion. The method has been applied to (a) a model problem, (b) hydrazine decomposition, (c) a hydrogen-oxygen system with 28 reactions with constant Dρ 2 approximation, and (d) a hydrogen-oxygen system (28 reactions) with trace diffusion approximation. Certain interesting aspects of behaviour of the solution with non-unity Lewis number are brought out in the case of hydrazine flame. The results of computation in the most complex case are shown to compare very favourably with those of Warnatz, both in terms of accuracy of results as well as computational time, thus showing that explicit methods can be effective in flame computations. Also computations using the Gear-Hindmarsh for chemistry and the present approach for diffusion have been carried out and comparison of the two methods is presented.

Pole placement in multi-input systems via elementary transformations

This paper is concerned with the development of an algorithm for pole placement in multi-input dynamic systems. The algorithm which uses a series of elementary transformations is believed to be simpler, computationally more efficient and numerically stable when compared with earlier methods. In this paper two methods have been presented.