Modeling as a means for making powerful ideas accessible to children at an early age

The SimCalc Vision and Contributions Advances in Mathematics Education 2013, pp 419-436 Modeling as a Means for Making Powerful Ideas Accessible to Children at an Early Age Richard Lesh, Lyn English, Serife Sevis, Chanda Riggs … show all 4 hide » Look Inside » Get Access Abstract In modern societies in the 21st century, significant changes have been occurring in the kinds of “mathematical thinking” that are needed outside of school. Even in the case of primary school children (grades K-2), children not only encounter situations where numbers refer to sets of discrete objects that can be counted. Numbers also are used to describe situations that involve continuous quantities (inches, feet, pounds, etc.), signed quantities, quantities that have both magnitude and direction, locations (coordinates, or ordinal quantities), transformations (actions), accumulating quantities, continually changing quantities, and other kinds of mathematical objects. Furthermore, if we ask, what kind of situations can children use numbers to describe? rather than restricting attention to situations where children should be able to calculate correctly, then this study shows that average ability children in grades K-2 are (and need to be) able to productively mathematize situations that involve far more than simple counts. Similarly, whereas nearly the entire K-16 mathematics curriculum is restricted to situations that can be mathematized using a single input-output rule going in one direction, even the lives of primary school children are filled with situations that involve several interacting actions—and which involve feedback loops, second-order effects, and issues such as maximization, minimization, or stabilizations (which, many years ago, needed to be postponed until students had been introduced to calculus). …This brief paper demonstrates that, if children’s stories are used to introduce simulations of “real life” problem solving situations, then average ability primary school children are quite capable of dealing productively with 60-minute problems that involve (a) many kinds of quantities in addition to “counts,” (b) integrated collections of concepts associated with a variety of textbook topic areas, (c) interactions among several different actors, and (d) issues such as maximization, minimization, and stabilization.

A quasi-maximum likelihood method for estimating the parameters of multivariate diffusions

A quasi-maximum likelihood procedure for estimating the parameters of multi-dimensional diffusions is developed in which the transitional density is a multivariate Gaussian density with first and second moments approximating the true moments of the unknown density. For affine drift and diffusion functions, the moments are exactly those of the true transitional density and for nonlinear drift and diffusion functions the approximation is extremely good and is as effective as alternative methods based on likelihood approximations. The estimation procedure generalises to models with latent factors. A conditioning procedure is developed that allows parameter estimation in the absence of proxies.

Environmental education through listening to children

Environmental education centres contribute to schools and communities in Environmental Education and Education for Sustainability through nature and urban -based, experiential learning and action learning approaches. An underlying assumption of these centres is that intensive, short-term, outdoor/environmental education experiences can change key attitudes and/or actions leading to positive environmental behaviour. This study reflects the interests of a researching professional who investigated aspects of a program that he designed and implemented as principal of an environmental education centre. Most evaluations of similar programs have used quasi-experimental designs to measure the program outcomes. However, this study considered the experiences of the program from the perspectives of a group of key stakeholders often overlooked in the literature; the children who participated in the program. This study examined children’s accounts of their own experiences in order to contribute new understandings of children’s perspectives and how they can be considered when designing and implementing environmental education programs. This research drew on key theoretical assumptions derived from the sociology of childhood. Within sociology of childhood, children are considered to be competent practitioners within their social worlds, who, through their talk and interaction, participate actively in the construction of their own social situations. This approach also views children as capable and competent learners who construct their knowledge through everyday participation in social experiences. This study set out to generate children’s own accounts of their experiences of a five day residential program at the Centre. In total, 54 children participated in the study that used a multi-faceted data collection approach that included conversations, drawings, photographs and journal writing. Using content analysis, data were analysed by means of an inductive approach to develop themes related to the children’s perspectives of their experiences. Three interrelated and co-dependent components of the experience emerged from the analysis; space and place; engagement and participation; and responsiveness and reflection. These components co-exist and construct the conditions for effective experiences in environmental education at the Centre. The first key finding was the emphasis that the children placed on being provided with somewhere where they could feel safe and comfortable to interact with their environment and engage in a range of outdoor experiences. The children identified that place was an outdoor classroom where they could participate in first-hand experiences and, at times, explore out-of-bound spaces; that is, a place where they had previously been limited, often by adults, in their opportunities to interact with nature. A second key finding was the emphasis that the children placed on engagement and participation in environmental experience. The children described participating in a range of new primary experiences that involved first-hand, experiences and also described participating in collaborative experiences that involved interacting with peers and with teachers, who appeared to behave differently to how they behaved at school. Finally, the children described a different type of interactional relationship with teachers, comparing the active educational role they played on camp to a more passive role at school where they sat at a table and the teacher wrote on the board. The final key finding was the emphasis that the children placed on responsiveness and reflection in the experience. In responding to their experiences, the children described the fun and excitement, confidence and satisfaction that they gained from the experience. The children also identified how their experiences contributed to the development of a caring-for-nature attitude and the value of a disorienting dilemma in promoting responsiveness to the environment. This disorienting dilemma was an event that caused the children to reassess their own beliefs and attitudes. From the three main findings, a theoretical framework that represented the children’s accounts of their experiences and a pedagogic approach that respected their accounts was developed. This pedagogic approach showed how a disorienting dilemma could create a disequilibrium in relation to a child’s existing ideas and experiences. As a result, children were challenged to reflect upon their existing environmental beliefs and practices. The findings of this research have implications for the field of environmental education. Adopting sociology of childhood provides an alternative foundation to research and can present a deeper understanding of what children believe, than an approach that relies solely on using scientific methods to undercover and analyse these understandings. This research demonstrates the value of gaining children’s accounts to assist educators to design environmental education programs as it can offer more than adult and educator perspectives. This study also provides understandings of environmental education practice by describing how the children engaged with informal learning situations. Finally, two sets of recommendations, drawn from this study, are made. The first set considers nine recommendations about and for future research and the second relates to redesigning of the environmental educational program at the research site, with six recommendations made.

Biodiesel with controlled physicochemical properties, a means to further reduce diesel engine particle emissions

The issue of particle emissions from diesel engines is still a matter of concern due its deleterious effects both on human health and environment(Ristovski et al., 2012). Recently, International Agency for Research on Cancer (IARC) inclusion of diesel engine exhaust particles as carcinogenic to human health added a new margin on it. Apart from the use of after treatment technology, biodiesel is also considered as potential way to reduce particle emission alongside with other emissions(Xue, Grift, & Hansen, 2011). Global biodiesel production is still reasonably small compared to its counterpart fossil diesel, but even this small amount comes from a wide variety of feed stocks. Contrary to fossil diesel, the important physicochemical properties of biodiesel vary among different feed stocks(Hoekman, Broch, Robbins, Ceniceros, & Natarajan, 2012).

What it means to be green : an examination of early stage environmental and sustainability focused firms

This paper examines ‘green’ entrepreneurial nascent and young firms in Australia. Findings of interest in this paper include: • Green entrepreneurs are more likely to be highly educated and have an extended depth of experience within their industry and are more likely to have started a business prior to their current venture. • Green entrepreneurs exhibit increased levels of innovation, with an increased focus on new & high technology, R&D and the development of proprietary technology. • Green entrepreneurs are most likely to be based upon a product rather than a service and have a higher emphasis upon growth when compared with non-green entrepreneurs. • Green entrepreneurial firms tend to have a longer venture creation process and draw financial resources from a larger number of sources and rely more upon equity as a means of financing their venture.

Transitioning from dependent to more independent learners : Using video tutorials as a means of helping students help themselves

This paper examines the use of short video tutorials in a post-graduate accounting subject, as a means of helping students transition from dependent to more independent learners. Five short (three to five minute) video tutorials were introduced in an effort to shift the reliance for learning from the lecturer to the student. Students’ usage of video tutorials, comments by students, and reliance on teaching staff for individual assistance were monitored over three semesters from 2008 to 2009. Interviews with students were then conducted in late 2009 to more comprehensively evaluate the use and benefits of video tutorials. Findings reveal preliminary but positive outcomes in terms of both more efficient teaching and more effective learning.

Investigation of mediated oxidation of ascorbic acid by ferrocenemethanol using large-amplitude fourier transformed ac voltammetry under quasi-reversible electron-transfer conditions at an indium tin oxide electrode

The ability of the technique of large-amplitude Fourier transformed (FT) ac voltammetry to facilitate the quantitative evaluation of electrode processes involving electron transfer and catalytically coupled chemical reactions has been evaluated. Predictions derived on the basis of detailed simulations imply that the rate of electron transfer is crucial, as confirmed by studies on the ferrocenemethanol (FcMeOH)-mediated electrocatalytic oxidation of ascorbic acid. Thus, at glassy carbon, gold, and boron-doped diamond electrodes, the introduction of the coupled electrocatalytic reaction, while producing significantly enhanced dc currents, does not affect the ac harmonics. This outcome is as expected if the FcMeOH (0/+) process remains fully reversible in the presence of ascorbic acid. In contrast, the ac harmonic components available from FT-ac voltammetry are predicted to be highly sensitive to the homogeneous kinetics when an electrocatalytic reaction is coupled to a quasi-reversible electron-transfer process. The required quasi-reversible scenario is available at an indium tin oxide electrode. Consequently, reversible potential, heterogeneous charge-transfer rate constant, and charge-transfer coefficient values of 0.19 V vs Ag/AgCl, 0.006 cm s (-1) and 0.55, respectively, along with a second-order homogeneous chemical rate constant of 2500 M (-1) s (-1) for the rate-determining step in the catalytic reaction were determined by comparison of simulated responses and experimental voltammograms derived from the dc and first to fourth ac harmonic components generated at an indium tin oxide electrode. The theoretical concepts derived for large-amplitude FT ac voltammetry are believed to be applicable to a wide range of important solution-based mediated electrocatalytic reactions.

Interleukin-1β stimulates human renal fibroblast proliferation and matrix protein production by means of a transforming growth factor-β-dependent mechanism

One of the hallmarks of progressive renal disease is the development of tubulointerstitial fibrosis. This is frequently preceded by macrophage infiltration, raising the possibility that macrophages relay fibrogenic signals to resident tubulointerstitial cells. The aim of this study was to investigate the potentially fibrogenic role of interleukin-1beta (IL-1beta), a macrophage-derived inflammatory cytokine, on cortical fibroblasts (CFs). Primary cultures of human renal CFs were established and incubated for 24 hours in the presence or absence of IL-1beta. We found that IL-1beta significantly stimulated DNA synthesis (356.7% +/- 39% of control, P <.003), fibronectin secretion (261.8 +/- 11% of control, P <.005), collagen type 1 production, (release of procollagen type 1 C-terminal-peptide, 152.4% +/- 26% of control, P <.005), transforming growth factor-beta (TGF-beta) secretion (211% +/- 37% of control, P <.01), and nitric oxide (NO) production (342.8% +/- 69% of control, P <.002). TGF-beta (1 ng/mL) and the phorbol ester phorbol 12-myristate 13-acetate (PMA, 25 nmol/L) produced fibrogenic effects similar to those of IL-1beta. Neither a NO synthase inhibitor (N(G)-methyl-l-arginine, 1 mmol/L) nor a protein kinase C (PKC) inhibitor (bis-indolylmaleimide 1, 1 micromol/L) altered the enhanced level of fibronectin secretion or DNA synthesis seen in response to IL-1beta treatment. However, addition of a TGF-beta-neutralizing antibody significantly reduced IL-1beta-induced fibronectin secretion (IL-1beta + IgG, 262% +/- 72% vs IL-1beta + alphaTGF-beta 156% +/- 14%, P <.02), collagen type 1 production (IL-1beta + IgG, 176% +/- 28% vs IL-1beta + alphaTGF-beta, 120% +/- 14%, P <.005) and abrogated IL-1beta-induced DNA synthesis (245% +/- 49% vs 105% +/- 21%, P <.005). IL-1beta significantly stimulated CF DNA synthesis and production of fibronectin, collagen type 1, TGFbeta, and NO. The fibrogenic and proliferative action of IL-1beta on CF appears not to involve activation of PKC or production of NO but is at least partly TGFbeta-dependent.

Regulatory compliance as a means to achieve environmental sustainability at some large coastal developments in Queensland

The growing public concern about the complexity, cost and uncertain efficacy of the statuary environmental impact assessment process applying to large-scale projects in Queensland is reviewed. This is based on field data gathered over the past six years sat large-scale marina developments that access major environmental reserves along the coast. An ecological design proposal to broaden the process consisted with both government aspirations and regional ecological parameters - termed Regional Landscape Strategies - would allow the existing Environmental Impact Asessment to be modified alone potentially more practicable and effective lines.

The effectiveness of information-sharing interventions as a means to reduce anxiety in families waiting for surgical patients undergoing an elective surgical procedure : a systematic review protocol

Review question/objective What are the most effective information sharing strategies used to reduce anxiety in families of patients undergoing elective surgery? This review seeks to synthesize the best available evidence in relation to the most effective information-sharing intervention to reduce anxiety for families waiting for patients undergoing an elective surgical procedure. The specific objectives are to review the effectiveness of evidence of interventions designed to reduce the anxiety of families waiting whilst their loved one undergoes a surgical intervention. A variety of interventions exist and include surgical nurse liaison services, intraoperative reporting either by face-to-face or telephone delivery, informational cards, visual information screens, and intraoperative paging devices for families. Inclusion criteria Types of participants All studies of family members over 18 years of age waiting for patients undergoing an elective surgical procedure will be included, including those waiting for both adult and paediatric patients. Studies of families waiting for other patient populations, eg emergency surgery, chemotherapy or intensive care patients will be excluded. Types of intervention(s)/phenomena of interest All information-sharing Interventions for families of patients undergoing an elective surgical procedure will be included, including but not limited to: surgical nurse liaison services, in-person intraoperative reporting, visual information screens, paging devices, informational cards and telephone delivery of intraoperative progress reports. Interventions that take place during the intraoperative phase of care only will be included in the review. Preadmission information sharing interventions will be excluded. Types of outcomes The outcomes of interest include: Primary outcome: the level of anxiety amongst family members or close relatives whilst waiting for patients undergoing surgery, as measured by a validated instrument (such as the S-Anxiety portion of the State-Trait Anxiety Inventory).4 Secondary outcomes: family satisfaction and other measurements that may be considered indicators of stress and anxiety, such as mean arterial pressure (MAP) and heart rate.

Exploring the fundamental theorem of arithmetic in excel 2007

This paper discusses how fundamentals of number theory, such as unique prime factorization and greatest common divisor can be made accessible to secondary school students through spreadsheets. In addition, the three basic multiplicative functions of number theory are defined and illustrated through a spreadsheet environment. Primes are defined simply as those natural numbers with just two divisors. One focus of the paper is to show the ease with which spreadsheets can be used to introduce students to some basics of elementary number theory. Complete instructions are given to build a spreadsheet to enable the user to input a positive integer, either with a slider or manually, and see the prime decomposition. The spreadsheet environment allows students to observe patterns, gain structural insight, form and test conjectures, and solve problems in elementary number theory.

Spreadsheet Conditional Formatting Illuminates Investigations into Modular Arithmetic

Modular arithmetic has often been regarded as something of a mathematical curiosity, at least by those unfamiliar with its importance to both abstract algebra and number theory, and with its numerous applications. However, with the ubiquity of fast digital computers, and the need for reliable digital security systems such as RSA, this important branch of mathematics is now considered essential knowledge for many professionals. Indeed, computer arithmetic itself is, ipso facto, modular. This chapter describes how the modern graphical spreadsheet may be used to clearly illustrate the basics of modular arithmetic, and to solve certain classes of problems. Students may then gain structural insight and the foundations laid for applications to such areas as hashing, random number generation, and public-key cryptography.

Generalized azimuthal shear deformations in compressible isotropic elastic materials

In this article we study the azimuthal shear deformations in a compressible Isotropic elastic material. This class of deformations involves an azimuthal displacement as a function of the radial and axial coordinates. The equilibrium equations are formulated in terms of the Cauchy-Green strain tensors, which form an overdetermined system of partial differential equations for which solutions do not exist in general. By means of a Legendre transformation, necessary and sufficient conditions for the material to support this deformation are obtained explicitly, in the sense that every solution to the azimuthal equilibrium equation will satisfy the remaining two equations. Additionally, we show how these conditions are sufficient to support all currently known deformations that locally reduce to simple shear. These conditions are then expressed both in terms of the invariants of the Cauchy-Green strain and stretch tensors. Several classes of strain energy functions for which this deformation can be supported are studied. For certain boundary conditions, exact solutions to the equilibrium equations are obtained. © 2005 Society for Industrial and Applied Mathematics.

p-type doping of ZnO by means of high-density inductively coupled plasmas

A custom-designed inductively coupled plasma assisted radio-frequency magnetron sputtering deposition system has been used to fabricate N-doped p-type ZnO (ZnO:N) thin films on glass substrates from a sintered ZnO target in a reactive Ar + N2 gas mixture. X-ray diffraction and scanning electron microscopy analyses show that the ZnO:N films feature a hexagonal crystal structure with a preferential (002) crystallographic orientation and grow as vertical columnar structures. Hall effect and X-ray photoelectron spectroscopy analyses show that N-doped ZnO thin films are p-type with a hole concentration of 3.32 × 1018 cm- 3 and mobility of 1.31 cm2 V- 1 s- 1. The current-voltage measurement of the two-layer structured ZnO p-n homojunction clearly reveals the rectifying ability of the p-n junction. The achievement of p-type ZnO:N thin films is attributed to the high dissociation ability of the high-density inductively coupled plasma source and effective plasma-surface interactions during the growth process.

Workflow patterns as a means to model task succession in games – a preliminary case study

Over about the last decade, people involved in game development have noted the need for more formal models and tools to support the design phase of games. It is argued that the present lack of such formal tools is currently hindering knowledge transfer among designers. Formal visual languages, on the other hand, can help to more effectively express, abstract and communicate game design concepts. Moreover, formal tools can assist in the prototyping phase, allowing designers to reason about and simulate game mechanics on an abstract level. In this paper we present an initial investigation into whether workflow patterns – which have already proven to be effective for modeling business processes – are a suitable way to model task succession in games. Our preliminary results suggest that workflow patterns show promise in this regard but some limitations, especially in regard to time constraints, currently restrict their potential.