Integrating engineering model eliciting activities in elementary school curricula

This paper argues for a future-oriented, inclusion of Engineering Model Eliciting Activities (EngMEAs) in elementary mathematics curricula. In EngMEAs students work with meaningful engineering problems that capitalise on and extend their existing mathematics and science learning, to develop, revise and document powerful models, while working in groups. The models developed by six groups of 12-year students in solving the Natural Gas activity are presented. Results showed that student models adequately solved the problem, although student models did not take into account all the data provided. Student solutions varied to the extent students employed the engineering context in their models and to their understanding of the mathematical concepts involved in the problem. Finally, recommendations for implementing EngMEAs and for further research are discussed.

A model eliciting framework for integrating mathematics and robotics learning

Robotics is taught in many Australian ICT classrooms, in both primary and secondary schools. Robotics activities, including those developed using the LEGO Mindstorms NXT technology, are mathematics-rich and provide a fertile round for learners to develop and extend their mathematical thinking. However, this context for learning mathematics is often under-exploited. In this paper a variant of the model construction sequence (Lesh, Cramer, Doerr, Post, & Zawojewski, 2003) is proposed, with the purpose of explicitly integrating robotics and mathematics teaching and learning. Lesh et al.’s model construction sequence and the model eliciting activities it embeds were initially researched in primary mathematics classrooms and more recently in university engineering courses. The model construction sequence involves learners working collaboratively upon product-focussed tasks, through which they develop and expose their conceptual understanding. The integrating model proposed in this paper has been used to design and analyse a sequence of activities in an Australian Year 4 classroom. In that sequence more traditional classroom learning was complemented by the programming of LEGO-based robots to ‘act out’ the addition and subtraction of simple fractions (tenths) on a number-line. The framework was found to be useful for planning the sequence of learning and, more importantly, provided the participating teacher with the ability to critically reflect upon robotics technology as a tool to scaffold the learning of mathematics.

Integrating Engineering Experiences within the Elementary Mathematics Curriculum

Engineering education for elementary school students is a new and increasingly important domain of research by mathematics, science, technology, and engineering educators. Recent research has raised questions about the context of engineering problems that are meaningful, engaging, and inspiring for young students. In the present study an environmental engineering activity was implemented in two classes of 11-year-old students in Cyprus. The problem required students to use the data to develop a procedure for selecting among alternative countries from which to buy water. Students created a range of models that adequately solved the problem although not all models took into account all of the data provided. The models varied in the number of problem factors taken into consideration and also in the different approaches adopted in dealing with the problem factors. At least two groups of students integrated into their models the environmental aspect of the problem (energy consumption, water pollution) and further refined their models. Results provide evidence that engineering model-eliciting activities can be successfully integrated in the elementary mathematics curriculum. These activities provide rich opportunities for students to deal with engineering contexts and to apply their learning in mathematics and science to solving real-world engineering problems.

Engineering-based modelling experiences in the elementary classroom

Introducing engineering-based model-eliciting experiences in the elementary curriculum is a new and increasingly important domain of research by mathematics, science, technology, and engineering educators. Recent research has raised questions about the context of engineering problems that are meaningful, engaging, and inspiring for young students. In the present study an environmental engineering activity was implemented in two classes of 11-year-old students in Cyprus. The problem required students to develop a procedure for selecting among alternative countries from which to buy water. Students created a range of models that adequately solved the problem although not all models took into account all of the data provided. The models varied in the number of problem factors taken into consideration and also in the different approaches adopted in dealing with the problem factors. At least two groups of students integrated into their models the environmental aspect of the problem (energy consumption, water pollution) and further refined their models. Results indicate that engineering model-eliciting activities can be introduced effectively into the elementary curriculum, providing rich opportunities for students to deal with engineering contexts and to apply their learning in mathematics and science to solving real-world engineering problems.

Modeling as a bridge between real world problems and school mathematics

This article argues for an interdisciplinary approach to mathematical problem solving at the elementary school, one that draws upon the engineering domain. A modeling approach, using engineering model eliciting activities, might provide a rich source of meaningful situations that capitalize on and extend students’ existing mathematical learning. The study reports on the developments of 48 twelve-year old students who worked on the Bridge Design activity. Results revealed that young students, even before formal instruction, have the capacity to deal with complex interdisciplinary problems. A number of students created quite appropriate models by developing the necessary mathematical constructs to solve the problem. Students’ difficulties in mathematizing the problem, and in revising and documenting their models are presented and analysed, followed by a discussion on the appropriateness of a modeling approach as a means for introducing complex problems to elementary school students.

Integrated Acquisition Engineering Model for acquiring heavy engineering assets

In asset intensive industries such as mining, oil & gas, utilities etc. most of the capital expenditure happens on acquiring engineering assets. Process of acquiring assets is called as “Procurement” or “Acquisition”. An asset procurement decision should be taken in consideration with the installation, commissioning, operational, maintenance and disposal needs of an asset or spare. However, such cross-functional collaboration and communication does not appear to happen between engineering, maintenance, warehousing and procurement functions in many asset intensive industries. Acquisition planning and execution are two distinct parts of asset acquisition process. Acquisition planning or procurement planning is responsible for determining exactly what is required to be purchased. It is important that an asset acquisition decision is the result of cross-functional decision making process. An acquisition decision leads to a formal purchase order. Most costly asset decisions occur even before they are acquired. Therefore, acquisition decision should be an outcome of an integrated planning & decision making process. Asset intensive organizations both, Government and non Government in Australia spent AUD 102.5 Billion on asset acquisition in year 2008-09. There is widespread evidence of many assets and spare not being used or utilized and in the end are written off. This clearly shows that many organizations end up buying assets or spares which were not required or non-conforming to the needs of user functions. It is due the fact that strategic and software driven procurement process do not consider all the requirements from various functions within the organization which contribute to the operation and maintenance of the asset over its life cycle. There is a lot of research done on how to implement an effective procurement process. There are numerous software solutions available for executing a procurement process. However, not much research is done on how to arrive at a cross functional procurement planning process. It is also important to link procurement planning process to procurement execution process. This research will discuss ““Acquisition Engineering Model” (AEM) framework, which aims at assisting acquisition decision making based on various criteria to satisfy cross-functional organizational requirements. Acquisition Engineering Model (AEM) will consider inputs from corporate asset management strategy, production management, maintenance management, warehousing, finance and HSE. Therefore, it is essential that the multi-criteria driven acquisition planning process is carried out and its output is fed to the asset acquisition (procurement execution) process. An effective procurement decision making framework to perform acquisition planning which considers various functional criteria will be discussed in this paper.

A decision support framework for prioritization of engineering asset management activities under uncertainty

Engineers and asset managers must often make decisions on how to best allocate limited resources amongst different interrelated activities, including repair, renewal, inspection, and procurement of new assets. The presence of project interdependencies and the lack of sufficient information on the true value of an activity often produce complex problems and leave the decision maker guessing about the quality and robustness of their decision. In this paper, a decision support framework for uncertain interrelated activities is presented. The framework employs a methodology for multi-criteria ranking in the presence of uncertainty, detailing the effect that uncertain valuations may have on the priority of a particular activity. The framework employs employing semi-quantitative risk measures that can be tailored to an organisation and enable a transparent and simple-to-use uncertainty specification by the decision maker. The framework is then demonstrated on a real world project set from a major Australian utility provider.

Surviving an avalanche of data

Open the sports or business section of your daily newspaper, and you are immediately bombarded with an array of graphs, tables, diagrams, and statistical reports that require interpretation. Across all walks of life, the need to understand statistics is fundamental. Given that our youngsters’ future world will be increasingly data laden, scaffolding their statistical understanding and reasoning is imperative, from the early grades on. The National Council of Teachers of Mathematics (NCTM) continues to emphasize the importance of early statistical learning; data analysis and probability was the Council’s professional development “Focus of the Year” for 2007–2008. We need such a focus, especially given the results of the statistics items from the 2003 NAEP. As Shaughnessy (2007) noted, students’ performance was weak on more complex items involving interpretation or application of items of information in graphs and tables. Furthermore, little or no gains were made between the 2000 NAEP and the 2003 NAEP studies. One approach I have taken to promote young children’s statistical reasoning is through data modeling. Having implemented in grades 3 –9 a number of model-eliciting activities involving working with data (e.g., English 2010), I observed how competently children could create their own mathematical ideas and representations—before being instructed how to do so. I thus wished to introduce data-modeling activities to younger children, confi dent that they would likewise generate their own mathematics. I recently implemented data-modeling activities in a cohort of three first-grade classrooms of six year- olds. I report on some of the children’s responses and discuss the components of data modeling the children engaged in.

Spatial stimulus : Model making in the architectural design studio

This action research examines the enhancement of visual communication within the architectural design studio through physical model making. „It is through physical model making that designers explore their conceptual ideas and develop the creation and understanding of space,‟ (Salama & Wilkinson 2007:126). This research supplements Crowther‟s findings extending the understanding of visual dialogue to include physical models. „Architecture Design 8‟ is the final core design unit at QUT in the fourth year of the Bachelor of Design Architecture. At this stage it is essential that students have the ability to communicate their ideas in a comprehensive manner, relying on a combination of skill sets including drawing, physical model making, and computer modeling. Observations within this research indicates that students did not integrate the combination of the skill sets in the design process through the first half of the semester by focusing primarily on drawing and computer modeling. The challenge was to promote deeper learning through physical model making. This research addresses one of the primary reasons for the lack of physical model making, which was the limited assessment emphasis on the physical models. The unit was modified midway through the semester to better correlate the lecture theory with studio activities by incorporating a series of model making exercises conducted during the studio time. The outcome of each exercise was assessed. Tutors were surveyed regarding the model making activities and a focus group was conducted to obtain formal feedback from students. Students and tutors recognised the added value in communicating design ideas through physical forms and model making. The studio environment was invigorated by the enhanced learning outcomes of the students who participated in the model making exercises. The conclusions of this research will guide the structure of the upcoming iteration of the fourth year design unit.

Complex modelling in the primary/middle school years

The world’s increasing complexity, competitiveness, interconnectivity, and dependence on technology generate new challenges for nations and individuals that cannot be met by continuing education as usual (Katehi, Pearson, & Feder, 2009). With the proliferation of complex systems have come new technologies for communication, collaboration, and conceptualisation. These technologies have led to significant changes in the forms of mathematical and scientific thinking that are required beyond the classroom. Modelling, in its various forms, can develop and broaden children’s mathematical and scientific thinking beyond the standard curriculum. This paper first considers future competencies in the mathematical sciences within an increasingly complex world. Next, consideration is given to interdisciplinary problem solving and models and modelling. Examples of complex, interdisciplinary modelling activities across grades are presented, with data modelling in 1st grade, model-eliciting in 4th grade, and engineering-based modelling in 7th-9th grades.

An endogenously deposited fibrin scaffold determines construct size in the surgically created arteriovenous loop chamber model of tissue engineering

Background: An arteriovenous loop (AVL) enclosed in a polycarbonate chamber in vivo, produces a fibrin exudate which acts as a provisional matrix for the development of a tissue engineered microcirculatory network. Objectives: By administering enoxaparin sodium - an inhibitor of fibrin polymerization, the significance of fibrin scaffold formation on AVL construct size (including the AVL, fibrin scaffold, and new tissue growth into the fibrin), growth, and vascularization were assessed and compared to controls. Methods: In Sprague Dawley rats, an AVL was created on femoral vessels and inserted into a polycarbonate chamber in the groin in 3 control groups (Series I) and 3 experimental groups (Series II). Two hours before surgery and 6 hours post-surgery, saline (Series I) or enoxaparin sodium (0.6 mg/kg, Series II) was administered intra-peritoneally. Thereafter, the rats were injected daily with saline (Series I) or enoxaparin sodium (1.5 mg/kg, Series II) until construct retrieval at 3, 10, or 21 days. The retrieved constructs underwent weight and volume measurements, and morphologic/morphometric analysis of new tissue components. Results: Enoxaparin sodium treatment resulted in the development of smaller AVL constructs at 3, 10, and 21 days. Construct weight and volume were significantly reduced at 10 days (control weight 0.337 ± 0.016 g [Mean ± SEM] vs treated 0.228 ± 0.048, [P < .001]: control volume 0.317 ± 0.015 mL vs treated 0.184 ± 0.039 mL [P < .01]) and 21 days (control weight 0.306 ± 0.053 g vs treated 0.198 ± 0.043 g [P < .01]: control volume 0.285 ± 0.047 mL vs treated 0.148 ± 0.041 mL, [P < .01]). Angiogenesis was delayed in the enoxaparin sodium-treated constructs with the absolute vascular volume significantly decreased at 10 days (control vascular volume 0.029 ± 0.03 mL vs treated 0.012 ± 0.002 mL [P < .05]). Conclusion: In this in vivo tissue engineering model, endogenous, extra-vascularly deposited fibrin volume determines construct size and vascular growth in the first 3 weeks and is, therefore, critical to full construct development.

Eliciting and encoding expert knowledge on variable selection into classical or Bayesian species distribution models

The quality of species distribution models (SDMs) relies to a large degree on the quality of the input data, from bioclimatic indices to environmental and habitat descriptors (Austin, 2002). Recent reviews of SDM techniques, have sought to optimize predictive performance e.g. Elith et al., 2006. In general SDMs employ one of three approaches to variable selection. The simplest approach relies on the expert to select the variables, as in environmental niche models Nix, 1986 or a generalized linear model without variable selection (Miller and Franklin, 2002). A second approach explicitly incorporates variable selection into model fitting, which allows examination of particular combinations of variables. Examples include generalized linear or additive models with variable selection (Hastie et al. 2002); or classification trees with complexity or model based pruning (Breiman et al., 1984, Zeileis, 2008). A third approach uses model averaging, to summarize the overall contribution of a variable, without considering particular combinations. Examples include neural networks, boosted or bagged regression trees and Maximum Entropy as compared in Elith et al. 2006. Typically, users of SDMs will either consider a small number of variable sets, via the first approach, or else supply all of the candidate variables (often numbering more than a hundred) to the second or third approaches. Bayesian SDMs exist, with several methods for eliciting and encoding priors on model parameters (see review in Low Choy et al. 2010). However few methods have been published for informative variable selection; one example is Bayesian trees (O’Leary 2008). Here we report an elicitation protocol that helps makes explicit a priori expert judgements on the quality of candidate variables. This protocol can be flexibly applied to any of the three approaches to variable selection, described above, Bayesian or otherwise. We demonstrate how this information can be obtained then used to guide variable selection in classical or machine learning SDMs, or to define priors within Bayesian SDMs.

Concurrent multi-scale modeling of civil infrastructures for analyses on structural deteriorating—Part II : Model updating and verification

This paper is a continuation of the paper titled “Concurrent multi-scale modeling of civil infrastructure for analyses on structural deteriorating—Part I: Modeling methodology and strategy” with the emphasis on model updating and verification for the developed concurrent multi-scale model. The sensitivity-based parameter updating method was applied and some important issues such as selection of reference data and model parameters, and model updating procedures on the multi-scale model were investigated based on the sensitivity analysis of the selected model parameters. The experimental modal data as well as static response in terms of component nominal stresses and hot-spot stresses at the concerned locations were used for dynamic response- and static response-oriented model updating, respectively. The updated multi-scale model was further verified to act as the baseline model which is assumed to be finite-element model closest to the real situation of the structure available for the subsequent arbitrary numerical simulation. The comparison of dynamic and static responses between the calculated results by the final model and measured data indicated the updating and verification methods applied in this paper are reliable and accurate for the multi-scale model of frame-like structure. The general procedures of multi-scale model updating and verification were finally proposed for nonlinear physical-based modeling of large civil infrastructure, and it was applied to the model verification of a long-span bridge as an actual engineering practice of the proposed procedures.