Integrating engineering education in the middle school mathematics curriculum

Many nations are experiencing a decline in the number of graduating engineers, an overall poor preparedness for engineering studies in tertiary institutions, and a lack of diversity in the field. Given the increasing importance of mathematics, science, engineering, and technology in our world, it is imperative that we foster an interest and drive to participate in engineering from an early age. This discuission paper argues for the intergration of engineering education within the elementary and middle school mathematics curricula. In doing so, we offer a definition of engineering education and address its core goals; consider some perceptions of engineering and engineering education held by teachers and students; and offer one approach to promoting engineering education within the elementary and middle school mathematics curriculum, namely through mathematical modeling.

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.

Theory and its role in mathematics education

The increased recognition of the theory in mathematics education is evident in numerous handbooks, journal articles, and other publications. For example, Silver and Herbst (2007) examined ―Theory in Mathematics Education Scholarship‖ in the Second Handbook of Research on Mathematics Teaching and Learning (Lester, 2007) while Cobb (2007) addressed ―Putting Philosophy to Work: Coping with Multiple Theoretical Perspectives‖ in the same handbook. And a central component of both the first and second editions of the Handbook of International Research in Mathematics Education (English, 2002; 2008) was ―advances in theory development.‖ Needless to say, the comprehensive second edition of the Handbook of Educational Psychology (Alexander & Winne, 2006) abounds with analyses of theoretical developments across a variety of disciplines and contexts. Numerous definitions of ―theory‖ appear in the literature (e.g., see Silver & Herbst, in Lester, 2007). It is not our intention to provide a ―one-size-fits-all‖ definition of theory per se as applied to our discipline; rather we consider multiple perspectives on theory and its many roles in improving the teaching and learning of mathematics in varied contexts.

Kava Anxiety Depression Spectrum Study (KADSS): a mixed methods RCT using an aqueous extract of Piper methysticum

Objectives: To report on the design, significance and potential impacts of the first documented human clinical trial assessing the anxiolytic and thymoleptic efficacy of an aqueous monoextract of Piper methysticum (kava). The significance of the qualitative element of our clinical trial is also explored. The Kava Anxiety Depression Spectrum Study (KADSS) is a 3-week placebocontrolled, double-blind, cross-over trial involving 60 adult participants (18—65) with elevated stable anxiety and varying levels of depressive symptoms. Aims: The aims of KADSS are: (1) to determine whether an aqueous standardised extract of kava is effective for the treatment of anxiety; (2) to assess the effects of kava on differing levels of depression; and (3) to explore participants’ experience of taking kava via qualitative research. The study also provides preliminary assessment of the safety of an aqueous extract of kava in humans. Conclusion: If results reveal that the aqueous kava preparation exerts significant anxiolytic effects and appears safe, potentially beneficial impacts may occur. Data supporting a safe and effective kava extract may encourage a re-introduction of kava to Europe, UK and Canada. This may provide a major socioeconomic benefit to Pacific Island nations, and to sufferers of anxiety disorders.

Recognising and respecting Torres Strait Islander mathematics knowledges and home languages through mainstream mathematics education [Abstract]

This abstract provides a preliminary discussion of the importance of recognising Torres Strait Islander knowledges and home languages of mathematics education. It stems from a project involving Torres Strait Islander Teachers and Teacher Aides and university based researchers who are working together to enhance the mathematics learning of students from Years 4-9. A key focus of the project is that mathematics is relevant and provides students with opportunities for further education, training and employment. Veronica Arbon (2008) questions the assumptions underpinning Western mainstream education as beneficial for Aboriginal and Torres Strait Islander people which assumes that it enables them to better participate in Australian society. She asks “how de we best achieve outcomes for and with Indigenous people conducive to our cultural, physical and economic sustainability as defined by us from Indigenous knowledge positions?” (p. 118). How does a mainstream education written to English conventions provide students with the knowledge and skills to participate in daily life, if it does not recognise the cultural identity of Indigenous students as it should (Priest, 2005; cf. Schnukal, 2003)? Arbon (2008) states that this view is now brought into question with calls for both ways education where mainstream knowledge and practices is blended with Indigenous cultural knowledges of learning. This project considers as crucial that cultural knowledges and experiences of Indigenous people to be valued and respected and given the currency in the same way that non Indigenous knowledge is (Taylor, 2003) for both ways education to work.

Torres Strait Island parents' involvement in their children's mathematics learning : a discussion paper

This paper is a beginning point for discussing what the literature states about parents’ involvement in their children’s mathematics education. Where possible it will focus on Torres Strait Islander Peoples. Little is known about how Torres Strait Islander parents approach their children’s learning of mathematics and how important early mathematics is to mothers. What is known is that is they are keen for their children to receive an education that provides them with opportunities for their present and future lives. However, gaining access to education is challenging given that the language of instruction in schools is written to English conventions, decontextualised and disconnected from the students’ culture, community and home language. This paper discusses some of the issues raised in the literature about what parents are confronted with when making decisions about their children’s education.

Integrating engineering education within the elementary and middle school mathematics curriculum

Many nations are experiencing a decline in the number of graduating engineers, an overall poor preparedness for engineering studies in tertiary institutions, and a lack of diversity in the field. Given the increasing importance of mathematics, science, engineering, and technology in our world, it is imperative that we foster an interest and drive to participate in engineering from an early age. This discussion paper argues for the integration of engineering education within the elementary and middle school mathematics curricula. In doing so, we offer a definition of engineering education and address its core goals; consider some perceptions of engineering and engineering education held by teachers and students; and offer one approach to promoting engineering education within the elementary and middle school mathematics curriculum, namely through mathematical modeling.

The use of income valuation methods to value rural property

Despite the advances that have been made in relation to the valuation of commercial, industrial and retail property, there has not been the same progress in relation to the valuation of rural property. Although the majority of rural property valuations also require the valuer to carry out a full analysis of the economic performance of the farming operations, this information is rarely used to assess the value of the property, nor is it even used for a secondary valuation method. Over the past 20 years the nature of rural valuation practice has required rural valuers to undertake studies in both agriculture (farm management) and valuation, especially if carrying out valuation work for financial institutions. The additional farm financial information obtained by rural valuers exceeds that level of information required to value commercial, retail and industrial by the capitalisation of net rent/profit valuation method and is very similar to the level of information required for the valuation of commercial and retail property by the Discounted Cash Flow valuation method. On this basis the valuers specialising in rural valuation practice should have the necessary skills and information to value rural properties by an income valuation method. Although the direct comparison method of valuation has been sufficient in the past to value rural properties the future use of the method as the main valuation method is limited and valuers need to adopt an income valuation method as at least a secondary valuation method to overcome the problems associated with the use of direct comparison as the only rural property valuation method. This paper will review the results of an extensive survey carried out by rural property valuers in New South Wales (NSW), Australia, in relation to the impact of farm management on rural property values and rural property income potential.

Virtual reality or virtually real : blended teaching and learning in a Master's level research methods class

This paper examines the enabling effect of using blended learning and synchronous internet mediated communication technologies to improve learning and develop a Sense of Community (SOC) in a group of post-graduate students consisting of a mix of on-campus and off-campus students. Both quantitative and qualitative data collected over a number of years supports the assertion that the blended learning environment enhanced both teaching and learning. The development of a SOC was pivotal to the success of the blended approach when working with geographically isolated groups within a single learning environment.

The role of fluency in a mathematics item with an embedded graphic: Interpreting a pie chart.

The purpose of this study was to identify the pedagogical knowledge relevant to the successful completion of a pie chart item. This purpose was achieved through the identification of the essential fluencies that 12–13-year-olds required for the successful solution of a pie chart item. Fluency relates to ease of solution and is particularly important in mathematics because it impacts on performance. Although the majority of students were successful on this multiple choice item, there was considerable divergence in the strategies they employed. Approximately two-thirds of the students employed efficient multiplicative strategies, which recognised and capitalised on the pie chart as a proportional representation. In contrast, the remaining one-third of students used a less efficient additive strategy that failed to capitalise on the representation of the pie chart. The results of our investigation of students’ performance on the pie chart item during individual interviews revealed that five distinct fluencies were involved in the solution process: conceptual (understanding the question), linguistic (keywords), retrieval (strategy selection), perceptual (orientation of a segment of the pie chart) and graphical (recognising the pie chart as a proportional representation). In addition, some students exhibited mild disfluencies corresponding to the five fluencies identified above. Three major outcomes emerged from the study. First, a model of knowledge of content and students for pie charts was developed. This model can be used to inform instruction about the pie chart and guide strategic support for students. Second, perceptual and graphical fluency were identified as two aspects of the curriculum, which should receive a greater emphasis in the primary years, due to their importance in interpreting pie charts. Finally, a working definition of fluency in mathematics was derived from students’ responses to the pie chart item.

Teaching and learning science and mathematics through technology practice

In this chapter we review studies of the engagement of students in design projects that emphasise integration of technology practice and the enabling sciences, which include physics and mathematics. We give special attention to affective and conceptual outcomes from innovative interventions of design projects. This is important work because of growing international concern that demand for professionals with technological expertise is increasing rapidly, while the supply of students willing to undertake the rigors of study in the enabling sciences is proportionally reducing (e.g., Barringtion, 2006; Hannover & Kessels, 2004; Yurtseven, 2002). The net effect is that the shortage in qualified workers is having a detrimental effect upon economic and social potential in Westernised countries (e.g., Department of Education, Science and Training [DEST], 2003; National Numeracy Review Panel and National Numeracy Review Secretarial, 2007; Yurtseven, 2002). Interestingly, this trend is reversed in developing economies including China and India (Anderson & Gilbride, 2003).

Comparison of methods for processing drinking water samples for the isolation of Myocbacterium avium and intracellulare

Several protocols for isolation of mycobacteria from water exist, but there is no established standard method. This study compared methods of processing potable water samples for the isolation of Mycobacterium avium and Mycobacterium intracellulare using spiked sterilized water and tap water decontaminated using 0.005% cetylpyridinium chloride (CPC). Samples were concentrated by centrifugation or filtration and inoculated onto Middlebrook 7H10 and 7H11 plates and Lowenstein-Jensen slants and into mycobacterial growth indicator tubes with or without polymyxin, azlocillin, nalidixic acid, trimethoprim, and amphotericin B. The solid media were incubated at 32°C, at 35°C, and at 35°C with CO2 and read weekly. The results suggest that filtration of water for the isolation of mycobacteria is a more sensitive method for concentration than centrifugation. The addition of sodium thiosulfate may not be necessary and may reduce the yield. Middlebrook M7H10 and 7H11 were equally sensitive culture media. CPC decontamination, while effective for reducing growth of contaminants, also significantly reduces mycobacterial numbers. There was no difference at 3 weeks between the different incubation temperatures.

A Numerical Solution Using an Adaptively Preconditioned Lanczos Method for a Class of Linear Systems Related with the Fractional Poisson Equation

This study considers the solution of a class of linear systems related with the fractional Poisson equation (FPE) (−∇2)α/2φ=g(x,y) with nonhomogeneous boundary conditions on a bounded domain. A numerical approximation to FPE is derived using a matrix representation of the Laplacian to generate a linear system of equations with its matrix A raised to the fractional power α/2. The solution of the linear system then requires the action of the matrix function f(A)=A−α/2 on a vector b. For large, sparse, and symmetric positive definite matrices, the Lanczos approximation generates f(A)b≈β0Vmf(Tm)e1. This method works well when both the analytic grade of A with respect to b and the residual for the linear system are sufficiently small. Memory constraints often require restarting the Lanczos decomposition; however this is not straightforward in the context of matrix function approximation. In this paper, we use the idea of thick-restart and adaptive preconditioning for solving linear systems to improve convergence of the Lanczos approximation. We give an error bound for the new method and illustrate its role in solving FPE. Numerical results are provided to gauge the performance of the proposed method relative to exact analytic solutions.

Inducing shades of meaning by matrix methods : a first step towards thematic analysis of opinion

This article explores two matrix methods to induce the ``shades of meaning" (SoM) of a word. A matrix representation of a word is computed from a corpus of traces based on the given word. Non-negative Matrix Factorisation (NMF) and Singular Value Decomposition (SVD) compute a set of vectors corresponding to a potential shade of meaning. The two methods were evaluated based on loss of conditional entropy with respect to two sets of manually tagged data. One set reflects concepts generally appearing in text, and the second set comprises words used for investigations into word sense disambiguation. Results show that for NMF consistently outperforms SVD for inducing both SoM of general concepts as well as word senses. The problem of inducing the shades of meaning of a word is more subtle than that of word sense induction and hence relevant to thematic analysis of opinion where nuances of opinion can arise.