Investigating the effectiveness of an ecological approach to learning design in a first year mathematics for engineering unit

This paper reports on the results of a project aimed at creating a research-informed, pedagogically reliable, technology-enhanced learning and teaching environment that would foster engagement with learning. A first-year mathematics for engineering unit offered at a large, metropolitan Australian university provides the context for this research. As part of the project, the unit was redesigned using a framework that employed flexible, modular, connected e-learning and teaching experiences. The researchers, interested in an ecological perspective on educational processes, grounded the redesign principles in probabilistic learning design (Kirschner et al., 2004). The effectiveness of the redesigned environment was assessed through the lens of the notion of affordance (Gibson, 1977,1979, Greeno, 1994, Good, 2007). A qualitative analysis of the questionnaire distributed to students at the end of the teaching period provided insight into factors impacting on the successful creation of an environment that encourages complex, multidimensional and multilayered interactions conducive to learning.

An algorithm for constructing Hjelmslev planes

Projective Hjelmslev planes and affine Hjelmslev planes are generalisations of projective planes and affine planes. We present an algorithm for constructing projective Hjelmslev planes and affine Hjelmslev planes that uses projective planes, affine planes and orthogonal arrays. We show that all 2-uniform projective Hjelmslev planes, and all 2-uniform affine Hjelmslev planes can be constructed in this way. As a corollary it is shown that all $2$-uniform affine Hjelmslev planes are sub-geometries of $2$-uniform projective Hjelmslev planes.

Changing agendas in international research in mathematics education

Handbooks serve an important function for our research community in providing state-of-the-art summations, critiques, and extensions of existing trends in research. In the intervening years between the second and third editions of the Handbook of International Research in Mathematics Education, there have been stimulating developments in research, as well as new challenges in translating outcomes into practice. This third edition incorporates a number of new chapters representing areas of growth and challenge, in addition to substantially updated chapters from the second edition. As such, the Handbook addresses five core themes, namely, Priorities in International Mathematics Education Research, Democratic Access to Mathematics Learning, Transformations in Learning Contexts, Advances in Research Methodologies, and Influences of Advanced Technologies...

Problem solving in a 21st century mathematics curriculum

Research on problem solving in the mathematics curriculum has spanned many decades, yielding pendulum-like swings in recommendations on various issues. Ongoing debates concern the effectiveness of teaching general strategies and heuristics, the role of mathematical content (as the means versus the learning goal of problem solving), the role of context, and the proper emphasis on the social and affective dimensions of problem solving (e.g., Lesh & Zawojewski, 2007; Lester, 2013; Lester & Kehle, 2003; Schoenfeld, 1985, 2008; Silver, 1985). Various scholarly perspectives—including cognitive and behavioral science, neuroscience, the discipline of mathematics, educational philosophy, and sociocultural stances—have informed these debates, often generating divergent resolutions. Perhaps due to this uncertainty, educators’ efforts over the years to improve students’ mathematical problem-solving skills have had disappointing results. Qualitative and quantitative studies consistently reveal mathematics students’ struggles to solve problems more significant than routine exercises (OECD, 2014; Boaler, 2009)...

Challenges in embedding numeracy throughout the curriculum in three Queensland secondary schools

The Australian Curriculum identified seven General Capabilities, including numeracy, to be embedded in all learning areas. However, it has been left to individual schools to manage this. Whilst there is a growing body of literature about pedagogies that embed numeracy in various learning areas, there are few studies from the management perspective. A social constructivist perspective and a multiple case study approach were used to explore the actions of school managers and mathematics teachers in three Queensland secondary schools, in order to investigate how they meet the Australian Curriculum requirement to embed numeracy throughout the curriculum. The study found a lack of coordinated cross-curricular approaches to numeracy in any of the schools studied. It illustrates the difficulties that arise when teachers do not share the Australian Curriculum cross-curricular vision of numeracy. Schools and curriculum authorities have not acknowledged the challenges for teachers in implementing cross-curricular numeracy, which include: limited understanding of numeracy; a lack of commitment; and inadequate skills. Successful embedding of numeracy in all learning areas requires: the commitment and support of school leaders, a review of school curriculum documents and pedagogical practices, professional development of teachers, and adequate funding to support these activities.

Ability of commonly used prediction equations to predict resting energy expenditure in children with inflammatory bowel disease

Background: Paediatric onset inflammatory bowel disease (IBD) may cause alterations in energy requirements and invalidate the use of standard prediction equations. Our aim was to evaluate four commonly used prediction equations for resting energy expenditure (REE) in children with IBD. Methods: Sixty-three children had repeated measurements of REE as part of a longitudinal research study yielding a total of 243 measurements. These were compared with predicted REE from Schofield, Oxford, FAO/WHO/UNU, and Harris-Benedict equations using the Bland-Altman method. Results: Mean (±SD) age of the patients was 14.2 (2.4) years. Mean measured REE was 1566 (336) kcal per day compared with 1491 (236), 1441 (255), 1481 (232), and 1435 (212) kcal per day calculated from Schofield, Oxford, FAO/WHO/UNU, and Harris-Benedict, respectively. While the Schofield equation demonstrated the least difference between measured and predicted REE, it, along with the other equations tested, did not perform uniformly across all subjects, indicating greater errors at either end of the spectrum of energy expenditure. Smaller differences were found for all prediction equations for Crohn's disease compared with ulcerative colitis. Conclusions: Of the commonly used equations, the equation of Schofield should be used in pediatric patients with IBD when measured values are not able to be obtained. (Inflamm Bowel Dis 2010;) Copyright © 2010 Crohn's & Colitis Foundation of America, Inc.

The correlation between reading and mathematics ability at age twelve has a substantial genetic component

Dissecting how genetic and environmental influences impact on learning is helpful for maximizing numeracy and literacy. Here we show, using twin and genome-wide analysis, that there is a substantial genetic component to children’s ability in reading and mathematics, and estimate that around one half of the observed correlation in these traits is due to shared genetic effects (so-called Generalist Genes). Thus, our results highlight the potential role of the learning environment in contributing to differences in a child’s cognitive abilities at age twelve.

Shock propagation in gas dynamics: explicit form of higher order compatibility conditions

With the use of tensor analysis and the method of singular surfaces, an infinite system of equations can be derived to study the propagation of curved shocks of arbitrary strength in gas dynamics. The first three of these have been explicitly given here. This system is further reduced to one involving scalars only. The choice of dependent variables in the infinite system is quite important, it leads to coefficients free from singularities for all values of the shock strength.

Unsteady flow and heat transfer between rotating coaxial disks

A study is made on the flow and heat transfer of a viscous fluid confined between two parallel disks. The disks are allowed to rotate with different time dependent angular velocities, and the upper disk is made to approach the lower one with a constant speed. Numerical solutions of the governing parabolic partial differential equations are obtained through a fourth-order accurate compact finite difference scheme. The normal forces and torques that the fluid exerts on the rotating surfaces are obtained at different nondimensional times for different values of the rate of squeezing and disk angular velocities. The temperature distribution and heat transfer are also investigated in the present analysis.

Stochastic differential games with multiple modes

We have studied two person stochastic differential games with multiple modes. For the zero-sum game we have established the existence of optimal strategies for both players. For the nonzero-sum case we have proved the existence of a Nash equilibrium.

Is that all there is? The limitations of global/local, PISA, and the dilemma of transnational curriculum research

Sob o rótulo da globalização, as ciências humanas e sociais têm sido forçadas a rever seu pensamento para encontrar novas maneiras de falar sobre as situações de mudança ao nosso redor e para reorientar-se conceitualmente em um aparente ‘mundo sem fronteiras’. Este artigo analisa algumas dessas formas, sugerindo que a pesquisa em currículo transnacional como tarefa, como talvez inclusiva de algo para além dos estudos curriculares como subárea, tem preocupações, pontos de entrada e horizontes de promulgação amplos, inconstantes, imprevisíveis, que levantam uma série de questões e considerações éticas que exigem maior compromisso nos espaços em que as fronteiras percebidas forem transgredidas no ato da investigação. Usando os relatórios sobre os resultados do PISA como disparador intelectual, este artigo discute quatro questões que surgem no ato investigativo em currículo transnacional: a comparação como princípio de produção de conhecimento; as estratégias de agrupamento onto-teo-filosóficas e a delimitação da ética; o retorno do sujeito centrado, humanista, racional e as críticas a esse sujeito inspirado no Iluminismo; as questões relativas à causalidade, ou seja, como os processos de atribuição são forjados e que tipos de ‘legitimação via procedimento’ operam na crítica social. Em vez de sugerir uma nova ordem, este artigo busca um questionamento mais profundo dos repetitivos pressupostos ocidentalistas.

Approximate Controllability Of Semilinear Systems Using Integral Contractors

In this article, a non-autonomous (time-varying) semilinear system is considered and its approximate controllability is investigated. The notion of 'bounded integral contractor', introduced by Altman, has been exploited to obtain sufficient conditions for approximate controllability. This condition is weaker than Lipschitz condition. The main theorems of Naito [11, 12] are obtained as corollaries of our main results. An example is also given to show how our results weaken the conditions assumed by Sukavanam[17].

Approximate solution of u'=-A2u using a relation between exp(-tA2) and exp(itA)

Let A be a positive definite operator in a Hilbert space and consider the initial value problem for u(t) = -A(2)u. Using a representation of the semigroup exp(-A(2)t) in terms of the group exp(iAt) we express u in terms of the solution of the standard heat equation w(t) = W-yy, with initial values v solving the initial value problem for v(y) = iAv. This representation is used to construct a method for approximating u in terms of approximations of v. In the case that A is a 2(nd) order elliptic operator the method is combined with finite elements in the spatial variable and then reduces the solution of the 4(th) order equation for u to that of the 2(nd) order equation for v, followed by the solution of the heat equation in one space variable.

“I have to rest all the time because you are not allowed to play”: Exploring children’s perceptions of autonomy during sleep-time in long day care services

Daytime sleep is a significant part of the daily routine for children attending early childhood education and care (ECEC) services in Australia and many other countries. The practice of sleep-time can account for a substantial portion of the day in ECEC and often involves a mandated sleep/rest period for all children, including older preschool-aged children. Yet, there is evidence that children have a reduced need for daytime sleep as they approach school entry age and that continuation of mandated sleep-time in ECEC for preschool-aged children may have a negative impact on their health, development, learning and well-being. Mandated sleep-time practices also go against current quality expectations for services to support children’s agency and autonomy in ECEC. This study documents children’s reports of their experiences of sleep-time in ECEC. Semi-structured interviews were conducted with 54 preschool-aged children (44–63 months) across four long day ECEC services that employed a range of sleep-time practices. Findings provide a snapshot of children’s views and experiences of sleep-time and perceptions of autonomy-supportive practices. These provide a unique platform to support critical reflection on sleep-time policies and practices, with a view to continuous quality improvement in ECEC. This study forms part of a programme of work from the Sleep in Early Childhood research group. Our work examines sleep practices in ECEC, the subsequent staff, parent and child experiences and impacts on family and child learning and development outcomes.