Mathematical thinking of preschool children in rural and regional Australia : research and practice

At what age do young children begin thinking mathematically? Can young children work on mathematical problems? How do early childhood educators ensure young children feel good about mathematics? Where do early childhood educators learn about suitable mathematics activities?

A good early childhood start in mathematics is critical for later mathematics success. Parents, carers and early childhood educators are teaching mathematics, either consciously or unconsciously, in any social interaction with a child.

Mathematical Thinking of Preschool Children in Rural and Regional Australia is an extension of a conference of Australian and New Zealand researchers that identified a number of important problems related to the mathematical learning of children prior to formal schooling. A project team of 11 researchers from top Australian universities sought to investigate how early childhood education can best have a positive influence on early mathematics learning.

The investigation complements and extends the work of Project Good Start by focusing attention on critical aspects of parents, carers and early childhood educators who care for young children. Early childhood educators from regional and rural New South Wales, Queensland and Victoria were interviewed, following a set of structured questions. The questions focused on: children’s mathematics learning; support for mathematics teaching; use of technology; attitudes to mathematics; and assessment and record keeping.

The researchers also reviewed research focusing on the mathematical capacities and potential foundations for further mathematical development in young children (0–5 years) published in the last decade and produced an annotated bibliography. This should provide a good basis for further research and reading.

Based upon the results of this investigation, the researchers make 11 recommendations for improving the practices of early childhood education centres in relation to young children’s mathematical thinking and development. The implications for policy and decision makers are outlined for teacher education, the provision of resources and further research.

Assessment of mathematical development in early childhood : some views of preschool practitioners in regional and rural Australia

As part of the project Mathematical Thinking of Preschool Children in Rural and Regional Australia: Research and Practice directors, teachers, and assistants in prior-to-school settings from regional and rural eastern Australia were interviewed to ascertain their beliefs and practices concerning early childhood mathematics. This paper reports the responses to  uestions about their assessment of children’s mathematical activity and development. The practitioners provided examples of both incidental and planned assessment activities, the different forms these took, methods of recording, and how the results were used.

Shaping practice: worksheets as social artefacts

Part of a broader research project on the development of mathematical understanding in primary classrooms, the research reported in this paper focused on how opportunities to learn about percentage in two classrooms were shaped by worksheets. The words in the text, the way that the teachers replicated these orally, a grid used to illustrate the concept of percentage, the genre of both mathematical and non-mathematical aspects of the worksheet's presentation, and the calculation methods presented were all potentially influential aspects. It is argued that the "knowledge" conveyed by the texts of the worksheets was distributed over a much wider field than the classrooms involved.

Longitudinal examination of the family food environment and weight status among children

Objective. To examine whether aspects of the family food environment were associated with body mass index (BMI) z-score and weight status in children, cross-sectionally and prospectively over 3 years.

Methods. Four aspects of the family food environment (breakfast eating patterns, food consumption while watching television, parental provision of energy-dense foods and child consumption of energy-dense food at home and away from home) were assessed with a questionnaire completed by parents of 161 children aged 5-6 years and 132 children aged 10-12 years in Melbourne, Australia in 2002/03. In 2002/03 and 2006, children's BMI z-score and weight status (non-overweight or overweight) was calculated from measured height and weight. Results. At baseline, 19% of younger and 21% of older children were overweight. Three years later, a greater proportion of younger (now aged 8-9 years) compared with older (aged 13-15 years) children were classified as overweight (28% versus 18%). Few of the family food environment variables were associated with children's BMI z-score and weight status cross-sectionally and longitudinally. However, among older children, more frequent dinner consumption while watching television was associated with a higher BMI z-score longitudinally (B = 0.3, 95% CI = 0.0, 0.6), less frequent breakfast consumption was associated with higher odds of overweight longitudinally (OR = 2.2, 95% CI = 1.1-4.7), and more frequent fast food consumption at home was associated with higher odds of overweight cross-sectionally (OR = 3.1, 95% CI = 1.4-7.0).

Conclusions. This study found few significant associations between aspects of the family food environment and BMI z-score or weight status in a sample of Australian children.

Estimates of Heterozostera tasmanica, Zostera muelleri and Ruppia megacarpa distribution and biomass in the Hopkins Estuary, western Victoria, by GIS

Knowledge of the spatial arrangement of the seagrass distribution and biomass within the Hopkins Estuary is an essential step towards gaining an understanding of the functioning of the estuarine ecosystem. This study marks the first attempt to map seagrass distribution and model seagrass biomass and epiphyte biomass along depth gradients by the use of global positioning system (GPS) and geographical information system (GIS) technologies in the estuary. For mapping seagrass in small estuaries, ground-surveying the entire system is feasible. Three species of seagrasses, Heterozostera tasmanica (Martens ex Aschers), Zostera muelleri (Irmisch ex Aschers) and Ruppia megacarpa (Mason), were identified in the Hopkins Estuary. All beds investigated contained a mixed species relationship. Three harvest techniques were trialed in a pilot study, with the 25 × 25-cm quadrat statistically most appropriate. Biomass of seagrasses and epiphytes was found to vary significantly with depth, but not between sites. The average estimate of biomass for total seagrasses and their epiphytes in the estuary in January 2000 was 222.7 g m^–2 (dry weight). Of the total biomass, 50.6% or 112.7 g m^–2 (dry weight) was contributed by seagrasses and 49.4% of the biomass (110.0 g m^–2) were epiphytes. Of the 50.6% of the total biomass represented by seagrasses, 39.3% (87.5 g m^–2) were leaves and 11.3% (25.2 g m^–2) were rhizomes. The total area of seagrasses present in the Hopkins Estuary was estimated to be 0.4 ± 0.005 km², with the total area of the estuary estimated to be 1.6 ± 0.02 km² (25% cover). The total standing crop of seagrasses and epiphytes in the Hopkins Estuary in January 2000 was estimated to be 102.3 ± 57 t in dry weight, 56% (56.9 ± 17 t, dry weight) seagrasses and 44% (45.4 ± 19 t, dry weight) epiphytes. Of the seagrass biomass, 39% (39.7 ± 13 t, dry weight) was contributed by leaves and 17% (17.3 ± 7 t, dry weight) by rhizomes.

Computational aspects of the numerical solution of SDEs

In the last 30 to 40 years, many researchers have combined to build the knowledge base of theory and solution techniques that can be applied to the case of differential equations which include the effects of noise. This class of ``noisy'' differential equations is now known as stochastic differential equations (SDEs). Markov diffusion processes are included within the field of SDEs through the drift and diffusion components of the Itô form of an SDE. When these drift and diffusion components are moderately smooth functions, then the processes' transition probability densities satisfy the Fokker-Planck-Kolmogorov (FPK) equation -- an ordinary partial differential equation (PDE). Thus there is a mathematical inter-relationship that allows solutions of SDEs to be determined from the solution of a noise free differential equation which has been extensively studied since the 1920s. The main numerical solution technique employed to solve the FPK equation is the classical Finite Element Method (FEM). The FEM is of particular importance to engineers when used to solve FPK systems that describe noisy oscillators. The FEM is a powerful tool but is limited in that it is cumbersome when applied to multidimensional systems and can lead to large and complex matrix systems with their inherent solution and storage problems. I show in this thesis that the stochastic Taylor series (TS) based time discretisation approach to the solution of SDEs is an efficient and accurate technique that provides transition and steady state solutions to the associated FPK equation. The TS approach to the solution of SDEs has certain advantages over the classical techniques. These advantages include their ability to effectively tackle stiff systems, their simplicity of derivation and their ease of implementation and re-use. Unlike the FEM approach, which is difficult to apply in even only two dimensions, the simplicity of the TS approach is independant of the dimension of the system under investigation. Their main disadvantage, that of requiring a large number of simulations and the associated CPU requirements, is countered by their underlying structure which makes them perfectly suited for use on the now prevalent parallel or distributed processing systems. In summary, l will compare the TS solution of SDEs to the solution of the associated FPK equations using the classical FEM technique. One, two and three dimensional FPK systems that describe noisy oscillators have been chosen for the analysis. As higher dimensional FPK systems are rarely mentioned in the literature, the TS approach will be extended to essentially infinite dimensional systems through the solution of stochastic PDEs. In making these comparisons, the advantages of modern computing tools such as computer algebra systems and simulation software, when used as an adjunct to the solution of SDEs or their associated FPK equations, are demonstrated.

Mathematical modelling of linear motion error for Hexarot parallel manipulators

Hexarot is a robotic manipulator that belongs to the family of axis symmetric parallel mechanisms. The robot is able to move the robot platform or tool center point in six degrees of freedom (DOF). This paper presents the kinematics model of the robot including the inverse and forward kinematics, and its time derivatives. Then using the kinematics formulations, investigation of the nonlinear motion of the Hexarot robot for a desired linear motion path is performed. For this purpose, the concept of curvature of the robot path is used for measuring the nonlinearity of the actual motion of the robot. The nonlinear motion error of the robot is analyzed for the scenario where the platform moves on a linear path between two arbitrary points of the robot workspace. The effects of different parameters on the nonlinear motion error of the mechanism are demonstrated and strategies for motions with low error values are proposed.

Combinatorial aspects of jump codes

We develop an approach to jump codes concentrating on their combinatorial and symmetry properties. The main result is a generalization of a theorem previously proved in the context of isodual codes. We show that several previously constructed jump codes are instances of this theorem.

An investigation of middle secondary students' mathematical conceptions of rate

This study identified four educationally critical aspects of ‘rate’ through analysis of phenomenographic, video-recorded interviews with Year 10 students. Further analysis indicated understandings in one representation or context were not necessarily transferable.

Neuromuscular mechanics and hopping training in elderly

Purpose: The present study examined the effects of repetitive hopping training on muscle activation profiles and fascicle–tendon interaction in the elderly.Methods: 20 physically active elderly men were randomly assigned for training (TG) and control groups (CG). TG performed supervised bilateral short contact hopping training with progressively increasing training volume. Measurements were performed before the training period (BEF) as well as after 2 weeks (2 W) and 11 weeks (11 W) of training. During measurements, the gastrocnemius medialis–muscle (GaM) fascicle and its outer Achilles tendon length changes during hopping were examined by ultrasonography together with electromyographic (EMG) activities of calf muscles, kinematics, and kinetics.Results: At 2 W, the ankle joint stiffness was increased by 21.0 ± 19.3 % and contact time decreased by 9.4 ± 7.8 % in TG. Thereafter, from 2–11 W the jumping height increased 56.2 ± 18.1 % in TG. Simultaneously, tendon forces increased 24.3 ± 19.0 % but tendon stiffness did not change. GaM fascicles shifted to shorter operating lengths after training without any changes in their length modifications during the contact phase of hopping. Normalized EMG amplitudes during hopping did not change with training.Conclusions: The present study shows that 11 W of hopping training improves the performance of physically active elderly men. This improvement is achieved with shorter GaM operating lengths and, therefore, increased fascicle stiffness and improved tendon utilization after training. Based on these results, hopping training could be recommended for healthy fit elderly to retain and improve rapid force production capacity. © 2014 Springer-Verlag Berlin Heidelberg