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)...

Export of radioactive cesium from agricultural fields under simulated rainfall in Fukushima

In this study, we investigated the impact of rainfall on runoff, soil erosion and consequently on the discharge of radioactive cesium in agricultural fields in Fukushima prefecture using a rainfall simulator. Simulated heavy rainfalls (50 mm h-1) generated significant runoff and soil erosion. The average concentration of radioactive cesium (the sum of 134Cs and 137Cs) in the runoff sediments was [similar]3500 Bq kg-1 dry soil, more than double the concentrations measured in the field soils which should be considered in studies using the 137Cs loss to estimate long-term soil erosion. However, the estimated mass of cesium discharged through one runoff event was less than 2% of the cesium inventory in the field. This suggested that cesium discharge via soil erosion is not a significant factor in reducing the radioactivity of contaminated soils in Fukushima prefecture. However, the eroded sediment carrying radioactive cesium will deposit into the river systems and potentially pose a radioactivity risk for aquatic living organisms.

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.

Design and flight testing of an integrated solar powered UAV and WSN for greenhouse gas monitoring emissions in agricultural farms

There is an increased interest in measuring the amount of greenhouse gases produced by farming practices . This paper describes an integrated solar powered Unmanned Air Vehicles (UAV) and Wireless Sensor Network (WSN) gas sensing system for greenhouse gas emissions in agricultural lands. The system uses a generic gas sensing system for CH4 and CO2 concentrations using metal oxide (MoX) and non-dispersive infrared sensors, and a new solar cell encapsulation method to power the unmanned aerial system (UAS)as well as a data management platform to store, analyze and share the information with operators and external users. The system was successfully field tested at ground and low altitudes, collecting, storing and transmitting data in real time to a central node for analysis and 3D mapping. The system can be used in a wide range of outdoor applications at a relatively low operational cost. In particular, agricultural environments are increasingly subject to emissions mitigation policies. Accurate measurements of CH4 and CO2 with its temporal and spatial variability can provide farm managers key information to plan agricultural practices. A video of the bench and flight test performed can be seen in the following link: https://www.youtube.com/watch?v=Bwas7stYIxQ

Evaluation of a Multispectral Camera on a UAV for Agricultural Applications

Australian farmers have used precision agriculture technology for many years with the use of ground – based and satellite systems. However, these systems require the use of vehicles in order to analyse a wide area which can be time consuming and cost ineffective. Also, satellite imagery may not be accurate for analysis. Low cost of Unmanned Aerial Vehicles (UAV) present an effective method of analysing large plots of agricultural fields. As the UAV can travel over long distances and fly over multiple plots, it allows for more data to be captured by a sampling device such as a multispectral camera and analysed thereafter. This would allow farmers to analyse the health of their crops and thus focus their efforts on certain areas which may need attention. This project evaluates a multispectral camera for use on a UAV for agricultural applications.

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

This is presentation of the refereed paper accepted for the Conferences' proceedings. The presentation was given on Tuesday, 1 December 2015.

Mathematics, programming, and STEM

Learning mathematics is a complex and dynamic process. In this paper, the authors adopt a semiotic framework (Yeh & Nason, 2004) and highlight programming as one of the main aspects of the semiosis or meaning-making for the learning of mathematics. During a 10-week teaching experiment, mathematical meaning-making was enriched when primary students wrote Logo programs to create 3D virtual worlds. The analysis of results found deep learning in mathematics, as well as in technology and engineering areas. This prompted a rethinking about the nature of learning mathematics and a need to employ and examine a more holistic learning approach for the learning in science, technology, engineering, and mathematics (STEM) areas.

Modeling dynamic demand response using Monte Carlo simulation and interval mathematics for boundary estimation

With the rapid development of various technologies and applications in smart grid implementation, demand response has attracted growing research interests because of its potentials in enhancing power grid reliability with reduced system operation costs. This paper presents a new demand response model with elastic economic dispatch in a locational marginal pricing market. It models system economic dispatch as a feedback control process, and introduces a flexible and adjustable load cost as a controlled signal to adjust demand response. Compared with the conventional “one time use” static load dispatch model, this dynamic feedback demand response model may adjust the load to a desired level in a finite number of time steps and a proof of convergence is provided. In addition, Monte Carlo simulation and boundary calculation using interval mathematics are applied for describing uncertainty of end-user's response to an independent system operator's expected dispatch. A numerical analysis based on the modified Pennsylvania-Jersey-Maryland power pool five-bus system is introduced for simulation and the results verify the effectiveness of the proposed model. System operators may use the proposed model to obtain insights in demand response processes for their decision-making regarding system load levels and operation conditions.

Crude oil and agricultural futures: An analysis of correlation dynamics

Correlations between oil and agricultural commodities have varied over previous decades, impacted by renewable fuels policy and turbulent economic conditions. We estimate smooth transition conditional correlation models for 12 agricultural commodities and WTI crude oil. While a structural change in correlations occurred concurrently with the introduction of biofuel policy, oil and food price levels are also key influences. High correlation between biofuel feedstocks and oil is more likely to occur when food and oil price levels are high. Correlation with oil returns is strong for biofuel feedstocks, unlike with other agricultural futures, suggesting limited contagion from energy to food markets.

Science, ICT and Mathematics Education in Rural and Regional Australia: The SiMERR National Survey

The SiMERR National Survey was one of the first priorities of the National Centre of Science, Information and Communication Technology and Mathematics Education for Rural and Regional Australia (SiMERR Australia), established at the University of New England in July 2004 through a federal government grant. With university based ‘hubs’ in each state and territory, SiMERR Australia aims to support rural and regional teachers, students and communities in improving educational outcomes in these subject areas. The purpose of the survey was to identify the key issues affecting these outcomes. The National Survey makes six substantial contributions to our understanding of issues in rural education. First, it focuses specifically on school science, ICT and mathematics education, rather than on education more generally. Second, it compares the different circumstances and needs of teachers across a nationally agreed geographical framework, and quantifies these differences. Third, it compares the circumstances and needs of teachers in schools with different proportions of Indigenous students. Fourth, it provides greater detail than previous studies on the specific needs of schools and teachers in these subject areas. Fifth, the analyses of teacher ‘needs’ have been controlled for the socio-economic background of school locations, resulting in findings that are more tightly associated with geographic location than with economic circumstances. Finally, most previous reports on rural education in Australia were based upon focus interviews, public submissions or secondary analyses of available data. In contrast, the National Survey has generated a sizable body of original quantitative and qualitative data.

Tutoring with higher mathematics and the use of technology

We discuss three approaches to the use of technology as a teaching and learning tool that we are currently implementing for a target group of about one hundred second level engineering mathematics students. Central to these approaches is the underlying theme of motivating relatively poorly motivated students to learn, with the aim of improving learning outcomes. The approaches to be discussed have been used to replace, in part, more traditional mathematics tutorial sessions and lecture presentations. In brief, the first approach involves the application of constructivist thinking in the tertiary education arena, using technology as a computational and visual tool to create motivational knowledge conflicts or crises. The central idea is to model a realistic process of how scientific theory is actually developed, as proposed by Kuhn (1962), in contrast to more standard lecture and tutorial presentations. The second approach involves replacing procedural or algorithmic pencil-and-paper skills-consolidation exercises by software based tasks. Finally, the third approach aims at creating opportunities for higher order thinking via "on-line" exploratory or discovery mode tasks. The latter incorporates the incubation period method, as originally discussed by Rubinstein (1975) and others.

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.

Building teachers' pedagogy practices in reasoning, to improve students' dispositions towards mathematics

Drawing on participatory action research, this study identifies the pedagogies necessary to advance reasoning, which is one of the proficiencies from the Australian Curriculum Mathematics, and explores how reasoning leads to greater productive disposition. With the current emphasis on STEM in schools, this research is timely. This thesis makes an original and substantive contribution to the understanding of why and how teachers can most effectively advance student proficiency in reasoning through targeted instructional strategies and style of instruction. The study explores the ways in which teacher practices, when focused on reasoning, enhance the disposition of students towards greater mathematical proficiency.

Rural first year university students: As engaged, aspirational and motivated as anyone – but different science ‘choices’ in year 12 and university

This paper reports on findings from the Interests and Recruitment in Science study, which explored the experiences of first year students studying science, technology, engineering and mathematics (STEM) courses in Australian universities. First year STEM students who went to school in rural or regional areas were as engaged, aspirational and motivated as their more metropolitan counterparts. However, they were less likely to have studied physics or advance mathematics, and more likely to have enrolled in an Agricultural or Environmental Science degree. The relationships between these results and broader contextual issues such as employment and Higher Education budgetary and policy settings are discussed.