Assessing the potential of mathematics textbooks to promote deep learning

Curriculum documents for mathematics emphasise the importance of promoting depth of knowledge rather than shallow coverage of the curriculum. In this paper, we report on a study that explored the analysis of junior secondary mathematics textbooks to assess their potential to assist in teaching and learning aimed at building and applying deep mathematical knowledge. The method of analysis involved the establishment of a set of specific curriculum goals and associated indicators, based on research into the teaching and learning of a particular field within the mathematics curriculum, namely proportion and proportional reasoning. Topic selection was due to its pervasive nature throughout the school mathematics curriculum at this level. As a result of this study, it was found that the five textbook series examined provided limited support for the development of multiplicative structures required for proportional reasoning, and hence would not serve well the development of deep learning of mathematics. The study demonstrated a method that could be applied to the analysis of junior secondary mathematics in many parts of the world.

Bayesian modelling of surveillance and proof of freedom : the mathematical, logical & psychological challenges

Keeping exotic plant pests out of our country relies on good border control or quarantine. However with increasing globalization and mobilization some things slip through. Then the back up systems become important. This can include an expensive form of surveillance that purposively targets particular pests. A much wider net is provided by general surveillance, which is assimilated into everyday activities, like farmers checking the health of their crops. In fact farmers and even home gardeners have provided a front line warning system for some pests (eg European wasp) that could otherwise have wreaked havoc. Mathematics is used to model how surveillance works in various situations. Within this virtual world we can play with various surveillance and management strategies to "see" how they would work, or how to make them work better. One of our greatest challenges is estimating some of the input parameters : because the pest hasn't been here before, it's hard to predict how well it might behave: establishing, spreading, and what types of symptoms it might express. So we rely on experts to help us with this. This talk will look at the mathematical, psychological and logical challenges of helping experts to quantify what they think. We show how the subjective Bayesian approach is useful for capturing expert uncertainty, ultimately providing a more complete picture of what they think... And what they don't!

Resources for improving journalists' understanding of the economic and financial parameters of Australia's agricultural and commodity producers

The research addresses how an understanding of the fundamentals of economics will better inform general journalists who report on issues or events affecting rural and regional Australia. The research draws on practice-based experience of the author, formal economics studies, interviews with news editors from Australian television news organisations, and interviews from leading economists. A guidebook has also been written to help journalists apply economic theories to their reporting. The guidebook enables reporters to think strategically and consider the 'big picture' when they inform society about policies, commodity trade, the environment, or any issues involving rural and regional Australia.

Data and measurement in Year 4 of the national curriculum : Mathematics

The activities introduced here were used in association with a research project in four Year 4 classrooms and are suggested as a motivating way to address several criteria for Measurement and Data in the Australian Curriculum: Mathematics. The activities involve measuring the arm span of one student in a class many times and then of all students once.

Perspectives on Reconceptualizing Early Mathematics Learning

This introductory section provides an overview of the different perspectives on reconceptualizing early mathematics learning. The chapters provide a broad scope in their topics and approaches to advancing young children’s mathematical learning. They incorporate studies that highlight the importance of pattern and structure across the curriculum, studies that target particular content such as statistics, early algebra, and beginning number, and studies that consider how technology and other tools can facilitate early mathematical development. Reconceptualizing the professional learning of teachers in promoting young children’s mathematics, including a consideration of the role of play, is also addressed. Although these themes are diffused throughout the chapters, we restrict our introduction to the core focus of each of the chapters.

Reconceptualizing Early Mathematics Learning : The Fundamental Role of Pattern and Structure

The Pattern and Structure Mathematics Awareness Program (PASMAP) was developed concurrently with the studies of AMPS and the development of the Pattern and Structure Assessment (PASA) interview. We summarize some early classroom-based teaching studies and describe the PASMAP that resulted. A large-scale two-year longitudinal study, Reconceptualizing Early Mathematics Learning (REML) resulted. We provide an overview of the REML study and discuss the consequences for our view of early mathematics learning. A purposive sample of four large primary schools, two in Sydney and two in Brisbane, representing 316 students from diverse socio-economic and cultural contexts, participated in an evaluation of the PASMAP intervention throughout the 2009 school year and a follow-up assessment in 2010. Two different mathematics programs were implemented: in each school, two Kindergarten teachers implemented the PASMAP and another two implemented their regular program. The study shows that both groups of students made substantial gains on the ‘I Can Do Maths’ standardized assessment and the PASA interview, but highly significant differences were found on the latter with PASMAP students outperforming the regular group on PASA scores. Qualitative analysis of students’ responses for structural development showed increased levels for the PASMAP students. Implications for pedagogy and curriculum are discussed.

Accelerating the Mathematics Learning of Low Socio-Economic Status Junior Secondary Students : an early report

The Accelerating the Mathematics Learning of Low Socio-Economic Status Junior Secondary Students project aims to address the issues faced by very underperforming mathematics students as they enter high school. Its aim is to accelerate learning of mathematics through a vertical curriculum to enable students to access Year 10 mathematics subjects, thus improving life chances. This paper reports upon the theory underpinning this project and illustrates it with examples of the curriculum that has been designed to achieve acceleration.

A conceptual framework for the cultural integration of cooperative learning : a Thai primary mathematics education perspective

The Thailand education reform adopted cooperative learning to improve the quality of education. However, it has been reported that the introduction and maintenance of cooperative learning has been difficult and uncertain because of the cultural differences. The study proposed a conceptual framework developed based on making a connection between Thai cultures and cooperative learning elements, and implemented a small-scale research project in a Thai primary mathematics class with a teacher and thirty-two Grade 4 students. The results uncovered that the three components including preparation of teachers, instructional strategies and preparation of students can be vehicles for the culture integration in cooperative learning.

Rural masculinities and the internalisation of violence in agricultural communities

This article is based on research we conducted in two agricultural communities as part of a broader study that included mining communities in rural Australia. The data from the agricultural locations tell a different story to that of the mining communities. In the latter, alcohol-fuelled, male-on-male assaults in public places caused considerable anxiety among informants. By contrast, people in the agricultural communities seemed more troubled by hidden violent harms which were largely privatised and individualised, including self-harm, suicide, isolation and threats to men’s general wellbeing and mental health; domestic violence; and other forms of violence largely unreported and thus unacknowledged within the wider community (including sexual assault and bullying linked to homophobia). We argue one reason for the different pattern in the agricultural communities is the decline of pub(lic) masculinity, and with this, the increasing isolation of rural men and the increasing propensity to internalise violence. We argue that the relatively high rates of suicide in agricultural communities experiencing rural decline are symptomatic of the internalisation of violence.

Low cost localisation for agricultural robotics

This paper presents a pose estimation approach that is resilient to typical sensor failure and suitable for low cost agricultural robots. Guiding large agricultural machinery with highly accurate GPS/INS systems has become standard practice, however these systems are inappropriate for smaller, lower-cost robots. Our positioning system estimates pose by fusing data from a low-cost global positioning sensor, low-cost inertial sensors and a new technique for vision-based row tracking. The results first demonstrate that our positioning system will accurately guide a robot to perform a coverage task across a 6 hectare field. The results then demonstrate that our vision-based row tracking algorithm improves the performance of the positioning system despite long periods of precision correction signal dropout and intermittent dropouts of the entire GPS sensor.

Modelling as a vehicle for philosophical inquiry in the mathematics curriculum

Philosophical inquiry in the teaching and learning of mathematics has received continued, albeit limited, attention over many years (e.g., Daniel, 2000; English, 1994; Lafortune, Daniel, Fallascio, & Schleider, 2000; Kennedy, 2012a). The rich contributions these communities can offer school mathematics, however, have not received the deserved recognition, especially from the mathematics education community. This is a perplexing situation given the close relationship between the two disciplines and their shared values for empowering students to solve a range of challenging problems, often unanticipated, and often requiring broadened reasoning. In this article, I first present my understanding of philosophical inquiry as it pertains to the mathematics classroom, taking into consideration the significant work that has been undertaken on socio-political contexts in mathematics education (e.g., Skovsmose & Greer, 2012). I then consider one approach to advancing philosophical inquiry in the mathematics classroom, namely, through modelling activities that require interpretation, questioning, and multiple approaches to solution. The design of these problem activities, set within life-based contexts, provides an ideal vehicle for stimulating philosophical inquiry.

An evaluation of the Australian ‘reconceptualising early mathematics learning’ project : key findings and implications

The Pattern and Structure Mathematics Awareness Project (PASMAP) has investigated the development of patterning and early algebraic reasoning among 4 to 8 year olds over a series of related studies. We assert that an awareness of mathematical pattern and structure (AMPS) enables mathematical thinking and simple forms of generalization from an early age. This paper provides an overview of key findings of the Reconceptualizing Early Mathematics Learning empirical evaluation study involving 316 Kindergarten students from 4 schools. The study found highly significant differences on PASA scores for PASMAP students. Analysis of structural development showed increased levels for the PASMAP students; those categorised as low ability developed improved structural responses over a short period of time.

Retailer-driven agricultural restructuring - Australia, the UK and Norway in comparison

In recent decades, the governance of food safety, food quality, on-farm environmental management and animal welfare has been shifting from the realm of 'the government' to that of the private sector. Corporate entities, especially the large supermarkets, have responded to neoliberal forms of governance and the resultant 'hollowed-out' state by instituting private standards for food, backed by processes of certification and policed through systems of third party auditing. Today's food regime is one in which supermarkets impose 'private standards' along the food supply chain to ensure compliance with a range of food safety goals-often above and beyond those prescribed by government. By examining regulatory governance in Australia, Norway and the United Kingdom we highlight emerging trajectories of food governance. We argue that the imposition of the new private forms of monitoring and compliance continue the project of agricultural restructuring that began with government support for structural adjustment schemes in agriculture and that these are most evident in the UK and Australia where neoliberalism is an entrenched philosophy. However, despite Norway's identity as a social democracy, we also identify neoliberal 'creep' into the system of food governance. Small-scale producers in all three nations are finding themselves increasingly subject to governance through private, market-based mechanisms that, to varying degrees, are dominated by major supermarket chains. The result is agricultural restructuring not through the traditional avenues of elected governments, but via non-elected market operatives.

Starting out in STEM : a study of young men and women in first year science, technology, engineering and mathematics courses

In late 2011, first year university students in science, technology, engineering and mathematics (STEM) courses across Australia were invited to participate in the international Interests and Recruitment in Science (IRIS) study. IRIS investigates the influences on young people's decisions to choose university STEM courses and their subsequent experiences of these courses. The study also has a particular focus on the motivations and experiences of young women in courses such as physics, IT and engineering given the low rates of female participation in these fields. Around 3500 students from 30 Australian universities contributed their views on the relative importance of various school and non-school influences on their decisions, as well as insights into their experiences of university STEM courses so far. It is hoped that their contributions will help improve recruitment, retention and gender equity in STEM higher education and careers.