Greek or not : the use of symbols and abbreviations in mathematics

The use of symbols and abbreviations adds uniqueness and complexity to the mathematical language register. In this article, the reader’s attention is drawn to the multitude of symbols and abbreviations which are used in mathematics. The conventions which underpin the use of the symbols and abbreviations and the linguistic difficulties which learners of mathematics may encounter due to the inclusion of the symbolic language are discussed. 2010 NAPLAN numeracy tests are used to illustrate examples of the complexities of the symbolic language of mathematics.

A framework for mathematics graphical tasks : The influence of the graphic element on student sense making

Graphical tasks have become a prominent aspect of mathematics assessment. From a conceptual stance, the purpose of this study was to better understand the composition of graphical tasks commonly used to assess students’ mathematics understandings. Through an iterative design, the investigation described the sense making of 11–12-year-olds as they decoded mathematics tasks which contained a graphic. An ongoing analysis of two phases of data collection was undertaken as we analysed the extent to which various elements of text, graphics, and symbols influenced student sense making. Specifically, the study outlined the changed behaviour (and performance) of the participants as they solved graphical tasks that had been modified with respect to these elements. We propose a theoretical framework for understanding the composition of a graphical task and identify three specific elements which are dependently and independently related to each other, namely: the graphic; the text; and the symbols. Results indicated that although changes to the graphical tasks were minimal, a change in student success and understanding was most evident when the graphic element was modified. Implications include the need for test designers to carefully consider the graphics embedded within mathematics tasks since the elements within graphical tasks greatly influence student understanding.

Recombination, decreased host specificity and increased mobility may have driven the emergence of maize streak virus as an agricultural pathogen

Maize streak virus (MSV; family Geminiviridae, genus Mastrevirus), the causal agent of maize streak disease, ranks amongst the most serious biological threats to food security in subSaharan Africa. Although five distinct MSV strains have been currently described, only one of these - MSV-A - causes severe disease in maize. Due primarily to their not being an obvious threat to agriculture, very little is known about the 'grass-adapted' MSV strains, MSV-B, -C, -D and -E. Since comparing the genetic diversities, geographical distributions and natural host ranges of MSV-A with the other MSV strains could provide valuable information on the epidemiology, evolution and emergence of MSV-A, we carried out a phylogeographical analysis of MSVs found in uncultivated indigenous African grasses. Amongst the 83 new MSV genomes presented here, we report the discovery of six new MSV strains (MSV-F to -K). The non-random recombination breakpoint distributions detectable with these and other available mastrevirus sequences partially mirror those seen in begomoviruses, implying that the forces shaping these breakpoint patterns have been largely conserved since the earliest geminivirus ancestors. We present evidence that the ancestor of all MSV-A variants was the recombinant progeny of ancestral MSV-B and MSV-G/-F variants. While it remains unknown whether recombination influenced the emergence of MSV-A in maize, our discovery that MSV-A variants may both move between and become established in different regions of Africa with greater ease, and infect more grass species than other MSV strains, goes some way towards explaining why MSV-A is such a successful maize pathogen. © 2008 SGM.

Teacher aides and their pedagogical contributions in the underachieving Indigenous mathematics classroom

This study examines the pedagogical contributions made by teacher aides in underperforming Indigenous mathematics secondary classrooms. Three teaching teams, each consisting of a teacher and their teacher aide, responded to semi-structured interviews. Their mathematics classrooms were observed for details of pedagogical contributions to the mathematics lessons. It was found that the pedagogical contributions of the teacher aides varied from co-teaching contributions, to the provision of menial support and behaviour management. The techniques used by the teacher aides to provide student feedback, to support behaviour management and to undertake questioning vary greatly, and this variance is also evident in the classroom atmosphere. Teacher aides are providing pedagogical contributions, and are engaged in instructional interactions, and are in a sense “teaching”.

Does 'habitus' count in Chinese Australians' mathematics achievement?

Large-scale international comparative studies and cross-ethnic studies have revealed that Chinese students, whether living in China or overseas, consistently outperform their counterparts in mathematics achievement. These studies tended to explain this result from psychological, educational, or cultural perspectives. However, there is scant sociological investigation addressing Chinese students’ better mathematics achievement. Drawing on Bourdieu’s sociological theory, this study conceptualises Chinese Australians’ “Chineseness” by the notion of ‘habitus’ and considers this “Chineseness” generating but not determinating mechanism that underpins Chinese Australians’ mathematics learning. Two hundred and thirty complete responses from Chinese Australian participants were collected by an online questionnaire. Simple regression model statistically significantly well predicted mathematics achievement by “Chineseness” (F = 141.90, R = .62, t = 11.91, p < .001). Taking account of “Chineseness” as a sociological mechanism for Chinese Australians’ mathematics learning, this study complements psychological and educational impacts on better mathematics achievement of Chinese students revealed by previous studies. This study also challenges the cultural superiority discourse that attributes better mathematics achievement of Chinese students to cultural factors.

ICT driven pedagogies and its impact on learning outcomes in high school mathematics

ICT (Information and Communication Technology) creates numerous opportunities for teachers to re-think their pedagogies. In subjects like mathematics which draws upon abstract concepts, ICT creates such an opportunity. Instead of a mimetic pedagogical approach, suitably designed activities with ICT can enable learners to engage more proactively with their learning. In this quasi-experimental designed study, ICT was used in teaching mathematics to a group of first year high school students (N=25) in Australia. The control group was taught predominantly through traditional pedagogies (N=22). Most of the variables that had previously impacted on the design of such studies were suitably controlled in this yearlong investigation. Quantitative and qualitative results showed that students who were taught by ICT driven pedagogies benefitted from the experience. Pre and post-test means showed that there was a difference between the treatment and control groups. Of greater significance was that the students (in the treatment group) believed that the technology enabled them to engage more with their learning.

Theories of learning mathematics

According to Karl Popper, widely regarded as one of the greatest philosophers of science in the 20th century, falsifiability is the primary characteristic that distinguishes scientific theories from ideologies – or dogma. For example, for people who argue that schools should treat creationism as a scientific theory, comparable to modern theories of evolution, advocates of creationism would need to become engaged in the generation of falsifiable hypothesis, and would need to abandon the practice of discouraging questioning and inquiry. Ironically, scientific theories themselves are accepted or rejected based on a principle that might be called survival of the fittest. So, for healthy theories on development to occur, four Darwinian functions should function: (a) variation – avoid orthodoxy and encourage divergent thinking, (b) selection – submit all assumptions and innovations to rigorous testing, (c) diffusion – encourage the shareability of new and/or viable ways of thinking, and (d) accumulation – encourage the reuseability of viable aspects of productive innovations.

Evaluation of the "reconceptualising early mathematics learning" project

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 enables mathematical thinking and simple forms of generalisation from an early age. The project aims to promote a strong foundation for mathematical development by focusing on critical, underlying features of mathematics learning. This paper provides an overview of key aspects of the assessment and intervention, and analyses of the impact of PASMAP on students’ representation, abstraction and generalisation of mathematical ideas. 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 the evaluation 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’ assessment and a Pattern and Structure Assessment (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; those categorised as low ability developed improved structural responses over a relatively short period of time.

Modeling as a bridge between real world problems and school mathematics

This article argues for an interdisciplinary approach to mathematical problem solving at the elementary school, one that draws upon the engineering domain. A modeling approach, using engineering model eliciting activities, might provide a rich source of meaningful situations that capitalize on and extend students’ existing mathematical learning. The study reports on the developments of 48 twelve-year old students who worked on the Bridge Design activity. Results revealed that young students, even before formal instruction, have the capacity to deal with complex interdisciplinary problems. A number of students created quite appropriate models by developing the necessary mathematical constructs to solve the problem. Students’ difficulties in mathematizing the problem, and in revising and documenting their models are presented and analysed, followed by a discussion on the appropriateness of a modeling approach as a means for introducing complex problems to elementary school students.

Agricultural biodiversity, farm level technical efficiency and conservation benefits : an empirical investigation

The issues involved in agricultural biodiversity are important and interesting areas for the application of economic theory. However, very little theoretical and empirical work has been undertaken to understand the benefits of conserving agricultural biodiversity. Accordingly, the main objectives of this PhD thesis are to: (1) Investigate farmers’ valuation of agricultural biodiversity; (2) Identify factors influencing farmers’ demand for agricultural biodiversity; (3) Examine farmers’ demand for biodiversity rich farming systems; (4) Investigate the relationship between agricultural biodiversity and farm level technical efficiency. This PhD thesis investigates these issues by using primary data in small-scale farms, along with secondary data from Sri Lanka. The overall findings of the thesis can be summarized as follows. Firstly, owing to educational and poverty issues of those being interviewed, some policy makers in developed countries question whether non-market valuation techniques such as Choice Experiment (CE) can be applied to developing countries such as Sri Lanka. The CE study in this thesis indicates that carefully designed and pre-tested nonmarket valuation techniques can be applied in developing countries with a high level of reliability. The CE findings support the priori assumption that small-scale farms and their multiple attributes contribute positively and significantly to the utility of farm families in Sri Lanka. Farmers have strong positive attitudes towards increasing agricultural biodiversity in rural areas. This suggests that these attitudes can be the basis on which appropriate policies can be introduced to improve agricultural biodiversity. Secondly, the thesis identifies the factors which influence farmers’ demand for agricultural biodiversity and farmers’ demands on biodiversity rich farming systems. As such they provide important tools for the implementation of policies designed to avoid the loss agricultural biodiversity which is shown to be a major impediment to agricultural growth and sustainable development in a number of developing countries. The results illustrate that certain key household, market and other characteristics (such as agricultural subsidies, percentage of investment of owned money and farm size) are the major determinants of demand for agricultural biodiversity on small-scale farms. The significant household characteristics that determine crop and livestock diversity include household member participation on the farm, off-farm income, shared labour, market price fluctuations and household wealth. Furthermore, it is shown that all the included market characteristics as well as agricultural subsidies are also important determinants of agricultural biodiversity. Thirdly, it is found that when the efficiency of agricultural production is measured in practice, the role of agricultural biodiversity has rarely been investigated in the literature. The results in the final section of the thesis show that crop diversity, livestock diversity and mix farming system are positively related to farm level technical efficiency. In addition to these variables education level, number of separate plots, agricultural extension service, credit access, membership of farm organization and land ownerships are significant and direct policy relevant variables in the inefficiency model. The results of the study therefore have important policy implications for conserving agricultural biodiversity in Sri Lanka.

Assessing eco-environmental performance of agricultural production in OECD countries : combination of soil surface, soil system and farm gate methods of nutrient auditing

Nitrogen balance is increasingly used as an indicator of the environmental performance of agricultural sector in national, international, and global contexts. There are three main methods of accounting the national nitrogen balance: farm gate, soil surface, and soil system. OECD (2008) recently reported the nitrogen and phosphorus balances for member countries for the 1985 - 2004 period using the soil surface method. The farm gate and soil system methods were also used in some international projects. Some studies have provided the comparison among these methods and the conclusion is mixed. The motivation of this present paper was to combine these three methods to provide a more detailed auditing of the nitrogen balance and flows for national agricultural production. In addition, the present paper also provided a new strategy of using reliable international and national data sources to calculate nitrogen balance using the farm gate method. The empirical study focused on the nitrogen balance of OECD countries for the period from 1985 to 2003. The N surplus sent to the total environment of OECD surged dramatically in early 1980s, gradually decreased during 1990s but exhibited an increasing trends in early 2000s. The overall N efficiency however fluctuated without a clear increasing trend. The eco-environmental ranking shows that Australia and Ireland were the worst while Korea and Greece were the best.

A comparison of Chinese and Australian early childhood mathematics

In the 21st century mathematics proficiency is synonymous with a numerate citizenry. In the past few decades young children’s ability to reason mathematically and develop mathematical proficiencies has been recognised. This paper explores the history of early childhood mathematics (ECME) that may explicate differences in Chinese and Australian contexts. Results of this review established that China and Australia are diametrically positioned in ECME. Influencing each countries philosophies and practices are their cultural beliefs. ECME in China and Australia must be culturally sustainable to achieve excellent outcomes for young children. Ongoing critique and review is necessary to ensure that ECME is meeting the needs of all teachers and children in their particular context. China and Australia with their rich contrasting philosophies can assist each other in their journeys to create exemplary ECME for the 21st century.

Mathematics learning in prep

Most teachers recognise the importance of mathematics teaching and learning in early years but there is not consensus on how and when this learning should occur. Young-Loveridge (cited in de Vries, Thomas, and Warren, 2010) suggests that quality early mathematical experiences are a key determinant to later achievement.