The continuing decline of science and mathematics enrolments in Australian high schools

Is there a crisis in Australian science and mathematics education? Declining enrolments in upper secondary Science and Mathematics courses have gained much attention from the media, politicians and high-profile scientists over the last few years, yet there is no consensus amongst stakeholders about either the nature or the magnitude of the changes. We have collected raw enrolment data from the education departments of each of the Australian states and territories from 1992 to 2012 and analysed the trends for Biology, Chemistry, Physics, two composite subject groups (Earth Sciences and Multidisciplinary Sciences), as well as entry, intermediate and advanced Mathematics. The results of these analyses are discussed in terms of participation rates, raw enrolments and gender balance. We have found that the total number of students in Year 12 increased by around 16% from 1992 to 2012 while the participation rates for most Science and Mathematics subjects, as a proportion of the total Year 12 cohort, fell (Biology (-10%), Chemistry (-5%), Physics (-7%), Multidisciplinary Science (-5%), intermediate Mathematics (-11%), advanced Mathematics (-7%) in the same period. There were increased participation rates in Earth Sciences (+0.3%) and entry Mathematics (+11%). In each case the greatest rates of change occurred prior to 2001 and have been slower and steadier since. We propose that the broadening of curriculum offerings, further driven by students' self-perception of ability and perceptions of subject difficulty and usefulness, are the most likely cause of the changes in participation. While these continuing declines may not amount to a crisis, there is undoubtedly serious cause for concern.

A survey in mathematics for industry: Two-timing and matched asymptotic expansions for singular perturbation problems

Following the derivation of amplitude equations through a new two-time-scale method [O'Malley, R. E., Jr. & Kirkinis, E (2010) A combined renormalization group-multiple scale method for singularly perturbed problems. Stud. Appl. Math. 124, 383-410], we show that a multi-scale method may often be preferable for solving singularly perturbed problems than the method of matched asymptotic expansions. We illustrate this approach with 10 singularly perturbed ordinary and partial differential equations. © 2011 Cambridge University Press.

Making meaning in mathematics problem solving using the Reciprocal Teaching approach

This paper examines the application of the Reciprocal Teaching instructional approach to Mathematical word problems in the middle years. The Reciprocal Teaching process is extended from the four traditional strategies of predicting, clarifying, questioning and summarising, to include further cognitive reading comprehension strategies applied to the context of solving Mathematical word problems.

Vision-based simultaneous localization and mapping in changing outdoor environments

For robots operating in outdoor environments, a number of factors, including weather, time of day, rough terrain, high speeds, and hardware limitations, make performing vision-based simultaneous localization and mapping with current techniques infeasible due to factors such as image blur and/or underexposure, especially on smaller platforms and low-cost hardware. In this paper, we present novel visual place-recognition and odometry techniques that address the challenges posed by low lighting, perceptual change, and low-cost cameras. Our primary contribution is a novel two-step algorithm that combines fast low-resolution whole image matching with a higher-resolution patch-verification step, as well as image saliency methods that simultaneously improve performance and decrease computing time. The algorithms are demonstrated using consumer cameras mounted on a small vehicle in a mixed urban and vegetated environment and a car traversing highway and suburban streets, at different times of day and night and in various weather conditions. The algorithms achieve reliable mapping over the course of a day, both when incrementally incorporating new visual scenes from different times of day into an existing map, and when using a static map comprising visual scenes captured at only one point in time. Using the two-step place-recognition process, we demonstrate for the first time single-image, error-free place recognition at recall rates above 50% across a day-night dataset without prior training or utilization of image sequences. This place-recognition performance enables topologically correct mapping across day-night cycles.

Changes in outdoor workers' sun-related attitudes, beliefs, and behaviors : a pre-post workplace intervention

OBJECTIVE To evaluate changes in outdoor workers' sun-related attitudes, beliefs, and behaviors in response to a health promotion intervention using a participatory action research process. METHODS Fourteen workplaces across four outdoor industry types worked collaboratively with the project team to develop tailored sun protection action plans. Workers were assessed before and after the 18-month intervention. RESULTS Outdoor workers reported increases in workplace support for sun protection (P < 0.01) and personal use of sun protection (P < 0.01). More workers reported seeking natural shade (+20%) and wearing more personal protective equipment, including broad-brimmed hats (+25%), long-sleeved collared shirts (+19%), and long trousers (+16%). The proportion of workers reporting sunburn over the past 12 months was lower at postintervention (-14%) (P = 0.03); however, the intensity of reported sunburn increased. CONCLUSIONS This intervention was successful in increasing workers' sun protective attitudes, beliefs, and behaviors.

Indigenous students transitioning to school : responses to pre-foundational mathematics

Australian Indigenous students' mathematics performance continues to be below that of non-Indigenous students. This occurs from the early years of school, due largely to knowledge and social differences on entry to formal schooling. This paper reports on a mathematics research project conducted in one Aboriginal community school in New South Wales, Australia. The project aimed to identify and explain the ways that young Australian Indigenous students (age 2-4 years) learn number language and processes, specifically attribute language, sorting, 1-1 correspondence and, counting. The project adopted a mixed methods approach. That is, the methodology was decolonising (Smith 1999) in that it collaborated with and gave benefit back to the Indigenous community and school being researched. It was qualitative and interpretative (Burns 2000) and incorporated an action-research teaching-experiment approach where and teachers collaborated with the researchers to try new teaching methods. This paper draws on data pertaining to students' response to diagnostic interview questions, the pre- and post-test results of the interview and photographic evidence as observations during mathematics learning time. Participants referred to in this paper include one female principal (N = 1), and the transition class of students' pre- (N = 6) and post-test (N = 3) results of the pre-foundational processes (also referred to as attributes). The results were encouraging with improvements in colour (34%), patterns (33%); capacity (38%). As a result of this project, our epistemology regarding the importance of finding out about students' pre-foundational knowledge and understandings and providing a culturally appropriate learning environment with resources has been built upon.

Language and literacy in mathematics: stepping stones or stumbling blocks in accelerating junior-secondary students

The authors have collaborated in the development and initial evaluation of a curriculum for mathematics acceleration. This paper reports upon the difficulties encountered with documenting student understanding using pen-and-paper assessment tasks. This leads to a discussion of the impact of students’ language and literacy on mathematical performance and the consequences for motivation and engagement as a result of simplifying the language in the tests, and extending student work to algebraic representations. In turn, implications are drawn for revisions to assessment used within the project and the language and literacy focus included within student learning experiences.

Use of genetic decompositions to scaffold the development of a structurally sequenced curriculum for mathematics acceleration

The authors have collaboratively used a graphical language to describe their shared knowledge of a small domain of mathematics, which has in turn scaffolded their re-development of a related curriculum for mathematics acceleration. This collaborative use of the graphical language is reported as a simple descriptive case study. This leads to an evaluation of the graphical language’s usefulness as a tool to support the articulation of the structure of mathematics knowledge. In turn, implications are drawn for how the graphical language may be utilised as the detail of the curriculum is further elaborated and communicated to teachers.

Developing young students’ meta-representational competence through integrated mathematics and science investigations

This paper describes students’ developing meta-representational competence, drawn from the second phase of a longitudinal study, Transforming Children’s Mathematical and Scientific Development. A group of 21 highly able Grade 1 students was engaged in mathematics/science investigations as part of a data modelling program. A pedagogical approach focused on students’ interpretation of categorical and continuous data was implemented through researcher-directed weekly sessions over a 2-year period. Fine-grained analysis of the developmental features and explanations of their graphs showed that explicit pedagogical attention to conceptual differences between categorical and continuous data was critical to development of inferential reasoning.

Chinese Australians’ Chineseness and their mathematics achievement : the role of habitus

Large-scale international comparative studies and cross-ethnic studies have revealed that Chinese students, living either in China or overseas, consistently outperform their counterparts in mathematics. Empirical research has discussed psychological, educational, and cultural reasons behind Chinese students’ better mathematics performance. However, there is scant sociological investigation of this phenomenon. The current mixed methods study aims to make a contribution in this regard. The study conceptualises Chineseness through Bourdieu’s sociological notion of habitus and considers this habitus of Chineseness generating, but not determining, mechanism that underpins commitment to mathematics learning. The study firstly analyses the responses of 230 Chinese Australian participants to a set of questionnaire items. Results indicate that the habitus of Chineseness significantly mediates the relationship between participants’ commitment to mathematics learning and their mathematics achievement. The study then reports on the interviews with five participants to add nuances and dynamics to the mediating role of habitus of Chineseness. The study complements the existing literature by providing sociological insight into the better mathematics achievement of Chinese students.

Accelerating junior-secondary mathematics

Unfortunately, in Australia there is a prevalence of mathematically underperforming junior-secondary students in low-socioeconomic status schools. This requires targeted intervention to develop the affected students’ requisite understanding in preparation for post-compulsory study and employment and, ultimately, to increase their life chances. To address this, the ongoing action research project presented in this paper is developing a curriculum of accelerated learning, informed by a lineage of cognitivist-based structural sequence theory building activity (e.g., Cooper & Warren, 2011). The project’s conceptual framework features three pillars: the vertically structured sequencing of concepts; pedagogy grounded in students’ reality and culture; and professional learning to support teachers’ implementation of the curriculum (Cooper, Nutchey, & Grant, 2013). Quantitative and qualitative data informs the ongoing refinement of the theory, the curriculum, and the teacher support.

Estimating the burden of disease attributable to urban outdoor air pollution in South Africa in 2000

Objectives To quantify the mortality burden attributed to urban outdoor air pollution in South Africa in 2000. Design The study followed comparative risk assessment (CRA) methodology developed by the World Heath Organization (WHO). In most urban areas, annual mean concentrations of particulate matter (PM) with diameters less than 10 μum (PM10) from monitoring network data and PM with diameters less than 2.5 μm (PM2.5) derived using a ratio method were weighted according to population size. PM10 and PM2.5 data from air-quality assessment studies in areas not covered by the network were also included. Population-attributable fractions calculated using risk coefficients presented in the WHO study were weighted by the proportion of the total population (33%) in urban environments, and applied to revised estimates of deaths and years of life lost (YLLs) for South Africa in 2000. Setting South Africa. Subjects Children under 5 years and adults 30 years and older. Outcome measures Mortality and YLLs from lung cancer and cardiopulmonary disease in adults (30 years and older), and from acute respiratory infections (ARIs) in children aged 0 - 4 years. Results Outdoor air pollution in urban areas in South Africa was estimated to cause 3.7% of the national mortality from cardiopulmonary disease and 5.1% of mortality attributable to cancers of the trachea, bronchus and lung in adults aged 30 years and older, and 1.1% of mortality from ARIs in children under 5 years of age. This amounts to 4 637 or 0.9% (95% uncertainty interval 0.3 - 1.5%) of all deaths and about 42 000 YLLs, or 0.4% (95% uncertainty interval 0.1 - 0.7%) of all YLLs in persons in South Africa in 2000. Conclusion Urban air pollution has under-recognised public health impacts in South Africa. Fossil fuel combustion emissions and traffic-related air pollution remain key targets for public health in South Africa.