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.

Using annotations to inform an understanding of achievement standards

The implementation of a new national curriculum and standards-referenced assessment in Australia has been an opportunity and a challenge for teacher assessment practices. In this case study of teachers in two Queensland schools, we explore how annotating student or exemplar assessment tasks could support teacher assessment practice. Three learning conversations between the researchers and the teacher teams are interpreted through the lens of Bernstein’s (1999) horizontal and vertical discourses to understand the complexities of coming to know an assessment standard. The study contributes to the literature on the use of annotations by exploring how teachers negotiated the purposes and processes of annotation, how annotating student work or exemplars before teaching commenced supported teachers to experience greater clarity about assessment standards and, finally, some of the tensions experienced by the teachers as they considered this practice within the practicalities of their daily work.

Family structure and change through middle childhood : the impact on children's adjustment and achievement

This research project investigated the influence of family transitions on children's adjustment and school achievement across the primary school years, in single-parent, re-partnered and two-parent families. The quality of children's relationships with parents, teachers and peers were predictive of more positive outcomes, regardless of family structure. The research analysed data from the Kindergarten Cohort participating in Growing Up in Australia: The Longitudinal Study of Australian Children. Across the age span of the children studied, cumulative effects of any residential or school changes, or decreased family income, associated with family transitions, were more likely to predict poorer child outcomes in behaviour adjustment and school achievement.

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.

Self-reflection as an intervention to influence achievement goal orientations and intrinsic motivation

In the context of physical activity, intrinsic motivation refers to the inherent satisfaction associated with participation in the activity. Interest-enjoyment, perceived competence, and effort have been identified as three underlying components of intrinsic motivation. Achievement goal theory stipulates that achievement goals guide our beliefs and behavior. The two main achievement goal orientations identified in the sport and physical activity literature are task and ego orientations. A person with a strong task orientation defines success in self-referenced terms, as improving one’s own performance or mastering new skills. Someone with a strong ego orientation defines success normatively, as being better than others. The majority of research suggests that having a strong task orientation is a good thing, whether with regard to motivationally adaptive responses, sources of sport confidence, students’ satisfaction with learning, or the use of cognitive and self-regulatory strategies. Although the literature supporting the potential benefits of having a strong task orientation is vast, considerably less research has tested interventions designed to strengthen task orientations and intrinsic motivation. A climate that emphasises individual mastery has resulted in increased interest-enjoyment and perceived competence, whereas an emphasis on competition and comparison with others has resulted in a decrease in interest-enjoyment and an increase in tension-pressure. One possible intervention is the use of structured self-reflection. Using self-reflection sheets that cause respondents to focus on specific elements of technique or skills, and rate one’s own performance, should theoretically promote a task focus. Hanrahan suggested that engaging in self-reflection may enhance intrinsic motivation. Perceived competence could be positively affected, as self-analysis and self-monitoring have been found to positively influence the acquisition of physical skills. The purpose of this study was to determine if the use of structured self-reflection in community dance classes would influence achievement goal orientations or levels of intrinsic motivation.

Dulux Study Tour for Australian Achievement in Architecture Awards Recipient Report 2008

The Dulux Study Tour is a collaborative initiative between Dulux, the Australian Institute of Architects and EmAGN. Each year five (5) architectural professionals (within 10 years of graduation) are selected to join the Dulux Study Tour, an international tour visiting leading architectural firms, recently completed projects and architecturally rich locations. The Dulux Study Tour acknowledges the contribution the selected emerging architects make to practice, research and the culture of architecture, and seeks to further inspire the next generation of emerging architects.

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.

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.