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.

Adaptive finite element analysis of elliptic problems based on bubble-type local mesh generation

A new mesh adaptivity algorithm that combines a posteriori error estimation with bubble-type local mesh generation (BLMG) strategy for elliptic differential equations is proposed. The size function used in the BLMG is defined on each vertex during the adaptive process based on the obtained error estimator. In order to avoid the excessive coarsening and refining in each iterative step, two factor thresholds are introduced in the size function. The advantages of the BLMG-based adaptive finite element method, compared with other known methods, are given as follows: the refining and coarsening are obtained fluently in the same framework; the local a posteriori error estimation is easy to implement through the adjacency list of the BLMG method; at all levels of refinement, the updated triangles remain very well shaped, even if the mesh size at any particular refinement level varies by several orders of magnitude. Several numerical examples with singularities for the elliptic problems, where the explicit error estimators are used, verify the efficiency of the algorithm. The analysis for the parameters introduced in the size function shows that the algorithm has good flexibility.

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.

Versatility of polymethacrylate monoliths for chromatographic purification of biomolecules

Polymethacrylate monoliths, specifically poly(glycidyl methacrylate-co-ethylene dimethacrylate) or poly(GMA-co-EDMA) monoliths, are a new generation of chromatographic supports and are significantly different from conventional particle-based adsorbents, membranes, and other monolithic supports for biomolecule purification. Similar to other monoliths, polymethacrylate monoliths possess large pores which allow convective flow of mobile phase and result in high flow rates at reduced pressure drop, unlike particulate supports. The simplicity of the adsorbent synthesis, pH resistance, and the ease and flexibility of tailoring their pore size to that of the target biomolecule are the key properties which differentiate polymethacrylate monoliths from other monoliths. Polymethacrylate monoliths are endowed with reactive epoxy groups for easy functionalization (with anion-exchange, hydrophobic, and affinity ligands) and high ligand retention. In this review, the structure and performance of polymethacrylate monoliths for chromatographic purification of biomolecules are evaluated and compared to those of other supports. The development and use of polymethacrylate monoliths for research applications have grown rapidly in recent times and have enabled the achievement of high through-put biomolecule purification on semi-preparative and preparative scales.

Effects of strain artefacts arising from a pre-defined callus domain in models of bone healing mechanobiology

Iterative computational models have been used to investigate the regulation of bone fracture healing by local mechanical conditions. Although their predictions replicate some mechanical responses and histological features, they do not typically reproduce the predominantly radial hard callus growth pattern observed in larger mammals. We hypothesised that this discrepancy results from an artefact of the models’ initial geometry. Using axisymmetric finite element models, we demonstrated that pre-defining a field of soft tissue in which callus may develop introduces high deviatoric strains in the periosteal region adjacent to the fracture. These bone-inhibiting strains are not present when the initial soft tissue is confined to a thin periosteal layer. As observed in previous healing models, tissue differentiation algorithms regulated by deviatoric strain predicted hard callus forming remotely and growing towards the fracture. While dilatational strain regulation allowed early bone formation closer to the fracture, hard callus still formed initially over a broad area, rather than expanding over time. Modelling callus growth from a thin periosteal layer successfully predicted the initiation of hard callus growth close to the fracture site. However, these models were still susceptible to elevated deviatoric strains in the soft tissues at the edge of the hard callus. Our study highlights the importance of the initial soft tissue geometry used for finite element models of fracture healing. If this cannot be defined accurately, alternative mechanisms for the prediction of early callus development should be investigated.

A meshless method based on Point Interpolation Method (PIM) for the space fractional diffusion equation

This paper aims to develop a meshless approach based on the Point Interpolation Method (PIM) for numerical simulation of a space fractional diffusion equation. Two fully-discrete schemes for the one-dimensional space fractional diffusion equation are obtained by using the PIM and the strong-forms of the space diffusion equation. Numerical examples with different nodal distributions are studied to validate and investigate the accuracy and efficiency of the newly developed meshless approach.

Investigation into chemistry of new particle formation and growth in subtropical urban environment

The role of different chemical compounds, particularly organics, involved in the new particle formation (NPF) and its consequent growth are not fully understood. Therefore, this study was conducted to investigate the chemistry of aerosol particles during NPF events in an urban subtropical environment. Aerosol chemical composition was measured along with particle number size distribution (PNSD) and several other air quality parameters at five sites across an urban subtropical environment. An Aerodyne compact Time-of-Flight Aerosol Mass Spectrometer (c-TOF-AMS) and a TSI Scanning Mobility Particle Sizer (SMPS) measured aerosol chemical composition and PNSD, respectively. Five NPF events, with growth rates in the range 3.3-4.6 nm, were detected at two sites. The NPF events happened on relatively warmer days with lower humidity and higher solar radiation. Temporal percent fractions of nitrate, sulphate, ammonium and organics were modelled using the Generalised Additive Model (GAM), with a basis of penalised spline. Percent fractions of organics increased after the NPF events, while the mass fraction of ammonium and sulphate decreased. This uncovered the important role of organics in the growth of newly formed particles. Three organic markers, factors f43, f44 and f57, were calculated and the f44 vs f43 trends were compared between nucleation and non-nucleation days. f44 vs f43 followed a different pattern on nucleation days compared to non-nucleation days, whereby f43 decreased for vehicle emission generated particles, while both f44 and f43 decreased for NPF generated particles. It was found for the first time that vehicle generated and newly formed particles cluster in different locations on f44 vs f43 plot and this finding can be used as a tool for source apportionment of measured particles.

Unlocking the learning potential of incarcerated Indigenous and low SES young people; Mathematics outcomes for future success: a discussion paper

This presentation provides a beginning discussion about what the literature reports about incarcerated young people. Incarcerated Indigenous and low SES young people typically have very low literacy and mathematics skills which precludes them from future education and or employment opportunities, thus continuing the cycle of disadvantage, exclusion and despair(Payne, 2007). Being locked out of learning, they are stuck in a cycle of underachievement, a scenario which contributes to unacceptably high levels of recidivism(ACER, 2014). Success at education is considered an important protective factor against delinquent behaviours such as offending, substance abuse and truancy. Youth education and training centres provide educational opportunities for the incarcerated Indigenous youth but achievement continues to be lower than expected, particularly in mathematics. This presentation provides an introductory literature review focusing on incarcerated young people and education. It is also the preliminary writing for a small pilot project currently being conducted in one Youth Education and Training Centre in Australia.

Preparing engineering graduates for the knowledge economy through blended delivery of mathematics

Contemporary higher education institutions are making significant efforts to develop cohesive, meaningful and effective learning experiences for Science, Technology, Engineering and Mathematics (STEM) curricula to prepare graduates for challenges in the modern knowledge economy, thus enhancing their employability (Carnevale et al, 2011). This can inspire innovative redesign of learning experiences embedded in technology-enhanced educational environments and the development of research-informed, pedagogically reliable strategies fostering interactions between various agents of the learning-teaching process. This paper reports on the results of a project aimed at enhancing students’ learning experiences by redesigning a large, first year mathematics unit for Engineering students at a large metropolitan public university. Within the project, the current study investigates the effectiveness of selected, technology-mediated pedagogical approaches used over three semesters. Grounded in user-centred instructional design, the pedagogical approaches explored the opportunities for learning created by designing an environment containing technological, social and educational affordances. A qualitative analysis of mixed-type questionnaires distributed to students indicated important inter-relations between participants’ frames of references of the learning-teaching process and stressed the importance (and difficulty) of creating appropriate functional context. Conclusions drawn from this study may inform instructional design for blended delivery of STEM-focused programs that endeavor to enhance students’ employability by educating work-ready graduates.