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.

Butterfly catastrophe for fronts in a three-component reaction–diffusion system

We study the dynamics of front solutions in a three-component reaction–diffusion system via a combination of geometric singular perturbation theory, Evans function analysis, and center manifold reduction. The reduced system exhibits a surprisingly complicated bifurcation structure including a butterfly catastrophe. Our results shed light on numerically observed accelerations and oscillations and pave the way for the analysis of front interactions in a parameter regime where the essential spectrum of a single front approaches the imaginary axis asymptotically.

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.

Tropomyosin Tm5NM1 spatially restricts src kinase activity through perturbation of rab11 vesicle trafficking

In order for cells to stop moving, they must synchronously stabilize actin filaments and their associated focal adhesions. How these two structures are coordinated in time and space is not known. We show here that the actin association protein Tm5NM1, which induces stable actin filaments, concurrently suppresses the trafficking of focal-adhesion-regulatory molecules. Using combinations of fluorescent biosensors and fluorescence recovery after photobleaching (FRAP), we demonstrate that Tm5NM1 reduces the level of delivery of Src kinase to focal adhesions, resulting in reduced phosphorylation of adhesion-resident Src substrates. Live imaging of Rab11-positive recycling endosomes that carry Src to focal adhesions reveals disruption of this pathway. We propose that tropomyosin synchronizes adhesion dynamics with the cytoskeleton by regulating actin-dependent trafficking of essential focal-adhesion molecules.

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.

Characterization of alluvial formation by stochastic modelling of paleo-fluvial processes: The concept and method

Modelling fluvial processes is an effective way to reproduce basin evolution and to recreate riverbed morphology. However, due to the complexity of alluvial environments, deterministic modelling of fluvial processes is often impossible. To address the related uncertainties, we derive a stochastic fluvial process model on the basis of the convective Exner equation that uses the statistics (mean and variance) of river velocity as input parameters. These statistics allow for quantifying the uncertainty in riverbed topography, river discharge and position of the river channel. In order to couple the velocity statistics and the fluvial process model, the perturbation method is employed with a non-stationary spectral approach to develop the Exner equation as two separate equations: the first one is the mean equation, which yields the mean sediment thickness, and the second one is the perturbation equation, which yields the variance of sediment thickness. The resulting solutions offer an effective tool to characterize alluvial aquifers resulting from fluvial processes, which allows incorporating the stochasticity of the paleoflow velocity.

Bhutanese eighth grade students' and teachers' perceptions of their classroom learning environment in relation to the new mathematics curriculum

This thesis examined how Bhutanese eighth grade students and teachers perceived their classroom learning environment in relation to a new standards-based mathematics curriculum. Data were gathered from administering surveys to a sample of 608 students and 98 teachers, followed by semi-structured interviews with selected participants. The findings of the study indicated that participants generally perceived their learning environments favorably. However, there were differences in terms of gender, school level, and school location. The study provides teachers, educational leaders, and policy-makers in Bhutan new insights into students' and teachers' perceptions of their mathematics classroom environments.

Mathematics knowledge for teaching and the classroom environment

This study investigated the classroom environment in an underperforming mathematics classroom. The objectives were: (1) to investigate the classroom environment and identify influences upon it, and (2) to further explore those influences (i.e., teacher knowledge). This was completed using a diachronic case study approach in which data were gathered during lesson observations and coaching sessions. These data were analysed to describe and exemplify the classroom environment, then further described against forms of teacher knowledge. Conjectures regarding the importance of teacher knowledge of content were made which formed a base for developing a model of teacher planning and pedagogy.

STEM: Challenges and opportunities for mathematics education

Climbing Mountains, Building Bridges is a rich theme for exploring some of the “challenges, obstacles, links, and connections” facing mathematics education within the current STEM climate (Science, Technology, Engineering and Mathematics). This paper first considers some of the issues and debates surrounding the nature of STEM education, including perspectives on its interdisciplinary nature. It is next argued that mathematics is in danger of being overshadowed, in particular by science, in the global urgency to advance STEM competencies in schools and the workforce. Some suggestions are offered for lifting the profile of mathematics education within an integrated STEM context, with examples drawn from modelling with data in the sixth grade.