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.

Analysis of genome survey sequences and SSR marker development for Siamese Mud Carp, Henicorhynchus siamensis, using 454 Pyrosequencing

Siamese mud carp (Henichorynchus siamensis) is a freshwater teleost of high economic importance in the Mekong River Basin. However, genetic data relevant for delineating wild stocks for management purposes currently are limited for this species. Here, we used 454 pyrosequencing to generate a partial genome survey sequence (GSS) dataset to develop simple sequence repeat (SSR) markers from H. siamensis genomic DNA. Data generated included a total of 65,954 sequence reads with average length of 264 nucleotides, of which 2.79% contain SSR motifs. Based on GSS-BLASTx results, 10.5% of contigs and 8.1% singletons possessed significant similarity (E value < 10–5) with the majority matching well to reported fish sequences. KEGG analysis identified several metabolic pathways that provide insights into specific potential roles and functions of sequences involved in molecular processes in H. siamensis. Top protein domains detected included reverse transcriptase and the top putative functional transcript identified was an ORF2-encoded protein. One thousand eight hundred and thirty seven sequences containing SSR motifs were identified, of which 422 qualified for primer design and eight polymorphic loci have been tested with average observed and expected heterozygosity estimated at 0.75 and 0.83, respectively. Regardless of their relative levels of polymorphism and heterozygosity, microsatellite loci developed here are suitable for further population genetic studies in H. siamensis and may also be applicable to other related taxa.

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.

Identification of long intergenic region sequences involved in maize streak virus replication

The main cis-acting control regions for replication of the single-stranded DNA genome of maize streak virus (MSV) are believed to reside within an approximately 310 nt long intergenic region (LIR). However, neither the minimum LIR sequence required nor the sequence determinants of replication specificity have been determined experimentally. There are iterated sequences, or iterons, both within the conserved inverted-repeat sequences with the potential to form a stem-loop structure at the origin of virion-strand replication, and upstream of the rep gene TATA box (the rep-proximal iteron or RPI). Based on experimental analyses of similar iterons in viruses from other geminivirus genera and their proximity to known Rep-binding sites in the distantly related mastrevirus wheat dwarf virus, it has been hypothesized that the iterons may be Rep-binding and/or -recognition sequences. Here, a series of LIR deletion mutants was used to define the upper bounds of the LIR sequence required for replication. After identifying MSV strains and distinct mastreviruses with incompatible replication-specificity determinants (RSDs), LIR chimaeras were used to map the primary MSV RSD to a 67 nt sequence containing the RPI. Although the results generally support the prevailing hypothesis that MSV iterons are functional analogues of those found in other geminivirus genera, it is demonstrated that neither the inverted-repeat nor RPI sequences are absolute determinants of replication specificity. Moreover, widely divergent mastreviruses can trans-replicate one another. These results also suggest that sequences in the 67 nt region surrounding the RPI interact in a sequence-specific manner with those of the inverted repeat.

Restoration of native folding of single-stranded DNA sequences through reverse mutations: an indication of a new epigenetic mechanism

We used in vivo (biological), in silico (computational structure prediction), and in vitro (model sequence folding) analyses of single-stranded DNA sequences to show that nucleic acid folding conservation is the selective principle behind a high-frequency single-nucleotide reversion observed in a three-nucleotide mutated motif of the Maize streak virus replication associated protein (Rep) gene. In silico and in vitro studies showed that the three-nucleotide mutation adversely affected Rep nucleic acid folding, and that the single-nucleotide reversion [C(601)A] restored wild-type-like folding. In vivo support came from infecting maize with mutant viruses: those with Rep genes containing nucleotide changes predicted to restore a wild-type-like fold [A(601)/G(601)] preferentially accumulated over those predicted to fold differently [C(601)/T(601)], which frequently reverted to A(601) and displaced the original population. We propose that the selection of native nucleic acid folding is an epigenetic effect, which might have broad implications in the evolution of plants and their viruses.

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.

Kernel analysis on Grassmann manifolds for action recognition

Modelling video sequences by subspaces has recently shown promise for recognising human actions. Subspaces are able to accommodate the effects of various image variations and can capture the dynamic properties of actions. Subspaces form a non-Euclidean and curved Riemannian manifold known as a Grassmann manifold. Inference on manifold spaces usually is achieved by embedding the manifolds in higher dimensional Euclidean spaces. In this paper, we instead propose to embed the Grassmann manifolds into reproducing kernel Hilbert spaces and then tackle the problem of discriminant analysis on such manifolds. To achieve efficient machinery, we propose graph-based local discriminant analysis that utilises within-class and between-class similarity graphs to characterise intra-class compactness and inter-class separability, respectively. Experiments on KTH, UCF Sports, and Ballet datasets show that the proposed approach obtains marked improvements in discrimination accuracy in comparison to several state-of-the-art methods, such as the kernel version of affine hull image-set distance, tensor canonical correlation analysis, spatial-temporal words and hierarchy of discriminative space-time neighbourhood features.

Improved foreground detection via block-based classifier cascade with probabilistic decision integration

Background subtraction is a fundamental low-level processing task in numerous computer vision applications. The vast majority of algorithms process images on a pixel-by-pixel basis, where an independent decision is made for each pixel. A general limitation of such processing is that rich contextual information is not taken into account. We propose a block-based method capable of dealing with noise, illumination variations, and dynamic backgrounds, while still obtaining smooth contours of foreground objects. Specifically, image sequences are analyzed on an overlapping block-by-block basis. A low-dimensional texture descriptor obtained from each block is passed through an adaptive classifier cascade, where each stage handles a distinct problem. A probabilistic foreground mask generation approach then exploits block overlaps to integrate interim block-level decisions into final pixel-level foreground segmentation. Unlike many pixel-based methods, ad-hoc postprocessing of foreground masks is not required. Experiments on the difficult Wallflower and I2R datasets show that the proposed approach obtains on average better results (both qualitatively and quantitatively) than several prominent methods. We furthermore propose the use of tracking performance as an unbiased approach for assessing the practical usefulness of foreground segmentation methods, and show that the proposed approach leads to considerable improvements in tracking accuracy on the CAVIAR dataset.

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.

Slid pairs in the initialisation of the A5/1 stream cipher

A5/1 is a shift register based stream cipher which uses a majority clocking rule to update its registers. It is designed to provide privacy for the GSM system. In this paper, we analyse the initialisation process of A5/1. We demonstrate a sliding property of the A5/1 cipher, where every valid internal state is also a legitimate loaded state and multiple key-IV pairs produce phase shifted keystream sequences. We describe a possible ciphertext only attack based on this property.

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.