Learning power and language expressiveness

The topic of the present work is to study the relationship between the power of the learning algorithms on the one hand, and the expressive power of the logical language which is used to represent the problems to be learned on the other hand. The central question is whether enriching the language results in more learning power. In order to make the question relevant and nontrivial, it is required that both texts (sequences of data) and hypotheses (guesses) be translatable from the “rich” language into the “poor” one. The issue is considered for several logical languages suitable to describe structures whose domain is the set of natural numbers. It is shown that enriching the language does not give any advantage for those languages which define a monadic second-order language being decidable in the following sense: there is a fixed interpretation in the structure of natural numbers such that the set of sentences of this extended language true in that structure is decidable. But enriching the original language even by only one constant gives an advantage if this language contains a binary function symbol (which will be interpreted as addition). Furthermore, it is shown that behaviourally correct learning has exactly the same power as learning in the limit for those languages which define a monadic second-order language with the property given above, but has more power in case of languages containing a binary function symbol. Adding the natural requirement that the set of all structures to be learned is recursively enumerable, it is shown that it pays o6 to enrich the language of arithmetics for both finite learning and learning in the limit, but it does not pay off to enrich the language for behaviourally correct learning.

Implementing a Pattern and Structure Mathematics Awareness Program (PASMAP) in kindergarten

This paper provides an interim report of a large empirical evaluation study in progress. An intervention was implemented to evaluate the effectiveness of the Pattern and Structure Mathematical Awareness Program (PASMAP) on Kindergarten students’ mathematical development. Four large schools (two from Sydney and two from Brisbane), 16 teachers and their 316 students participated in the first phase of a 2-year longitudinal study. Eight of 16 classes implemented the PASMAP program over three school terms. This paper provides an overview of key aspects of the intervention, and preliminary analysis of the impact of PASMAP on students’ representation, abstraction and generalisation of mathematical ideas.

Development of a novel rolling-circle amplification technique to detect Banana streak virus which also discriminates between integrated and episomal virus sequences

Bananas are hosts to a large number of banana streak virus (BSV) species. However, diagnostic methods for BSV are inadequate because of the considerable genetic and serological diversity amongst BSV isolates and the presence of integrated BSV sequences in some banana cultivars which leads to false positives. In this study, a sequence non-specific, rolling-circle amplification (RCA) technique was developed and shown to overcome these limitations for the detection and subsequent characterisation of BSV isolates infecting banana. This technique was shown to discriminate between integrated and episomal BSV DNA, specifically detecting the latter in several banana cultivars known to contain episomal and/or integrated sequences of Banana streak Mysore virus (BSMyV), Banana streak OL virus (BSOLV) and Banana streak GF virus (BSGFV). Using RCA, the presence of BSMyV and BSOLV was confirmed in Australia, while BSOLV, BSGFV, Banana streak Uganda I virus (BSUgIV), Banana streak Uganda L virus (BSUgLV) and Banana streak Uganda M virus (BSUgMV) were detected in Uganda. This is the first confirmed report of episomally-derived BSUglV, BSUgLV and BSUgMV in Uganda. As well as its ability to detect BSV, RCA was shown to detect two other pararetroviruses, Sugarcane bacilliform virus in sugarcane and Cauliflower mosaic virus in turnip.

Interaction of NPR1 with basic leucine zipper protein transcription factors that bind sequences required for salicylic acid induction of the PR–1 gene

The Arabidopsis thaliana NPR1 has been shown to be a key regulator of gene expression during the onset of a plant disease-resistance response known as systemic acquired resistance. The npr1 mutant plants fail to respond to systemic acquired resistance-inducing signals such as salicylic acid (SA), or express SA-induced pathogenesis-related (PR) genes. Using NPR1 as bait in a yeast two-hybrid screen, we identified a subclass of transcription factors in the basic leucine zipper protein family (AHBP-1b and TGA6) and showed that they interact specifically in yeast and in vitro with NPR1. Point mutations that abolish the NPR1 function in A. thaliana also impair the interactions between NPR1 and the transcription factors in the yeast two-hybrid assay. Furthermore, a gel mobility shift assay showed that the purified transcription factor protein, AHBP-1b, binds specifically to an SA-responsive promoter element of the A. thaliana PR-1 gene. These data suggest that NPR1 may regulate PR-1 gene expression by interacting with a subclass of basic leucine zipper protein transcription factors.

Culture-fair assessment : challenging Indigenous students through effortful mathematics teaching

This paper reports on a mathematics education research project centred on teachers’ pedagogical practices and capacity to assess Indigenous Australian students in a culture-fair manner. The project has been funded by the Australian Research Council Linkage program and is being conducted in seven Catholic and Independent primary schools in north Queensland. Our Industry Partners are Catholic Education and the Association of Independent Schools, Queensland. The study aims to provide greater understanding about how to build more equitable assessment practices to address the issue of underperforming Aboriginal and Torres Strait Islander (ATSI) students in regional and remote Australia. The goal is to identify ways forward by attending to culture-fair assessment practice. The research is exploring the attitudes, beliefs and responses of Indigenous students to assessment in the context of mathematics learning with particular focus on teacher knowledge in these educational settings in relation to the design of assessment tasks that are authentic and engaging for these students in an accountability context. This approach highlights how teachers need to distinguish the ‘funds of knowledge’ (González, Moll, Floyd Tenery, Rivera, Rendón, Gonzales & Amanti, 2008) that Indigenous students draw on and how teachers need to be culturally responsive in their pedagogy to open up curriculum and assessment practice to allow for different ways of knowing and being

Teaching and learning mathematics with robotics in middle-years of schooling

Engaging and motivating students in mathematics lessons can be challenging. The traditional approach of chalk and talk can sometimes be problematic. The new generation of educational robotics has the potential to not only motivate students but also enable teachers to demonstrate concepts in mathematics by connecting concepts with the real world. Robotics hardware and the software are becoming increasing more user-friendly and as a consequence they can be blended in with classroom activities with greater ease. Using robotics in suitably designed activities promotes a constructivist learning environment and enables students to engage in higher order thinking through hands-on problem solving. Teamwork and collaborative learning are also enhanced through the use of this technology. This paper discusses a model for teaching concepts in mathematics in middle year classrooms. It will also highlight some of the benefits and challenges of using robotics in the learning environment.

Comparison of Nucleotide Sequences between Northern and Southern Philippine Isolates of Rice Grassy Stunt Virus Indicates Occurrence of Natural Genetic Reassortment

Rice grassy stunt virus is a member of the genus Tenuivirus, is persistently transmitted by a brown planthopper, and has occurred in rice plants in South, Southeast, and East Asia (similar to North and South America). We determined the complete nucleotide (nt) sequences of RNAs 1 (9760 nt), 2 (4069 nt), 3 (3127 nt), 4 (2909 nt), 5 (2704 nt), and 6 (2590 nt) of a southern Philippine isolate from South Cotabato and compared them with those of a northern Philippine isolate from Laguna (Toriyama et al., 1997, 1998). The numbers of nucleotides in the terminal untranslated regions and open reading frames were identical between the two isolates except for the 5′ untranslated region of the complementary strand of RNA 4. Overall nucleotide differences between the two isolates were only 0.08% in RNA 1, 0.58% in RNA 4, and 0.26% in RNA 5, whereas they were 2.19% in RNA 2, 8.38% in RNA 3, and 3.63% in RNA 6. In the intergenic regions, the two isolates differed by 9.12% in RNA 2, 11.6% in RNA 3, and 6.86% in RNA 6 with multiple consecutive nucleotide deletion/insertions, whereas they differed by only 0.78% in RNA 4 and 0.34% in RNA 5. The nucleotide variation in the intergenic region of RNA 6 within the South Cotabato isolate was only 0.33%. These differences in accumulation of mutations among individual RNA segments indicate that there was genetic reassortment in the two geographical isolates; RNAs 1, 4, and 5 of the two isolates came from a common ancestor, whereas RNAs 2, 3, and 6 were from two different ancestors.

Towards a classification of criterion referenced assessment models in mathematics courses : student and academic perspectives

We present the findings of a study into the implementation of explicitly criterion- referenced assessment in undergraduate courses in mathematics. We discuss students' concepts of criterion referencing and also the various interpretations that this concept has among mathematics educators. Our primary goal was to move towards a classification of criterion referencing models in quantitative courses. A secondary goal was to investigate whether explicitly presenting assessment criteria to students was useful to them and guided them in responding to assessment tasks. The data and feedback from students indicates that while students found the criteria easy to understand and useful in informing them as to how they would be graded, it did not alter the way the actually approached the assessment activity.

Direct instruction in mathematics : issues for schools with high Indigenous enrolments : a literature review

Direct instruction, an approach that is becoming familiar to Queensland schools that have high Aboriginal and Torres Strait Islander populations, has been gaining substantial political and popular support in the United States of America [USA], England and Australia. Recent examples include the No Child Left Behind policy in the USA, the British National Numeracy Strategy and in Australia, Effective Third Wave Intervention Strategies. Direct instruction, stems directly from the model created in the 1960s under a Project Follow Through grant. It has been defined as a comprehensive system of education involving all aspects of instruction. Now in its third decade of influencing curriculum, instruction and research, direct instruction is also into its third decade of controversy because of its focus on explicit and highly directed instruction for learning. Characteristics of direct instruction are critiqued and discussed to identify implications for teaching and learning for Indigenous students.

Students' perceptions of the relevance of mathematics in engineering

In this paper, we report on the findings of an exploratory study into the experience of students as they learn first year engineering mathematics. Here we define engineering as the application of mathematics and sciences to the building and design of projects for the use of society (Kirschenman and Brenner 2010)d. Qualitative and quantitative data on students' views of the relevance of their mathematics study to their engineering studies and future careers in engineering was collected. The students described using a range of mathematics techniques (mathematics skills developed, mathematics concepts applied to engineering and skills developed relevant for engineering) for various usages (as a subject of study, a tool for other subjects or a tool for real world problems). We found a number of themes relating to the design of mathematics engineering curriculum emerged from the data. These included the relevance of mathematics within different engineering majors, the relevance of mathematics to future studies, the relevance of learning mathematical rigour, and the effectiveness of problem solving tasks in conveying the relevance of mathematics more effectively than other forms of assessment. We make recommendations for the design of engineering mathematics curriculum based on our findings.