Individual differences in learning from worked examples by senior secondary mathematics students

The primary purpose of this research was to examine individual differences in learning from worked examples. By integrating cognitive style theory and cognitive load theory, it was hypothesised that an interaction existed between individual cognitive style and the structure and presentation of worked examples in their effect upon subsequent student problem solving. In particular, it was hypothesised that Analytic-Verbalisers, Analytic-Imagers, and Wholist-lmagers would perform better on a posttest after learning from structured-pictorial worked examples than after learning from unstructured worked examples. For Analytic-Verbalisers it was reasoned that the cognitive effort required to impose structure on unstructured worked examples would hinder learning. Alternatively, it was expected that Wholist-Verbalisers would display superior performances after learning from unstructured worked examples than after learning from structured-pictorial worked examples. The images of the structured-pictorial format, incongruent with the Wholist-Verbaliser style, would be expected to split attention between the text and the diagrams. The information contained in the images would also be a source of redundancy and not easily ignored in the integrated structured-pictorial format. Despite a number of authors having emphasised the need to include individual differences as a fundamental component of problem solving within domainspecific subjects such as mathematics, few studies have attempted to investigate a relationship between mathematical or science instructional method, cognitive style, and problem solving. Cognitive style theory proposes that the structure and presentation of learning material is likely to affect each of the four cognitive styles differently. No study could be found which has used Riding's (1997) model of cognitive style as a framework for examining the interaction between the structural presentation of worked examples and an individual's cognitive style. 269 Year 12 Mathematics B students from five urban and rural secondary schools in Queensland, Australia participated in the main study. A factorial (three treatments by four cognitive styles) between-subjects multivariate analysis of variance indicated a statistically significant interaction. As the difficulty of the posttest components increased, the empirical evidence supporting the research hypotheses became more pronounced. The rigour of the study's theoretical framework was further tested by the construction of a measure of instructional efficiency, based on an index of cognitive load, and the construction of a measure of problem-solving efficiency, based on problem-solving time. The consistent empirical evidence within this study that learning from worked examples is affected by an interaction of cognitive style and the structure and presentation of the worked examples emphasises the need to consider individual differences among senior secondary mathematics students to enhance educational opportunities. Implications for teaching and learning are discussed and recommendations for further research are outlined.

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.