99 resultados para Sequences (Mathematics)

em Deakin Research Online - Australia


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The article explores the conceptual complexity and apparent contradictions in the language of mathematics and suggests ways to handle these problems. Mathematics, as described the author, is a formal, artificially constructed language. One problem arises from the changes of gradient and rates of change of gradient, continuous functions. Conceptual conflicts also arise when least upperbounds and greatest lower-bounds in discussing sequences and series, convergence and limits are considered.

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Various applications of electronic technology have contributed to the field of mathematics teacher education, but the array of tools now' available to teacher educators in developed countries can be somewhat daunting. In this chapter, the authors present an overview of some of these tools and the ways that they are being used. In addition, they address issues surrounding the development and applications of digital technology in teacher education programs in a number of countries. In particular, they present recent applications of videotapes, multimedia resources, internet-based communities, and tutorial conferencing facilities in pre-service and in-service education of mathematics teachers. As professionals who have used technology in teacher education, the authors blend their own insights into this review of technological tools and relevant issues.

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Leicha Bragg shares an effective activity for integrating visual arts, technology and mathematics. Such an approach has the potential to enhance students' visual reasoning and spatial ability by using multiple perspectives of learning. 

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In the first stage of a three-year study in which the effects of using computers for the teaching and learning of mathematics are being explored, a questionnaire was developed and administered to teachers of students in grades 7–10 in a representative sample of co-educational post-primary schools in Victoria, Australia. Using open and closed response formats, the information sought included data on the teachers' professional backgrounds, computer ownership and use, and their beliefs and practices in using computers for the teaching of mathematics. In this article, findings related to ownership, professional development, perceptions of technological skills, beliefs about the efficacy of computer use in mathematics, and data on how teachers are using computers for teaching secondary mathematics are presented and discussed.

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One of the most important requirements for systematic and phylogenetic studies is the identification of gene regions with the appropriate level of variation for the question of interest. Molecular phylogenetic and systematic studies of freshwater crayfish have made use of DNA sequences mainly from ribosomal genes, especially the 16S rRNA gene region. Thus, little information is available on other potentially useful mitochondrial gene regions for systematic studies in these animals. In this study, we look at nucleotide variation and phylogenetic relations within and between four species of freshwater crayfish of the genus Cherax from the southwest of Western Australia using four fragments amplified from the 16S rRNA, 12S rRNA, Cytochrome Oxidase I (COI), and Cytochrome b (Cyt b) gene regions. Samples of Engaeus strictifrons, Euastacus bispinosus, and Geocharax falcata were also sequenced for comparative purposes. The size of the fragments varied from 358 bp to 600 bp. Across all samples, the four fragments showed significant phylogenetic signal and showed similar proportions of variable sites (28.81–37.33%). Average divergence within species for the mitochondrial gene regions varied from 1.18% to 4.91%, with the 16S rRNA being the least variable and Cyt b the most variable. Average divergence between species ranged 7.63–15.53%, with 16S rRNA being the least variable and COI the most variable. At the generic level, average divergence ranged 17.21–23.82%. Phylogenetic analyses of the 16S rRNA, 12S rRNA, and COI regions generated four clades consistent with the presence of four species previously identified on the basis of allozyme and morphological studies. The relationships among samples were largely congruent across the data set, although some relationships remained unresolved. Not all samples could be amplified using the Cyt b primers, and some of those that were showed quite anomalous relationships, suggesting that one or more Cyt b pseudogenes were being amplified.

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This study uses nucleotide sequences from the 16S rRNA mitochondrial gene to investigate the taxonomy and phylogeny of freshwater crayfish belonging to the 'Cherax destructor' complex. The sequencing of an approximately 440-bp fragment of this gene region from freshwater crayfish sampled from 14 locations identified significant haplotype diversity. Phylogenetic analysis found three distinct clades that correspond to the species C. rotundus, C. setosus and C. destructor. C. rotundus is largely confined to Victoria, and C. setosus is restricted to coastal areas north of Newcastle in New South Wales. C. destructor is widely distributed in eastern Australia and shows significant phylogeographic structure, with three well supported clades. None of these clades, however, correspond to species previously recognised as C. esculus, C. davisi or C. albidus. The failure to genetically distinguish these morphologically defined species is consistent with reproductive information and morphological plasticity relating to habitat similar to that documented for other Cherax species.

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Descriptive measurement reliability and validity data are reported on scores from the Mathematics Self-Efficacy Scale (MSES) in two contexts—class and test—for a sample of 302 Australian high school students. Summated scores on the MSES correlated r = .74, and together these items yielded one component that explained 49% of the variance. MSES scores demonstrated internal reliability for both class and test (Cronbach alphas = .86 and .90). Statistically significant correlations between MSES scores, past mathematics grades, and Marsh’s Self-Description Questionnaire III (Math) were used to indicate the convergent validity of scores for the MSES. Discriminant validity of the MSES scores was suggested by the lack of significant correlations between the MSES measures and students’ desired English grades. Statistically significant correlations between MSES scores and students’ desired mathematics grades indicated concurrent validity of the MSES measures. A statistically significant difference between class and test scores supported Bandura’s prescription for context specificity in efficacy research.

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The evolutionary relationships of the freshwater prawn genus Macrobrachium are obscure. Members of this genus are widely distributed across tropical and subtropical regions. The phylogenetic relationships among the seven endemic and six non-endemic Australian Macrobrachium, along with five non-Australian species, were inferred from the mitochondrial 16S rRNA gene sequences. Methods of analysis yielded phylogenetic trees of differing topologies; however, none supported a monophyletic origin for endemic Australian Macrobrachium. Enforced monophyly of a single origin of endemic Macrobrachium was statistically tested and rejected. These results support the view that the endemic Australian Macrobrachium arose from multiple origins. Previous biogeographical hypotheses related to the radiation of Macrobrachium into Australia are re-examined in the context of these results.

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Nucleotide sequence data were used to re-examine systematic relationships and species boundaries within the genus Cherax from eastern Australia. Partial sequences were amplified from the 12S (~365 bp) and 16S (~545 bp) rRNA mitochondrial gene regions. Levels of intra- and inter-specific divergence for Cherax species were very similar between the two gene regions and similar to that reported for other freshwater crayfish for 16S rRNA. Phylogenetic analyses using the combined data provided strong support for a monophyletic group containing 11 eastern Australian species and comprising three well-defined species-groups: the 'C. destructor' group containing three species, the 'C. cairnsensis' group containing four species and the 'C. cuspidatus' group containing two species. Cherax dispar and C. robustus are distinct from all other species and each other. In addition, two northern Australian and a New Guinean species were placed in the 'Astaconephrops' group, which is the sister-group to the eastern Australian Cherax lineage. Several relationships were clarified, including: the status of northern and southern C. cuspidatus as separate species; a close relationship between C. cairnsensis and C. depressus; the validity of C. rotundus and C. setosus as separate species and their close affinities with C. destructor; and the distinctiveness of the northern forms of Cherax. The analysis of the 12S rRNA and 16S rRNA data is highly concordant with the results of previous allozyme studies.

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Fish of the genus Gadopsis are a distinctive component of the freshwater fish fauna of south-eastern Australia. Gadopsis marmoratus and G. bispinosus are the only two species recognised within the genus, with the former of uncertain taxonomic status, as it is thought to be composed of at least two distinct geographical forms based on morphological and allozyme data. The objective of this study was to investigate DNA sequence divergence in Gadopsis, especially in the western portion of its distribution, using an approximately 400 base pair fragment of the mitochondrial small subunit 12S rRNA gene region in order to reassess the taxonomy of the genus. Individuals from 11 locations were sequenced and confirm that G. marmoratus and G. bispinosus are genetically distinct, and further that the G. marmoratus complex consists of two divergent clades representing the previously identified northern and southern forms. The degree of divergence between the three Gadopsis clades was similar (5–6% nucleotide substitutions), suggesting that they diverged from a common ancestor at approximately the same period in geological time. These results are consistent with previous allozyme studies and highlight the usefulness of mitochondrial DNA data coupled with allozyme information for clarifying taxonomic boundaries in morphologically conservative aquatic organisms.

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Direct sequencing of mitochondrial DNA (mtDNA) D-loop (745 bp) and MTATPase6/MTATPase8 (857 bp) regions was used to investigate genetic variation within common carp and develop a global genealogy of common carp strains. The D-loop region was more variable than the MTATPase6/MTATPase8 region, but given the wide distribution of carp the overall levels of sequence divergence were low. Levels of haplotype diversity varied widely among countries with Chinese, Indonesian and Vietnamese carp showing the greatest diversity whereas Japanese Koi and European carp had undetectable nucleotide variation. A genealogical analysis supports a close relationship between Vietnamese, Koi and Chinese Color carp strains and to a lesser extent, European carp. Chinese and Indonesian carp strains were the most divergent, and their relationships do not support the evolution of independent Asian and European lineages and current taxonomic treatments.

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The complete mitochondrial DNA sequence was determined for the Australian giant crab Pseudocarcinns gigas (Crustacea: Decapoda: Menippidae) and the giant freshwater shrimp Macrobrachium rosenbergii (Crustacea: Decapoda: Palaemonidae). The Pse gigas and Mrosenbergii mitochondrial genomes are circular molecules, 15,515 and 15,772 bp in length, respectively, and have the same gene composition as found in other metazoans. The gene arrangement of M. rosenbergii corresponds with that of the presumed ancestral arthropod gene order, represented by Limulus polyphemus, except for the position of the tRNALeu(UUR) gene. The Pse. gigas gene arrangement corresponds exactly with that reported for another brachyuran, Portunus trituberculatus, and differs from the M. rosenbergii gene order by only the position of the tRNAHis gene. Given the relative positions of intergenic nonoding nucleotides, the “duplication/random loss” model appears to be the most plausible mechanism for the translocation of this gene. These data represent the first caridean and only the second brachyuran complete mtDNA sequences, and a source of information that will facilitate surveys of intraspecific variation within these commercially important decapod species.

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TATA box is one of the most important transcription factor binding sites. But the exact sequences of TATA box are still not very clear yet. In this study, we conducted a dedicated analysis on the frequency distribution of TATA Box and its extension sequences on human promoters. Sixteen TATA elements derived from TATA Box motif, TATAWAWN, were classified into three distribution patterns: peak, bottom-peak and bottom. Fourteen TATA extension sequences (up to two base extensions) were predicted to be the new TATA Box elements because of their high motif factors, which indicate their statistical significance. Statistical analysis on the promoters of mouse, zebrafish and drosophila melanogaster verified seven of these elements. It was also observed that the distribution of TATA elements on the promoters of housekeeping genes are very similar with their distribution on the promoters of tissue specific genes in human.

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This article presents an examination of the use of Rasch modelling in a major research project, 'Improving Middle Years Mathematics and Science' (IMYMS). It is unarguable that it is important to take students' perceptions, or views, into account when planning learning and teaching for them. The IMYMS student perceptions survey is an attempt to make visible these student viewpoints, and report them in a way that is accessible to teachers and researchers involved in the project. The project involves four clusters of schools from urban and regions of Victoria to investigate the role of mathematics and science knowledge and subject cultures in mediating change processes in the middle years of schooling. There are five secondary and twenty-eight primary schools. The project has generated both qualitative and quantitative data, with much of the qualitative data being ordinal in nature. Reporting the results of analyses for a range of audiences necessitates careful, well-designed report formats. Some useful new report formats based on Rasch modeling -the Modified Variable Map, the Ordinal Map, the Threshold Map, and the Annotated Ordinal Map - are illustrated using data from the IMYMS project. The Rasch analysis and the derived reporting formats avoid the pitfalls that exist when working with ordinal data and provide insights into the respondents' views about their experiences in schools unavailable by other approaches.