Mathematical practices and mathematical modes of enquiry: Same or different?

Background: In this paper, I share a case study of a teacher’s work on mathematics tasks in the context of a ‘mathematics for teaching’ course aiming to develop mathematical content understandings and mathematical practices among primary teachers in one South African province. The course was developed in a national context of concerns about the nature and levels of primary teachers’ mathematical knowledge. Theories viewing mathematical practices as fundamental, contrasted with those that view mathematical practices and mathematical content in more separate and ‘to be integrated’ ways, are used to frame the analysis and ritically reflect on the findings. Results: Data from this teacher’s pre-test and selected course assessments and interactions suggest that while he was able to develop some aspects of the mathematical practices described in the literature, his overall orientation remained attuned to memorization and recall. Findings also pointed to an ongoing reliance on external validation of the ‘correctness’ of his answers. Conclusions: The data suggest that the presence of elements of mathematical practices cannot be viewed as equivalent to the presence of mathematical modes of enquiry. The analysis presented in this paper suggests that while elements of mathematical practices can be developed, moving towards an encompassing orientation to mathematical modes of enquiry may require more central focus on problem-solving approaches to achieve a change in orientation

Tortricid Moths Reared from the Invasive Weed Mexican Palo Verde, Parkinsonia aculeata, with Comments on their Host Specificity, Biology, Geographic Distribution, and Systematics

As part of efforts to identify native herbivores of Mexican palo verde, Parkinsonia aculeata L. (Leguminosae: Caesalpinioideae), as potential biological control agents against this invasive weed in Australia, ten species of Tortricidae (Lepidoptera) were reared from Guatemala, Mexico, Nicaragua, and Venezuela: Amorbia concavana (Zeller), Platynota rostrana (Walker), Platynota helianthes (Meyrick), Platynota stultana Walsingham (all Tortricinae: Sparganothini), Rudenia leguminana (Busck), Cochylis sp. (both Tortricinae: Cochylini), Ofatulena duodecemstriata (Walsingham), O. luminosa Heinrich, Ofatulena sp. (all Olethreutinae: Grapholitini), and Crocidosema lantana Busck (Olethreutinae: Eucosmini). Significant geographic range extensions are provided for O. duodecemstriata and R. leguminana. These are the first documented records of P. aculeata as a host plant for all but O. luminosa. The four species of Sparganothini are polyphagous; in contrast, the two Cochylini and three Grapholitini likely are specialists on Leguminosae. Ofatulena luminosa is possibly host specific on P. aculeata. Host trials with Rudenia leguminana also provide some evidence of specificity, in contrast to historical rearing records. To examine the possibility that R. leguminana is a complex of species, two data sets of molecular markers were examined: (1) a combined data set of two mitochondrial markers (a 781-basepair region of cytochrome c oxidase I (COI) and a 685-basepair region of cytochrome c oxidase II) and one nuclear marker (a 531-basepair region of the 28S domain 2); and (2) the 650-basepair “barcode” region of COI. Analyses of both data sets strongly suggest that individuals examined in this study belong to more than one species

HIV-Specific T-Cells Accumulate in the Liver in HCV/HIV Co-Infection

BACKGROUND AND AIMS: Hepatitis C Virus (HCV)-related liver disease progresses more rapidly in individuals co-infected with Human Immunodeficiency Virus-1 (HIV), although the underlying immunologic mechanisms are unknown. We examined whether HIV-specific T-cells are identified in the liver of HCV/HIV co-infected individuals and promote liver inflammation through bystander immune responses. METHODS: Ex-vivo intra-hepatic lymphocytes from HCV mono-infected and HCV/HIV co-infected individuals were assessed for immune responses to HIV and HCV antigens by polychromatic flow cytometry. RESULTS: HCV/HIV liver biopsies had similar frequencies of lymphocytes but lower percentages of CD4+ T-cells compared to HCV biopsies. In co-infection, intra-hepatic HIV-specific CD8+ and CD4+ T-cells producing IFN-gamma and TNF-alpha were detected and were comparable in frequency to those that were HCV-specific. In co-infected individuals, viral-specific CD8+ T-cells produced more of the fibrogenic cytokine, TNF-alpha. In both mono- and co-infected individuals, intra-hepatic HCV-specific T-cells were poorly functional compared to HIV-specific T-cells. In co-infection, HAART was not associated with a reconstitution of intra-hepatic CD4+ T-cells and was associated with reduction in both HIV and HCV-specific intra-hepatic cytokine responses. CONCLUSION: The accumulation of functional HIV-specific T-cells in the liver during HCV/HIV co-infection may represent a bystander role for HIV in inducing faster progression of liver disease

Bayesian Denoising of Visual Images in the Wavelet Domain

The use of multi-scale decompositions has led to significant advances in representation, compression, restoration, analysis, and synthesis of signals. The fundamental reason for these advances is that the statistics of many natural signals, when decomposed in such bases, are substantially simplified. [...] In this chapter, we examine the empirical statistical properties of visual images within two fixed multi-scale bases, and describe two statistical models for the coefficients in these bases. The first is a non-Gaussian marginal model, previously described in [icip-96]. The second is a joint non-Gaussian Markov model for wavelet subbands, previous versions of which have been described in [icassp-97,asilomar-97]. We demonstrate the use of each of these models in Bayesian estimation of an image contaminated by additive Gaussian white noise

Assessing the Performance of Independent Component Analysis in Remote Sensing Data Processing

Independent component analysis (ICA) is a novel method to be considered as a powerful type of analysis in the process of source signal separation. Based on the capabilities of this particular analysis, there will be a hypothesis of applying ICA in the image processing of remote sensing data. This paper aims to introduce the ability of ICA in contrasting and highlighting some area with potential of mineralization. Considering and applying ICA transformation on the ETM+ image of southern Masule, Iran has resulted in finding some favorable points for further investigation. Moreover, sampling program on the indicated area has led to identify some huge, unexpected lithology and dikes. ICA analysis is a robust method even in remote sensing data processing with the high speed and capabilities in separating source signals from noise. © 2012 Indian Society of Remote Sensing

Papilio aegeus Donovan (Lepidoptera : Papilionidae) host plant range evaluated experimentally on ancient angiosperms

Chemical similarities among ancient Angiosperms presumably played a role in the ecological and evolutionary diversification of the swallowtail butterflies (Papilionidae). The abilities of neonate larvae of the Citrus swallowtail, Papilio (=Princeps) aegeus (from Queensland, Australia), to eat, survive and grow on leaves (a choice of young and old) of 34 plant species from families of ancient Angiosperms; 8 Rutaceae, 3 Magnoliaceae, 13 Lauraceae, 3 Monimiaceae, 1 Aristolochiaceae, 2 Apiaceae, 1 Sapotaceae, 1 Winteraceae and 2 Annonaceae were tested. It was apparent that there is genetic variation in populations of Rutaceae-specialised Australian P. aegeus for acceptance, consumption and larval growth, reflecting differential suitability of some native Australian Lauraceae species as food plants (as well as certain Winteraceae, Monimiaceae and non-Australian Magnoliaceae, Lauraceae and Annonaceae). No consumption or survival of P. aegeus was seen on Aristolochia elegans (Aristolochiaceae) or Pouteria australis (Sapotaceae) despite literature records alluding to this possibility. The Rutaceae specialist P. aegeus appears to have the fundamental detoxification capabilities for processing many existing species of the basal Angiosperm families, without having direct ancestors that historically had fed on them

Significance of a new field oviposition record for Graphium eurypylus (L.) (Lepidoptera: Papilionidae) on Michelia champaca (Magnoliaceae)

Phytochemical similarities among ancient Angiosperms presumably played a role in the ecological and evolutionary diversification of the swallowtail butterflies (Papilionidae). Host family feeding specialisation is typical of most Papilionidae species, but field records of oviposition are rare for most swallowtail butterflies. It is even more uncommon to witness oviposition and larval feeding on new host plant species, especially in plant families not previously reported for the butterfly species. Oviposition by a female on a new host, or even on a toxic plant, may represent ancestral behaviour (with a loss of larval acceptance, detoxification or processing abilities) or novel behaviour (providing genetic variation for a potential expansion of host range, or host shift). We document the oviposition, larval use and pupation of the Annonaceae specialised and geographically widespread Graphium eurypylus on a Magnoliaceae species, all under field conditions in Queensland, Australia. This is the first time such field observations of oviposition and larval feeding on Michelia champaca (Magnoliaceae) have been documented anywhere for this species