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The enquiry is an interpreting of the phenomenon of school mathematical texts consequent upon, in the first instance, certain difficulties I experienced in school-teaching with such texts. It was an attempt to reach a developed interpretative understanding of school mathematical texts in order that particular problems I experienced teaching with and about such texts be resolved. Initially I enquired into the experience of reading school mathematical texts and developed an understanding of reading based upon studies from semiotics (in particular the work of Ferdinand de Saussure), and on the work of Frank Smith. With such a developed understanding I produced readings of several instances of school mathematical text and in the light of these readings particular essential features of school mathematical texts emerged. My enquiring proceeded with an interpretation of school mathematical texts as objects becoming within the practices of school mathematics teaching, which was based upon both my own experiences with such texts and conversations with forty eight primary school children concerning theirs. With respect to understanding my own experiences with these texts I drew particularly upon the work of Umberto Eco and of David Olson, and with respect to understanding both my own and children's experiences I drew especially upon Martin Heidegger's 'Being and Time'. Finally I addressed the changing nature of the phenomenon of school mathematical texts. My developed understanding of school mathematical texts includes the view that such texts necessarily become authoritarian in character when written so as to preserve, impart, or emphasise a `Textual' mathematics.

Cyanobacterial harmful algal blooms (cHABs) pose significant ecological and public health concerns in freshwater ecosystems. Viruses, specifically phages (viruses that infect bacteria), are increasingly recognized as influential players in microbial community dynamics, yet their roles within cHABs remain poorly understood. This dissertation explores the intricate interactions between phages and their microbial hosts within the context of cHABs, revealing their potential impacts on bloom dynamics and genetic diversity. Chapter 2 delves into the temporal dynamics of phages infecting bloom-forming Microcystis aeruginosa populations in Lake Erie, a region susceptible to recurrent cHABs. Through extensive genomic analyses and a novel machine-learning model, we unveil the complex web of viral interactions within cHABs, highlighting the potential for cross-species exchange of genetic material and potential phage-driven alterations in key metabolic pathways crucial for Microcystis persistence in cHABs. Chapter 3 further explores the role of phages in cHABs more broadly by unraveling the viral community structure and its relationship with the bacterial host community beyond Microcystis. Using metagenomic data, we identify and characterize thousands of viral operational taxonomic units (vOTUs), decipher their metabolic functions, and predict their bacterial hosts. This chapter underscores the dynamic nature of viral communities within cHABs and emphasizes the impact of spatiotemporal variation on viruses and how community turnover affects virus-host interactions. Chapter 4 shifts focus to how Microcystis host evolutionary distance affects their infection profiles, by using a collection of Lake Erie Microcystis multispecies enrichments. We reveal a significant association between Microcystis strain phylogenetic relatedness and infection profiles, suggesting that hosts with similar phylogenies share comparable infection profiles. Furthermore, evidence of infection dynamics within the multispecies colonies formed by Microcystis and its associated bacteria assemblage emerges, as multiple phages are predicted to infect both Microcystis and non-Microcystis hosts within a culture. Collectively, this dissertation advances our understanding of the intricate interplay between phages and their bacterial hosts within cHABs. As such, it provides valuable insights into viral ecology as it pertains to cHABs, paving the way for future research to bolster our understanding of viruses in the wild.