Vagueness in mathematics talk

The Cockcroft Report claimed that "mathematics provides a means of communication which is powerful, concise and unambiguous". Such precision in language may be a conventional aim of mathematics, particularly when communicated in writing. Nonetheless, as this thesis demonstrates, vagueness is commonplace when people talk about mathematics. In this thesis, I examine the circumstances in which vagueness arises in mathematics talk, and consider the practical purposes which speakers achieve by means of vague utterances in this context. The empirical database, which is considered in Chapters 4 to 7, consists almost entirely of transcripts of mathematical conversations between adult interviewers (including myself) and one or two children. The data were collected from clinical interviews focused on a small number of tasks, and from fragments of teaching. For the most part, the pupils involved in the study were aged between 9 and 12, although the age-range in Chapter 7 extends from 4 to 25. I draw on a number of approaches to discourse associated with 'pragmatics' -a field of linguistics - to analyse the motives and communicative effectiveness of speakers who deploy vagueness in mathematics talk. I claim that, for these speakers, vagueness fulfills a number of purposes, especially 'shielding', i. e. self-protection against accusation of being wrong. Another purpose is to give approximate information; sometimes to achieve shielding, but also to provide the level of detail that is deemed to be appropriate in a given situation. A different purpose, associated with a particular form of vagueness (of reference), is to compensate for lexical gaps in pursuit of effective communication of concepts and ideas. I show, in particular, how speakers use the pronouns 'it' and 'you' in mathematics talk to communicate concepts and generalisations. Some consideration is given to the intentions of 'expert speakers of mathematics when they deploy vague language. Their purposes include some of those identified for novices. Teachers also use vagueness as a means of indirectness in addressing pupils; this strategy is associated with the redress of 'face threatening acts'. My thesis is that vagueness can be viewed and presented, not as a disabling feature of language, but as a subtle and versatile device which speakers can and do deploy to make mathematical assertions with as much precision, accuracy or as much confidence as they judge is warranted by both the content and the circumstances of their utterances. I report on the validation and generalisation of my findings by an Informal Research Group of school teachers, who transcribed and analysed their own classroom interactions using the methods I had developed

Upward Influence in Organizations: Test of A Model

A causal model of upward influence in organizations was proposed and tested on a sample of staff nurses and their supervisors in a hospital setting. LISREL results demonstrated that the proposed model fit the data well, and reflected a better fit than several alternative models that were estimated. The contributions and limitations of the present study are discussed, in addition to challenges and directions for future research

The Changing Role of Pharmacists as Evidenced by the Strong Vocational Interest Blank

The Strong Vocational Interest Blank/Strong Campbell Interest Inventory-Merged Form, or simply Strong Vocational Interest Blank (SVIB), is widely used to determine the suitability of a student\u27s interests to a particular field. In the process of norming the instrument, data concerning the satisfaction of practitioners of a field and their responses on the instrument are gathered. Such data lend themselves to analysis of trends in the characteristics of those practitioners both over time and over the satisfaction spectrum. Hence changes in the field and characteristics lending themselves to satisfaction can be ascertained

PUBLIC FAMILY SPENDING, LABOUR PRODUCTIVITY, INCOME INEQUALITY AND POVERTY GAP IN THE GROUP OF SEVEN COUNTRIES: EMPIRICAL EVIDENCE FROM PANEL DATA

Purpose. Comparable data on distribution of family income provide reference point for determining economic performance of any country, opportunity to assess effects of income inequality and poverty drivers that are either country- or region-specific. This study analysed the effectiveness of composite indices of public spending on family benefits, labour productivity, macroeconomic performance indicators and moderating factors in reducing income inequality and poverty gap in the Group of Seven (G7) countries from 1980 to 2019. Methodology. The study employed fixed effects Least Squares regression model in panel environment within the framework of empirical econometric methodologies. The composite indices comprised public spending on family benefits in cash and kind, unemployment allowance payments, tax on personal income, labour productivity, harmonised unemployment rate, consumer price index, real GDP growth rate, GDP per capita and per hour worked, fertility rate and trade. After graphical analysis of the data, order of integration was via unit root tests. Hausman test was carried out to choose between fixed and random effects models. Subsequently, parameters of the models were estimated and evaluated for significance at the 0.05 critical level. Findings. The results showed that percentage changes in income inequality and poverty gap indices differed for same percentage change in components of the composite indices. Some variable-specific percentage changes in income inequality and poverty gap were statistically significant, while others were not. However, the overall percentage changes was statistically significant. The paper concluded that while some specific effectiveness of the explanatory variables in reducing income inequality and poverty gap was not significant, their joint effectiveness significantly reduced poverty. Therefore, it is pertinent that family-oriented fiscal policy thrusts should be strengthened and sustained so as to continually reduce income inequality and, ultimately, narrow poverty gap in the countries. Limitations. The study considered the G7 countries for a period of 40 years. The limitations were that the variables considered to influence income inequality and poverty gap in the countries were both exhaustive. Also, the results were conditioned to the method used, and different methods can alternatively be used by other researchers and the results compared with this. Originality. The study is original research paper. It has neither been published in any other peer-reviewed journal not under consideration for publication by any other journal

Chemical analysis of flotsam ambergris

The natural product ambergris is only found rarely on beaches, as jetsam. Even more scarce, or even absent, are accounts of flotsam ambergris. Here, we report the chemical analysis of a rare, large piece (\u3e100kg) of flotsam found in the Atlantic in 2019. About 95% of subsamples from the outside of the coprolith was soluble in dichloromethane. Of this, FTIR spectroscopy, APCI-MS and GC-MS indicated the presence of ambrein. Radiocarbon dating indicated that the sample was post 1950s in age. The 13C/12C isotope ratio (−22.5 ‰) was typical of those reported to date for whale ‘body’ ambergris. Metals of ambergris have hardly been reported previously. The distribution found here for the flotsam, was dominated by copper and zinc, which is similar to that of several squid species. This is also consistent with the presence of squid beaks in the coprolith. Squid are a major prey species of sperm whales

A duck with four legs: Investigating the structure of conceptual knowledge using picture drawing in semantic dementia

In Study 1, six patients with semantic dementia were asked to produce drawings of concrete concepts from dictation of their names. The drawings were characterised by a loss of distinctive features. In the artefact domain, this feature loss resulted in representations that were increasingly box-like. In the living domain, as well as distinctive features being lost, there was a tendency for patients to include incorrect features that resulted in more familiar and "prototypical" representations. A second study included two further conditions in the drawing assessment: immediate and delayed copying of line drawings of concrete concepts. Analysis of the drawings produced by three patients with semantic dementia confirmed that overall performance was significantly influenced by the task condition (immediate delayed) and severity of disease. The rate of intruding features, but not of omitted ones, was influenced by the domain of the item, with a greater proportion of intrusions in the living than in the nonliving domain. There was also a significant effect of feature distinctiveness on the proportions of these error types: Intruded features were most likely to come from the pool of properties that are shared across domain

Soaking beans for 12 h reduces split percent and cooking time regardless of type of water used for cooking

Beans are one of the most important cheap source of protein in developing countries. However, their utilisation in the diets of many people remains limited due to long cooking time, among others. Therefore, it is imperative to identify ways to enhance utilisation of beans. The aim of the current study was to assess the effects of soaking and cooking in different types of water (tap, borehole, acidulated- 1.0 percent citric acid and soda- 0.2 percent sodium bicarbonate) on cooking time (CT), split percentage (SP) and total soluble solids (TSS) in broth of different va rieties of beans. Results show that soaking significantly reduced CT across eight varieties from an average CT of 109.5–84.6 min in tap water, 109.5–85.2 min in borehole water, 115.9–92.7 min in acidulated water and 82.0–51.2 min in soda water representing 22.7%, 22.1%, 20.0% and 37.6% reduction in CT, respectively. Soaking generally decreased SP and varietal differences were observed suggesting beans are less likely to break when soaking precede cooking. Although cooking in soda water significantly reduced CT, unfortunately, it increased SP. Acidulated water extended CT but reduced SP in almost all varieties. Soaking generally decreased TSS in broth from 7.0 to 6.7% in tap water, 6.1–5.8% in borehole water and 11.3–7.7% in soda water while it increased TSS in acidulated water from 18.2 to 20.6% across all the eight varieties which suggest reduction in leaching out of bean solids into cooking water which is consistent with reduced SP of soaked beans. While use of soda water reduced cooking time and therefore saved time and energy, its effect of increasing split percent may not be appealing to some consumers. This study has demonstrated that bean soaking significantly reduced cooking time and split percent and these can also be affected by type of cooking water

Linking hydraulic traits to tropical forest function in a size-structured and trait-driven model (TFS v.1-Hydro)

Forest ecosystem models based on heuristic water stress functions poorly predict tropical forest response to drought partly because they do not capture the diversity of hydraulic traits (including variation in tree size) observed in tropical forests. We developed a continuous porous media approach to modeling plant hydraulics in which all parameters of the constitutive equations are biologically interpretable and measurable plant hydraulic traits (e.g., turgor loss point πtlp, bulk elastic modulus ε, hydraulic capacitance Cft, xylem hydraulic conductivity ks,max, water potential at 50 % loss of conductivity for both xylem (P50,x) and stomata (P50,gs), and the leaf : sapwood area ratio Al : As). We embedded this plant hydraulics model within a trait forest simulator (TFS) that models light environments of individual trees and their upper boundary conditions (transpiration), as well as providing a means for parameterizing variation in hydraulic traits among individuals. We synthesized literature and existing databases to parameterize all hydraulic traits as a function of stem and leaf traits, including wood density (WD), leaf mass per area (LMA), and photosynthetic capacity (Amax), and evaluated the coupled model (called TFS v.1-Hydro) predictions, against observed diurnal and seasonal variability in stem and leaf water potential as well as stand-scaled sap flux.Our hydraulic trait synthesis revealed coordination among leaf and xylem hydraulic traits and statistically significant relationships of most hydraulic traits with more easily measured plant traits. Using the most informative empirical trait–trait relationships derived from this synthesis, TFS v.1-Hydro successfully captured individual variation in leaf and stem water potential due to increasing tree size and light environment, with model representation of hydraulic architecture and plant traits exerting primary and secondary controls, respectively, on the fidelity of model predictions. The plant hydraulics model made substantial improvements to simulations of total ecosystem transpiration. Remaining uncertainties and limitations of the trait paradigm for plant hydraulics modeling are highlighted