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Emma-Louise Lord Title of study: Calculation fluency: A mixed methods study in English primary classrooms The teaching and learning of written calculation strategies remains a high priority in many national curricula. However, the available literature was dominated by quantitative studies which explored a restricted range of arithmetic operations, paying limited attention to the role of confidence or the reasons behind the selection of their calculation strategies with the learners themselves. The literature revealed that calculation fluency was generally accepted to require flexibility, efficiency, accuracy, and conceptual understanding, yet recent curriculum reforms in English schools prioritised formal algorithms and thus appeared to restrict calculation fluency in the classroom. This study explored calculation fluency among the first cohort of Year 6 learners (10- to 11-year-olds) studying under the reforms by asking: To what extent does calculation fluency among Year 6 learners vary by gender, confidence level and prior attainment? Phase 1 of this sequential mixed methods explanatory study involved a large-scale survey (N = 590) where each participant was presented with a ten-question, Likert-style mathematics confidence questionnaire followed by a workbook specifically developed for this study containing 16 age-related, context-free multi-digit calculations covering addition, subtraction, multiplication and division. The participants' answers were compared by gender, mathematical confidence and previous attainment using regression analysis. Phase 2 consisted of a purposeful sample of learners drawn from Phase 1 (n = 23) who attended individual semi-structured interviews exploring their workbook responses in more depth. Their comments were examined using framework analysis, then the findings from both phases were integrated together to address the research question. The findings indicated that too many learners failed to satisfy the stated criteria for calculation fluency. Many learners worked inaccurately, inflexibly and inefficiently by prioritising formal algorithms irrespective of the merits of individual calculations. They either failed to recognise situations where other strategies might have been more efficient and less likely to lead to error, or they were unwilling to deviate from using formal algorithms. The findings indicated that confidence, rather than gender or prior attainment, had the greatest effect of the three predictor variables on use of the formal algorithm; confident learners were less likely to deviate from using formal algorithms than other learners. The findings also revealed that girls were significantly less likely to deviate from using formal algorithms than boys. However, most of the variance in calculation fluency was determined by factors other than gender, prior attainment or confidence. Calculation fluency was also affected by practice, knowledge of testing procedures and an individual's checking procedures. Hence, it is recommended that future researchers consider adopting a mixed methods research design due to the insights gained in this thesis. Moreover, by addressing all four operations, I was able to identify patterns in my findings across the operations. Regarding policymakers, my findings indicated that the decision to prioritise formal algorithms in the primary curriculum may need further consideration. Schools should consider encouraging their learners to calculate more flexibly to increase their accuracy rates, calculation efficiency and conceptual understanding. Further research should be undertaken to ascertain the longer-term effects on both genders and differing mathematical confidence levels of limiting calculation flexibility at primary level when those learners will experience a curriculum dominated by problem-solving, rather than calculation, later in their education.

Digital technology has radically disrupted the established ways of organising the film industry. However, digital initiatives such as marketing and distribution strategies involving social media and online distribution have also provided means through which filmmakers manage this environment. I investigate the role of the digital data involved, which I term Digital Engagement Metrics (DEMs), in market reconfiguration. Through exploratory, longitudinal case study of market construction for independent films, the thesis articulates the interdependent combination of attributes that co-constitute DEMs' highly mobile, and multifaceted valuation capacities, and develops a conceptualisation of their role as a market device. I engage with the literature of translation, calculation, and the performativity and materiality of markets. I then develop an approach for tracing market activity to understand the interaction of networked agencies that shape the arrangement of economic transactions. My analysis is delivered in three empirical chapters, which provide rare data on the emergent digital practice of a film production company. I chart the progressive establishment of DEMs' role in the hybridisation of established market attachment frameworks, and the instantiation of new modes of coordinating market actors. I conclude that the dynamic assembly, content and distributed architecture of market arrangements involving DEMs simultaneously shape the product and enable its calculation. In addition to extending the reach of market studies into a new empirical field, I make a number of contributions to the theoretical literature. My findings bring two coordinating kinds of performativity into focus. These are the creation of felicitous conditions required to mobilise DEMs as an organisational concept, and the digital materialisation of the audience both as the market, and as a qualified property of the market object. Reading DEMs through the market devices lens renders previously hidden modes of calculation visible, and this has implications for developing assemblage-oriented research in the creative industries.

Methods to automatically extract and validate data from the chemical literature in legacy formats to machine-understandable forms are examined. The work focuses of three types of data: analytical data reported in articles, computational chemistry output files and crystallographic information files (CIFs). It is shown that machines are capable of reading and extracting analytical data from the current legacy formats with high recall and precision. Regular expressions cannot identify chemical names with high precision or recall but non-deterministic methods perform significantly better. The lack of machine-understandable connection tables in the literature has been identified as the major issue preventing molecule-based data-driven science being performed in the area. The extraction of data from computational chemistry output files using parser-like approaches is shown to be not generally possible although such methods work well for input files. A hierarchical regular expression based approach can parse > 99.9% of the output files correctly although significant human input is required to prepare the templates. CIFs may be parsed with extremely high recall and precision, contain connection tables and the data is of high quality. The comparison of bond lengths calculated by two computational chemistry programs show good agreement in general but structures containing specific moieties cause discrepancies. An initial protocol for the high-throughput geometry optimisation of molecules extracted from the CIFs is presented and the refinement of this protocol is discussed. Differences in bond length between calculated and experimentally determined values from the CIFs of less than 0.03 Angstrom are shown to be expected by random error. The final protocol is used to find high-quality structures from crystallography which can be reused for further science.

We present a complete calculation of the photon +1 jet rate in e(^+)e(^-) annihilation up to O(aa(_s)). Although formally of next-to-leading order in perturbation theory, this calculation contains several ingredients appropriate to a next-to-next-to-leading order calculation of jet observables. No such calculation has been performed before, and the work discussed here represents a first step in that direction. In particular, we describe a generalization of the commonly used phase space slicing method to isolate the singularities present when more than one particle is unresolved. More precisely, we provide an analytic evaluation of the following multiple unresolved factors: triple collinear factor, soft/collinear factor and double single collinear factor. By comparing the results of our calculation with the existing data on the photon +1 jet rate from the ALEPH Collaboration at CERN, we make a new determination of the process-independent non-perturbative quark-to-photon fragmentation function D(_q-γ)(z,μ(_F)) at O(aa(_s)). at As a first application of this measurement allied with our improved perturbative calculation, we determine the dependence of the isolated photon -fl jet cross section in a democratic clustering approach on the jet resolution parameter y(_cut) at next-to-leading order. Inclusion of the next-to-leading order corrections to this observable considerably improves the agreement between theoretical prediction and experimental data.

The idea that friendship is an illusory connection that may only exist in philosophers’ writings was a subject of interest for many of the early modern writers. Writers like Thomas Elyot, Thomas Churchyard, and Michel de Montaigne attempted to uphold idealized traditions of friendship; conversely, Shakespeare, along with writers such as Francis Bacon, presented early modern perceptions of idealized friendship only to confront and challenge the precepts. In The Merchant of Venice and Othello, the Moor of Venice, Shakespeare expresses a sometimes cynical yet realistic approach toward idealized friendship. He exposes the problem of upholding the idealized early modern version of amity in order to present a more realistic representation of friendship.

While working as an intern in the corporate pensions department of Rudd and Wisdom, Inc., Consulting Actuaries, I learned about the different kinds of pension plans available to businesses and became familiar with the process of benefit calculation. I performed several benefit calculations for clients under different scenarios and plan specifications. When a participant of a pension plan retires, terminates employment, dies, or becomes disabled, the participant (or his or her beneficiary) may request a calculation to illustrate benefit options. In each case, the methods used to perform such a calculation and the benefit options available to the participant or beneficiary are different. In this report, I will demonstrate a number of scenarios illustrating plan provisions and methods of calculation.

In this dissertation I present an analysis of the practices of calculation needed to create carbon forestry offsets in Costa Rica, with special attention to the spaces that are produced through such practices. Carbon forestry offsets are a mechanism by which a person, nation, or corporation can offset the climactic impact of their greenhouse gas emissions by purchasing a credit, which funds a forestry project that sequesters an equivalent amount of carbon. I explore the function and effects of the scientific and technical work that is undertaken so that carbon may be rendered as a source of value. Drawing on the writings of Martin Heidegger, I argue that the calculations needed to bring a carbon forestry offset into being as a commodity is a process that is grounded in a technological metaphysics, where the world becomes disclosed to us as an object of orderability. This ontological orientation allows for the objects and subjects of the world – carbon commodities as well as producers and consumers of carbon offsets – to become relationally embedded in the world through the production of bounded Cartesian space. Building on this argument about the ontological grounds of carbon offsets, I also investigate the bodily performances needed to maintain spaces of carbon sequestration. I do so by examining the transitive movement between the abstract and the material that ultimately produces the spaces of the forest as a commodified forestry offset. I argue that this oscillation is part of the performance of the space of an offset. Through the performative oscillation between the abstract and the material, the commodity-object and the “carbon market” itself, are mutually emergent and sustained. In addition to focusing on the performative materiality of carbon offsets, I also examine the discursive practices that are necessary for the spaces of commodified carbon storage to emerge. Through a historical-discursive analysis of the spaces of the indigenous body in the 19th and early 20th century, I argue that carbon offsets in indigenous communities in Costa Rica today occur within a spatial and territorial frame that is an effect of the transitive position of the indigenous body as a discursive object – where it is at once part of the Costa Rican nation yet outside of its normalized spaces of accumulation – a position that became hegemonic in the early 20th century. Finally, I explore how the discursive conception of the indigenous body, and its spaces of agriculture has changed in the late 20th century, where its contemporary discursive status as a rational user of land and labor has allowed for carbon offsets to emerge as a solution to a specific socio-spatial development problematic: “fixing” the ecologically unsustainable landscapes that are produced by economically rational actors. The use of cost-benefit calculations in the implementation of carbon offsets, however, results in new representations of agricultural space, which has contributed to the “opening up” of some spaces for receiving commodified carbon, while foreclosing on others.

The calculation of infrared limb emission from the middle atmosphere to space by ozone in the 9$\mu$m to 11$\mu$m spectral region is discussed. The departure from local thermodynamic equilibrium (LTE) in the vibration-rotation bands of ozone is investigated, considering the processes of collisional excitation, collisional quenching, chemical pumping, photochemical reaction loss, radiative emission and radiative absorption. As the database of kinetic and spectroscopic rates necessary to construct statistical equilibrium models is very sparse, three different models are developed and their results are compared. The source functions for the $\nu\sb3$ hot bands and combination bands are calculated from the surface to 110 km in altitude for noon and midnight conditions during mid-latitude winter. Source function enhancements relative to LTE are a result of the chemical pumping and radiative absorption processes. Diurnal variations in the source functions are a result of diurnally varying photochemical processes. The radiance emitted by ozone is calculated for six bands for two of the three statistical equilibrium models considered using a high-resolution, line-by-line infrared emission model. A maximum 32% difference in the spectrally integrated radiance between 925 cm$\sp{-1}$ and 1141 cm$\sp{-1}$ exists between the two sets of model radiances for tangent paths in the upper mesosphere. The difference in radiance is primarily the result of the differences in the hot band emission. The agreement between the radiances predicted by these two models is best in the lower thermosphere where radiative processes control the populations and also in the middle stratosphere where collisional effects control the populations. The contribution to the total radiance due to emission from two combination bands of carbon dioxide (CO$\sb2$) that emit in the 9$\mu$m to 11$\mu$m spectral region is also calculated. These calculations show that CO$\sb2$ emission will be the dominant source of infrared radiance in this spectral interval in the daytime upper mesosphere and lower thermosphere. The nighttime limb radiance from the upper mesosphere and lower thermosphere is governed by emission from the $\nu\sb3$ fundamental and is much closer in magnitude to the LTE limb emission. CO$\sb2$ emission constitutes only a small fraction of the total nighttime limb radiance. The ozone and carbon dioxide radiance calculations are discussed with respect to the remote sensing of ozone by the measurement of infrared emission.

This research is an investigation of the phenomenon of abacus-based mental addition among 11-year-old Chinese children. The children, all trained in abacus calculation, report doing mental calculation by visualizing a mental image of the abacus, and by moving beads on this mental abacus as they would on a real abacus. Studying this phenomenon enables one to investigate the nature and function of mental imagery, and the mechanisms involved in acquiring images. This study had two specific purposes: first, to gather basic information about the abacus and children's skill in both abacus and mental abacus calculation; second, to gather evidence that might clarify the nature of the mental representation involved in mental abacus calculation. Three groups of four children each were studied, representing expert, intermediate, and novice abacus operators. Response times and errors were recorded for both abacus and mental addition of a large and varied set of problems. Four American adults also performed mental calculations on the same set of problems. The Chinese children also performed a task requiring them, both mentally and using the abacus, to answer questions about intermediate states in abacus addition problems. The abacus experts were found to be amazingly fast at both abacus and mental calculation, and faster when using mental solution than when using the physical abacus. Response times for both abacus and mental addition were a linear function of the total number of digits in the problem, calculated as number of digits (per addend) times number of addends. With total digits held constant, number of digits per addend was positively related to Chinese mental calculation time, but not abacus or American mental calculation times. Several pieces of evidence converged in showing the mental abacus to be an analog representation, isomorphic with the structure and function of the physical abacus. Evidence supporting this conclusion were the facts that subjects mentally were able to answer questions about intermediate states unique to abacus calculation, and errors in mental calculation showed that Chinese, but not Americans, made errors predicted from analysis of abacus operation.

A description of an improved non-LTE model together with earlier two-level and multi-level models is presented. Effects of collisional and radiative energy transfer paths among CO$\sb2$ vibrational levels on source functions are discussed. We take into account the 10 $\mu$m bands, i.e. (00$\sp0$1) - (02$\sp0$0/10$\sp0$0) bands, which were previously neglected. A line-by-line calculation of transmission functions with Voigt line shape is tested and employed for evaluation of the mean specific intensity and flux divergence for a vibrational-rotational band. The cooling rate from the atmospheric carbon dioxide is evaluated for altitudes ranging from 40 km to 140 km. Above 105 km, departures of source functions for the 15 $\mu$m fundamental and hot bands from LTE are so significant that non-LTE effects on band strength and transmission function cannot be neglected. The non-LTE effects increase the cooling rate for the 15 $\mu$m fundamental band, but decrease the cooling rates for the hot bands. The mixing ratio of CO$\sb2$ above 100 km during the day is smaller than at night, due to photodissociation of CO$\sb2$. This reduces the cooling rate, in particular, for the fundamental band. Contributions to the total cooling rate from the hot bands for the 40 to 75 km range are comparable to the contribution from the fundamental band. Above 110 km, the hot and 4.3 $\mu$m bands make considerable contributions to the cooling, but cooling from the 10 $\mu$m band is negligible. However, the 10 $\mu$m band contribution would be significant if the non-LTE effects on the band strength and transmission function were neglected. Cooling rates of minor isotopic species are small, but are not negligible. We obtain a maximum total cooling rate of 7.4 K day$\sp{-1}$ at the stratopause for the U.S. Standard Atmosphere (1976) and a minimum cooling of 1.7 K day$\sp{-1}$ at about 70 km, in good agreement with previous results. Above about 105 km, however, our total cooling rate is, in general, larger than those of earlier workers. During the night, a second maximum at about 135 km is as large as 29.8 K day$\sp{-1}$. For day-time, this second maximum appears at about 125 km with the smaller cooling rate of 17.5 K day$\sp{-1}$. Solar radiation corresponding to the 4.3 $\mu$m band gives rise to heating in the stratosphere and mesosphere, and enhances the vibrational temperature of the (00$\sp0$1) state particularly at the mesopause, where the vibrational temperature is about 105 K higher than the kinetic temperature. The N$\sb2$(v = 1) and CO$\sb2$(00$\sp0$1) states are in LTE up to about 100 km, and above this altitude the vibrational temperature for N$\sb2$(v = 1) tends to follow the kinetic temperature. These vibrational temperatures also agree well with earlier results.

Many computer programs have been developed to calculate the Fast Fourier Transform (FFT). It is the intention of this thesis to develop the tree graph idea, presented by E. 0. Brigham and R. E. Morrow in the article "The fast Fourier transform," into another computer program that will calculate both the forward and inverse Fourier transforms using nonsymmetrical periodic functions. Most of the information obtained was from periodicals with relatively little available in text books. General matrix equations and calculations presented in proofs were developed by this thesis. The tree graph idea was also expanded to a general form. First the matrix equations for the Discrete Fourier Transform (DFT) were developed. Starting with the Fourier transform pair for an aperiodic continuous function and the matrix equations for the DFT, steps were taken to show how these equations were tied together. Two methods for the FFT were evaluated and proven equal to the DFT matrix equations. The more efficient method was written into a computer program which was explained in detail. Finally examples using this computer program were presented. The forward FFT was approximated using input functions such as a rectangular wave, a step function, a sawtooth wave, and a constant. A test for accuracy was also presented using a rectangular wave input time function.

The purpose of this paper is to describe the mechanization of the basic equations of motion for the performance and maneuver characteristics of an airplane with some simplifications which render solutions more practicable. The results of a study made to program these equations for calculation by the IBM MODEL 650 digital computer are presented as well as the steps to be taken in using this method of calculation.

This paper is an extension of various projects that the writer has been associated with at Chance Vought Aircraft, Incorporated.