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Interleaving Effects in Mathematics: Comparing interleaving, blocking and exposition strategies for teaching secondary school pupils how to classify mathematical images
Full text link‘Interleaving’ is a strategy that has become increasingly popular in secondary school mathematics teaching over recent years. It is often defined as being the opposite of another strategy called ‘blocking’, with blocking referring to when content from different categories is grouped together by type (e.g., AAAABBBBCCCCDDDD) and interleaving referring to when different categories are mixed together (ABCDABCDABCD). Some research has investigated the potential benefits of interleaving for revision during mathematics practice assignments; other research has investigated its benefits for inductively learning how to classify images into categories. Based on findings from this research, recommendations in professional literature advise teachers to use interleaving more often during mathematics lessons. However, this thesis proposes two problems with this: the conditions in which interleaving effects have previously been found in research are not authentic to school-based mathematics learning; and that blocking and interleaving are not the only two strategies available to teachers and pupils.
The aim of the research in this thesis has been to investigate whether interleaving effects found in the inductive learning strand of research also apply to category learning in secondary school mathematics, while also comparing blocking and interleaving with a third alternative strategy: learning through exposition. The empirical research took the form of three randomised controlled trials involving secondary school pupils learning to classify mathematical images into categories. The results found no main effects of any study conditions on participants’ accuracy during the classification tests in any of the three experiments. These findings led to considerations about the differences between the types of categories that are learned about in mathematics and the types of categories that have been used in research where interleaving effects have previously been found. The thesis concludes by reflecting on the difficulties and discrepancies that can occur when transferring findings from laboratory-based research into classroom-based practice
Routines and Applications of Symbolic Algebra Software
Full text linkComputing has become an essential resource in modern research and has found application
across a wide range of scientific disciplines. Developments in symbolic algebra tools have been
particularly valuable in physics where calculations in fields such as general relativity, quantum
field theory and physics beyond the standard model are becoming increasing complex and
unpractical to work with by hand. The computer algebra system Cadabra is a tensor-first
approach to symbolic algebra based on the programming language Python which has been used
extensively in research in these fields while also having a shallow learning curve making it an
excellent way to introduce students to methods in computer algebra.
The work in this thesis has been concentrated on developing Cadabra, which has involved
looking at two different elements which make up a computer algebra program. Firstly, the
implementation of algebraic routines is discussed. This has primarily been focused on the
introduction of an algorithm for detecting the equivalence of tensorial expressions related by
index permutation symmetries. The method employed differs considerably from traditional
canonicalisation routines which are commonly used for this purpose by using Young projection
operators to make such symmetries manifest.
The other element of writing a computer algebra program which is covered is the infrastruc-
ture and environment. The importance of this aspect of software design is often overlooked by
funding committees and academic software users resulting in an anti-pattern of code not being
shared and contributed to in the way in which research itself is published and promulgated.
The focus in this area has been on implementing a packaging system for Cadabra which allows
the writing of generic libraries which can be shared by the community, and interfacing with
other scientific computing packages to increase the capabilities of Cadabra
Approaches to Evaluating Teaching for Mastery in Secondary Mathematics Education
Full text linkTeaching for Mastery (TfM) in mathematics education is a pedagogical approach which seeks to develop students’ depth of understanding to ensure that they ‘master maths’ and develop a deep, secure and adaptable understanding of the subject. The term was coined by the NCETM following
the England-Shanghai Teacher Exchange Programme of 2015 in a bid to address mathematics underperformance of students in England following transnational assessments.
This research explores observational methods for assessing the impact of TfM on secondary mathematics outcomes, and is the first of its kind in moving away from experimental approaches to attempt to ascribe cause to TfM at the individual, student level. The move away from an experimental approach comes from the need to overcome the risk of trial effects and bias that are inherent to approaches such as Randomised Controlled Trials (RCTs), and the wish to explore the longer-term impact of embedded TfM. This thesis explores the research field to date as well as other viable methods for ascribing cause, before justifying the use of propensity score matching methods.
Three individual school cases are considered, and propensity score matching methods applied and analysed, showing that observational methods may, to some extent, help evaluate curriculum interventions
1,2,4-Triazoliums: Applications in Biocatalysis, Organocatalysis and Stable Radical Synthesis
No full textHerein we report the exploration of carbenes derived from 1,2,4-triazoliums in the novel rearrangement reaction to stable Blatter radicals, biocatalysis and organocatalysis.
Nitron is an intriguing 1,2,4-triazolium, with a C(5)-N-anilino substituent which permits establishment of a tautomeric equilibrium between the C(3) and C(5)-N positions. This work continues from our initial report of the unusual rearrangement of Nitron to Blatter radicals. The synthesis of Nitron was revisited and contemporary synthetic strategies were employed to enhance isolated yields and scope. Evaluating the series of Nitron derivatives for propensity to form Blatter radicals enabled the isolation of seven new radicals and implicated the role of the carbenic tautomer in the initial hydrolytic ring opening step. Evaluation of the tautomeric equilibrium was performed by spectrophotometric determination of C(5)-NH pKa values and NMR spectroscopic kinetic monitoring of C(3)-H/D exchange. A 10-fold drop in carbene proportion at equilibrium when Nitron is substituted with a 4-F3CC6H4 group at the C(5)-N-anilino position was attributed to stabilisation of the formal N- charge in the zwitterionic form. The experimental evidence supports a faster ring opening from the carbene tautomer compared to the zwitterion.
Owing to the growing interest in stable organic diradicals, a range of synthetic strategies was explored to couple Blatter radicals. The intolerance of radical character to synthetic conditions and cross-reactivity of the ring and exocyclic nitrogen positions complicated this coupling. A synthetic strategy to a coupled di-Nitron was developed and evaluation for di-radical formation provided circumstantial evidence. The lack of a C(3)-H for carbene formation appears to limit hydrolytic ring opening. Future work could explore conditions to promote hydrolytic ring opening at the 1,2,4-triazolium C(3)-position.
The use of heterocyclic azolium-derived carbenes for organocatalysis originated from the mechanistic evaluation of thiamine (pyrophosphate, TPP) (a thiazolium) as a cofactor in TPP-dependent enzymes. Since this discovery, the field of NHC organocatalysis has grown exponentially, with chemists developing catalysts centred about the more acidic 1,2,4-triazolium scaffold. We report the first synthesis of a 1,2,4-triazolium replica of TPP in attempt to improve the yield, selectivity and scope of TPP-dependent biocatalytic transformations. Kinetic evaluation of H/D exchange of TPP and the isolated 1,2,4- triazolium mimic using NMR spectroscopy permitted estimation of C(2/3)-H pKa values and showed a ~1.5 unit decrease for 1,2,4-triazolium mimics in comparison to thiamine.
Initial evaluation of 1,2,4-triazolium mimics focussed on model benzoin condensation reactions, in the absence of enzyme. An approximate 10-fold enhancement in rates of initial hydroxyaryl adduct were determined through kinetic monitoring. Assessment of the 1,2,4-triazolium mimic as a cofactor was performed with TPP-dependent enzymes pyruvate decarboxylase from Saccharomyces cerevisiae and pyruvate oxidase from Aerococcus sp. via spectrophotometric coupled assays and direct NMR spectroscopic analysis. Loss of enzyme activity in the presence of the cofactor mimic was observed implying that binding to the active site occurred but the mimic was less active. This decreased activity was thought to be due to a conformational discrepancy within the active site. Future work will screen a greater range of more tolerant TPP-dependent enzymes to fully explore compatibility of the 1,2,4-triazolium mimic.
Complementary studies evaluated the hydrolytic stability of TPP by 31P NMR spectroscopy in a series of deuterated buffers from pD 0-13. Under physiological conditions (pD 4-7) TPP is very stable with minimal hydrolysis of the pyrophosphate over several months (t1/2 = 300-500 days). Under acidic conditions (pD < 3), hydrolysis of the pyrophosphate becomes more prevalent (t1/2 down to 2 days). Above pD 8, hydrolysis of the pyrophosphate group is negligible, but cleavage of the methylene linker occurs.
Finally, 1,2,4-triazoliums isolated within these projects were evaluated as catalysts to the benzoin condensation, a key NHC organocatalysed transformation. Intriguingly, Nitron derivatives showed no propensity for catalysis, despite showing similar rates constants for H/D-exchange as other commonly employed 1,2,4-triazolium catalysts. This result was unexpected and attributed to the unusual chemical nature of carbenes derived from Nitron derivatives. The evaluation of more sustainable reaction conditions for NHC organocatalysis led to the observation that rate enhancements were observed when the benzoin condensation was performed under aqueous conditions with a more traditional 1,2,4-triazolium catalyst. This observation paves the way for significant future work to develop an understanding of NHC-organocatalysed transformations in water
Conceptual Framework for Designing Virtual Field Trip Games
Full text linkThis thesis aimed to provide designing models to explore an alternative solution for a field trip when it becomes impossible for several reasons such as the limitation of cost and time. Virtual field trip games are relatively new means to create virtual field trips in game environments through adding game aspects to learning aspects to enhance the learning experience. The simple combining of game and learning aspects will not guarantee the desired effect of virtual field trips. Theoretical and logical connections should be established to form interweave between both aspects.
This thesis proposes a designing framework by establishing three links between game design aspects and learning aspects. The three links are constructed by modelling: the experiential learning theory (ELT), the gameplay, and the game world. ELT modelling quantifies the theory into the internal economy mechanic and balances the levels of game task difficulty with the player’s ability through game machinations, game modelling links the learning process to gameplay, and world modelling connects field environment to game environment. The internal economy mechanic and its components (resources, internal mechanic, feedback loop), formulating equations to define generic player’s interactions and identify indicators to capture evidence of achievements via a mathematical (evaluation) model. The game modelling includes skill models to design two important high-order skills (decision-making and teamwork) and connects them to the evaluation model. The game world is modelled through defining its variables and relationships’ rules to connect both environments (game and field) expanding the evaluation model. The framework is supported by essential learning theories (ELT, task-based learning, some aspects of social learning) and pedagogical aspects (assessment, feedback, field-based structure, high-order skills) and connected to the key game elements (interaction, multimodal presentation, control of choice…etc) of field-based learning along with suitable game mechanics.
The two research studies that were conducted as part of this thesis found that the designing framework is useful, usable, and provides connections between learning and game aspects and the designed VFTG based on the framework improved learning performance along with providing motivation and presence. This suggests the effectiveness of the framework
Hegemonic Practices in the GCC Political Complex (GPC): Evolvement of Counter-Hegemonic Formations
No full textThe thesis contributes to the international relations and political science literature on the GCC countries by theorizing intra-GCC rivalries around organic and conjunctural crises, with a focus on the concepts of hegemony, power, and crisis from the perspective of post-structural discourse theory. The purpose of this study is to examine dislocated, deconstructed, and transformed hegemonic formations as well as emerging hegemonic practices within the GCC.
The GCC Political Complex (the GPC) is a technical term developed in this study to depict the main arguments for conceptualizing the political paradigms of this sub-region. In its political complex, the GPC prioritizes the importance of hegemonic formations and acknowledges the cultural and generic values of Arab monarchies. Looking at the importance of hegemony, power and crisis in the GPC, the thesis takes a poststructuralist approach. This theoretical interpretation helps the research to reach a solid and comprehensive discussion on the hegemonic projects and formations that are emerged around the GCC's unique political structure. The research aims to improve theoretical and conceptual discussions regarding the policy making of these states by describing intra-GCC hegemonic struggles, focusing primarily on the two oil monarchies (Saudi Arabia and Qatar) but also taking into account other states' reactions (Kuwait, Bahrain, the UAE, and Oman). There are other actors that are briefly examined in the thesis in relation to Qatar's counter-hegemonic discourse, including Iran and Turkey.
The concept of hegemony in this specific context is not the predominance of one nation over another. Rather it refers to a comprehensive set of relations under leadership with a combination of coercion and persuasion for material and non-material means. The thesis does not focus solely on Qatari foreign policy or the Saudi role in the region. It is a theoretical discussion with case studies of the articulation of sectarian polarity and political Islam in two monarchies’ policies over Egypt, Syria, and the intra-GCC crises of 2013 and 2017. In looking at these articulations, there are two primary levels of analysis. The research delves into sub-regional rivalries, first, looking at intra-GCC tensions and second looking at Middle East wide implications of the sub-regional antagonism. Hence, the thesis first examines how hegemonic and counter-hegemonic practices manifested themselves in the GPC after the Arab Uprisings. The second focus is on institutionalizing these emerging hegemonic practices, questioning whether a counter-hegemonic Qatari “myth” has been incorporated into a hegemonic power “imaginary”
Scalable Methodologies and Analyses for Modality Bias and Feature Exploitation in Language-Vision Multimodal Deep Learning
Full text linkMultimodal machine learning benchmarks have exponentially grown in both capability and popularity over the last decade. Language-vision question-answering tasks such as Visual Question Answering (VQA) and Video Question Answering (video-QA) have ---thanks to their high difficulty--- become a particularly popular means through which to develop and test new modelling designs and methodology for multimodal deep learning. The challenging nature of VQA and video-QA tasks leaves plenty of room for innovation at every component of the deep learning pipeline: from dataset to modelling methodology. Such circumstances are ideal for innovating in the space of language-vision multimodality. Furthermore, the wider field is currently undergoing an incredible period of growth and increasing interest. I therefore aim to contribute to multiple key components of the VQA and video-QA pipeline, but specifically in a manner such that my contributions remain relevant, ‘scaling’ with the revolutionary new benchmark models and datasets of the near future instead of being rendered obsolete by them. The work in this thesis: highlights and explores the disruptive and problematic presence of language bias in the popular TVQA video-QA dataset, and proposes a dataset-invariant method to identify subsets that respond to different modalities; thoroughly explores the suitability of bilinear pooling as a language-vision fusion technique in video-QA, offering experimental and theoretical insight, and highlighting the parallels in multimodal processing with neurological theories; explores the nascent visual equivalent of languague modelling (`visual modelling') in order to boost the power of visual features; and proposes a dataset-invariant neurolinguistically-inspired labelling scheme for use in multimodal question-answering. I explore the positive and negative results that my experiments across this thesis yield. I conclude by discussing the limitations of my contributions, and conclude with proposals for future directions of study in the areas I contribute to
Dynamics of Pakistan’s Ballistic Missile Acquisition
Full text linkArms dynamic studies are concerned with explaining the causes and consequences of state’s decision to acquire arms. Such studies are dominated by two opposing models. First, the action-reaction model, which posits a state’s decision to acquire arms as a rational response to external threats and consequently it enables them to deter belligerent adversaries. Second, the domestic structure model, which holds that arms acquisitions are an outcome of domestic interests and consequently create instability and strain political relations. Traditionally the two models have competed for exclusivity in explaining armament phenomena. However, more recent studies argue that they are, in fact, not mutually exclusive but complementary to each other. The basic underlying assumption of these studies is, while external security threats may provide a rationale for a state to acquire arms the scale and manner by which the state arms itself will be determined by domestic forces.
The basic generalisations for the two models have been extracted from the armament dynamics of the Cold War superpowers or the major arms producing states from the Western Hemisphere or Global North. In the case of less industrialised weapons producer like Pakistan the literature takes a narrow approach, identifying its behaviour as congruent with action- reaction model and downplaying the importance of domestic-structure model. This thesis argues that not only the action-reaction process in the case of Pakistan’s ballistic missile competition vis-à-vis that of India is less understood but domestic factors have also played a crucial role in the ballistic missile acquisition. In accordance with this argument this thesis hopes to conduct a twofold analysis into the external and internal dynamics of Pakistan’s ballistic missile acquisition. The research postulates that while external threats have provided rationale for Pakistan’s ballistic missile programme, domestic factors have intervened to influence certain missile developments in the programme
Facies Control on Fluvial Reservoir Quality
Full text linkFluvial sandstones form important hydrocarbon reservoirs and aquifers in many regions of the world and more recently been identified as potential sites for carbon dioxide and hydrogen subsurface storage. The characterization of fluvial reservoirs is however challenging due to the complex heterogeneities (internal and external) associated with the variable lithologies and sedimentary architecture. Understanding the main controls on the heterogeneities is essential for building accurate reservoir models. One of the main controls is depositional facies, which in turn has a major influence on early and late burial diagenesis. Although depositional facies is widely known to exert a primary control on fluvial lithological variability and heterogeneity, its role in clay-coat distribution and authigenesis remains poorly constrained. In this study, a multidisciplinary approach involving outcrop analogues, core analysis, petrography, electron microscopy, burial history/quartz cement modelling, clay coat and stable isotope analysis has been employed to understand the controls on fluvial reservoir quality and overall heterogeneity. A total of 293 samples comprising of core and outcrop samples from the Triassic Skagerrak Formation (UK Central North Sea), St Bees Sandstone Formation (West Cumbria, UK) and Buntsandstein facies (Central Iberian Basin, Spain) were investigated. This research clearly identifies that reservoir quality/heterogeneity is controlled by facies, grain size and clay/ductile grains content. Channel facies offer the best reservoir quality while floodplain facies offer poor quality. In the channel sandstones, porosity and permeability range from 0-24% and 0.01-1150 mD, respectively, while in the floodplain facies, they range from 0-7.3% and 0.004-0.51 mD, respectively. Grain size is a first order control on reservoir quality. Coarser-grained channel sandstones have a higher reservoir quality than finer-grained channel sandstones due to their lower clay and ductile grains content. This study reveals that within channel bodies, there is a significant variation in reservoir quality, with the channel centres having the best reservoir quality. Furthermore, this research reveals that the extent of coverage of clay coats governs its ability to effectively inhibit quartz cementation, and significantly correlates with grain size, clay content, and depositional energy. The most extensive clay coat coverage (70-98%) is associated with the finer-grained, low energy channel sandstones and possibly crevasse channel intervals containing between 5 and 10% clay coat by volume. The results of this study have significant implications for reservoir quality prediction and development of fluvial reservoir models especially in high pressure high temperature (HPHT) environments. Finer-grained, dirty sandstones that are often overlooked during exploration offer potentially better reservoir quality at depth and could provide better underground storage sites
Endoplasmic Reticulum Resident Chaperones and their Implications in Health and Disease
No full textThe endoplasmic reticulum (ER) is a key organelle in the eukaryotic cell and is responsible for protein folding and quality control, mediated by protein chaperones. It is also home to the oxidoreductase system which is required for disulphide bond formation and is the main theme of this thesis. Two of the vital proteins in the ER-localised oxidoreductase system are protein disulphide isomerase (PDI) and endoplasmic reticulum oxidoreductase 1 α (Ero1α). These proteins work alongside other specialist PDI family members such as anterior gradient 2 (AGR2). This thesis examines the role of both PDI and AGR2 in protein quality control, together with important clients such as collagen, a major component of the extracellular matrix (ECM) and a secreted product of fibroblast cells present in the skin. The role of AGR2 in oesophageal cancer was explored, with data dependant acquisition (DDA) mass spectrometry (MS) used to identify novel interacting partners of AGR2. AGR2 was found to be over expressed in certain oesophageal cell lines and key interacting partners such as MUC5AC and SQSTM1 were identified. Research was undertaken in this thesis to compare the effectiveness and application of the reducing agent dithiobutylamine (DTBA) to biological systems and how this reducing agent affects the cellular proteome and the redox state of PDI. Live cell imaging was used to see how the structure of the ER was affected by reductive stress. Data independent acquisition (DIA) MS was used to identify new molecular players in the cellular response to reductive stress, in the response to PDI inhibitors, in the response to growth factors (PDGF) and in the response to skin bioactive (e.g. niacinamide). Taken together, these analyses lay the foundations for understanding new mechanistic control points in the quality control of protein secretion and homeostasis
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