This thesis is an investigation into conceptions of ‘understanding mathematics in depth’, as articulated by two specific groups of novice secondary mathematics teachers in the UK. Most participants in the sample interviewed have completed one of two government funded mathematics subject knowledge enhancement courses, which were devised with an aim of strengthening students’ understanding of fundamental mathematics. Qualitative data was drawn from semi-structured interviews with 21 subjects and more in-depth case studies of two of the sample. The data reveals some key themes common to both groups, and also some clear differences. The data also brings to light some new emergent theory which is particularly relevant in novice teachers’ contexts. To provide background context to this study, quantitative data on pre-service mathematics Postgraduate Certificate in Education (PGCE) students is also presented, and it is shown that, at the university in the study, there is no relationship between degree classification on entry to PGCE, and effectiveness as a teacher as measured on exit from the course. The data also shows that there are no significant differences in subject knowledge and overall performance on exit from PGCE, between students who have previously followed a subject knowledge enhancement course, and those who have followed more traditional degree routes.

The purpose of this study is to investigate how education managers conceptualise due process and how their understanding of due process influences the way in which they discipline learners. It adopted a qualitative approach that was based on an interpretative paradigm and followed a case study design. The data collection techniques that were used include semi-structured interviews and document analysis. Research was conducted in eight secondary schools. The findings of this study indicate that the majority of education managers have a good understanding of preliminary disciplinary investigation, a right to information, the disciplinary committee, who should participate in a disciplinary hearing and the appeal process. The minutes of few selected schools provide that schools do consider the school’s code of conduct for learners when disciplining learners. The study found that education managers lack sufficient understanding the implementation of due process and the correct steps to follow when conducting fair disciplinary hearings. Misunderstandings about the learners’ right to information, who should be involved in disciplinary committees, the involvement of witnesses and learner representation were common. Most schools did not include sufficient information in their notices for hearings. Some participants indicated that, for various reasons, they often avoid holding hearings and others avoid following correct procedures of learner discipline. In addition, there is a lack of understanding that the reasons given for a decision by a disciplinary committee must based on the evidence presented during the hearing. Some participants do not know which acts/laws/policies and learner disciplinary documents apply to learner discipline and did not ensure the safekeeping of minutes for their disciplinary hearings. Most schools do not keep detailed minutes of the hearings conducted and the majority did not have disciplinary policies. Moreover, thre is still a lack of understanding about which learner behaviours constitute serious misconduct and whether a disciplinary hearing should be organised for learners who have committed criminal offences in a school. Only about a half of participants consider the age of learners when they discipline them. Some are not sure about number of days that are required for learner and parents to lodge an appeal. / Thesis (PhD)--University of Pretoria, 2015. / tm2015 / Education Management and Policy Studies / PhD / Unrestricted

Many epistemic attitudes including belief and knowledge have already been examined to determine the extent to which they can be attributed to collectives. The epistemological literature on explanatory understanding and objectual understanding, on the other hand, has focused almost exclusively on individual subjects. However, there are many situations that can be described by sentences of the form “We understand P”, “We understand why p”, “Group G understands P”, or “G understands why p”. As I shall show, these situations can be classified into five categories: distributive, common, joint, deferential, and cooperative understanding. Based on a definitional scheme, according to which the general concept of understanding has a cognitive component, a factivity component, and an epistemic-pro-attitude component, this paper aims to analyse these five types.

This thesis is about moods in works of art, and how moods expressed in art can change how we view the world. Among those who speak of the value of discussing moods in philosophical aesthetics, it is normally assumed that the value of moods is in the way they are induced in the viewer of the work. In this thesis, I will argue that such an argument is not the best. Those who think moods are not relevant to aesthetics have only to argue either that being induced with emotions is not an ideal way of approaching art, or that such reactions as being induced with mood belong to the more rare cases of approaching art. Therefore, focusing on how moods are induced hinders the potential of discussing moods in art. Instead I argue that the value of moods is in the way they are expressed. I argue that moods can be understood as a form of symbolic schemas. They affect how the world appears, and how one sorts and organizes things in the world. One can therefore use moods as resources for getting knowledge about the world. Because some works of art express moods, where expression is understood as metaphorical exemplification, they make the viewer epistemically aware of the mood. Thus one can imagine being in the mood expressed. Thereby moods can lead to knowledge, also in cases where they are not literally induced. When one succesfully imagines being in an expressed mood, parts of the world are sorted and organized differently as in accordance with the mood.

Low levels of learner performance in Mathematics in the Senior Phase (Grades 7-9) in South Africa is often attributed to insufficient mathematics content knowledge among teachers. Although this view might be justifiable, it is often incorrect to assume that content knowledge alone will solve the problem of low performance in mathematics. This study, therefore, argues that understanding learner misconceptions and/or errors and their underlying intricacies could provide the basis for instructional decision making, subsequently improved performance in mathematics. The purpose of the study was to explore the implications of teachers’ understanding of learner errors for mathematics learning. The study was guided by qualitative methods using a case study design which involved data collection from two schools, followed by in-depth data analysis. Two theoretical lenses, namely, Cognitively Guided Instruction (CGI) and Constructivist theory were used to explore the main research question: What are the implications of the teachers’ understanding of learner errors on the learning of school mathematics in the Senior Phase (specifically Grade 9)? Data was collected through lesson observations, analysis of learners’ test responses and interviews. The findings revealed that teachers’ understanding of learner errors from written responses differed notably from intricacies of same errors emanating from interviewing the learners as well as the same errors analysed by the researcher. The implications of these findings suggest the likelihood of a mismatch between teachers’ instructional decision making and learner misconception/errors and this may hamper effective learning of mathematics. / Dissertation (MEd)--University of Pretoria, 2020. / Science, Mathematics and Technology Education / MEd / Unrestricted

<p>Physicians must explain medical information to patients in a way that patients can understand, and physician use of analogies is one strategy that may help patients better understand health information. The present dissertation, guided by patient-centered communication, investigated whether the use of analogies by a physician within a medical encounter enhances participants’ objective understanding, perceived understanding, and perceptions of clarity regarding information about a health condition, and perceptions of the physician in areas of liking, similarity, satisfaction, and affective communication. The experiment consisted of eight conditions with a 2 (familiar/unfamiliar health condition) x 4 (no analogies, diagnosis analogies, treatment analogies, both diagnosis and treatment analogies) design, and the conditions varied by being exposed to the familiar or unfamiliar health issue first. An actor physician delivered a 1-2 minute video-recorded message, diagnosing the participants, serving as analogue patients, with the familiar or unfamiliar health issue. After watching the video and responding to the dependent variable measures based on their perceptions of the physician and video message, U.S. adult participants read a vignette of another physician diagnosing them with the other (familiar or unfamiliar) health issue, and answered the same dependent variable measures regarding the physician and vignette message. Open-ended questions sought to understand what participants remembered from the message and whether they recalled analogies in their retelling of the physician messages, whether they (dis)liked the analogies, what they (dis)liked about the physicians and whether these perceptions differed by analogy conditions, whether they remembered any analogies from their own clinicians, and in which medical situations they found provider analogies to be useful. Findings indicated when including health literacy as a covariate, analogies did not enhance perceptions of clarity, perceived understanding, or objective understanding. Regarding positive perceptions, analogies did not influence liking, similarity, satisfaction, or affective communication. There was no significant interaction between use of analogies and health issues, nor a difference in the effectiveness of the analogies based on whether they were used to describe diagnosis or treatment. Explanations containing analogies resulted in increased objective understanding for the vignette compared to the video format. When recalling the physician’s message, participants rarely recalled analogies, nor explicitly mentioned them as something they liked or disliked. However, some participants recalled clinician use of particular analogies, and most of them indicated they found clinician analogies to be useful, especially when describing complex health issues that are difficult for patients to understand. The dissertation results indicate that healthcare providers may want to use analogies when interacting with patients, which could potentially improve the doctor-patient relationship. </p>

One of the long-standing problems in artificial intelligence is the development of intelligent agents with complete visual understanding. Understanding entails recognition of scene attributes such as actors, objects and actions as well as reasoning about the common semantic structure that combines these attributes into a coherent description. While significant milestones have been achieved in the field of computer vision, majority of the work has been concentrated on supervised visual recognition where complex visual representations are learned and a few discrete categories or labels are assigned to these representations. This implies a closed world where the underlying assumption is that all environments contain the same objects and events, which are in one-to-one correspondence with the ground evidence in the image. Hence, the learned knowledge is limited to the annotated training set. An open world, on the other hand, does not assume the distribution of semantics and requires generalization beyond the training annotations. Increasingly complex models require massive amounts of training data and offer little to no explainability due to the lack of transparency in the decision-making process. The strength of artificial intelligence systems to offer explanations for their decisions is central to building user confidence and structuring smart human-machine interactions. In this dissertation, we develop an inherently explainable approach for generating rich interpretations of visual scenes. We move towards an open world open-domain visual understanding by decoupling the ideas of recognition and reasoning. We integrate common sense knowledge from large knowledge bases such as ConceptNet and the representation learning capabilities of deep learning approaches in a pattern theory formalism to interpret a complex visual scene. To be specific, we first define and develop the idea of contextualization to model and establish complex semantic relationships among concepts grounded in visual data. The resulting semantic structures, called interpretations allow us to represent the visual scene in an intermediate representation that can then be used as the source of knowledge for various modes of expression such as labels, captions and even question answering. Second, we explore the inherent explainability of such visual interpretations and define key components for extending the notion of explainability to intelligent agents for visual recognition. Finally, we describe a self-supervised model for segmenting untrimmed videos into its constituent events. We show that this approach can segment videos without the need for supervision - neither implicit nor explicit. Combined, we argue that these approaches offer an elegant path to inherently explainable, open domain visual understanding while negating the need for human supervision in the form of labels and/or captions. We show that the proposed approach can advance the state-of-the-art results in complex benchmarks to handle data imbalance, complex semantics, and complex visual scenes without the need for vast amounts of domain-specific training data. Extensive experiments on several publicly available datasets show the efficacy of the proposed approaches. We show that the proposed approaches outperform weakly-supervised and unsupervised baselines by up to 24% and achieves competitive segmentation results compared to fully supervised baselines. The self-supervised approach for video segmentation complements this top-down inference with efficient bottom-up processing, resulting in an elegant formalism for open-domain visual understanding.

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Effective collaboration in a team is a crucial skill. When people interact together to perform physical tasks, they rely on gestures to convey instructions. This thesis explores gestures as means to assess physical collaborative task understanding. This research proposes a framework to represent, compare, and assess gestures’ morphology, semantics, and pragmatics, as opposed to traditional approaches that rely mostly on the gestures’ physical appearance. By leveraging this framework, functionally equivalent gestures can be identified and compared. In addition, a metric to assess the quality of assimilation of physical instructions is computed from gesture matchings, which acts as a proxy metric for task understanding based on gestural analysis. The correlations between this proposed metric and three other task understanding proxy metrics were obtained. Our framework was evaluated through three user studies in which participants completed shared tasks remotely: block assembly, origami, and ultrasound training. The results indicate that the proposed metric acts as a good estimator for task understanding. Moreover, this metric provides task understanding insights in scenarios where other proxy metrics show inconsistencies. Thereby, the approach presented in this research acts as a first step towards assessing task understanding in physical collaborative scenarios through the analysis of gestures.

Every day robots are becoming more common in the society. Consequently, they must have certain basic skills in order to interact with humans and the environment. One of these skills is the capacity to understand the places where they are able to move. Computer vision is one of the ways commonly used for achieving this purpose. Current technologies in this field offer outstanding solutions applied to improve data quality every day, therefore producing more accurate results in the analysis of an environment. With this in mind, the main goal of this research is to develop and validate an efficient object-based scene understanding method that will be able to help solve problems related to scene identification for mobile robotics. We seek to analyze state-of-the-art methods for finding the most suitable one for our goals, as well as to select the kind of data most convenient for dealing with this issue. Another primary goal of the research is to determine the most suitable data input for analyzing scenes in order to find an accurate representation for the scenes by meaning of semantic labels or point cloud features descriptors. As a secondary goal we will show the benefits of using semantic descriptors generated with pre-trained models for mapping and scene classification problems, as well as the use of deep learning models in conjunction with 3D features description procedures to build a 3D object classification model that is directly related with the representation goal of this work. The research described in this thesis was motivated by the need for a robust system capable of understanding the locations where a robot usually interacts. In the same way, the advent of better computational resources has allowed to implement some already defined techniques that demand high computational capacity and that offer a possible solution for dealing with scene understanding issues. One of these techniques are Convolutional Neural Networks (CNNs). These networks have the capacity of classifying an image based on their visual appearance. Then, they generate a list of lexical labels and the probability for each label, representing the likelihood of the present of an object in the scene. Labels are derived from the training sets that the networks learned to recognize. Therefore, we could use this list of labels and probabilities as an efficient representation of the environment and then assign a semantic category to the regions where a mobile robot is able to navigate, and at the same time construct a semantic or topological map based on this semantic representation of the place. After analyzing the state-of-the-art in Scene Understanding, we identified a set of approaches in order to develop a robust scene understanding procedure. Among these approaches we identified an almost unexplored gap in the topic of understanding scenes based on objects present in them. Consequently, we propose to perform an experimental study in this approach aimed at finding a way of fully describing a scene considering the objects lying in place. As the Scene Understanding task involves object detection and annotation, one of the first steps is to determine the kind of data to use as input data in our proposal. With this in mind, our proposal considers to evaluate the use of 3D data. This kind of data suffers from the presence of noise, therefore, we propose to use the Growing Neural Gas (GNG) algorithm to reduce noise effect in the object recognition procedure. GNGs have the capacity to grow and adapt their topology to represent 2D information, producing a smaller representation with a slight noise influence from the input data. Applied to 3D data, the GNG presents a good approach able to tackle with noise. However, using 3D data poses a set of problems such as the lack of a 3D object dataset with enough models to generalize methods and adapt them to real situations, as well as the fact that processing three-dimensional data is computationally expensive and requires a huge storage space. These problems led us to explore new approaches for developing object recognition tasks. Therefore, considering the outstanding results obtained by the CNNs in the latest ImageNet challenge, we propose to carry out an evaluation of the former as an object detection system. These networks were initially proposed in the 90s and are nowadays easily implementable due to hardware improvements in the recent years. CNNs have shown satisfying results when they tested in problems such as: detection of objects, pedestrians, traffic signals, sound waves classification, and for medical image processing, among others. Moreover, an aggregate value of CNNs is the semantic description capabilities produced by the categories/labels that the network is able to identify and that could be translated as a semantic explanation of the input image. Consequently, we propose using the evaluation of these semantic labels as a scene descriptor for building a supervised scene classification model. Having said that, we also propose using semantic descriptors to generate topological maps and test the description capabilities of lexical labels. In addition, semantic descriptors could be suitable for unsupervised places or environment labeling, so we propose using them to deal with this kind of problem in order to achieve a robust scene labeling method. Finally, for tackling the object recognition problem we propose to develop an experimental study for unsupervised object labeling. This will be applied to the objects present in a point cloud and labeled using a lexical labeling tool. Then, objects will be used as the training instances of a classifier mixing their 3D features with label assigned by the external tool.