Doctor of Philosophy / Department of Physics / Nobel S. Rebello / Conventional wisdom has long advised that students’ learning is best supported by interaction with physical manipulative. Thus, in the physics laboratory, students typically spend their time conducting experiments with physical equipment. However, computer simulations offer a tempting alternative to traditional physical experiments. In a virtual experiment, using a computer simulation, students can gather data quickly, and measurement errors and frictional effects can be explicitly controlled. This research investigates the relative support for students’ learning offered by physical and virtual experimentation in the context of simple machines. Specifically, I have investigated students’ learning as supported by experimentation with physical and virtual manipulative from three different angles-- what do students learn, how do students learn, and what do students think about their learning. The results indicate that the virtual manipulative better supported students’ understanding of work and potential energy than the physical manipulative did. Specifically, in responding to data analysis questions, students who used the virtual manipulative before the physical manipulative were more likely to describe work as constant across different lengths of frictionless inclined planes (or pulley systems) and were more likely to adequately compare work and potential energy, whereas students who used the physical manipulative first were more likely to talk about work and potential energy separately. On the other hand, no strong support was found to indicate that the physical manipulative better supported students’ understanding of a specific concept. In addition, students’ responses to the survey questions indicate that students tend to value data from a computer simulation more than from a physical experiment. The interview analysis indicates that the virtual environment better supported the students to create new ideas than the physical environment did. These results suggest that the traditional wisdom that students learn best from physical experiments is not necessarily true. Thus, researchers should continue to investigate how to best interweave students’ experiences with physical and virtual manipulatives. In addition, it may be useful for curriculum designers and instructors to spend more of their efforts designing learning experiences that make use of virtual manipulatives.

Doctor of Philosophy / Electrical and Computer Engineering / Steven Warren / Linear Systems (a.k.a., Signals and Systems) is an important class in an Electrical Engineering curriculum. A clear understanding of the topics in this course relies on a well-developed notion of lower-level mathematical constructs and procedures, including the roles these procedures play in system analysis. Students with an inadequate math foundation regularly struggle in this class, as they are typically able to perform sequences of the underlying calculations but cannot piece together the higher-level, conceptual relationships that drive these procedures. This dissertation describes an investigation to assess and improve students’ higher-level understanding of Linear Systems concepts. The focus is on the topics of (a) time-domain, linear time-invariant (LTI) system response visualization and (b) Fourier series conceptual understanding, including trigonometric Fourier series (TFS), compact trigonometric Fourier series (CTFS), and exponential Fourier series (EFS). Support data, including exam and online homework data, were collected since 2004 from students enrolled in ECE 512 - Linear Systems at Kansas State University. To assist with LTI response visualization, two online homework modules, Zero Input Response and Unit Impulse Response, were updated with enhanced plots of signal responses and placed in use starting with the Fall 2009 semester. To identify students’ conceptual weaknesses related to Fourier series and to help them achieve a better understanding of Fourier series concepts, teaching-learning interviews were applied between Spring 2010 and Fall 2012. A new concept-based online homework module was also introduced in Spring 2011. Selected final exam problems from 2007 to 2012 were analyzed, and these data were supplemented with detailed mid-term and final exam data from 77 students enrolled in the Spring 2010 and Spring 2011 semesters. In order to address these conceptual learning issues, two frameworks were applied: Bloom’s Taxonomy and APOS theory. The teaching-learning interviews and online module updates appeared to be effective treatments in terms of increasing students’ higher-level understanding. Scores on both conceptual exam questions and more traditional Fourier series exam questions were improved relative to scores received by students that did not receive those treatments.

The topic of students’ application of conceptual knowledge in physics is constantly being researched. It is a common occurrence that students are able to solve numerical problems without understanding the concepts involved. The primary focus of this dissertation is to investigate the extent to which a group of first year physics students are able to identify and use the correct physics concepts when solving problems set in different contexts. Furthermore, this study aims to identify underlying factors giving way to students not applying appropriate physics concepts. A questionnaire was designed in test-format in which all the problems dealt with two objects whose movement had to be compared to each other. The physical quantities describing or influencing the objects’ movement differed in each consecutive problem; whilst the nature of the concept under consideration remained the same. The problems were set in various contexts namely: i. Formal conceptual questions, some with numeric values; ii. Questions set in every day context with/without numeric values; iii. Questions on vertical upward, vertical downward and horizontal motion. The questionnaire was distributed to 481 students in the first-year physics course in 2014 at the Potchefstroom Campus of the North West University. It was expected that the percentage of correct answers would reveal discrepancies in the responses to contextual, numeric and formal conceptual questions. The outcome of the statistical analysis confirmed this expectation. In addition, it seemed that only a few students were able to correctly identify the appropriate variables when considering vertical and horizontal movement while the majority of the students did not apply the same physics principle in isomorphic vertical upward and vertical downward problems. It appears that the context in which the question was posed determined whether the problem was seen as an item that would require “physics reasoning” or as a setting where physics reasoning did not apply. The results revealed students inability to relate physics concepts to appropriate mathematical equations. Two important results from this work are: (1) the presentation of a questionnaire that can be implemented to investigate various aspects regarding the contexts of physics problems; and (2) expanding the concept of context to include the direction of movement as a separate context. / MSc (Natural Science Education), North-West University, Potchefstroom Campus, 2015

Physics education research found that graphs in kinematics have been a problem to students, even at university level. The study hence investigates what deficiencies first-year Physics students at the Central University of Technology, Bloemfontein, South Africa have in terms of transferring mathematics knowledge and understanding when solving kinematics problems. According to the National Department of Education (DoE, 2003), mathematics enables learners to have creative and logical reasoning about problems in the physical and social worlds. Graphs in kinematics are one of the domains that need that skill in mathematics. DoE (2011) further emphasises that learners should be able to collect, analyze, organize and critically evaluate information at the end of their FET sector and that include graphing in kinematics. The study started by exploring graph sense and comprehension from literature. The study further explored from a literature review students‘ problems and possible solutions in transferring their mathematics understanding and knowledge to solve physics problems. The literature study served as conceptual framework for the empirical study, i.e. the design and interpretation of questionnaires, and interview questions. The mathematics and kinematics questions of the questionnaire were divided into four constructs, namely area, gradient, reading coordinates and form/expression of graphs. The participants undertook the questionnaire and interviews voluntarily according to the research ethics. Hundred and fifty two (152) out of 234 students registered for first-year physics from the faculties of humanities (natural science), health and environmental science and engineering and information technology undertook the questionnaire. The researcher interviewed 14 students of these participants as a follow up to the responses of the questionnaire. The responses of the participants were analysed statistically to conclude this study. The average percentages of the questionnaire showed that the majority (62.7% participants) have the mathematics knowledge compared to the low percentage of 34.7 % on physics knowledge. With regard to the constructs the participants generally performed similarly on gradient, reading coordinates and form/expression, i.e. they could either answer both the corresponding mathematics and physics questions and neither of them. In the area construct, most participants with the mathematics knowledge did not transfer it to the physics context. The study further revealed that the majority of interviewees do not have an understanding of the basic physics concepts such as average velocity and acceleration. The researcher therefore recommends that physical science teachers in the FET schools should also undergo constant training in data handling and graphs by subject specialists and academic professionals from Higher Education Institutions. Other remedial actions are also proposed in the dissertation. / MSc (Natural Science Education), North-West University, Potchefstroom Campus, 2015

The topic of students’ application of conceptual knowledge in physics is constantly being researched. It is a common occurrence that students are able to solve numerical problems without understanding the concepts involved. The primary focus of this dissertation is to investigate the extent to which a group of first year physics students are able to identify and use the correct physics concepts when solving problems set in different contexts. Furthermore, this study aims to identify underlying factors giving way to students not applying appropriate physics concepts. A questionnaire was designed in test-format in which all the problems dealt with two objects whose movement had to be compared to each other. The physical quantities describing or influencing the objects’ movement differed in each consecutive problem; whilst the nature of the concept under consideration remained the same. The problems were set in various contexts namely: i. Formal conceptual questions, some with numeric values; ii. Questions set in every day context with/without numeric values; iii. Questions on vertical upward, vertical downward and horizontal motion. The questionnaire was distributed to 481 students in the first-year physics course in 2014 at the Potchefstroom Campus of the North West University. It was expected that the percentage of correct answers would reveal discrepancies in the responses to contextual, numeric and formal conceptual questions. The outcome of the statistical analysis confirmed this expectation. In addition, it seemed that only a few students were able to correctly identify the appropriate variables when considering vertical and horizontal movement while the majority of the students did not apply the same physics principle in isomorphic vertical upward and vertical downward problems. It appears that the context in which the question was posed determined whether the problem was seen as an item that would require “physics reasoning” or as a setting where physics reasoning did not apply. The results revealed students inability to relate physics concepts to appropriate mathematical equations. Two important results from this work are: (1) the presentation of a questionnaire that can be implemented to investigate various aspects regarding the contexts of physics problems; and (2) expanding the concept of context to include the direction of movement as a separate context. / MSc (Natural Science Education), North-West University, Potchefstroom Campus, 2015

Physics education research found that graphs in kinematics have been a problem to students, even at university level. The study hence investigates what deficiencies first-year Physics students at the Central University of Technology, Bloemfontein, South Africa have in terms of transferring mathematics knowledge and understanding when solving kinematics problems. According to the National Department of Education (DoE, 2003), mathematics enables learners to have creative and logical reasoning about problems in the physical and social worlds. Graphs in kinematics are one of the domains that need that skill in mathematics. DoE (2011) further emphasises that learners should be able to collect, analyze, organize and critically evaluate information at the end of their FET sector and that include graphing in kinematics. The study started by exploring graph sense and comprehension from literature. The study further explored from a literature review students‘ problems and possible solutions in transferring their mathematics understanding and knowledge to solve physics problems. The literature study served as conceptual framework for the empirical study, i.e. the design and interpretation of questionnaires, and interview questions. The mathematics and kinematics questions of the questionnaire were divided into four constructs, namely area, gradient, reading coordinates and form/expression of graphs. The participants undertook the questionnaire and interviews voluntarily according to the research ethics. Hundred and fifty two (152) out of 234 students registered for first-year physics from the faculties of humanities (natural science), health and environmental science and engineering and information technology undertook the questionnaire. The researcher interviewed 14 students of these participants as a follow up to the responses of the questionnaire. The responses of the participants were analysed statistically to conclude this study. The average percentages of the questionnaire showed that the majority (62.7% participants) have the mathematics knowledge compared to the low percentage of 34.7 % on physics knowledge. With regard to the constructs the participants generally performed similarly on gradient, reading coordinates and form/expression, i.e. they could either answer both the corresponding mathematics and physics questions and neither of them. In the area construct, most participants with the mathematics knowledge did not transfer it to the physics context. The study further revealed that the majority of interviewees do not have an understanding of the basic physics concepts such as average velocity and acceleration. The researcher therefore recommends that physical science teachers in the FET schools should also undergo constant training in data handling and graphs by subject specialists and academic professionals from Higher Education Institutions. Other remedial actions are also proposed in the dissertation. / MSc (Natural Science Education), North-West University, Potchefstroom Campus, 2015

The subject of teacher competencies or knowledge has been a key issue in mathematics education reform. This study attempts to identify and analyze teacher competencies necessary in the orchestration of a problem-centred approach to dynamic geometry teaching and learning. The advent of dynamic geometry environments into classrooms has placed new demands and expectations on mathematics teachers. In this study the Teacher Development Experiment was used as the main method of investigation. Twenty third-year mathematics major teachers participated in workshop and microteaching sessions involving the use of the Geometer's Sketchpad dynamic geometry software in the teaching and learning of the geometry of triangles and quadrilaterals. Five intersecting categories of teacher competencies were identified: mathematical/geometrical competencies. pedagogical competencies. computer and software competences, language and assessment competencies. / Mathematical Sciences / M. Ed. (Mathematical Education)

Bakgrund: Demens är en sjukdom som utgör minnesförluster, kommunikationssvårigheter och nedsatt förmåga att klara av vardagliga aktiviteter. Patientens problem med beteendet kan orsaka oro, aggressivitet och förvirring mot anhöriga och vårdare. När patienten inte kan förmedla sin önskan i kommunikationen så bidrar det att patienten inte kan uppnå hälsa. Missförstånd kan ha uppstått av det som patienten har försökt att förmedla. Patientens livsvärld kommer inte fram till följd av den oförmåga som sjukdomen kan ge upphov till. Det medför att patientens behov inte kommer fram. Problem: Det behövs mer kunskaper om kommunikation för patienter som lever med demenssjukdom. Syfte: Syfte är att beskriva kommunikationens betydelse för att underlätta omvårdnaden för patienter som lever med demens, ur ett vårdarperspektiv. Metod: En litteraturöversikt utfördes med tio vårdvetenskapliga artiklar i en beskrivande syntes som sammanställdes och beskrevs i resultatet. Resultat: Sjuksköterskan ska vara medveten om sitt förhållningssätt och tillämpa en individanpassad kommunikationsmetod för att patientens behov ska kunna tillgodoses. Vidare uppkommer det vikten av förståelse för människan bakom sjukdomen. Genom att känna till olika kommunikations metoder kan relationen förbättras. Slutsats: Det framkommer ett ökat behov av att kunna utöva kunskaper i kommunikationen, för vårdare och tillåta sig bli berörd av patienten genom att se patientens resurser och inte bara patientens sjukdom. / Background: Dementia is a disease`s which constitute memory disorder, communication difficulties and the ability to manage daily activities become reduced. The patient´s behaviour problem cause expressions like anxiety, aggression, confusion against relatives and carers. When the patient is unable to convey his desire of communication contributes the patient cannot achieve health. Misunderstandings may have arisen from what the patient has tried to convey. The patient's lifeworld cannot arrive due to the inability of the disease may cause. This means that the patient need is not being identified. Problem: There is a need for more knowledge on communication for patients living with dementia. Aim: The purpose is to describe the importance of communication to facilitate the care for patients living with dementia, from a caring perspective. Method: A literature review was conducted by ten nursing research articles in a descriptive synthesis compiled and described in the result. Results: The nurse should be aware of their approach and apply an individualized method of communication to the patient's needs can be met. Moreover, it arises as the importance of understanding of the human being behind the disease. By knowing the different methods of communication, the relationship improved. Conclusion: There is an increased need for being able to exercise skills in communication, for nurses and allow themselves to be touched by the patient by patient's resources and not just the patient's disease.

Lung cancer is a disease affecting millions of people every year and poses a serious threat to global public health. Accurate lung cancer staging is crucial to choose an appropriate treatment protocol and to determine prognosis, this requires the acquisition of contrast-enhanced diagnostic CT (d-CT) that is usually followed by a PET/CT scan. Information from both d-CT and PET scan is used by the clinician in the staging process; however, these images are not intrinsically aligned because they are acquired on different days and on different scanners. Establishing anatomical correspondence, i.e., aligning the d-CT and the PET images is an inherently difficult task due to the absence of a direct relationship between the intensities of the images. The CT acquired during the PET/CT scan is used for attenuation correction (AC-CT) and is implicitly aligned with the PET image as they are acquired at the same time using a hybrid scanner. Patients are required to maintain shallow breathing for both scans. In contrast to that, the d-CT image is acquired after the injection of a contrast agent, and patients are required to maximally inhale, for better view of the lungs. Differences in the AC-CT and d-CT image volumes are thus due to differences in breathhold positions and image contrast. Nonetheless, both images are from the same modality. In this thesis, we present a new approach that aligns the d-CT with the PET image through an indirect registration process that uses the AC-CT. The deformation field obtained after the registration of the AC-CT to d-CT is used to align the PET image to the d-CT. Conventional image registration techniques deform the entire image using homogeneous regularization without taking into consideration the physical properties of the various anatomical structures. This homogeneous regularization may lead to physiologically and physically implausible deformations. To register the d-CT and AC-CT images, we developed a 3D registration framework based on a fluid transformation model including three physically motivated properties: (i) sliding motion of the lungs against the pleura; (ii) preservation of rigid structures; and (iii) preservation of topology. The sliding motion is modeled using a direction dependent regularization that decouples the tangential and the normal components of the external force term. The rigid shape of the bones is preserved using a spatially varying filter for the deformations. Finally, the topology is maintained using the concept of log-unbiased deformations. To solve the multi-modal registration problem due to the contrast injected for the d-CT, but lack thereof in the AC-CT, we use local cross correlation (LCC) as the similarity measure. To illustrate and validate the proposed registration framework, different intra-patient CT datasets are used, including the NCAT phantom, EMPIRE10 and POPI datasets. Results show that our proposed registration framework provides improved alignment and physically motivated deformations when compared to the classic elastic and fluid registration techniques. The final goal of our work was to demonstrate the clinical utility of our new approach that aligns d-CT and PET/AC-CT images for fusion. We apply our method to ten real patients. Our results show that the PET images have much improved alignment with the d-CT images using our proposed registration technique. Our method was successful in providing a good overlap of the lungs, improved alignment of the tumours and a lower target registration error for landmarks in comparison to the classic fluid registration. The main contribution of this thesis is the development of a comprehensive registration framework that integrates important physical properties into a state-of-the-art transformation model with application to lung imaging in cancer.

Object category detection, the task of determining if one or more instances of a category are present in an image with their corresponding locations, is one of the fundamental problems of computer vision. The task is very challenging because of the large variations in imaged object appearance, particularly due to the changes in viewpoint, illumination and intra-class variance. Although successful solutions exist for learning object category detectors, they require massive amounts of training data. Transfer learning builds upon previously acquired knowledge and thus reduces training requirements. The objective of this work is to develop and apply novel transfer learning techniques specific to the object category detection problem. This thesis proposes methods which not only address the challenges of performing transfer learning for object category detection such as finding relevant sources for transfer, handling aspect ratio mismatches and considering the geometric relations between the features; but also enable large scale object category detection by quickly learning from considerably fewer training samples and immediate evaluation of models on web scale data with the help of part-based indexing. Several novel transfer models are introduced such as: (a) rigid transfer for transferring knowledge between similar classes, (b) deformable transfer which tolerates small structural changes by deforming the source detector while performing the transfer, and (c) part level transfer particularly for the cases where full template transfer is not possible due to aspect ratio mismatches or not having adequately similar sources. Building upon the idea of using part-level transfer, instead of performing an exhaustive sliding window search, part-based indexing is proposed for efficient evaluation of templates enabling us to obtain immediate detection results in large scale image collections. Furthermore, easier and more robust optimization methods are developed with the help of feature maps defined between proposed transfer learning formulations and the “classical” SVM formulation.