This study investigated the use of an advanced technological development (free GeoGebra software) within the secondary educational setting in four relatively under-resourced schools in the Gauteng Province of South Africa. This advancement is viewed as having the potential to promote the teaching and learning of complex ideas in mathematics, even within traditionally deprived communities. The focus in this study was on the teaching and learning of transformation geometry at Grade 9 and attainment was reflected in terms of the van Hieles' levels of geometrical thinking. A mixed methods approach was followed, where data was collected through lesson observations, written tests and semi-structured interviews. Four Grade 9 teachers from four schools were purposively selected, while twenty-four mathematics learners (six from each school) in the Tshwane metropolitan region were randomly selected. The teachers' lesson observations and interview outcomes were coded and categorised into themes, and the learners' test scripts were marked and captured. The analysis of test scores was structured according to the van Hieles' levels of geometric thought development. As far as the use of GeoGebra is concerned, it was found that teachers used the program in preparation for, as well as during lessons; learners who had access to computers or android technology, used GeoGebra to help them with practice and exercises. As far as the effect of the use of GeoGebra is concerned, improved performance in transformation geometry was demonstrated. / Dissertation (MEd)--University of Pretoria, 2016. / Science, Mathematics and Technology Education / MEd / Unrestricted

Thesis (MComm) -- Stellenbosch University, 2002. / ENGLISH ABSTRACT: Consider a data set with a categorical response variable and a set of explanatory variables. The response variable can have two or more categories and the explanatory variables can be numerical or categorical. This is a typical setup for a classification analysis, where we want to model the response based on the explanatory variables. Traditional statistical methods have been developed under certain assumptions such as: the explanatory variables are numeric only and! or the data follow a multivariate normal distribution. hl practice such assumptions are not always met. Different research fields generate data that have a mixed structure (categorical and numeric) and researchers are often interested using all these data in the analysis. hl recent years robust methods such as classification trees have become the substitute for traditional statistical methods when the above assumptions are violated. Classification trees are not only an effective classification method, but offer many other advantages. The aim of this thesis is to highlight the advantages of classification trees. hl the chapters that follow, the theory of and further developments on classification trees are discussed. This forms the foundation for the CART software which is discussed in Chapter 5, as well as other software in which classification tree modeling is possible. We will compare classification trees to parametric-, kernel- and k-nearest-neighbour discriminant analyses. A neural network is also compared to classification trees and finally we draw some conclusions on classification trees and its comparisons with other methods. / AFRIKAANSE OPSOMMING: Beskou 'n datastel met 'n kategoriese respons veranderlike en 'n stel verklarende veranderlikes. Die respons veranderlike kan twee of meer kategorieë hê en die verklarende veranderlikes kan numeries of kategories wees. Hierdie is 'n tipiese opset vir 'n klassifikasie analise, waar ons die respons wil modelleer deur gebruik te maak van die verklarende veranderlikes. Tradisionele statistiese metodes is ontwikkelonder sekere aannames soos: die verklarende veranderlikes is slegs numeries en! of dat die data 'n meerveranderlike normaal verdeling het. In die praktyk word daar nie altyd voldoen aan hierdie aannames nie. Verskillende navorsingsvelde genereer data wat 'n gemengde struktuur het (kategories en numeries) en navorsers wil soms al hierdie data gebruik in die analise. In die afgelope jare het robuuste metodes soos klassifikasie bome die alternatief geword vir tradisionele statistiese metodes as daar nie aan bogenoemde aannames voldoen word nie. Klassifikasie bome is nie net 'n effektiewe klassifikasie metode nie, maar bied baie meer voordele. Die doel van hierdie werkstuk is om die voordele van klassifikasie bome uit te wys. In die hoofstukke wat volg word die teorie en verdere ontwikkelinge van klassifikasie bome bespreek. Hierdie vorm die fondament vir die CART sagteware wat bespreek word in Hoofstuk 5, asook ander sagteware waarin klassifikasie boom modelering moontlik is. Ons sal klassifikasie bome vergelyk met parametriese-, "kernel"- en "k-nearest-neighbour" diskriminant analise. 'n Neurale netwerk word ook vergelyk met klassifikasie bome en ten slote word daar gevolgtrekkings gemaak oor klassifikasie bome en hoe dit vergelyk met ander metodes.

The purpose of this study was to investigate the effects of teaching linear equations with Dynamic Mathematics Software (GeoGebra) on seventh grade students&rsquo / achievement compared to the regular instruction. Randomized posttest-only control group design was utilized in the study. 60 seventh grade students (32 girls and 28 boys) of a public school in Yenimahalle district in Ankara participated in the study. The study was conducted in 2011-2012 fall semester, lasting 9 class hours in three weeks. The data was collected by three Mathematics Achievement Tests: Cartesian coordinate system achievement test (MAT1), linear relation achievement test (MAT2) and graph of linear equation achievement test (MAT3). The quantitative analysis was conducted by using analysis of covariance (ANCOVA). The results revealed that teaching Cartesian coordinate system and linear relation by using Dynamic Mathematics Software had no significant effect on seventh grade students&rsquo / achievement compared to the regular instruction. On the other hand, the results also indicated that teaching graph of linear equations by using Dynamic Mathematics Software had a significant effect on seventh grade students&rsquo / achievement positively.

The overall problem that formed the basis for this thesis is that students get limited opportunity to develop their mathematical reasoning ability while, at the same time, there are dynamic mathematics software available which can be used to foster this ability. The aim of this thesis is to contribute to knowledge in this area by focusing on task design in a dynamic software environment and by studying the reasoning that emerges when students work on tasks in such an environment. To analyze students’ mathematical reasoning, a new analytical tool was developed in the form of an expanded version of Toulmin’s model. Results from one of the studies in this thesis show that exploratory tasks in a dynamic software environment can promote mathematical reasoning in which claims are formulated, examined and refined in a cyclic process. However, this reasoning often displayed a lack of the more conceptual, analytic and explanatory reasoning normally associated with mathematics. This result was partly confirmed by another of the studies. Hence, one key question in the thesis has been how to design tasks that promote conceptual and explanatory reasoning. Two articles in the thesis deal with task design. One of them suggests a model for task design with a focus on exploration, explanation, and generalization. This model aims, first, to promote semantic proof production and then, after the proof has been constructed, to encourage further generalizations. The other article dealing with task design concerns the design of prediction tasks to foster student reasoning about exponential functions. The research process pinpointed key didactical variables that proved crucial in designing these tasks. / Baksidestext Det övergripande problem som legat till grund för denna avhandling är att elever får begränsad möjlighet att utveckla sin resonemangsförmåga samtidigt som det finns dynamiska matematikprogram som kan utnyttjas för att stimulera denna förmåga. Syftet med avhandlingen är att bidra till den samlade kunskapen inom detta problemområde, dels genom att fokusera på design av uppgifter i en lärandemiljö med dynamiska matematikprogram och dels genom att studera och karakterisera de resonemang som utvecklas när elever jobbar med olika uppgifter i denna miljö. För att analysera elevernas resonemang utvecklades ett nytt analysverktyg i form av en utökad version av Toulmins modell. Resultat från en av studierna i avhandlingen visar att dynamiska matematikprogram i kombination med utforskande uppgifter kan stimulera till matematiska resonemang där hypoteser formuleras, undersöks och förfinas i en cyklisk process. Samtidigt visar samma studie att de resonemang som utvecklas i stor utsträckning saknar matematiskt grundade förklaringar. Detta resultat bekräftas till viss del av ytterligare en studie.  Frågan hur uppgifter bör designas för att främja matematiskt grundade resonemang har därför varit central i avhandlingen. Två av artiklarna behandlar uppgiftsdesign, men utifrån olika utgångspunkter.

Orientador: Janito Vaqueiro Ferreira / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-19T00:39:11Z (GMT). No. of bitstreams: 1 Souza_GustavoFurtadode_M.pdf: 3361483 bytes, checksum: 72dc9fa21313b39aa7b0b797d45f7793 (MD5) Previous issue date: 2011 / Resumo: A indústria de motores de um modo geral utiliza-se de testes de final de linha para assegurar a funcionalidade de seus produtos. Na indústria de motores estes testes são normalmente funcionais e verificam características de desempenho do motor, porém características construtivas são difíceis de avaliar e dependem de operadores habilidosos para serem identificadas. A dependência da habilidade dos operadores torna o processo subjetivo, pois não é possível aferir as habilidades dos operadores. A análise de vibrações surge como uma importante ferramenta para avaliação destas características, permitindo verificações não intrusivas nos motores. A implementação da transformada de wavelet packet - WTP aos sinais de vibração permite determinar o nível de energia em cada uma das bandas de freqüência, comparando então motor a motor. Para facilitar a análise, os coeficientes de energia são compactados e um polinômio de resposta pode ser determinado com auxilio da análise de componentes principais - ACP. A utilização de um polinômio de resposta, aplicado a um conjunto de resultados conhecidos, permite que seja definida uma assinatura mecânica padrão para os motores / Abstract: The engine industry in general is used for end of line testing to ensure the functionality of its products. In the engine industry these tests are usually functional and verify performance characteristics of the engine, but construction features are difficult to assess and depend on skilled operators to be identified. The dependence of the ability of operators makes the subjective process, it is not possible to assess the skills of operators. Vibration analysis emerges as an important tool for evaluation of these features, enabling non-intrusive checks on the engines. The implementation of wavelet packet transform - WTP to vibration signals to determine the energy level in each frequency bands, then comparing the motor engine. To make the analysis easy, the coefficients of energy is compressed and a polynomial response can be determined with the aid of main component analysis - PCA. The use of a polynomial response, applied to a set of known results, allows us to define a signature pattern for mechanical engines / Mestrado / Projetos / Mestre em Engenharia Automobilistica

This thesis concerns the challenge of integrating dynamic software environments into the teaching of mathematics. It investigates particular aspects of the design of tasks which employ this type of computer-based system, with a focus on improvement, both of the tasks themselves and of the design process through which they are developed and refined. The thesis reports two research projects: a small initial one preceding a larger main project. The initial case study, involving two graduate students in mathematics, develops a task design model for geometrical locus problems. The main study constitutes the first iteration of a design-based study, conducted in collaboration with four upper-secondary school teachers and their classes. It seeks to identify task design characteristics that foster students’ mathematical reasoning and proficient use of software tools, and examines teachers’ organisation of ‘follow-up’ lessons. The findings concern three particular aspects: features of tasks and task environment relevant to developing a specific plan of action for a lesson; orchestration of a particular task environment to support the instrumental genesis of specific dynamic software tools; how to follow up students’ work on computer-based tasks in a whole-class discussion.

This dissertation discusses novel techniques for interpolation-based software model checking, an approximate method which uses Craig interpolation to compute invariants of programs. Our work addresses two aspects of program analyses based on model checking: verification (the construction of correctness proofs for programs) and falsification (the detection of counterexamples that violate the specification). In Hoare's calculus, a proof of correctness comprises assertions which establish that a program adheres to its specification. The principal challenge is to derive appropriate assertions and loop invariants. Contemporary software verification tools use Craig interpolation (as opposed to traditional predicate transformers such as the weakest precondition) to derive approximate assertions. The performance of the model checker is contingent on the Craig interpolants computed. We present novel interpolation techniques which provide the following advantages over existing methods. Firstly, the resulting interpolants are sound with respect to the bit-level semantics of programs, which is an improvement over interpolation systems that use linear arithmetic over the reals to approximate bit-vector arithmetic and/or do not support bit-level operations. Secondly, our interpolation systems afford us a choice of interpolants and enable us to fine-tune their logical strength and structure. In contrast, existing procedures are limited to a single ad-hoc choice of an interpolant. Interpolation-based verification tools are typically forced to refine an initial approximation repeatedly in order to achieve the accuracy required to establish or refute the correctness of a program. The detection of a counterexample containing a repetitive construct may necessitate one refinement step (involving the computation of additional interpolants) for each iteration of the loop. We present a heuristic that aims to avoid the repeated and computationally expensive construction of interpolants, thus enabling the detection of deeply buried defects such as buffer overflows. Finally, we present an implementation of our techniques and evaluate them on a set of standardised device driver and buffer overflow benchmarks.

Early this century "S-shaped" curves, sigmoids, gained popularity among demographers. However, by 1940, the approach had "fallen out of favour", being criticised for giving poor results and having no theoretical validity. It was also considered that models of total population were of little practical interest, the main forecasting procedure currently adopted being the bottom-up "cohort-component" method. In the light of poor forecasting performance from component methods, a re-assessment is given in this thesis of the use of simple trend models. A suitable means of fitting these models to census data is developed, using a non-linear least squares algorithm based on minimisation of a proportionately weighted residual sum of squares. It is demonstrated that useful models can be obtained from which, by using a top-down methodology, component populations and vital components can be derived. When these models are recast in a recursive parameterisation, it is shown that forecasts can be obtained which, it is argued, are superior to existing official projections. Regarding theoretical validity, it is argued that sigmoid models relate closely to Malthusian theory and give a mathematical statement of the demographic transition. In order to judge the suitability of extrapolating from sigmoid models, a framework using Catastrophe Theory is developed. It is found that such a framework allows one qualitatively to model population changes resulting from subtle changes in influencing variables. The use of Catastrophe Theory has advantages over conventional demographic models as it allows a more holistic approach to population modelling.

Mathematics learning seems to be a demanding and time-consuming task for many learners. Information and communication technology (ICT) is an attractive tool of learning for students at any level and it can provide an effective atmosphere for understanding mathematics. The question is how to combine mathematics teaching contents, approaches, curricula, and syllabus with new media. The key issue in European educational policy (and other countries as well) is exchange and sharing digital learning resources (learning objects) among countries. In order to accumulate the practice of various countries and use the best digital resources created by different countries, it is necessary to localize learning objects (LO). The paper deals with some problems connected with localization of LO, developed for mathematics education, and presents some solution. Software localization is mainly referred to as language translation (e.g., translation of user interface texts and help documents). However, there are many other important elements depending on the country and people who will use the localized software. In this paper, the main attention is paid to localization of learning objects used for teaching and learning mathematics.

Submitted by Maike Costa (maiksebas@gmail.com) on 2016-03-28T12:29:14Z No. of bitstreams: 1 arquivototal.pdf: 800250 bytes, checksum: 42e76ab05ea580b4fd24a3312b9b4212 (MD5) / Made available in DSpace on 2016-03-28T12:29:14Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 800250 bytes, checksum: 42e76ab05ea580b4fd24a3312b9b4212 (MD5) Previous issue date: 2014-08-29 / In this work we present a study of the regular polyhedra, comparing and discussing the concepts and de nitions given in the study of regular polyhedra in textbooks most widely used in Brazilian high schools. We prove the theorem of Euler, we calculate surface areas and volumes of regular polyhedra. Finally, we present some mathematical software that can be used by students and mathematics teachers in the spatial geometry classes as auxiliary material in the teaching and learning of this subject in the classroom. / Neste trabalho apresentamos um estudo sobre os poliedros regulares, comparando e discutindo os conceitos e as de nições que são dadas no estudo dos poliedros regulares nos livros didáticos mais utilizados nas escolas brasileiras de Ensino Médio. Provamos o teorema de Euler, calculamos áreas de superfícies e os volumes dos poliedros regulares. Por m, apresentamos alguns softwares matemáticos que podem ser utilizados pelos alunos e professores de Matemática nas aulas de geometria espacial como material auxiliar no processo de ensino e aprendizagem deste tema em sala de aula.