Title: Problems of pupils of high school in solving geometric construction exercises Author: Miroslava Dyntarová Department: Department of Mathematics and Mathematical Education Supervisor: Mgr. Michal Zamboj, Ph.D., Department of Mathematics and Mathema- tical Education Abstract: The aim of this thesis is to reveal various errors and issues that high school students face in triangle construction problems. The thesis is divided into two parts for clarity. In the theoretical part we deal with construction problems in general and look into their various solution methods and formal procedures recommended by high school textbooks. Next, we focus on sets of points of a given property (that are part of the high school curriculum), give related denitions, basic properties and use cases. For better understanding of the demonstrated problems the thesis is lled with au- xiliary graphs made in the program GeoGebra. In the last chapter of the theoretical part, we introduce various problems that are expected to occur during geometry con- struction problem solving by students themselves. Those were the main focus of the following study. The preparation of the study, its implementation and subsequent ana- lysis of collected data is described in the practical part of the thesis. The study was conducted with 10 students....

Sedan 1907 har det upplåtits fastigheter med tomträtt i Sverige. Tomträtt innebär att kommun eller stat, mot en årlig avgäld, upplåter mark med nyttjanderätt till en tomträttshavare med avgäldsperioder om minst tio år. Att inneha bebyggelse på mark som är förenad med tomträtt kan, beroende på tomträttshavarens ekonomiska situation, leda till ett skräckscenario. En kombination av kraftiga markvärdestegringar och långa avgäldsperioder resulterar i chockhöjda tomträttsavgälder för tomträttshavare, på nivåer som är svåra att förutspå. I nuläget saknas tydliga direktiv för hur bestämmelse av tomträttsavgälden vid ny avgäldsperiod ska ske och trots förslag om att förenkla regleringen har inga ändringar gjorts.  Syftet med denna uppsats är att undersöka rättsläget kring bestämmelse av tomträttsavgälden inför ny avgäldsperiod och på så sätt försöka bringa klarhet i den problematik som finns. Genom en rättsvetenskaplig metod där rättskällor har tolkats, utretts och analyserats kunde vi dra slutsatsen att den reglering som finns kring bestämmande av tomträttsavgälden bör ses över. Tills vidare får denna undersökning och de riktlinjer vi funnit ses som en vägledning.

[pt] Este trabalho tem como objetivo principal apresentar uma proposta de atividades para o ensino dos conteúdos de lugares geométricos e pontos notáveis do triângulo, sendo aplicados no oitavo e nono ano escolares, conforme previsto na Base Nacional Comum Curricular (BNCC). As atividades possuem como base metodológica a teoria elaborada pelo casal de matemáticos Dina van Hiele-Geldof e Pierre van Hiele, a qual demonstra as relações que aquela metodologia possui com o Construtivismo, ao possuir as principais características das teorias pedagógicas de Piaget, Vygotsky e Ausubel. Tal escolha baseia-se especialmente no fato da teoria ter sido desenvolvida para o ensino de geometria. Além disso, este trabalho discorre sobre as definições e propriedades dos elementos geométricos que serão os objetos das práticas propostas. Estas são orientadas por meio de roteiros que exploram, sob a metodologia adotada, diferentes registros semióticos. A execução de algumas atividades fomenta, por um lado, a manipulação de materiais concretos, e por outro, o uso de tecnologia, no caso, o software de geometria dinâmica Geogebra para realização das construções geométricas. Estas atividades buscam cativar o interesse do aluno pelo processo de descoberta na geometria. / [en] The main objective of this project is to propose activities for the teaching of geometric locations and notable points of the triangle, being applied at the eighth and ninth years of elementary school, as provided for in the National Common Curricular Base (BNCC). The activities have as methodological basis the theory elaborated by the mathematician couple Dina van Hiele-Geldof and Pierre van Hiele, which demonstrates the relationship that that methodology has with Constructivism, by having the main characteristics of the pedagogical theories of Piaget, Vygotsky and Ausubel. This choice is based especially on the fact that the theory was developed for the teaching of geometry. In addition, this work discusses the definitions and properties of the geometric elements that will be the objects of the proposed practices. These are guided by scripts that explore, under the adopted methodology, different semiotic records. The execution of some activities encourages, on the one hand, the manipulation of concrete materials, and on the other, the use of technology, in this case, the Geogebra dynamic geometry software for the realization of geometric constructions. These activities seek to captivate the student s interest in the process of discovering geometry.

[pt] O Triângulo Norte da América Central é composto por El Salvador, Honduras e Guatemala. Esses países compartilham um histórico de desigualdades socioeconômicas, violência e intervenções estrangeiras em seus territórios. Intensos fluxos emigratórios são registrados nesses países, com seus nacionais buscando chegar aos Estados Unidos percorrendo o território mexicano, razão pela qual consideramos esses quatro países como uma região de emigração, devido aos fluxos neles originados e atravessados. Essas migrações geralmente ocorrem de maneira forçada e em fluxos maciços. Consoante à mobilidade, ocorre um processo de contenção desses migrantes por parte dos Estados Unidos, que desenvolve mecanismos físicos e políticos para impedir a entrada dessas pessoas em seu território, além de imporem políticas migratórias e fronteiriças ao México e aos países do Triângulo Norte da América Central para impedirem os fluxos de chegarem em sua fronteira. Assim sendo, percebemos esses quatro países como uma região de fronteira que se traduz em região de i-mobilidade migratória, pois nela ocorrem dois processos concomitantes, o de trânsito e o de controle do mesmo. Nesta dissertação, investigamos a violência como elemento deflagrador dessas migrações e como ela atinge os sujeitos migrantes ao longo de seu percurso à Terra Prometida, os Estados Unidos. Analisaremos as migrações ocorridas entre 2018 e 2021, com foco nas caravanas de migrantes centro-americanos, apresentando as inovações de sua organização e o perfil demográfico daqueles que as integraram, bem como as medidas tomadas pelos Estados Unidos e México para impedir essa mobilidade. / [en] The Northern Triangle of Central America is composed by El Salvador, Honduras and Guatemala. These countries share a history of socioeconomic inequalities, violence, and foreign interventions in their territories. Intense emigration flows are recorded in these countries, with their nationals seeking to reach the United States by traveling through Mexican territory, in what we consider these four countries as a region of emigration, due to the flows originating and crossing through them. These migrations usually occur in a forced way and in massive flows. The United States develops physical and political mechanisms to prevent these people from entering its territory and imposes migration and border policies to Mexico and to the countries of the Northern Triangle of Central America to prevent the flows from reaching its borders. Thus, we perceive these four countries as a border region that translates into a region of migratory i-mobility, because two concomitant processes occur there, that of transit and that of control of it. In this dissertation, we investigate violence as a triggering element of these migrations and how it affects the migrant subjects along their journey to the Promised Land, the United States. We will analyze the migrations that occurred between 2018 and 2021, focusing on the Central American migrant caravans, presenting the innovations of their organization and the demographic profile of those who integrated them, as well as the measures taken by the United States and Mexico to prevent this mobility.

Необходимость в написании программы для расчета рассеянного поля телом вращения возникла в связи с неоднозначностью решения рассеянного поля таких объектов средствами электродинамического моделирования FEKO и Ansoft HFSS. В частности, в HFSS при повороте объекта (конуса) и соответствующем изменении характеристик падающей волны (направления распространения и поляризации) количество сегментов могло меняться более, чем на порядок. Отметим, что в качестве подхода к решению использовался метод физической оптики. Трудности расчета в FEKO вызваны по большей части ресурсами компьютера, а также сложностью последующей трактовки и математической обработки полученных результатов. Программа, описываемая в работе, позволит подойти к решению рассеянного на теле вращения поля более индивидуально и избежать таких неоднозначностей, что могут встречаться при расчетах в пакетах электродинамического моделирования. По результатам рассмотрения ряда задач сделан выбор в пользу метода физической оптики и его численной реализации на базе алгоритмов MATLAB. / The solution of diffraction from perfectly conducting convex solids of revolution is considered. The main aim is obtainment of an optimal approach for diffraction solution from large-scale solids. The implementation of a numerical solution of diffraction with physical optics method using MATLAB is considered. The realized program allows description of the solid of revolution with the analytic form equation of the curve. The possibility of curve description with a few functions defined on disjoint intervals is taken into consideration. The surface meshing with the required value is assured. The measure method of scattering characteristics is touched upon. The experimental results of the solid with three equations of curve are presented. The results of MATLAB modeling are compared with the experimental ones. The upgradability of mathematical modeling algorithms is proposed.

Based on students’ declining reading comprehension there is a need to develop systematic explicit instruction in teaching reading. This study is based on theories of metacognition, reading comprehension, reading instruction and Legitimation Code Theory and has the reading triangle as a model for teaching expository texts. The model has been tested in one class with eighth-grade students. The students have estimated their own reading comprehension and how they worked before, during and after reading an expository text, both before and after work with the reading triangle. The students in this survey have been taught and have worked with texts based on three levels of the reading triangle. The materials in the study are students’ self-assessments, texts with underlining and comments and interviews with the students and their teacher. The results show that the model, the reading triangle, as a part of an approach to develop literacy, with modelling and metacognitive textual conversations, can contribute to an understanding of the students’ reading process and knowledge of how global and local aspects of texts – such as purpose, text structure and choice of words – are connected with and influence reading comprehension. The study shows that the link between local and global levels must be explicit, since a focus on details can be detrimental to the overall understanding of texts. The use of the reading triangle in the classroom can also help the teaching move between the concrete and the abstract, enabling students to use the acquired knowledge and insights in new texts and reading situations.

This project investigates the Norwegian wine market and attempts to provide models of how the sales volume is influenced by different product attributes. The purpose was to examine if and how such relationship can be modelled using multiple linear regression. Additionally, the aim was to give insights in what drives the sales - which is especially valuable and useful for wine producers in order to efficiently enhance their business strategies. Accordingly, the research questions were: which wine attributes have a positive respectively negative effect on sales, and how can wine producers improve their business using this information? The data was retrieved from Vinmonopolet (which has monopoly on wine sales in Norway) and consisted of the best-selling red wines and white wines during January-June of 2020. The model building and analysis were separated for red wines and white wines, hence resulting in two final models. Evaluation of the models showed that they were reasonable for describing the interaction between sales volume and product attributes. For instance, the model validation generated R^2 values of approximately 56% for red wine and 61% for white wine. For both red wine and white wine, the final models indicated that high-volume packages have a positive effect on sales volume. Conversely, high sales prices and high alcohol contents, as well as ordering items and bag-in-box packaging, were negative properties in respect of sales volume. In addition, the red wine model implied that sales are improved by high sugar contents, the grape Rondinella and the food recommendations cattle, vegetables and big game - while high acid contents and France (as the production country) have negative effects on sales. Furthermore, the white wine model pointed out that younger wines and the food recommendation cheese increase sales, whereas high sugar contents and the food recommendation fish decrease sales. The discussion presents interpretations of the results in conjunction with economic theory and articles about wine. The marketing mix model (the 4 Ps) was also applied to employ the project results and thus provide wine producers guidance in marketing and product development. In conclusion, this project offers a deeper understanding of wine markets - in particular, the Norwegian market. The research questions are answered and the purpose and aim are satisfied. Moreover, proposed further research is for example to conduct a similar analysis but with adjustments of taxes and fees on wine and to further investigate the balance between alcohol, acidity, tannins and sweetness. / Det här projektet undersöker den norska vinmarknaden och försöker utforma modeller för hur försäljningsvolymen påverkas av olika produktattribut. Syftet var att undersöka om och hur ett sådant samband kan modelleras med hjälp av multipel linjär regression. Därutöver var målet med arbetet att ge insikt om vad som driver försäljningen - vilket är speciellt värdefullt och användbart för vinproducenter i syfte att effektivt utveckla sina affärsstrategier. Följaktligen var projektets frågeställningar: vilka vinattribut har en positiv respektive negativ effekt på försäljningen, och hur kan vinproducenter använda informationen för att förbättra sina affärer? Data hämtades från Vinmonopolet (vilka har monopol på vinförsäljningen i Norge) och bestod av de bästsäljande rödvinerna och vitvinerna under januari-juni 2020. Modellbyggandet och analysen separerades för rött och vitt vin, vilket ledde till två slutgiltiga modeller. Granskningen av modellerna visade att de var rimliga för att beskriva interaktionen mellan försäljningsvolym och produktattribut. Till exempel modellvalideringen genererade R^2-värden på ungefär 56% för rött vin och 61% för vitt vin. För både rött vin och vitt vin indikerade de slutgiltiga modellerna att storvolymsförpackningar har en positiv effekt på försäljningsvolymen. Däremot var höga försäljningspriser och högt alkoholinnehåll, samt beställningsvaror och bag-in-box-paketering, negativa egenskaper vad gäller försäljningsvolym. Rödvinsmodellen antydde dessutom att försäljningen förbättras av högt sockerinnehåll, druvan Rondinella samt matrekommendationerna nötkreatur, grönsaker och storvilt - samtidigt som högt syrainnehåll och Frankrike (som produktionsland) har negativa effekter på försäljningen. Därtill påpekade vitvinsmodellen att yngre viner och matrekommendationen ost ökar försäljningen, medan högt sockerinnehåll och matrekommendationen fisk minskar försäljningen. Diskussionen presenterar tolkningar av resultaten i samband med ekonomisk teori och artiklar om vin. Marknadsmixmodellen (de 4 Pna) användes också för att tillämpa projektresultaten och på så sätt ge vinproducenter vägledning i marknadsföring och produktutveckling. Sammanfattningsvis ger projektet en djupare förståelse för vinmarknaden - speciellt den norska. Frågeställningarna besvarades samt syftet och målet tillgodosågs. Som vidare undersökning föreslogs bland annat en liknande studie men med justeringar för skatter och avgifter på vin samt en djupare undersökning av balansen mellan alkohol, syra, tanniner och sötma.

School constantly changes and adapts methods to teach and contents according to the society. The change has led to a growing trend for digitalcurriculum resources in the classroom and mathematic as a subject. Thepurpose of this paper is therefore to investigate usage of digital curriculum resources in learning mathematics and teachers’ opinion about thedigital curriculum resources. The data was collected by a questionnaire,in total 87 respondents participated. The data was interpreted with thedidactic triangle and external factors.As a result, teachers express that the digital curriculum resources can leadto a wider scale of teaching methods and increases motivation for the pupils. On the other hand, teachers also express that the digital curriculumresources can lead to a distraction for the pupils and that they tend to hassle. The result shows that less teachers express that digital curriculum resources are used rather than analogue material. / Skolan är i ständig förnyelse och anpassar sig både i arbetssätt och innehållsmässigt utefter hur samhället ser ut och fungerar. Det har bidragit tillatt det i matematikundervisningen idag finns ett stort intresse för att använda digitala läromedel. Denna studie har därför som syfte att utforskaanvändningen av digitala läromedel i matematikundervisning samt vadlärare som undervisar i årskurs 1–3 uttrycker om de digitala läromedlen.Studien genomfördes med forskningsmetoden enkät och 87 respondenterhar använts till studien. Empirin som samlats in har tolkats med den didaktiska triangeln och ramfaktorer.Resultatet av studien visar att lärarna uttrycker att de digitala läromedlenkan bidra till ökad variation i undervisningen och till att öka motivationenhos eleverna. Lärarna uttrycker även att de kan bidra till en distraktionhos eleverna och att de digitala läromedlen krånglar. Resultatet visarockså att det är en mindre andel lärare som uttrycker att de använder digitala läromedel i sin matematikundervisning än analoga läromedel.

Syftet med studien är att ta reda på om lärare i årskurs 4–6 undervisar i engelsk grammatik och vilka undervisningsstrategier de använder sig av under sina grammatiklektioner i ämnet engelska i årskurs 4–6. För att undersöka studiens syfte har sex klassrumsobservationer och fyra semistrukturerade intervjuer med lärare på fyra skolor i södra Sverige genomförts. Den didaktiska triangeln har använts som teoretisk utgångspunkt. Resultatet visar att lärare använder sig av en integrerad undervisning för att lära ut engelsk grammatik. Lärare använder ett läromedel som utgångspunkt och sedan väljer att komplettera grammatikundervisningen för att få en fördjupad och ökad förståelse av grammatiken.

Cary-Cortona is a city that lies on the periphery of two realities; the reality of pragmatism and the reality of abstraction. It was conceived as a response to the pragmatic questions posed by an uncertain, yet impending future. It was nurtured by the correlation of vaguely related information until the facts and figures themselves became an abyss of abstraction. From the cavernous depths of information came a night of dreams when Cary-Cortona first emerged as walls and columns that began to form a city of arcades and courtyards. On that night the inhabitants walked the streets and alleys and the fragments of a dream became the very real elements of a living town. The subconscious residue of that dream flowed together as expressions of order, hierarchy, and form, drawn into existence through the media of models, drawings and sketches. Those formal expressions have taken on a reality of their own even when seen as abstractions through pragmatic eyes because they represent aspirations not yet realized. Cary-Cortona is very much alive in the realm of ideas, and as an idea it can emote a different series of images from each viewer who sees it. Just as there are limitless images of the future each tied to the individual, Cary-Cortona represents only one aspiration for a small corner of a vast future. In its present form Cary-Cortona is an adolescent in a purgatory between the two realities of abstraction and pragmatism, belonging to neither world completely, yet existing to be judged and scrutinized by both. / Master of Architecture