CAPES / Este trabalho mostra um estudo sobre as sete indeterminações matemáticas. Apresenta uma análise de livros didáticos de Cálculo e mostra que esse assunto é tratado de forma semelhante por todos eles, mediante aplicação da Regra de L’Hôspital. A proposta deste trabalho é fornecer explicações mais completas e adequadas ao entendimento de estudantes, professores e entusiastas da Matemática sobre indeterminações. O texto contém uma lista de exemplos sobre todas as possibilidades de interminações através de limites cujo resultado pode ser igual: a zero, infinito, constante não nula, ou limite não existente. Além disso, tráz uma análise contextualizada dessas expressões através da História da Matemática e de como a tentativa de compreender o infinito trouxe avanços significativos tanto na Matemática quanto na Filosofia, para resolver problemas como o hotel de Hilbert e os paradoxos de Zenão. / This work is about the seven mathematical indeterminate forms. It presents a review of many Calculus textbooks and shows that all of them treat the subject of indeterminate forms in similar way, by using the L’Hôspital’s rule. This study aims to provide a more general explanation of indeterminate forms to Math students, teachers, and enthusiasts. For each indeterminate form, it shows examples of limits that are equal to zero, infinite, a non-zero constant, or does not exist. It also discusses how the notion of infinity solved paradoxes in Mathematics and Philosophy throughout the history, such as Hilbert Hotel and Zeno paradoxes.

In this diploma thesis I look at the Analysis of selected textbook health education through the eyes of teachers who use it in their lessons. The theoretical part of this thesis serves as an introduction to the complex topic of textbooks and lays out the criteria according to which a textbook is chosen. In the practical part I carry out a didactic analysis of the textbook and I present a summary of experience of teachers who have worked with it. The practical part shows that teachers's experience does not differ significantly from the findings of the didactic analysis. The textbook's unusual approach to teaching health education is prominent in both surveys. This thesis aims to help junior health education teachers decide whether and how this particular textbook will benefit their own teaching method. KEYWORDS analysis of textbooks, teaching resources, textbooks, function and structure of textbooks, textbook evaluation

This thesis concern with the teaching of the literature of the czech national revival at the secondary school. Its aim is to analyze selected textbooks and manuals used in secondary schools and based on this analysis it tries to characterize the most important aspects of this period. It describes how the term "national revival" is explained to high school students, what is the time range of this period, which authors of this section of czech literary history are included in individual textbooks and also in the canon of works required for the final school- leaving examination. It compares individual aspects with the starting points of the professional literature. The work raises the question of whether and to what extent textbooks create an image of this topic for school purposes, how they affect students' awareness of the topic. Finally, it proposes specific procedures and activities that can be used in teaching the literature of the czech national revival at secondary schools and grammar schools.

Som ett led i att stärka den digitala kompetensen i den svenska skolan så beslöt regeringen2017 att införa användandet av programmering i matematikämnet. Sedan höstterminen 2018 så har flertalet matematikkurser för gymnasiet fått uppdaterade kursplaner med tillägget att programmering ska användas som verktyg för problemlösning. I praktiken innebär detta att drygt hälften av de nationella gymnasieprogrammen nu får programmering som antingen obligatorisk eller valbar genom någon av matematikkurserna i c-spåret eller matematik 3b. I samband med de uppdaterade styrdokumenten så har förlagen givit ut reviderade läromedel i matematik eller webresurser med programmeringsuppgifter. I detta arbete utreds i vilken utsträckning dessa programmeringsuppgifter relaterar till problemlösning. Analysen visar att endast en dryg fjärdedel av samtliga analyserade programmeringsuppgifter kategoriseras som problemlösningsuppgifter. Metoden för dataanalys bygger på Lithners ramverk för imitativa och kreativa resonemang. Metoden definierar tre olika lösningstyper (kategorier) av matematikuppgifter; High relatedness tasks (HR), Local low relatedness tasks (LLR) och Global low relatedness tasks (GLR). När lösningen till en uppgift är en procedur tagen från läroboken så räknas det till HR kategorin och räknas då som ett imitativt resonemang. När en uppgift tillhör någon av de två övriga kategorierna (LLR eller GLR) så innebär det att eleven själv behövt konstruera stora delar av lösningen till en uppgift. För att främja utvecklingen av problemlösningsförmågan som räknas som ett kreativt resonemang, så måste eleven få arbeta med uppgifter som tillhör LLR eller GLR kategorierna. Metoden för datainsamling är en innehållsanalys av läromedel i matematik som utgörs av förlaget Natur & Kulturs serie Matematik 5000+ samt förlaget Gleerups serie Exponent med en tillhörande webresurs. I arbetet analyserades 86 programmeringsuppgifter ur Matematik 5000+ samt ytterligare 20 programmeringsuppgifter publicerade som en webresurs med hänvisning till Exponent. Ett antal av de 20 programmeringsuppgifterna relaterade till två läromedel vilket ledde till att det totala antalet analyserade programmeringsuppgifter blev 113. Det visade sig att en delmängd av de analyserade uppgifterna var sådana att någon lösningsalgoritm inte behövdes för att lösa uppgiften, exempelvis genom att facit varit givet i problemformuleringen. Eftersom den typen av uppgifter inte kunde kategoriseras till någon av de tre befintliga kategorierna så definierades en ny fjärde kategori None relatedness tasks (NR). Resultatet visar att nästan hälften av de analyserade uppgifterna (55 av 113) tillhör NR kategorin. En del av förklaringen ligger i att Matematik 5000+ introducerar eleverna till programmering genom färdiga exempel. Analysen visade att ytterligare 28 uppgifter hamnade i HR kategorin vilket således innebär att endast en dryg fjärdedel av samtliga analyserade programmeringsuppgifter klassas som problemlösning. För matematik 3c derivata och matematik 3c integraler så analyserades totalt tio uppgifter där ingen av dessa relaterade till problemlösning. Här används programmeringen istället som ett verktyg för att förklara viktiga begrepp som ingår i dessa kapitel. De matematiska moment som visade sig lämpa sig väl för problemlösningsuppgifter var bl.a. matematik 1c aritmetik och matematik 2c linjär algebra. Sammanfattningsvis så visar studien att en stor majoritet av programmeringsuppgifterna leder till att eleven introduceras till programmering eller leder till att eleven får arbeta med procedurförmågan. Exponent hade en jämförelsevis stor andel programmeringsuppgifter för problemlösning, med sina 44 %. Matematik 5000+ i sin tur presenterar ett större antal uppgifter för problemlösning med deras 18, vilket dock motsvarar endast 21 % av de totalt 86 uppgifterna. / As part of increasing the digital competence in the Swedish school, the government decided in 2017 to introduce the use of programming in the subject of mathematics. Since the autumn term 2018, several mathematics courses for upper secondary school have received updated syllabi with the addition that programming will be used as a tool for problem solving. In practice, this means that just over half of the national upper secondary school programs now receive programming that is either compulsory or elective through one of the mathematics courses in the c-track or mathematics course 3b. In conjunction with the updated governing documents, the publishers have published revised teaching aids in mathematics or webresources with programming tasks. In this thesis, it is investigated to what extent these programming tasks relate to problem solving. The analysis shows that only just over a quarterof all analyzed programming tasks are categorized as problem-solving tasks.The method of data analysis is based on Lithner's framework for imitative and creative reasoning. The method defines three different solution types (categories) of mathematical problems; High relatedness tasks (HR), Local low relatedness tasks (LLR) and Global low relatedness tasks (GLR). When the solution to a task is a procedure taken from the textbook, it is considered part of the HR category and is then categorized as an imitative reasoning. When a task belongs to one of the other two categories (LLR or GLR), it means that the student has had to construct large parts of the solution for the task. In order to promote the development of problem-solving ability, which is considered as creative reasoning, the student must be allowed to work with tasks that belong to the LLR or GLR categories. The method of data collection is content analysis of teaching aids in mathematics, which consists of the publisher Natur & Kultur’s series Matematik 5000+ and the publisher Gleerups's series Exponent with an associated web resource. In this study, 86 programming tasks from Matematik 5000+ were analyzed and another 20 programming tasks published as a web resource with reference to Exponent. Some of the 20 programming tasks referred to two teaching aids, which led to the total number of analyzed programming tasks becoming 113. It turned out that a subset of the analyzed tasks was such that no solution algorithm was needed to solve them, for example by the fact that the results had been given in the problem formulation. As this type of data could not be categorized into any of the three existing categories, a new fourth category None relatedness tasks (NR) was defined. The results show that almost half of the analyzed tasks (55 of 113) belong to the NR category. Part of the explanation lies in the fact that Matematik 5000+ introduce the students to programming through ready-made examples. The analysis showed that a further 28 tasks ended up in the HR category, which thus means that only just over a quarter of all analyzed programming tasks are classified as problem solving. For mathematics 3c derivatives and mathematics 3c integrals, a total of ten tasks were analyzed, none of which related to problem solving. The programming tasks were instead used as a tool to explain important concepts from these chapters. The mathematical chapters that proved to be well suited for problem-solving tasks were e.g. mathematics 1c arithmetic and mathematics 2c linear algebra. In summary, this study shows that a large majority of the programming tasks rather introduce the student to programming or to tasks requiring mere procedural skills, than to tasks that require problemsolving skills. Exponent had a comparatively large proportion of programming tasks for problem solving, with its 44%. Matematik 5000+ in turn presents a larger number of tasks for problem solving with their 18, which, however, corresponds to only 21% of the total 86 tasks.

During the 19th century German language teaching as a foreaing language was significantly changing related to the development of education and the promotion of Czech language as the main teaching language at Czech schools. German language became optional foreign language even though there was a large number of pupils interested in learning German. German was offical language until the estabilishment of an independent Czechoslovak Republic also in Czech lands. In the introduction I focus on the organizational structure of the Czech education system in the Austria-Hungary monarchy between 1869 and 1918. Secondary vocational education was mostly changing and developing at this time, real gymnasiums and various specialization vocational schools were formed. I pay attention to teachers and their education too, since without good teachers there is no chance to have high quality education. The main focus of my work is an overview of the development of teaching methods of modern foreign languages. Development of methods is described chronologically from 17th century and in more detail in 19th century, when the most methods were invented. Instead of Grammar translation method, which was the standard in the teaching of foreaign languages for a very long time, new so called reform methods started to became...

The term of evolution and its understanding by students of secondary schools and high schools This Master's thesis deals with the conception of evolutionary topic in schools and textbooks. It introduces education systems and curricular documents of England, Scotland and the Czech Republic. Based on this information an analysis of biology textbooks was made, which was focused on the theme of evolution. The research included 62 textbooks distributed by 27 different publishers. Comparative SWOT analysis of these textbooks has shown that the concept of biology in general is presented differently, what is also reflected in the interpretation of the studies of evolution. The questionnaire research based on those findings was done in the Czech Republic. It is focused on secondary school and high school pupil's knowledge and their personal opinions about this topic. 586 pupils took part in this research. It was found that in the context of evolutionary processes the pupils have problems to use commonly known biological, or evolutionary terms (e.g. adaptation, evolution of the organisms). On the other hand some pupils can easily define some more complicated evolutionary topics such as Neo-Darwinism. Pupils have quite various personal opinions on the issue of the evolution. Some of them are not interested in...

Analiso nesta dissertação as representações sobre o ciclo de vida das plantas de onze coleções de livros didáticos de ciências aprovados pelo Programa Nacional de Livros Didático (PNLD) referente ao ano de 2011 para, em um segundo momento, focar nas mensagens visivas das representações de cada uma das divisões de plantas briófitas, pteridófitas, gimnospermas e angiospermas. As mensagens visivas permitir-me-iam caracterizar as transformações ocorridas tanto na forma de representar o ciclo quanto nas linguagens utilizadas nas estruturas representacionais que, na maioria das vezes, não condizem com os títulos empregados para nomeá-las. Lançando mão dos pressupostos da tríade pierciana (ícone-objeto-símbolo) a análise semiótica empreendida forneceu-me subsídios para, em uma terceira etapa da pesquisa, coletar desenhos junto aos sujeitos da pesquisa no que tange ao ciclo de vida das plantas, cujos ícones apresentaram os indícios que caracterizam o objeto, ou seja, o ciclo de vida das plantas - encerrado em simbologias com significados que reverberam em contextos históricos específicos, como uma lei própria das estruturas iconográficas. Nos ciclos de vida das plantas essas simbologias se encerram no círculo, envolvendo a vida das plantas como algo ininterrupto, isto é, a planta germina, cresce, desenvolve-se, reproduz e volta a germinar. Baseada nas premissas piercianas constatei que embora as imagens no ensino de ciências sejam de fundamental importância, elas interferem sobremaneira na aprendizagem dos fenômenos naturais, modificando percepções entre os ícones e o objeto real, fato este evidenciado quando comparei as representações imagéticas dos sujeitos desta pesquisa com as representações dos livros didáticos de ciências nos quais não há indícios da finalização do ciclo vital das plantas: a representação da senescência e da morte das plantas. / The object of this essay is the analysis of the representations about vegetables life cycle included in eleven science didactic books approved by PNLD related to the year of 2011. The intention is to focus on the visual messages delivered by the representations of each one of the vegetables division bryophytes, pteridophytes, gymnosperms and angiosperms. Those visual messages would allow me to identify the changes occurred both in the way to represent the cycle as well the language used to perform it. Most of the time these representations do not match with the titles used to designate them. In light of the pierciana triad (icon-object-symbol) the semiotics analysis used during the third phase of this study provided me subsidies to collect drawings from the research subjects regarding the vegetable life cycle. Such icons showed evidences that the feature of the object (vegetables life cycle) is enclosed in symbols linked to specific historic contexts like a particular law applied in iconographic structures. These symbols used to show the vegetables life cycle like something uninterrupted. In other words, the vegetables would germinate, grow, develop, breed and back to germinate in an endless cycle. Even though images are fundamental in the science teaching process I was able to conclude (Based on the PIERCIANAS premises) that the images may induce relevant misunderstandings between Icons and real objects. The perception of the natural phenomenon may be strongly corrupted. The evidences of this statement became crystal clear when I compared the image representations of the subjects of this research with the images of the science didactic books that dont clearly show the end of the life cycle of the vegetables: A senescence representation of the vegetables death.

Analiso nesta dissertação as representações sobre o ciclo de vida das plantas de onze coleções de livros didáticos de ciências aprovados pelo Programa Nacional de Livros Didático (PNLD) referente ao ano de 2011 para, em um segundo momento, focar nas mensagens visivas das representações de cada uma das divisões de plantas briófitas, pteridófitas, gimnospermas e angiospermas. As mensagens visivas permitir-me-iam caracterizar as transformações ocorridas tanto na forma de representar o ciclo quanto nas linguagens utilizadas nas estruturas representacionais que, na maioria das vezes, não condizem com os títulos empregados para nomeá-las. Lançando mão dos pressupostos da tríade pierciana (ícone-objeto-símbolo) a análise semiótica empreendida forneceu-me subsídios para, em uma terceira etapa da pesquisa, coletar desenhos junto aos sujeitos da pesquisa no que tange ao ciclo de vida das plantas, cujos ícones apresentaram os indícios que caracterizam o objeto, ou seja, o ciclo de vida das plantas - encerrado em simbologias com significados que reverberam em contextos históricos específicos, como uma lei própria das estruturas iconográficas. Nos ciclos de vida das plantas essas simbologias se encerram no círculo, envolvendo a vida das plantas como algo ininterrupto, isto é, a planta germina, cresce, desenvolve-se, reproduz e volta a germinar. Baseada nas premissas piercianas constatei que embora as imagens no ensino de ciências sejam de fundamental importância, elas interferem sobremaneira na aprendizagem dos fenômenos naturais, modificando percepções entre os ícones e o objeto real, fato este evidenciado quando comparei as representações imagéticas dos sujeitos desta pesquisa com as representações dos livros didáticos de ciências nos quais não há indícios da finalização do ciclo vital das plantas: a representação da senescência e da morte das plantas. / The object of this essay is the analysis of the representations about vegetables life cycle included in eleven science didactic books approved by PNLD related to the year of 2011. The intention is to focus on the visual messages delivered by the representations of each one of the vegetables division bryophytes, pteridophytes, gymnosperms and angiosperms. Those visual messages would allow me to identify the changes occurred both in the way to represent the cycle as well the language used to perform it. Most of the time these representations do not match with the titles used to designate them. In light of the pierciana triad (icon-object-symbol) the semiotics analysis used during the third phase of this study provided me subsidies to collect drawings from the research subjects regarding the vegetable life cycle. Such icons showed evidences that the feature of the object (vegetables life cycle) is enclosed in symbols linked to specific historic contexts like a particular law applied in iconographic structures. These symbols used to show the vegetables life cycle like something uninterrupted. In other words, the vegetables would germinate, grow, develop, breed and back to germinate in an endless cycle. Even though images are fundamental in the science teaching process I was able to conclude (Based on the PIERCIANAS premises) that the images may induce relevant misunderstandings between Icons and real objects. The perception of the natural phenomenon may be strongly corrupted. The evidences of this statement became crystal clear when I compared the image representations of the subjects of this research with the images of the science didactic books that dont clearly show the end of the life cycle of the vegetables: A senescence representation of the vegetables death.

This PhD thesis deals with a topic of food chemistry and nutrition in secondary school education in chemistry lessons. The theoretical part summarizes significance and evaluation of textbooks and furthermore it focuses on modern approaches in chemistry lessons with the main focus on interactive boards. The methodological part deals with the analysis of framework educational programs, textbook analysis, questionaire surveys and creation of teaching materials. The practical part of this thesis summarizes the results of analysis of framework educational programs and textbooks in relation to food chemistry and diseases related to nutrition. It shows results of a questionnaire survey which has examined knowledge of students in the area of proper nutrition, diet and diseases related to nutrition and also relationship of students to this issue and to the subject of chemistry in general. It also summarizes the results of verification of studying materials which have arisen in this thesis. The practical part also includes an educational text for teachers on the topic of lipids, which was developed based on the results of extensive analysis of secondary school chemistry and biology textbooks, framework analysis of educational programs and research at secondary schools in the Czech Republic. The topic of...

本研究是以1980年代以後的科學教育目標來分析我國國小自然科學教科書 之課本、教學指引及習作，探討教科書的內容、實驗活動及作業問題型態 ，並調查國小自然科教師對教科書的使用意見，了解現行教科書的優缺點 ，以供編撰教科書及學校、教師選擇教科書的參考。 為達上述之目的，本研究在內容分析部份採用的工具有科學知識本質年齡 層次分類表、ＳＴＳ科學教育目標、實驗活動發現開放層次分類法、科學 過程探究技能、教科書作業問題型態評估工具、以及 Bloom的目標分類法 ，在問卷調查方面採用國小自然科學教科書之意見調查表來蒐集和分析資 料。 本研究的主要發現如下: 一、國小自然科學教科書之課本內容在文字敘述上涉及科學知識本質的僅 佔0.084%，而這些文字敘述只提到科學知識是實證性的，雖如此，但其內 容仍含有科學知識本質之正面教學功能。 二、國小自然科學教科書的每個單元都提及個人需要及學術準備的科學教 育目標，而有25.53%的單元提及與科學有關的社會議題，但無提及有關生 涯職業教育的內容。 三、國小自然科學教科書的實驗活動無屬於層次０的單元，有55.32%的單 元屬於層次１，42.55%的單元屬於層次２，2.13% 的單元屬於層次３，是 屬相當不錯的實驗活動設計。 四、國小自然科學教科書習作的作業問題型態以及層次之分佈，有1.94% 的問題屬於非經驗性問題，98.06%的問題屬於經驗或實驗性問題；且屬於 高層次問題的比例較多，亦有一些價值性問題的設計，是相當重視學生高 層次問題解決的學習。以 Bloom目標分類來看，幾乎所有的作業問題都屬 於認知領域的問題，佔了99.72%，其中以理解和應用的問題為最多。 五、國小自然科教師對教科書的整體意見為滿意。可是教師對於教科書的 內容並不滿意但尚可接受；其他各項來說，教師對教科書的組織、閱讀層 次、圖表說明、課文中的實驗活動及習作、教學指引、教科書的容貌均呈 滿意的態度。 The purpose of this study was to analyze the science textbooks used in the elementary schools of Taiwan in terms of goals for science education. The following five components were studied and analyzed:(1)the nature of scientific knowledge, (2)the interaction of science, technology and society, (3)openness and process/skills of laboratory activities, (4)type and level of questioning style, and(5)opinions of science teachers concerning science textbooks. For the purposes described above, seven methods were adopted for this study; that is, the classification of the nature of scientific knowledge, the desired state of science in the elementary school, the level of discovery/openness, science process or inquity skills, and textbook questioning strategies assessment instrument, Bloom's taxonomy classifies educational objectives and science textbook rating system. The major findings include: 1.Only about 0.084% of the narrative page space is devoted to the nature of scientific knowledge in the science textbooks used in elementary school. Only empirical scientific knowledge was presented. 2.Every unit in the science textbooks used in elementary school is associated with the goals of personal needs and academic preparation. 25.53% of units are associated with the goals of societal issues, but no unit associated with the goals of career education. 3.Most of the laboratory activities in the science textbooks used in elementary schools, which provided the problems and the procedures to student's performance, belong to level 1 or 2. 4.Most of the questions are experiential questions(98.06%). And almost of the questions are cognitive domain(99.72%), and most of them are comprehension questions and application questions. 5.Most of the elementary school science teachers are satisfied with the science textbooks used in elementary schools , and their satisfaction goes beyond the contents of the textbooks.