A dissertação apresenta uma pesquisa que se situa no campo da História da Educação Matemática e que tomou por objeto de estudo a formação dos professores primários no Instituto de Educação General Flores da Cunha (IE), em Porto Alegre. Dialogando com autores da Histórica Cultural e da Histórica Oral busca-se compreender os modos de apropriação, aprender para ensinar os saberes matemáticos na instituição nas décadas de 1950 a 1970, período caracterizado pelo Movimento da Matemática Moderna (MMM). Inferiu-se, a partir das evidências verificadas em documentos localizados no acevo do Laboratório de Matemática da instituição e das entrevistas realizadas com as ex-alunas e ex-professoras, que o MMM norteou a formação das normalistas. Tal movimento materializou-se nas ações das professoras e estudantes que aprendiam e ensinavam a Moderna Matemática, nos materiais didáticos estudados e produzidos pelas normalistas no Laboratório de Matemática da instituição, bem como nos discursos das ex-alunas e da imprensa da época. Evidenciou-se que o envolvimento das normalistas com a renovação da Matemática, no interior do IE, partiu, inicialmente, das inquietações e ações da professora Odila Barros Xavier que almejava mudanças no ensino da Matemática desde o final da década de 1940. Na época, a professora já estudava mudanças no currículo da Matemática do Curso Normal, na incansável busca pela renovação na formação das professoras primárias Através da fundação e organização do Laboratório de Matemática, a partir dos anos 1950, a professora Odila amplia os espaços de formação de professores para além das portas do IE e contribui para a divulgação do pensamento modernizador, coordenando grupos de estudos, ministrando cursos sobre fundamentação teórica e metodológica da Matemática Moderna e incentivando práticas em aulas experimentais com materiais manipuláveis. O ápice deste percurso ocorre no final dos anos 1960 e início dos anos 1970 que, por conseguinte, é fundado o Grupo de Estudos sobre o Ensino da Matemática de Porto Alegre (GEEMPA), sob a liderança da professora Esther Grossi. Através do GEEMPA foram oportunizados cursos de formação de professores com a presença de vários estudiosos, entre eles, Zoltan Dienes, um dos principais autores estudados no Instituto de Educação General Flores da Cunha. Ao longo dos anos 1950 e 1970, a instituição tornou-se referência não só na formação inicial das normalistas, mas também na formação continuada dos professores de Matemática no Rio Grande do Sul, com reconhecimento nacional e internacional, no período marcado pelo MMM. / The dissertation presents a research that is located in the field of History of the Mathematics Education and that took as object of study, the formation of primary teachers at the Flores da Cunha (IE) General Education Institute in the city of Porto Alegre. In dialogue with authors from Cultural, Historical and Oral History, we sought to understand the ways of appropriation to learn how to teach the mathematical knowledge in the institution from 1950 to 1970, a period characterized by the Modern Mathematical Movement (MMM). We infer from the evidence verified in documents located in the acquis from the Laboratory of Mathematics from the institution and the interviews with the former students and the former teachers, that the MMM guided the formation of the normalists. This movement materialized in the actions of the teachers and students who learned and taught Modern Mathematics, in the didactic materials studied and produced by the normalists in the Mathematics Laboratory of the institution, as well as in the speeches of the former students and the press of the time. It was evidenced that the involvement of the normalists with the renewal of Mathematics, within IE, started, initially, from the concerns and the actions of the teacher Odila Barros Xavier, who aspired for changes in the teaching of Mathematics since the end of the 1940s At the time, the teacher was already studying changes in the curriculum of Normal Mathematics Course, in the relentless search for renewal in the training of primary teachers. Through the founding and organization of the Mathematics Laboratory, from the 1950s on wards, teacher Odila expanded the spaces for teacher training beyond IE's doors and contributed to the dissemination of modernizing thinking, coordinating study groups, giving courses on fundamentals theoretical and methodological approach of Modern Mathematics and encouraging practices in experimental classes with manipulative materials. The culmination of this course takes place in the late 1960s and early 1970s, which is why the Mathematics Teaching Group of Porto Alegre (GEEMPA) was founded under the leadership of teacher Esther Grossi. Through the GEEMPA, teacher training courses were offered in the presence of several scholars, among them Zoltan Dienes, one of the main authors studied at the Flores da Cunha General Education Institute. Throughout the 1950s and 1970s, the institution became a reference not only in the initial formation of the normalists, but also in the continuing formation of Mathematics teachers in Rio Grande do Sul, with national and international recognition, during the period marked by the MMM.

There are various digital teaching materials as expected due to the always increasing and changing digitization. Digitization is widespread in our everyday lives and our school system. Teaching mathematics is no exception. The national agency for education in Sweden describes digitization as closely connected to teaching mathematics which can be read in the national curriculum.   The purpose of the survey was to see to what extent teachers use digital teaching materials and how they use it in their mathematics teaching. There were 87 mathematics teachers who participated and answered the questions, to what extent teachers use digital teaching materials and how they use it in their mathematics teaching.    With support of PIC-RAT, MDTDK and Choppin- framework, the answers were analyzed and the results indicate that most teachers use digital teaching materials in mathematics teaching, at least once a week. Many teachers use digital teaching materials several times a week and as a variation and extending the context, by choosing exercises and making adjustments for the students needs and levels. / Det finns mycket olika digitala läromedel vilket kan ses som en effekt då digitaliseringen är en ständigt växande och föränderlig faktor som påverkar både i vardagen såsom i skolverksamheten. Matematikundervisningen är inte ett undantag. Skolverket beskriver digitaliseringen som nära kopplad till just matematikundervisningen vilket kan ses i läroplanen. Syftet med studien var att undersöka i vilken utsträckning som lärare använder digitala läromedel samt hur dem används i matematikundervisningen. I studien svarade 87 lärare som undervisar i matematik på en enkät om hur digitala läromedel används i matematikundervisningen och i vilken utsträckning det görs. Med hjälp av valda ramverken PIC-RAT, MDTDK samt Choppin analyserades svaren från respondenterna. Resultaten visar att en stor andel lärare använder digitala läromedel i matematikundervisningen vid minst ett tillfälle i veckan. Många lärare använder digitala läromedel flera gånger i veckan och för att skapa en variation i undervisningen men även för att bredda matematikundervisningens innehåll. Lärarna gör det genom att välja uppgifter och göra anpassningar i det digitala läromedlet utifrån elevernas behov och nivå.

In der Arbeit wird ein fächerverbindender Zugang zur Sinusfunktion entwickelt. Periodische Funktionen werden über die Analyse und das Aufzeichnen von Instrumenten untersucht. Die Sinusfunktion wird als Modell für Töne eingeführt. Auf Basis dieses Modells werden Synthesizer entwickelt an denen mathematische und musikalische Fragestellungen behandelt werden. Das Konzept wird exemplarisch erprobt und reflektiert.:1. Einleitung 2. Vergleich verschiedener Lehrbuchansätze 3. Unterrichtskonzept 3.1. Motivation 3.2. Fachliche Grundlagen und erste didaktische Überlegungen 3.2.1. Der Funktionsbegriff 3.2.2. Der Begriff Sinus und die zugehörigen Schüler*innenvorstellungen 3.2.3. Grundbegriffe zu periodischen Prozessen und Schwingungen 3.2.4. ModellierungvonInstrumenten 3.2.5. Schüler*innenvorstellungen zu Schwingungen, Wellen und Tönen 3.2.6. AnwendungderentwickeltenModelle 3.2.7. Diagramme und damit verbundene Schwierigkeiten im Unterricht 3.3. Didaktische Grundlagen 3.3.1. Rahmenbedingungen und Curriculumsbezug 3.3.2. DasKonzeptunddieKMKBildungsstandards 3.3.3. Vorwissen 3.4. Einführung: Instrumentenanalyse - Töne als Wahrnehmung von Schwingungen 3.4.1. Didaktisches Konzept Instrumentenanalyse 3.4.2. Verlaufsplan Instrumentenanalyse 3.5. Mathematische Modellierung der Töne - Die Sinusfunktion 3.5.1. Didaktisches Konzept mathematische Modellierung 3.5.2. Verlaufsplan mathematische Modellierung 3.6. Anwendung des Modells von Tönen als harmonische Schwingungen 3.6.1. Didaktisches Konzept Anwendung des Modells von Tönen als harmonische Schwingungen 3.6.2. Verlaufsplan Anwendung des Modells von Tönen als harmonische Schwingungen 3.7. Verwendete Software 3.7.1. Audacity 3.7.2. Geogebra 3.7.3. Viana 3.7.4. SonicVisualiser 3.7.5. VCV-Rack 4. Durchführung des Konzepts 4.1.Rahmenbedingungen, Lerngruppe und Vorwissen 4.2. Betrachtung der Einzelstunden 4.2.1. Erste Stunde 4.2.2. Zweite Stunde 4.2.3. Dritte Stunde 4.2.4. Vierte Stunde 4.2.5. Fünfte Stunde 4.2.6. Sechste Stunde 4.2.7. Siebte Stunde 4.2.8. Achte Stunde 5. Evaluation des Konzepts 5.1. Auswertung des Tests 5.2. Evaluationsgespräch mit SuS 6. Entwicklung eines Synthesizers für den Unterricht auf Basis eines Mikrocontrollers 6.1. Konzept 6.2. Umsetzung A. Arbeitsblätter 114 A.1. Einführung: Instrumentenanalyse A.1.1. Die Begriffe periodisch, Periode, Periodendauer und Amplitude A.1.2. Parameter einer periodischen Schwingung A.1.3. Parameter einer periodischen Schwingung (bearbeitet) A.2. Mathematische Modellierung der Töne - Die Sinusfunktion A.2.1. Modell einer harmonischen Schwingung A.2.2. Die Sinusfunktion A.2.3. Parameter der Sinusfunktion A.2.4. Die Sinusfunktion als Modell für Töne A.3. Anwendung des Modells von Tönen als harmonische Schwingungen A.3.1. Entwicklung eines Synthesizers auf Basis des Modells für harmonische Schwingungen A.3.2. Amplitudenverlauf A.3.3. Intervalle A.3.4. Obertoene B. Test C. Präsentationen C.1. Parameter der Sinusfunktion und Zeitabhängigkeit C.2. Ausblick zum Abschluss der Erprobung D. Verlaufspläne der Erprobung D.1. Erste Stunde D.2. Zweite Stunde D.3. Dritte Stunde D.4. Vierte Stunde D.5. Fünfte Stunde D.6. Sechste Stunde D.7. Siebte Stunde D.8. AchteStunde E. Programmcode Synthesizer F. Quellenverzeichnis G. Abbildungsverzeichnis H. Verzeichnis der Erklärboxen I. Selbstständigkeitserklärung

Matematikundervisningen har en flera hundra år lång historia och matematik är idag ett av de ämnen i grundskolan som det undervisas mest i. Trots det visar resultatet från den internationella undersökningen PISA 2022 att elever i den svenska skolan presterar lågt i jämförelse med tidigare PISA-studier i ämnet matematik. Forskning visar att det är lärarens kompetens som är den mest väsentliga faktorn för elevernas lärande och därmed behövs nya perspektiv på lärarens undervisning i matematik. Något som har väckt stort internationellt intresse under de senaste femton åren är den franska undervisningen i matematik där Brousseaus teori om didaktiska situationer i matematik är en central del. Därför är syftet med denna litteraturstudie att lyfta teorin samt hur forskningen använder den. Resultatet visar att teorin kan användas som undervisningsdesign för att främja elevernas lärande och som ett framgångsrikt verktyg för att observera och analysera lärares roll i undervisningen. Dessutom används teorin som grund för ett undervisningsprogram.

Thesis (MEd)--Stellenbosch University, 2012 / Includes bibliography / ENGLISH ABSTRACT: The use of information and communications technologies (ICTs) in the form of spreadsheet algebra programmes (SAPs) is important in the professional development of high school mathematics teachers. This is in line with The Namibian government‟s Vision 2030 in which ICT skills and competencies are regarded as core elements of living and participating in the 21st century. ICTs are also considered to be fundamental to the development of a dynamic knowledge-based economy (KBE) through the Education and Training Sector Improvement Program (ETSIP). ETSIP‟s aim is to embed ICT at all levels of the education system. It also aims to integrate the use of ICTs as tools in the delivery of curriculum and learning and in so doing, lead to a marked improvement in the quality of the learning and teaching process across all levels. Education has a key role in achieving Vision 2030. The aim of this research was to investigate mathematics teachers‟ perceptions of SAPs as curriculum materials in selected Namibian secondary (high) schools. This research adopted a qualitative methodology, which in this instance was a case study. The sample population consisted of five teachers from Okamu (pseudonym) secondary school in the Ohangwena Region of Namibia. Four of them had been teaching mathematics at different levels in the mentioned school for a period of four years, and one of them was teaching physical science. Three methods of data collection were used. The first two were semi-structured interviews and focus group interviews based on teachers‟ experiences using SAPs. The third method was an audio taped observation of a lesson taught by one of the teachers,. This research provides evidence about teachers‟ perceptions regarding time concerns and constraints with regards to the SAPs and the use of the SAPs. The teachers showed willingness and enthusiasm to use SAPs on linear and quadratic functions in their teaching. Some of the teachers became more aware of the epistemic dimensions associated with mathematical and algebraic symbols. Interview data reveal that the teachers had not considered these dimensions when teaching with the usual paper-and-pen format. The research also provides evidence of a teacher‟s early vision about the use of spreadsheets as an instrument to teach linear functions. This teacher did not consider any epistemic value for the instrumented spreadsheets techniques, or that they might contribute to a deeper understanding of the linear functions. His concern was focused more on getting the learners to acquire computer skills, such as learning how to use spreadsheets. It is recommended that in-service professional development about ICT integration into mathematics teaching be offered. This might help teachers to learn how their knowledge and skills could be used in the classroom more effectively in order to save time. It is also suggested that professional development programmes be designed to stimulate and promote teachers‟ willingness to develop an understanding of the characteristics of ICTs such as SAPs and their uses. Lastly, it is recommended that new SAPs be designed in order to deepen the understanding of algebra at the secondary level. / AFRIKAANSE OPSOMMING: Die gebruik van inligting- en kommunikasietegnologieë (IKT's) in die vorm van sigblad-algebra-programme (SAP's) is belangrik vir die professionele ontwikkeling van hoërskoolwiskunde-onderwysers. Dit is in pas met die Namibiese regering se visie vir 2030, Vision 2030, waarin IKT-vaardighede en -bevoegdhede beskou word as kernelemente van die lewe in en deelname aan die 21ste eeu. IKT's word ook beskou as grondliggend aan die ontwikkeling van ‟n dinamiese kennisekonomie (KE) deur middel van die Verbeteringsprogram vir die Onderwys- en Opleidingsektore (ETSIP). ETSIP het as oogmerk om IKT op alle vlakke van die onderwysstelsel vas te lê. Dit het ook ten doel om die gebruik van IKT's as hulpmiddele te integreer in die lewering van kurrikulum en leer en sodoende ‟n duidelike verbetering in die gehalte van die onderrig-en-leerproses oor alle vlakke heen tot gevolg te hê. Onderwys het ‟n sleutelrol te speel by die bereiking van Vision 2030. Die doel van hierdie navorsing was om wiskundeonderwysers se persepsies van SAP's as kurrikulummateriaal in geselekteerde Namibiese sekondêre (hoër-) skole te ondersoek. Hierdie navorsing het ‟n kwalitatiewe metode gevolg, in hierdie geval ‟n gevallestudie. Die proefgroep het bestaan uit vyf onderwysers van die sekondêre skool Okamu (skuilnaam) in die Ohangwena-streek van Namibië. Vier van hulle het reeds vier jaar lank wiskunde op verskillende vlakke in die betrokke skool gegee en een van hulle het fisiese wetenskap gegee. Drie metodes is ingespan om data in te samel. Die eerste twee was semigestruktureerde onderhoude en fokusgroeponderhoude gebaseer op onderwysers se ervaringe ten opsigte van die gebruik van SAP's. Die derde metode was ‟n klankopname van ‟n waarnemingsessie van ‟n les wat deur een van die onderwysers gegee is. Hierdie navorsing getuig van onderwysers se persepsies ten opsigte van tydskwessies en -beperkinge met betrekking tot die SAP's en die gebruik van die SAP's. Die onderwysers het ‟n gewilligheid en geesdrif geopenbaar om by lineêre en kwadratiese funksies SAP's in hul onderrig te gebruik. Party onderwysers het meer bewus geraak van die epistemiese dimensies in verband met wiskundige en algebraïese simbole. Onderhouddata onthul dat die onderwysers nie hierdie dimensies in ag geneem het toe hulle met die gewone papier-en-pen-formaat klasgegee het nie. Die navorsing bevestig ook ‟n onderwyser se aanvanklike insig oor die gebruik van sigblaaie as 'n instrument om lineêre funksies te onderrig. Hierdie onderwyser het nie die epistemiese waarde vir die geïnstrumenteerde sigbladtegnieke in ag geneem nie, of dat hulle sou kon bydra tot ‟n grondiger begrip van die lineêre funksies nie. Sy belangstelling was eerder daarop gefokus om die leerders sover te kry om rekenaarvaardighede, soos om sigblaaie te kan gebruik, te verwerf. Daar word aanbeveel dat indiens- professionele ontwikkeling oor IKT-integrasie in wiskundeonderrig aangebied word. Dit sal onderwysers moontlik help om te leer hoe hulle kennis en vaardighede meer doeltreffend in die klaskamer gebruik kan word om tyd te bespaar. Daar word ook voorgestel dat professionele ontwikkelingsprogramme ontwerp word, ter stimulering en bevordering van onderwysers se bereidwilligheid om ‟n begrip te ontwikkel van die kenmerke en gebruike van IKT's soos SAP's. Laastens word daar aanbeveel dat nuwe SAP's ontwerp word om die verstaan van algebra op sekondêre vlak te verdiep.

TITLE: Didactical situations in mathematics at lower secondary level. The classification of quadrilaterals based on selected characteristics. AUTHOR: Bc. Kateřina Vladyková DEPARTMENT: Department of Mathematics and Mathematical Education SUPERVISOR: Prof. RNDr. Jarmila Novotná, CSc. ABSTRACT: This thesis deals with the possible use of the Theory of didactical situations in mathematics at the lower secondary level of Czech school. It is specifically focused on the classification of quadrilaterals based on selected characteristics. The thesis consists of two parts, theoretical and practical. The theoretical part deals mainly with the introduction of Theory of didactical situations, defining and explaining their basic concepts. The thesis also briefly introduces currently existing curricula in the Czech Republic, in which quadrilaterals were the author's main focus. Furthermore, the topic is analyzed from educational materials (textbooks) used in Czech primary schools. In the experimental part of the thesis the author presents a detailed script of educational unit. It is a practical demonstration of a particular theory of didactic situations in teaching mathematics at the Czech elementary school, which is developed and implemented according to the principles of the theory of didactic situations. The thesis...

Made available in DSpace on 2017-07-10T16:38:39Z (GMT). No. of bitstreams: 1 DISSERT Odete Agostinho Fernando2.pdf: 5107247 bytes, checksum: 0dc430566be54ea4f745d91b63232a58 (MD5) Previous issue date: 2017-12-17 / This dissertation discusses how manipulable materials and games have been used in math education for deaf children. The question of this work was: how games and manipulative materials are used in mathematics education for deaf children? To answer this and other questions, interviews were conducted with teachers of three deaf education centers. The general objective was to analyze the games and manipulative materials used by math teachers in deaf education in schools of Cascavel and Foz do Iguaçu. To choose the schools the following criteria were used: only schools for the deaf, bilingual schools, schools where teachers use games to teach mathematics to deaf students. First, is presented a historical summary about deaf education and the main approaches: oralism, total communication and bilingualism. The oralist approach defends the teaching of oral speech for the deaf. Total communication defends all types of communication during the educational process of the deaf. Total communication is not recommended, because isn't systematized. In this work the bilingualism is defended. Bilingualism starts with the teaching of the sign language as the first language and of the written form of the portuguese as second language. In order to teach deaf students is necessary to consider that they learn different than listeners. Deaf people need a sensorial education. To address the games and manipulative materials in mathematics education, the theories of Piaget and Vygotsky are adopted. Piaget is the starting point to understand the play and its role in the construction of the number. Vygotsky's theory helps to understand the importance of sign language for a meaningful teaching to the deaf child. We conclude that the games are indispensable in the lives of deaf and hearing children, as they influence the development and the construction of the number. / Esta dissertação aborda os materiais manipuláveis e jogos usados na educação de matemática de crianças surdas. A investigação partiu da seguinte questão: como os jogos e materiais manipuláveis são utilizados no ensino de matemática de crianças surdas? Para responder esta e outras questões, foram realizadas entrevistas com as professoras de três centros de educação de surdos. O objetivo geral foi analisar os jogos e materiais manipuláveis utilizados pelas professoras de matemática em escolas de educação de surdos de Cascavel e Foz do Iguaçu. Para a escolha das escolas foram utilizados os seguintes critérios: escolas somente para surdos, escolas bilíngues, escolas com professores que usam jogos no ensino de matemática para alunos surdos. Primeiramente, o trabalho trata do histórico da educação de surdos e apresenta as três principais abordagens: oralismo, comunicação total e bilinguismo. O oralismo defende que a fala seja ensinada para o surdo. A comunicação total aceita todos os tipos de comunicação. Não é considerada uma abordagem recomendável, por não ser sintetizada. O bilinguismo, aqui defendido, parte do ensino da língua de sinais como primeira língua e o ensino da língua portuguesa como segunda língua na modalidade escrita. Tal abordagem é considerada mais adequada à educação de surdos. É necessário considerar que os surdos aprendem de modo diferente dos ouvintes. Os surdos precisam de uma educação visual. Para abordar os jogos e materiais manipuláveis no ensino de matemática, são adotadas as teorias de Piaget e Vygotsky. Piaget é o ponto de partida para entender o brincar e a construção do número pela criança. A teoria de Vygotsky ajuda a compreender a importância da língua de sinais para que o ensino seja significativo para a criança surda. Conclui-se que os jogos são indispensáveis na vida das crianças surdas e ouvintes, pois influenciam no desenvolvimento e na construção do número.

[pt] Esse trabalho visa demonstrar os lemas de Sperner e aplicá-los nasdemonstrações do teorema de Monsky em Q2 e do teorema do ponto fixo deBrouwer em R2. Além disso, relatamos como esses lemas foram abordados com alunos da educação básica tendo como ferramenta educacional jogos de tabuleiro. / [en] This work aims to prove the Sperner s Lemmas and to apply them in proving the Monsky s Theorem in Q2 and the Brouwer fixed point Theorem in R2. Moreover, we report how these lemmas were addressed with students in basic education using board games as educational tools.

This thesis deals with an introduction to variables. The aim of the thesis was to compare different approaches to teaching the introduction to variables in teachers who teach a method based on building schemes (known as Hejny method). The theoretical part of the thesis is a search of literature on the topic of introduction to variables and the theoretical background of teaching methods based on building schemes. Further, the thesis analyses textbooks designed for this method with a focus on tasks important for the propaedeutics of the variables. The research itself consisted of interviews with four teachers and observations of the lessons they taught in the 7th and 8th grades of secondary school, the topic of which was an introduction to the "language of letters". In total, there were fifteen lessons taught by these teachers in six classes (2-3 lessons in each class). Data were analyzed by qualitative methods. Although the observed teachers taught using the same method, I identified differences in the approach to the introduction of the variables and in the style of their teaching. There were differences in the organization of the lesson, in the selection of tasks and their style of assignments to pupils, teaching methods and ways in which teachers communicate with pupils. At the moment of entering the...

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.