The aim of this essay is to examine why and how three teachers who work in elementary classes choose to use ability grouping during math lessons and what they think of ability grouping as a method to individualize the activities according to the pupil’s needs. I chose one main question for this study that is the following: What is the teacher’s point of view and experience of ability grouping in teaching mathematics? And three sub-questions: What are the motives behind the choice of ability grouping? What are the advantages of ability grouping? What are the disadvantages of ability grouping? In order to be able to answer my questions, I used the qualitative method. I interviewed three teachers who work in the elementary classes (First to fifth grade) to find out what they think about ability grouping and how it is experienced in mathematic teaching.The result shows that the common thing between these three teachers is that they don’t use ability grouping as the only teaching method. They all agree that the whole class teaching has many benefits for the pupils. Regarding the teachers’ views on advantages of ability grouping, they all regard it as a method that contributes to differentiating the math activities according to the pupil's personal needs. My conclusion is that the teachers’ different experiences of ability grouping have an impact on their point of view of ability grouping.

The thesis consists of two equal parts - of a part dealing with didactic aspects of teaching linear algebra, and of an unconventionally approached textbook Fundamentals of Linear Algebra, which is appended as a separate attachment. The didactic part deals with teaching mathematics, especially linear algebra, at the University of Economics in Prague, namely from the historical and methodological point of view. The thesis also includes a detailed evaluation of students' knowledge tests. The conclusions are largely portable to other non- technically oriented universities. The textbook is designed with respect to two levels of difficulty; it is written in the form accessible for students with lighter assumptions for the study of mathematics. The textbook is designed especially for students of universities where mathematics is not the main focus; it may also serve to interested high schools students as an introduction to a more advanced study of linear algebra.

Submitted by Jean Medeiros (jeanletras@uepb.edu.br) on 2017-08-03T12:32:28Z No. of bitstreams: 1 PDF - Manoel Satiro de Medeiros Neto.pdf: 20066438 bytes, checksum: f40d582332be6a9a0db3d14b28616685 (MD5) / Approved for entry into archive by Secta BC (secta.csu.bc@uepb.edu.br) on 2017-08-29T15:43:18Z (GMT) No. of bitstreams: 1 PDF - Manoel Satiro de Medeiros Neto.pdf: 20066438 bytes, checksum: f40d582332be6a9a0db3d14b28616685 (MD5) / Made available in DSpace on 2017-08-29T15:43:18Z (GMT). No. of bitstreams: 1 PDF - Manoel Satiro de Medeiros Neto.pdf: 20066438 bytes, checksum: f40d582332be6a9a0db3d14b28616685 (MD5) Previous issue date: 2017-06-16 / Educational Robotics offers a standout under school, due to your use as teaching tool. In mathematics, it covers a field of opportunities that awakens in students the ability to question, think and look for solutions. The dissertation presents a model of low-cost robotic unit, used as additional tool for teaching and learning of mathematics. The ro- bot was prototype in a 3D printer and together with electronic kit Arduino project was implemented an algorithm, able to provide algebraic calculations that when performed, describe a circuit composed of line segments and circumferential arcs, taken from a pro- posed activities. / A robótica educacional oferece um destaque no âmbito escolar, devido a sua utiliza¸c˜ao como ferramenta pedagógica. Na matem´atica, ela abrange um campo de oportunidades que desperta nos alunos a capacidade de questionar, pensar e procurar soluções. Esta dissertação apresenta um modelo de robóotica de baixo custo, utilizado como ferramenta adicional ao ensino e aprendizagem da Matemática. O robô foi prototipado em uma impressora 3D e junto com kit de eletrônica do projeto Arduino foi implementado um algoritmo, capaz de proporcionar cálculos algébricos que ao serem realizados, descreve um circuito composto por segmentos de reta e arcos de circunferência, tomados a partir de uma proposta de atividades.

Submitted by Caroline Falcao (caroline.rfalcao@ufpe.br) on 2017-05-24T16:59:34Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) GUTEMBERG CAVALCANTI.pdf: 307338 bytes, checksum: f1ca085c8d4104f660d952b41399b2ca (MD5) / Made available in DSpace on 2017-05-24T16:59:34Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) GUTEMBERG CAVALCANTI.pdf: 307338 bytes, checksum: f1ca085c8d4104f660d952b41399b2ca (MD5) Previous issue date: 2012-05-16 / Esta pesquisa investigou o uso dos vídeos de Matemática do TV Escola pelo professor de Matemática da Rede Municipal de Ensino do Recife. Dados estatísticos dos empréstimos destas mídias do acervo da Diretoria Geral de Tecnologia na Educação e Cidadania - DGTEC indicaram que, desde 2001, nenhum vídeo de Matemática foi solicitado por estes profissionais. Averiguamos se os professores tinham acesso aos vídeos do TV Escola por outros meios, tais como os kits distribuídos nas escolas ou a internet. Questionamos se os professores de Matemática que têm acesso aos vídeos do TV Escola os utilizam como instrumentos de mediação pedagógica. A pesquisa baseou-se essencialmente na Teoria da Gênese Instrumental desenvolvida por Pierre Rabardel bem como nos estudos de José Manuel Moran, de Joan Ferrés e de Juana Maria Sancho. Em consonância com esses teóricos, para que se possa evidenciar o uso tecnológico de qualquer artefato, é preciso que o professor o tenha incorporado didaticamente aos processos pedagógicos, posicionando-se epistemologicamente frente às possibilidades e às limitações inerentes aos artefatos e esquemas de utilização individual. O método contemplou questionários, entrevistas, observações de aulas e sessões de trabalho coletivo. Dentre os professores de Matemática que responderam ao questionário, são raros os que utilizam tais mídias em sua prática pedagógica e nenhum deles declarou já ter utilizado vídeos do TV Escola como instrumentos de mediação pedagógica. A fim de aprofundar a análise das razões desse não uso, foi feito um estudo do tipo pesquisa-ação com duas professoras bem como visitas e entrevistas com gestores e coordenadores das escolas às quais as mesmas são vinculadas. A partir da análise desses dados, foram identificados impedimentos e limitações que se impõem na prática dos professores de Matemática e que geram entraves aos processos de instrumentação e instrumentalização para o uso do vídeo em sala de aula. Os sujeitos declaram saber da existência desse acervo e reconhecer seu potencial. As razões para o não uso foram agrupadas em nossa pesquisa em torno de sete focos interligados: questões de infraestrutura, como deficiências quanto às condições de conservação; dificuldades de acesso ao acervo do TV Escola e falta de informação; carência de formação específica para o uso adequado desse recurso; quantidade de alunos em sala de aula; resistência, por parte do professor com relação ao uso de tecnologias; crença de que os conhecimentos dos alunos não são compatíveis com o uso de vídeos; falta de tempo para preparação e para a vivência em sala de aula. / This research investigated the use of Mathematics’ videos of the TV Escola by the Mathematics teacher at the Municipal School of Recife. Statistical data on these loans from the collection of media General Directorate for Technology in Education and Citizenship - DGTEC indicated that since 2001, no Mathematics video was ask by these professionals. We checked if the teachers had access to the videos of TV Escola by other ways, such as the kits distributed in the schools or the internet, and made questions if the Mathematics’ teachers who have access to the videos of TV Escola use them as instruments of pedagogical mediation. The research was mainly based on the theory of Instrumental Genesis developed by Pierre Rabardel as well as in studies of José Manuel Moran, Joan Ferres and Juana Maria Sancho. In line with these theorists, so that we can demonstrate the use of any technological artifact, it is necessary that the teacher has incorporated didactically teaching processes, positioning itself epistemologically forward to the possibilities and limitations inherent in the artifacts and patterns of individual use. The method included questionnaires, interviews, classroom´s observations and workshops collective. Among mathematics teachers who answer the questionnaire, there are few who use the medias in their teaching pedagogical and none of them claimed that had used the TV Escola videos as teaching tools of mediation. In order to further analyze the reasons for any such use, a study was made by the type: action-research with two teachers as well as visits and interviews with managers and coordinators of the schools to which they are linked. From the analysis of these data, it was identified the constraints and limitations that are imposed on the Mathematics’ teachers practice and create barriers process´s instrumentation and instrumentalization for the use of video in the classroom The subjects claim to know the existence of this collection and recognize its potential. The reasons for not using it were grouped in our research around seven interrelated foci: infrastructure´s questions infrastructure issues, such as deficiencies in the conditions of preservation, difficulties of access to the collection of TV Escola and lack of information, , lack of specific training for the use that appropriate action; number of students in the classroom; resistance, from the teacher regarding the use of technology; belief that students' knowledge are not compatible with the use of videos, lack of preparation time and experience in the classroom.

Sedan läsåret 2018/2019 ska matematiklärare använda programmering som en problemlösningsmetod inom vissa kurser i ämnet matematik på gymnasiet samt i grundskolans senare år eftersom det finns i det centrala innehållet i kursplanerna. I grundskolans senare år är det i ämnena teknik och matematik där programmering ska ingå.Studiens syfte är att sammanställa på vilket sätt och inom vilka ämnesområden i matematiken som matematiklärare skapar programmeringsuppgifter för elever som går i grundskolans senare år eller gymnasieskolan. Studien har två frågeställningar. En av frågeställningarna är ”Inom vilka matematiska ämnesområden skapar matematiklärare uppgifter, är elever ska använda programmering som en lösningsmetod”. Den andra frågeställningar är ”Hur utformar matematiklärare uppgifter, där eleverna ska använda programmering som en problemlösningsmetod”.Metoden är en tematisk analys som är en kvalitativ metod, där tjugosju programmeringsuppgifter har undersökts utifrån frågeställningarna. Urvalet består av ett bekvämlighetsurval. Resultatet och analysen tyder på att lärarna skapar uppgifter där eleverna får möjlighet att på något sätt arbeta med en programkod eller det matematiska innehållet i programmeringsuppgiften i syfte att utveckla sin problemlösningsförmåga. Resultatet tyder på att ämneslärare skapar programmeringsuppgifter inom olika ämnesområden, men två matematiska ämnesområden var mer representerade än de andra. De två ämnesområdena är geometri och algebra. Slutsatsen är att alla lärare, förutom två, är förtrogna med att skapa programmeringsuppgifter där eleverna får möjlighet att utveckla deras problemlösningsförmåga. / Since the school year of 2018/2019 the teacher of mathematics is supposed to use programming as a problem-solving method in some of the courses in mathematics in upper secondary school and in the elementary school´s later years. In the elementary school´s later years, the subjects are technology and mathematics, which include programming.The purpose of the study is to compile how and in which disciplines of mathematics that mathematics teachers create programming-assignments to students of the later part of elementary school or in upper secondary school. The research has two questions. One of the questions are “In which disciplines of mathematics are math teachers creating assignments, where the students should use programming as a solving method”. The other question is “How do math teachers create assignments, where students are supposed to use programming as a problem-solving method”.The method is a thematic analysis that is a qualitative method, where twenty-seven assignments of programming has been analyzed based on the questions. The sample consists of a convenience selection.The result and the analysis indicates that the students are given the opportunity by working in some way with a program code or the mathematical content of the programming-assignments to develop their ability of problem solving. Math teachers create assignments in different disciplines of mathematics, but two disciplines were more represented than the others. The two disciplines are geometry and algebra. The conclusion is that all teachers, except two, is confidential to create programming assignments, where students can develop their ability of problem-solving.

A majority of students at the local University College of Science and Education (UCSE, pseudonym) in Jamaica do not have the conceptual understanding of mathematical principles to function in a competitive and highly globalized marketplace. In 2013 and 2014, 88% and 92% of freshmen education students scored at the lowest 2 levels on the Mathematics Diagnostic Test (MDT). The instructional language at UCSE is Standard English (SE) whereas most students speak Jamaican dialect (JD). The purpose of this study was to determine the effect that the language of instruction has on student achievement in math as measured by the MDT. Guided by Vygotsky's social development theory, the research questions focused on comparing MDT change scores between students who were taught using JD and those using SE as the instructional language. The quasi-experimental design used ex post facto data including pretest and posttest MDT scores from 40 freshmen of whom 20 were instructed in JD and 20 in SE. The results of an independent sample t test showed that the difference in the MDT change score was significant. The JD students had a higher improvement score. Consequently, it is recommended that math instructors use JD to instruct freshmen education students whose native language is JD. A professional development session for math teachers was created that demonstrates how to teach in JD while simultaneously scaffolding the instruction in a way that students can learn SE and be prepared for the following year at UCSE. If students understand the math concepts in their freshman year, they are more likely to continue their college education and to become productive members of Jamaica's economy which is dependent on employees that are proficient in math.

This study investigated the interaction of mathematics teachers with learners’ mathematical errors. The teachers’ verbal interaction with learners’ errors during learning periods and their written interaction in assessment tasks were explored. The study was contextualized in grade 9 secondary school classrooms in the Gauteng province of South Africa. The investigation was epistemologically underpinned by constructivism/socio-constructivism. The investigation was qualitatively approached through four case studies. Structured and semi-structured interviews, classroom observations and learners’ written assessment tasks were employed as sources of data. The participating teachers were described in terms of their beliefs about mathematics, their beliefs about learners’ mathematical errors, their observed prevalent teaching approach and their professed and enacted interaction with learners’ mathematical errors. Within-case and cross-case comparisons ensued. The findings proposed that when teachers believed that the value of learners’ errors was vested in the corrections thereof, rather than employing these opportunities for discussion, valuable opportunities for learners to develop and improve their meta-cognitive abilities might potentially be lost. The findings further indicated that a focus on the mere correction of learners’ errors probably denied learners opportunities to develop a mathematical discourse. The results of the investigation illuminated that an emphasis on achievement during assessment, together with a disapproving disposition towards errors among teachers and learners, were hindrances. They acted as barriers to engendering a socio-constructivist learning environment in which interactions with learners’ errors could enhance learning and establish a negotiating mathematical community. A concurrence between the teachers’ prevalent teaching approach and their mathematical beliefs was confirmed. However, in two of the four cases, a dissonance was revealed between their prevalent teaching approach and their interaction with learners’ errors. Interaction with learners’ mathematical errors was hence identified as a separate and discrete component of a teacher’s practice. The findings suggest the explicit inclusion of error-handling in reform-oriented teacher-training and professional development courses to utilize learners’ mathematical errors more constructively. / Dissertation (MEd)--University of Pretoria, 2010. / Science, Mathematics and Technology Education / unrestricted

The aim of this thesis is to explore the factors influencing the usage of modern technologies in teaching Mathematics. Modern technologies have been gradually earning their place in Czech schooling for a while now, but they are not always used in the way we might expect. To address such a question, upon consulting various literary sources, this thesis presents a model of factors which influence the usage of technologies in teaching Mathematics and aims to answer the following questions. What factors influence the intended usage of technologies in teaching Mathematics? How do these factors influence the intended usage of technologies in teaching Mathematics? What are the differences between the intended usage and the real usage and what factors influence them? How do these factors influence the real usage in teaching Mathematics? The individual factors have been further explored by a multiple-case study of three Czech Mathematics teachers during their teaching and subsequential interviews. It was the form of a multiple-case study which allowed for deeper observation of the mutual relationships between the individual factors in teachers with very different approaches to teaching and modern technologies. The differences between the considered cases then provided an insight into what could help...

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Den här litteraturstudien undersöker utmaningar vid användning av digitala verktyg i matematikundervisning på gymnasiet i Sverige, i ljuset av den senaste läroplanen för ämnet matematik. Studien undersöker balansen mellan skolans krav, samhällets behov av digital kompetens och den faktiska undervisningen. Syftet med studien är att få ökad kunskap om användningen av digitala verktyg i matematikundervisning och belyser de utmaningar och möjligheter som denna situation medför. Frågeställningen är: vilka är lärarnas utmaningar vid användning av digitala verktyg i matematikundervisning på gymnasiet? Metoden består av en tematisk analys av tio vetenskapligt granskade artiklar som sökts på databasen OneSearch med sökorden: “matematikundervisning, digitala verktyg, utmaningar och gymnasiet”. Utvalda material till analysen är artiklar som genomfördes i Sverige eller andra länder som följer upp västerländska skolsystem, liksom Tyskland, Nederländerna och USA. Tematisk analys resulterade i att identifiera fyra teman, det vill säga förkunskaper, användning av digitala verktyg, val av digitala verktyg och anpassning av uppgifter. Studien belyser också de potentiella fördelarna med digitala verktyg i matematikundervisningen, såsom förbättrade kommunikation av elev till elev samt elev till lärare, effektivare återkoppling och formativ bedömning, högre intresse till matematikinlärning och elevinflytande, respektive nackdelarna såsom försämrade kommunikation, förvirring och vilseledning av elever, förvärrade likvärdigheten i skolan och förhindrade kunskapsutveckling. En slutsats som kan dras här, är användning av digitala verktyg liksom andra icke digitala verktyg, kan ha fördelar, när användaren behärskar verktyget och använder det målinriktade, annars medför motsatta effekter. Studien är relevant för lärare inom matematikundervisning, eftersom den belyser dessa utmaningar på ett objektivt sätt. Det kan gynna lärare till att möta och hantera dessa utmaningar.