Orientador: Maria Aparecida Viggiani Bicudo / Banca: Marcelo de Carvalho Borba / Banca: Nilson José Machado / Resumo: Este estudo tem por objetivo conhecer o que os professores de Matemática pensam a respeito do uso da calculadora em sala de aula, buscando compreender o que consideram importante para essa prática pedagógica. A metodologia adotada para essa investigação teve inspiração fenomenológica, baseada na estrutura do fenômeno situado. Os sujeitos dessa pesquisa foram professores dos ensinos fundamental e médio, das redes pública e particular de ensino, nas cidades de Ponta Grossa - PR e Rio Claro - SP. Ao todo foram coletados 22 depoimentos, gravados, transcritos e analisados. A princípio, para a análise, foram consideradas as idéias individuais dos depoentes, com as quais foi construída a Matriz ldeográfica, que mostra uma das reduções feitas. Num segundo momento, partindo dessa Matriz, novas reduções foram efetuadas e delas emergiram três categorias abertas que apontam as características essenciais do uso da calculadora nas aulas de Matemática: domínio das operações básicas, a calculadora como recurso didátlco e formação do professor. Essas categorias foram interpretadas tendo em vista os depoimentos dos sujeitos e a literatura estudada. Finalizando o trabalho, apresentou-se a compreensão da pesquisadora sobre o estudo e, dessa interpretação e reflexão, foram levantados pontos relevantes que sugerem outras pesquisas e que indicam ações pedagógicas tendo em vista a calcufadora e a sala de aula. Esses pontos dizem de: conteúdos programáticos, avaliaçã e formação do professor. / Abstract: This study aims at knowing what mathematics teachers think about the use of calculators in the classroom, looking for an understanding of what they consider to be important in this pedagogical practice. The research methodology had a phenomenological inspiration based on the structure of situated phenomena. The subjects of this research were people teaching at primary, secondary and high school levels, at public and private schools in the cities of Ponta Grossa - PR and Rio Claro - SP. Twenty two testimonies were collected, recorded, transcribed and analysed. At first an Ideographical Matrix was assembled from the teachers' individual ideas, representing one of the reductions made. In a second moment, starting with this Matrix, new reductions were made and three open categories emerged. These categories point to the essential characteristics of the use of calculators in the Mathematics classroom: domain of basic operations, the calculator as didactic resource and teacher education. These categories were interpreted on the basis of the subjects' testimonies and the study of bibliography. Finally, the researcher comprehension of the study is presented. Based on her interpretation and reflection, relevant points suggesting new research and pedagogical action using the calculators in Mathematics classroom, were raised. These points refer to: subject matter, assessment and teacher education. / Mestre

Made available in DSpace on 2014-06-11T19:24:54Z (GMT). No. of bitstreams: 0 Previous issue date: 1997-12-08Bitstream added on 2014-06-13T20:27:25Z : No. of bitstreams: 1 mocrosky_lf_me_rcla.pdf: 17148221 bytes, checksum: b1f18d25688a3c8b09cd5974921da660 (MD5) / Este estudo tem por objetivo conhecer o que os professores de Matemática pensam a respeito do uso da calculadora em sala de aula, buscando compreender o que consideram importante para essa prática pedagógica. A metodologia adotada para essa investigação teve inspiração fenomenológica, baseada na estrutura do fenômeno situado. Os sujeitos dessa pesquisa foram professores dos ensinos fundamental e médio, das redes pública e particular de ensino, nas cidades de Ponta Grossa - PR e Rio Claro - SP. Ao todo foram coletados 22 depoimentos, gravados, transcritos e analisados. A princípio, para a análise, foram consideradas as idéias individuais dos depoentes, com as quais foi construída a Matriz ldeográfica, que mostra uma das reduções feitas. Num segundo momento, partindo dessa Matriz, novas reduções foram efetuadas e delas emergiram três categorias abertas que apontam as características essenciais do uso da calculadora nas aulas de Matemática: domínio das operações básicas, a calculadora como recurso didátlco e formação do professor. Essas categorias foram interpretadas tendo em vista os depoimentos dos sujeitos e a literatura estudada. Finalizando o trabalho, apresentou-se a compreensão da pesquisadora sobre o estudo e, dessa interpretação e reflexão, foram levantados pontos relevantes que sugerem outras pesquisas e que indicam ações pedagógicas tendo em vista a calcufadora e a sala de aula. Esses pontos dizem de: conteúdos programáticos, avaliaçã e formação do professor. / This study aims at knowing what mathematics teachers think about the use of calculators in the classroom, looking for an understanding of what they consider to be important in this pedagogical practice. The research methodology had a phenomenological inspiration based on the structure of situated phenomena. The subjects of this research were people teaching at primary, secondary and high school levels, at public and private schools in the cities of Ponta Grossa - PR and Rio Claro - SP. Twenty two testimonies were collected, recorded, transcribed and analysed. At first an Ideographical Matrix was assembled from the teachers' individual ideas, representing one of the reductions made. In a second moment, starting with this Matrix, new reductions were made and three open categories emerged. These categories point to the essential characteristics of the use of calculators in the Mathematics classroom: domain of basic operations, the calculator as didactic resource and teacher education. These categories were interpreted on the basis of the subjects' testimonies and the study of bibliography. Finally, the researcher comprehension of the study is presented. Based on her interpretation and reflection, relevant points suggesting new research and pedagogical action using the calculators in Mathematics classroom, were raised. These points refer to: subject matter, assessment and teacher education.

<p>Making mistakes is an inevitable part of mathematics learning and an essential aspect of teaching. The current study examined the patterns and key variations in teachers’ responses to children’s mistakes in kindergarten mathematics classrooms. I developed a coding scheme using both inductive and deductive approaches to document the discourse across a series of video-recorded mathematics lessons from a sample of 24 public school kindergarten teachers. Based on previous classroom observational studies, I first outlined four significant dimensions of teachers’ mistake-handling practices: (1) instructional support: the instructional strategies teachers use to elaborate on students’ mistakes and incorporate their mistakes into ongoing mathematics instructions, (2) emotional reactions: the valence of teachers’ affective reactions to students’ mistakes (i.e., positive, negative, or neutral), (3) locus of responsibility: the individual who is responsible for correcting the mistake, and (4) the nature of mistakes: teachers’ explicit communication about the causes, consequences, and value of making mistakes. Then, I followed an open-coding process to document emergent sub-categories related to each dimension. The study revealed distinct patterns of teachers’ mistake-related practices for the four major dimensions and the complexity of the teacher-child interaction surrounding mistakes. In addition, results indicated that teachers’ positive emotional reactions toward children’s mistakes were associated with their high-quality instructional support and adaptive statements regarding the nature of mistakes. The current study contributes to the understanding of adaptive strategies teachers could use to address children’s mistakes in mathematics classrooms.</p>

The sustainable development goals emphasise that gender equality within education is animportant problem. Furthermore, gender equality is more than just equal access for boys andgirls, it is important to look at what happens within the classroom. Thus, the aim of this studyis to explore gender within the mathematics classroom in Indonesia. More specifically, toexplore how gender is constructed and to get the pupils’ perspective on gender equality. Theresearch questions examined are:How is gender constructed in Indonesian mathematics classrooms?How do Indonesian pupils experience gender equality within the mathematics classrooms?To answer our research questions, we observed four mathematics classrooms in an Islamicprimary school in Indonesia. Furthermore, we handed out surveys to the pupils in order to gettheir perspective on gender equality. As a foundation for the analysis of these questions, weused the queer theory complemented with an interactionist view. According to the queertheory, gender is something that is constructed and all too often a dichotomy is used whendiscussing equality between the sexes. Thus, the intention of this study is to explore genderequality within mathematics by looking beyond this dichotomy.The results show that gender is being constructed both direct and indirect by the participantsin the mathematics classrooms. Both teachers and pupils act and behave in a way thatreinforces gender stereotypes. Although, when asked, the pupils thought that the teacherstreated the sexes equally and that the mathematics classroom was gender equal. Furthermore,the pupils agree that the girls are best in mathematics. However, girls tended to have lowerself-esteem than boys since they underestimated their knowledge to a greater extent.

Much research supports that student mindset influences how well students do in school and that teacher actions influence student mindset. Research has also shown that just because a teacher has a growth mindset, it does not imply that their students will also have a growth mindset. This research looks closer as to why a teacher's mindset does not correlate with their students' mindset by further examining teacher mindset and the connection between teacher mindset and teacher actions. In summary, teachers' mindsets do not directly influence student mindset for a few reasons: secondary mathematics teachers have different mindsets towards honors and regular students, while they have heard about mindset, they do not understand mindset deeply, and mathematics teachers do not know how to help their students develop a growth mindset.

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Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: The special needs community is in the midst of a philosophical and physical shift from a segregated system to an integrated system, not only in placement, but more importantly, in terms of learning and affording learners with special needs access to mainstream curricular materials. Mathematical modelling, or challenging mathematics problems solved in small groups, is part of the Australian mainstream curriculum. The purpose of the study was to investigate the way special needs learners learn mathematics from a modelling learning environment. To do this, it was necessary to identify the critical characteristics of the best practice in teaching and learning for learners with special needs, and the critical features of modelling. One theory of learning that has the capacity to promote special needs learners' interaction with mathematical modelling is Feuerstein’s theory of Structural Cognitive Modifiability. A hypothetical learning trajectory was designed for special needs learners at middle school according to general design principles from theory, which was adapted to the learning characteristics of the class. The learning environment comprised of three challenging modelling tasks, together with recommended implementation and support conditions in the classroom. Specifically, the research sought to investigate the ways in which special needs educators can support the higher reasoning processes of special needs students during modelling through design in general, and through mediation specific to each learner. The research took the form of a qualitative study, combining the phases of design-based research with a multiple case study approach. Three cases were analysed in depth. Empirical data were collected through a range of qualitative methods, which included data from student files, field observations, video and audio recordings, focus group interviews with students, and the input of various collaborators across the different phases of planning, design, implementation, and revision. Data were coded and analysed inductively according to emerging patterns and themes. Findings suggest that the use of modelling was successful when implemented with certain characteristics defined in the literature, and that it enabled learners to learn mathematics and also to develop additional outcomes such as social skills and language. During this study, learners' higher-order reasoning was supported through dynamic assessment and subsequent mediation. / AFRIKAANSE OPSOMMING: Die onderwysgemeenskap vir leerders met spesiale behoeftes bevind hulle in die middel van filosofiese en fisiese verskuiwings van 'n geskeide sisteem na 'n geïntegreerde sisteem. Dit omvat die plasing van leerders, maar meer belangrik ook die bemoontliking van toegang van hierdie leerders tot hoofstroom kurrikulêre materiale. Wiskundige modellering, en uitdagende wiskundeprobleme wat deur leerders in klein groepies opgelos word, is deel van die Australiese hoofstroomkurrikulum. Die doel van die studie was om die wyse te ondersoek waarvolgens leerders met spesiale behoeftes wiskunde in 'n modelleringsomgewing leer. Dit is gedoen deur die belangrike kenmerke van beste praktyk vir onderrig en leer in spesiale onderwys, asook die kritiese kenmerke van modellering, te vind. Een leerteorie wat die interaksie van leerders met spesiale behoeftes met wiskunde bevorder, is Feuerstein se teorie van Strukturele Kognitiewe Modifieerbaarheid. 'n Hipotetiese leertrajek was ontwerp vir leerders met spesiale behoeftes op middelskoolvlak. Empiriese data is deur 'n reeks kwalitatiewe aksies: data van studentelêers, veldwaar-nemings, video en klankopnames, fokusgroeponderhoude met studente, asook die insette van verskeie medewerkers oor die verskillende fases van beplanning, ontwerp, implementering en hersiening gegenereer. Die spesifieke leerkenmerke van hierdie leerders volgens algemeen-teoretiese en lokaalgekontekstualiseerde ontwerpbeginsels is nagekom. Die leertrajek het bestaan uit drie uitdagende modelleringsprobleme met aanbevole implementering en ondersteuningsriglyne in die klaskamer. Die navorsing het spesifiek gesoek na wyses waarop hierdie leerders se hoër beredeneringsvaardighede deur hul onderwysers, volgens elkeen se eie behoefte gedurende modellering, deur ontwerp in die algemeen en mediasie in die besonder, ondersteun kan word. Die navorsing, 'n kwalitatiewe studie, was gekombineer met fases van ontwikkelingsgebaseerde ontwerp wat uitgespeel het in 'n veelvuldige gevallestudiebenadering. Drie gevalle is in diepte ondersoek. Data was induktief gekodeer en geanaliseer volgens ontluikende patrone en temas. Bevindinge wys uit dat die gebruik van modellering suksesvol was wanneer die implementering volgens spesifieke kenmerke in die literatuur was. Dit het leerders instaat gestel om wiskunde te leer asook om addisionele uitkomste soos sosiale vaardighede en taal te ontwikkel. In hierdie studie is hoër-orde denke ondersteun deur dinamiese assessering en voortspruitende mediasie.

This is a qualitative research that draws on Fairclough’s Critical Discourse Analysis methodology to analyze the discourse practices of the mathematics teacher educators in initial teacher training colleges in Malawi. The study involved four mathematics teacher educators in two teacher training colleges located in two different regions of Malawi. Specifically the study explored the following questions: 1) What are the discourse practices that mathematics teacher educators display in their descriptions of multilingual mathematics classrooms? 2) a) What are the discourse practices that mathematics teacher educators display in a college mathematics classroom? b) How do they make available the discourse practices for the student teachers to draw on? Data was collected through pre-observation interviews, classroom observations, reflective interviews and focus group discussions with the mathematics teacher educators. This study has shown that while there are some disconnections between the discourse practices produced in a school multilingual mathematics classroom and a college mathematics classroom, some of the discourse practices that mathematics teachers produced in a college mathematics classroom reinforces the common discourse practices being produced in multilingual mathematics classroom. There are three common discourse practices that were displayed in a college mathematics classroom. These discourse practices are: Initial-Response-Evaluation (Pimm, 1987), traditional lecturing and group discussions. I observed that the IRE and traditional lecturing discourse practices were accompanied by directive discourses for procedural control, and the procedural discourse was the prevalent discourse in all the discourse practices produced. iv Three major themes have emerged from the data analysis. Firstly, the research findings indicate that the mathematics teacher educators regard multilingualism and the language practices that come with it such as code-switching more as a problem rather than a resource for teaching and learning. Secondly, code-switching in college mathematics classroom is not as spontaneous as is research shows it to be in schools; rather it is very much controlled and restricted. Thirdly, the dilemmas of code-switching as discussed by Adler (1998, 2001) are more acute in teacher training colleges, mainly because of the mismatch in the Language-in-Education Policy (LiEP) in schools and tertiary level.

Syftet med avhandlingen är att beskriva, analysera och förstå matematikundervisning på lågstadiet. Mer precist är syftet att undersöka vad denna undervisning ger elever i några klassrum möjlighet att lära då undervisningsinnehållet är skriftliga räknemetoder för addition och  ubtraktion. Centrala frågor är vad lärare och elever gör i matematikklassrummet och vad eleverna, som en följd av undervisningen har möjlighet att lära. En fältstudie har genomförts i fem klasser med början på våren i år 2 och fortsättning under hösten i år 3. Sammanlagt 24 lektioner har videofilmats. Materialet har analyserats i två etapper, med början i en empiri nära, tematisk analys. Verksamhetsteorin är teoretisk utgångspunkt och analysverktyget som inspirerats av Engeströms modell för verksamhetssystem har varit vägledande i den andra etappen av analysen. Resultatet visar fyra typer av undervisningsverksamheter i matematik, vilka resulterar i möjligt lärande som varierar i förhållande till de förmågemål som anges i Lgr11. Det framgår också att de utmärkande metoder som lärare och elever använder kan ordnas i fem grupper, i huvudsak beroende på vilka kunskapsaspekter metoderna riktas mot. Det gäller metoder där procedurer, begrepp och samband, matematisk kommunikation och resonemang samt intresse och tilltro är i centrum, tillsammans med metoder som bidrar till stötestenar, vilka innebär utmaningar för både lärare och elever. Resultatet diskuteras mot bakgrund av forskning om undervisning och lärande i matematik med inriktning mot språklig kommunikation, användning av laborativt material, klassrumskultur och klassrumsorganisation. / The aim of this study is to describe, analyse and understand teaching of mathematics in lower primary school. More precisely, the aim is to investigate what this teaching offers pupils in some classrooms in terms of learning, when the content of teaching is written calculation methods for addition and subtraction. Teachers’ and pupils’ activities are in focus, as well as what it is possible for the pupils to learn as a consequence of these activities. Collection of data has been carried out in five classes, starting in spring when the pupils were in second grade and finished by the end of the autumn, when the pupils were in third grade. The video-recorded material comprises a total of 24 lessons. The collected research material has been analysed in two steps, where the first step can be described as empirically oriented and thematical. The theoretical perspective is Activity theory (CHAT) and an analysing tool, inspired by Engeström’s model has guided the second step of the analysis. The result demonstrates four types of teaching activities in mathematics, which leads to possible learning that varies in relation to the educational goals set in the curriculum (Lgr11). It is also shown that teachers and pupils make use of a variety of characteristic methods, which can be sorted into five groups, primarily based on ability aspects that are actualised by different methods. These are methods, where (1) procedures, (2) concepts and connections, (3) mathematical communication and reasoning, and (4) interest and confidence are in focus. There is also a fifth group, but it deviates from the others, as it consists of methods that contribute to (5) stumbling blocks, which in turn means that they become challenges for teachers as well as pupils. The results are discussed in relation to other research about teaching and learning mathematics.

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