The main purpose of this thesis is to investigate how future pre- and primary school mathematics teachers change their approaches to mathematics and mathematics education during their subject studies, and also how this view has affected their teaching of mathematics after graduation. A qualitative interview method was used in combination with observations, notes, sound recordings, video recorded mathematics classes and materials produced by the teacher in order to answer the research questions. The research was carried out in two parts. The institutional theory has been used as theoretical framework throughout. This perspective was supplemented by a design theoretical perspective in part two. In the first investigation it became clear that the language used by the students is under change, and that they use terms from the national curriculum as well as the aims of the programme syllabus when they discuss mathematics teaching. The results from the observations later show that four out of five of the teachers have a clear connection to the sort of teaching they said they want to conduct, in that there is a clear relationship between the sort of teaching that they claim to perform and the sort of teaching they actually perform. From the overall results, it is apparent that teachers one year after graduation describe that they feel well prepared for teaching mathematics in preschool and primary school. This is interesting in the light of their dissatisfaction with the limited emphasis on concrete recommendations and "tips" directly after their graduation. In fact, the teachers said that in practice it turned out that their education provided a more stable and secure foundation than they described it to be shortly after having completed their mathematics studies. They say that during their education they developed knowledge and skills that enabled them to be better prepared for their future work roles than they believed themselves likely to become.

Studien syftar till att beskriva hur lärare i matematik upplever att de praktiskt hanterar elevers olika förutsättningar i sin matematikundervisning. Undersökningen genomfördes som en fallstudie av två lärare i matematik i grundskolans senare år. Det empiriska materialet består av fyra klassrumsobservationer, som analyserades för att identifiera olika typer av individualisering, samt fyra intervjuer, för att belysa lärarnas upplevelser av och tankar kring individualisering. Det framkom att det förekommer flera olika typer av individualisering. En del individualisering var ett resultat av lärarens medvetna val, men det förekom även individualisering som lärarna delvis var omedvetna om. / The study aims to describe how teachers of mathematics feel that they practically handle student differences in their mathematics teaching. The survey was conducted as a case study of two teachers of mathematics in secondary school. The empirical material consists of four classroom observations, which were analyzed to identify types of individualization, and four interviews, to highlight the teachers' experiences of and thoughts about individualization. It was found that there are several different types of individualization. Some individualization was the result of the teacher's conscious choice, but there were also individualization as teachers in part, were unaware of.

The current study, initially aimed to explore the problem solving skills of the sixth grade students within the four-process problem solving framework including the processes of understanding the problem, devising a plan, carrying out the plan, and looking back and evaluating. Secondly, it aimed to investigate the relationships between student and teacher related characteristics and problem solving skills of the students. In the study, a model was proposed based on the related literature and this proposed model was tested by using hierarchical linear modeling (HLM) technique. A total of 2562 sixth grade students from 37 public elementary schools in the eight central districts of Ankara completed a problem solving skills test developed by the researcher and a student questionnaire. At the same time, mathematics teachers of the students participated in the study completed a teacher questionnaire. The results indicated that in general the sixth grade students displayed low performance in the overall problem solving skills test. Moreover, the students performed best in the process of understanding problem whereas they showed the worst performance in the process of looking back and evaluating. The results of the hierarchical linear modeling technique indicated that the student characteristics significantly and positively related to the problem solving skills of the sixth grade students were socioeconomic status, mathematics self concept, extrinsic motivation, use of control strategies, preference for competitive learning situation, and teacher support, on the other hand student level characteristics significantly and negatively related to the problem solving skills of the sixth grade students were mathematics anxiety, giving homework, activities related with homework, and different types of homework. Furthermore, the teacher level characteristics significantly related to the problem solving skills of the sixth grade students were only teacher gender and perceptions about limitations aroused from students. The characteristic of perceptions about limitations aroused from students was negatively related to problem solving skills of the students on the other hand teacher gender was found to be related to problem solving skills of the students in favor of female teachers. It was also found that there was no teacher level characteristic influencing the relationship that was between student level characteristics and the problem solving skills of the students.

The Sediba project originated when investigations showed that there were many teachers in the North-West Province that did not possess sufficient subject knowledge to teach physical sciences and mathematics. In spite of many in-service training opportunities for teachers, the achievements of learners are still not satisfactory. From interviews with teachers in the Sediba Mathematics Programme the problem of unmotivated learners became apparent. From the literature it appeared that the motivation of teachers has an effect on the motivation of their learners. This study was undertaken as a result of those findings to determine whether the Sediba Mathematics Programme has an effect on the intrinsic motivation of the teachers in the programme. To understand the nature of motivation better, the motivation theories of Maslow, Herzberg, Adams and Vroom were investigated. This investigation made valuable contributions to the study and gave insight into the behaviour patterns of the teachers in certain situations. By means of the literature study a profile of a motivated mathematics teacher could be compiled. It was found that self-concept, self-efficacy, task value and the effect that change has on teachers, could be regarded as determinants of intrinsic motivation. Aided by a questionnaire, an empirical study was done to test the degree to which these determinants were present in the teachers. To bring about triangulation this was followed up by conducting interviews with a sample of the teachers. Furthermore, a mathematics competence test was done. Several models of in-service training were further investigated and the Sediba Mathematics Programme was evaluated on the basis of a set of essential elements for an ideal programme. It was found that the Sediba Programme fulfilled these requirements to a large degree. The empirical investigation, the mathematics competence test and the interviews that were held with teachers delivered the following results. It was found that the Sediba Mathematics Programme did have an effect on the intrinsic motivation of the teachers in the programme. The subject knowledge of the teachers improved significantly after only one year of study. The teachers' self-concept and self-efficacy improved, they regarded their task as important and endeavoured to implement change meaningfully in spite of existing uncertainties. Negative conditions such as overcrowded class-rooms, no/little aids, lack of safety and discipline at many schools that made it difficult for teachers to deliver quality teaching, could affect motivation negatively. Keywords for indexing: motivation, mathematics teacher, professional development, Sediba-program, in-service training and motivation, intrinsic motivation, extrinsic motivation, in-service training for mathematics teachers. / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2008.

South African learners underachieve in mathematics. The many different factors that influence this underachievement include mathematics teachers' role in teaching mathematics with understanding. The question arises as to how teachers' mathematical content knowledge states can be transformed to positively impact learners' achievement in mathematics. In this study, different kinds of teachers' knowledge needed for teaching mathematics were discussed against the background of research in this area, which included the work of Shulman, Ma and Ball. From this study an important kind of knowledge, namely mathematical content knowledge for teaching (MCKfT), was identified and a teacher's ability to unpack mathematical knowledge and understanding was highlighted as a vital characteristic of MCKfT. To determine further characteristics of MCKfT, the study focussed on the nature of mathematics, different kinds of mathematical content knowledge (procedural and conceptual), cognitive processes (problem solving, reasoning, communication, connections and representations) involved in doing mathematics and the development of mathematical understanding (instrumental vs. relational understanding). The influence of understanding different problem contexts and teachers' ability to develop reflective practices in teaching and learning mathematics were discussed and connected to a teacher's ability to unpack mathematical knowledge and understanding. In this regard, the role of teachers' prior knowledge or current mathematical content knowledge states was discussed extensively. These theoretical investigations led to identifying the characteristics of MCKfT, which in turn resulted in theoretical criteria for the development of MCKfT. The theoretical study provided criteria with which teachers' current mathematical content knowledge states could be analysed. This prompted the development of a diagnostic instrument consisting of questions on proportional reasoning and functions. A qualitative study was undertaken in the form of a diagnostic content analysis on teachers' current mathematical content knowledge states. A group of secondary school mathematics teachers (N=128) involved in the Sediba Project formed the study population. The Sediba Project is an in-service teacher training program for mathematics teachers over a period of two years. These teachers were divided into three sub-groups according to the number of years they had been involved in the Sediba Project at that stage. The teachers' current mathematical content knowledge states were analysed with respect to the theoretically determined characteristics of and criteria for the development of MCKfT. These criteria led to a theoretical framework for assessing teachers' current mathematical content knowledge states. The first four attributes consisted of the steps involved in mathematical problem solving skills, namely conceptual knowledge (which implies a deep understanding of the problem), procedural knowledge (which is reflected in the correct choice of a procedure), the ability to correctly execute the procedure and the insight to give a valid interpretation of the answer. Attribute five constituted the completion of these four attributes. The final six attributes were an understanding of different representations, communication of understanding in writing, reasoning skills, recognition of connections among different mathematical ideas, the ability to unpack mathematical understanding and understanding the context a problem is set in. Quantitative analyses were done on the obtained results for the diagnostic content analysis to determine the reliability of the constructed diagnostic instrument and to search for statistically significant differences among the responses of the different sub-groups. Results seemed to indicate that those teachers involved in the Sediba Project for one or two years had benefited from the in-service teacher training program. However, the impact of this teachers' training program was clearly influenced by the teachers' prior knowledge of mathematics. It became clear that conceptual understanding of foundation, intermediate and senior phase school mathematics that should form a sound mathematical knowledge base for more advanced topics in the school curriculum, is for the most part procedurally based with little or no conceptual understanding. The conclusion was that these teachers' current mathematical content knowledge states did not correspond to the characteristics of MCKfT and therefore displayed a need for the development of teachers' current mathematical content knowledge states according to the proposed criteria and model for the development of MCKfT. The recommendations were based on the fact that the training that these teachers had been receiving with respect to the development of MCKfT is inadequate to prepare them to teach mathematics with understanding. Teachers' prior knowledge should be exposed so that training can focus on the transformation of current mathematical content knowledge states according to the characteristics of MCKfT. A model for the development of MCKfT was proposed. The innermost idea behind this model is that a habit of reflective practices should be developed with respect to the characteristics of MCKfT to enable a mathematics teacher to communicate and unpack mathematical knowledge and understanding and consequently solve mathematical problems and teach mathematics with understanding. Key words for indexing: school mathematics, teacher knowledge, mathematical content knowledge, mathematical content knowledge for teaching, mathematical knowledge acquisition, mathematics teacher education / Thesis (Ph.D. (Education))--North-West University, Potchefstroom Campus, 2007.

The Sediba project originated when investigations showed that there were many teachers in the North-West Province that did not possess sufficient subject knowledge to teach physical sciences and mathematics. In spite of many in-service training opportunities for teachers, the achievements of learners are still not satisfactory. From interviews with teachers in the Sediba Mathematics Programme the problem of unmotivated learners became apparent. From the literature it appeared that the motivation of teachers has an effect on the motivation of their learners. This study was undertaken as a result of those findings to determine whether the Sediba Mathematics Programme has an effect on the intrinsic motivation of the teachers in the programme. To understand the nature of motivation better, the motivation theories of Maslow, Herzberg, Adams and Vroom were investigated. This investigation made valuable contributions to the study and gave insight into the behaviour patterns of the teachers in certain situations. By means of the literature study a profile of a motivated mathematics teacher could be compiled. It was found that self-concept, self-efficacy, task value and the effect that change has on teachers, could be regarded as determinants of intrinsic motivation. Aided by a questionnaire, an empirical study was done to test the degree to which these determinants were present in the teachers. To bring about triangulation this was followed up by conducting interviews with a sample of the teachers. Furthermore, a mathematics competence test was done. Several models of in-service training were further investigated and the Sediba Mathematics Programme was evaluated on the basis of a set of essential elements for an ideal programme. It was found that the Sediba Programme fulfilled these requirements to a large degree. The empirical investigation, the mathematics competence test and the interviews that were held with teachers delivered the following results. It was found that the Sediba Mathematics Programme did have an effect on the intrinsic motivation of the teachers in the programme. The subject knowledge of the teachers improved significantly after only one year of study. The teachers' self-concept and self-efficacy improved, they regarded their task as important and endeavoured to implement change meaningfully in spite of existing uncertainties. Negative conditions such as overcrowded class-rooms, no/little aids, lack of safety and discipline at many schools that made it difficult for teachers to deliver quality teaching, could affect motivation negatively. Keywords for indexing: motivation, mathematics teacher, professional development, Sediba-program, in-service training and motivation, intrinsic motivation, extrinsic motivation, in-service training for mathematics teachers. / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2008.

The purpose of this study was to investigate eighth grade students&rsquo / perceptions of their mathematics teachers&rsquo / interpersonal behaviors. The study also investigated mathematics teachers&rsquo / perceptions of their own interpersonal behaviors as well as relationships among students&rsquo / perceptions of their teachers&rsquo / interpersonal behaviors, attitudes towards mathematics, mathematics achievements, student gender, teacher gender, and socio-economical background. Questionnaire on Teacher Interaction (QTI) scale and a mathematics attitude scale were used for data collection. Data were collected from a sample of 1317 eighth grade students in public elementary schools in the following provinces: istanbul, Ankara, izmir, Adana, Bursa, and Hatay. Statistical analyses revealed that the Turkish version of QTI translated and adapted by the researcher had an acceptable degree of validity and reliability. Results showed that Turkish students perceive their mathematics teachers as displaying high levels of leadership, helpful/friendly, understanding, and displaying strict behaviors rather than uncertain, admonishing and dissatisfied behaviors. The results also indicated that students&rsquo / perceptions of their mathematics teachers&rsquo / interpersonal behaviors were associated with their attitudes towards mathematics and their mathematics achievement. While the leadership, helpful/friendly, and understanding behaviors had positive correlations with attitude scores of students, the uncertain, dissatisfied, admonishing and strict behaviors had negative correlations. Similarly, students who perceived their teacher as displaying leadership, helping/friendly and understanding behavior had higher achievement levels than the ones who perceive their teacher as strict, uncertain, admonishing and dissatisfied. Students with higher cultural and economical background perceived their teachers more favorably. The MANOVA results indicated that girls generally perceived their mathematics teacher more cooperative than boys did. Also students perceived their male teachers display more leadership, helping/friendly, and strict behaviors than their female teachers. Results also indicated that teachers generally perceived themselves in a more favorably manner than their students did.

Linha de pesquisa: Curr?culos, Avalia??o, Pr?ticas Pedag?gicas e Forma??o de Professores. / Na Capa, Folha de Rosto e Ficha Catalogr?fica do trabalho, constam o t?tulo: "Um estudo da identidade docente de licenciandos em Matem?tica da Unimontes". / Submitted by Jos? Henrique Henrique (jose.neves@ufvjm.edu.br) on 2018-07-23T22:28:07Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) marineide_almeida_rocha.pdf: 1622461 bytes, checksum: 5dafcb0275c404ba24bdcf413885c35f (MD5) / Approved for entry into archive by Rodrigo Martins Cruz (rodrigo.cruz@ufvjm.edu.br) on 2018-10-04T19:19:01Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) marineide_almeida_rocha.pdf: 1622461 bytes, checksum: 5dafcb0275c404ba24bdcf413885c35f (MD5) / Made available in DSpace on 2018-10-04T19:19:01Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) marineide_almeida_rocha.pdf: 1622461 bytes, checksum: 5dafcb0275c404ba24bdcf413885c35f (MD5) Previous issue date: 2017 / As quest?es que envolvem a profiss?o docente t?m se tornado cada vez mais presentes nos debates e f?runs educacionais, no cen?rio nacional e internacional, dada a necessidade de melhoria na qualidade do ensino, o que requer bons professores. Diante de reflex?es e de questionamentos sobre o tipo de forma??o adequada para o futuro professor, mediante a complexidade do trabalho docente na contemporaneidade, ? que surgiu o interesse pelo presente trabalho. O objetivo geral desta investiga??o foi desvelar ind?cios de constitui??o da identidade docente de licenciandos do Curso de Licenciatura em Matem?tica da Universidade Estadual de Montes Claros (Unimontes/Campus Montes Claros), tendo como objetivos espec?ficos: a) evidenciar as marcas de trajet?rias de forma??o e ind?cios de constitui??o de identidade profissional docente apresentados pelos sujeitos em forma??o em suas hist?rias de vida; e b) identificar os aspectos que os mesmos explicitam serem fundamentais para a forma??o docente, a partir das experi?ncias de forma??o proporcionadas pelo curso de Licenciatura em Matem?tica da Unimontes. O estudo utilizou como instrumento de produ??o e an?lise de dados as hist?rias de vida de oito licenciandos em Matem?tica da Unimontes, as quais foram obtidas por meio de memoriais de forma??o e complementadas por entrevistas semiestruturadas. Os dados analisados foram organizados em duas categorias: a) trajet?ria de forma??o anterior ao ingresso na licenciatura e b) trajet?ria de forma??o na licenciatura. Os dados evidenciam que o processo de constitui??o da identidade docente sofre influ?ncias m?ltiplas, que se inter-relacionam e apresentam-se de diversas formas, como elementos de uma hist?ria de vida, como acontecimentos ao longo de um percurso de vida e que configuram a representa??o que o professor tem de si pr?prio e de sua profiss?o. / Disserta??o (Mestrado Profissional) ? Programa de P?s-Gradua??o em Educa??o, Universidade Federal dos Vales do Jequitinhonha e Mucuri, 2017. / Considering the need to improve teaching quality, which requires good teachers, the issues related to teaching profession have become increasingly present at educational debates and forums in the national and international scenarios. In face of the reflections and questions about the appropriate education for the future teacher, through the complexity of the contemporary teaching work, the interest for this research theme has arisen. The aim of the investigation was to analyze the identity evidence of the undergraduate teaching students from the Prospective Mathematics Teacher Education Course offered by the Universidade Federal de Montes Claros (Unimontes) at Montes Claros Campus. The specific aims were: a) to highlight the evidence of the constitution of the teaching professional identity presented by the subjects in their life histories, and b) to identify the aspects that these subjects make explicit as being are fundamental for teacher education, based on the education experiences provided by the curricular proposal of the course Teaching mathematics education of the Unimontes. The study used as an instrumento of production and data analysys of life histories of eight Mathematics graduates, which were obtained through education memorial and complemented by semi structured interviews. Data analyzes were organized into two categories: a) trajectory of prior prospective teacher education and b) trajectory of the prospective teacher education. The data show that the process of constitution of the teacher identity suffers multiple influences, which are interrelated and presented in different ways, such as elements of a life history, as events along a life course and that configure the representation that the teacher has of himself and his profession.

Syftet med studien är att genom kvalitativa intervjuer undersöka hur lärare förhåller sig till det nya tillägget med digital kompetens i kursplanen för ämnet matematik, och om det kommer påverka matematikundervisningen. Intervjustudien inriktar sig på grundskollärare i någon av årskurserna 1-6. Resultatet av studien visar att lärarna inte är oroliga över sin egen digitala kompetens i undervisningssyfte. Detta trots det framkommit att dagens utbud av digitala verktyg bland lärarna var varierande men majoriteten av gångerna undermålig, samt att informationen kring tillägget många gånger hade kunnat varit informationsrikare. Resultatet visar även att lärarna tror på en framtida förändring av matematikundervsningen, varav flertalet ser en undervisningen där det finns ökad möjlighet till individualisering. Men trots detta finns det en staka unisonisk önskan av mer fortbildning inom området.

Orientador: Miriam Godoy Penteado / Banca: Antonio Carlos Carrera de Souza / Banca: Maria Elizabeth B.T.M.P. Almeida / Resumo: Este trabalho teve por objetivo analisar a formação continuada do professor de Matemática do o de São Paulo para o uso da informática na escola, tendo em vista as ações dos programas (MEC) e A Escola de Cara Nova na Era da Informática (SEEISP). A análise foi feita tanto r termos de proposta, isto é, considerando o planejamento das ações, quanto em termos de considerando as ações como elas efetivamente aconteceram. Por meio de uma Jrdagem qualitativa de pesquisa, acompanhei dois Núcleos Regionais de Tecnologia Educacional TEs) - órgãos responsáveis por capacitar os professores e oferecer suporte técnico e às escolas. Foram analisados documentos oficiais dos programas, registro das .bservações de duas oficinas na área de Matemática (uma em cada NRTE), questionários com os ores participantes destas oficinas e entrevistas com coordenadores de NRTEs e com - professores da Rede que capacitam os colegas por meio das oficinas pedagógicas. .j tensões entre a proposta e a implementação, reveladas na análise dos dados, foram discutidas à z da literatura sobre professores e computadores. O estudo apresenta também algumas sugestões ...a a formação continuada de professores de Matemática para o uso da informática na sala de aula. / Abstract: The objective of this study was to analyze the continuing education of mathematics teachers state of São Paulo for the use of computers in the schools, focusing on the actions of the iunent programs Prolnfo (Braziian Ministry of Education) and The New Face of the Schools omputer Age (São Paulo State Department of Education). The analysis looked at the posal of the programs, i.e., considering the planning of the actions, as well as the mentation, considering the actions as they went into effect. Using a qualitative research 1 followed two Regional Centers of Educational Technology (Núcleos Regionais de no1ogia Educational - NRTEs), responsible for training teachers and providing pedagogical and support to schools. The data analyzed included official program documents, field of observations of two mathematics workshops (one in each NRTE), questionnaires ninistered to workshop participants, and interviews with coordinators of the NRTEs as well as - teachers that administer workshops to their co-workers. The tensions between the roposal and the implementation that emerged from the data analysis are discussed in the light of literature on teachers and computers. Some suggestions are presented regarding continuing 1 ofmathematics teachers in the use of computers in the classroom. / Mestre