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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. / Disputationen sker den 2009-10-16, Tillbergsalen, Campus Konradsberg, hus T, Rålambsvägen 32, Stockholm, 10:00

Not often do mathematics teachers instruct to improve students' attitudes toward mathematics. The pressures to cover the state-mandated curriculum drive teachers to instruct for procedural understanding with few connections. The lack of real-life connections results in students with low motivation toward mathematics and results in poor mathematics attitude (Ma andamp; Kishor, 1997). The purpose of this mixed-methods research is to examine self-regulated learning as an instructional technique aimed at increasing mathematical attitudes while also increasing achievement and to reveal barriers to its implementation in the classroom.The research study involved an intervention in a Mid-South urban high school at the 9th grade level. All students who participated were enrolled in the middle track at the school, thus taking an Algebra I course. The intervention took place with four teachers in seven separate classes. Students were given the opportunity to regulate their own learning based on objectives for district and state requirements. In this pre/post design, students were surveyed for their mathematics attitude and achievement using the Attitude Toward Mathematics Inventory (Tapia, 1996) and a polynomial survey designed by the researcher. Teachers were surveyed and interviewed prior to the study to develop a sense of their teaching preferences. During the experiment classroom observations were conducted to assist in developing themes in the intervention. Following the study, extensive interviews took place with each participating teacher.Data analyses revealed no statistically significant difference between the control and experimental group in regards to mathematics attitude and achievement. Qualitative analysis using constant comparative strategies (Denzin andamp; Lincoln, 2000) revealed many teacher barriers and misconceptions. Teachers felt uncomfortable with the technique and were unable to allow the students to fully regulate their learning. The teachers imposed a timeline, quizzes, written tests, and direct instruction techniques on the students during the study. All of these created barriers to the students fully regulating their learning. Also, teachers' perceptions of learning and attitude were not valid. Teachers believed the students achieved at a lower level than with a traditional approach and viewed their attitudes as worse than normal. This was in direct contrast to the quantitative results.

The thesis called The Ways of Presentation of Mathematics in the 7th Grade of Montessori School provides with a description and detailed analysis of Montessori principles with regards to their use and fulfilling tasks during lessons of mathematics at Montessori Schools. Its further aim is to check out in the course of lessons if the three Montessori principles - discovering of facts by an individual, work with mistake and individual approach - are being applied during the presentations of new topics to the 7th grade students of Montessori school. The thesis consists of theoretical and practical parts. The theoretical part deals with establishing of educational areas of mathematics and its application within the "The Framework Education Programme for Elementary Education" and description of current trends in mathematics, didactic constructivism represented by Hejný and Kuřina. Further on, it describes Montessori principles and their application and use during the teaching of mathematics and ways of presentation of mathematic topics in Montessori classes. The end of theoretical part is a comparison of Montessori principles during the mathematic lessons and didactic constructivism. In its introduction, the practical part refers to the theoretical concept of education in the second cycle of Montessori...

This study has investigated the take-up, at a range of South African tertiary institutions, of Open Educational Resources (OER) designed for mathematics teacher education. Although numerous studies (e.g. Darling-Hammond, 2006; Jonassen & Rohrer-Murphy, 1999; Loughran, 2006) have identified criteria for the development of quality materials for teacher education, and have investigated ways in which these have been and should be used, little attention has been paid to the implications of these findings for the use of OER in teacher education. In 2006 the South African Institute of Distance Education (SAIDE) initiated the ACEMaths project to pilot a collaborative materials design and adaptation process in response to a Department of Education call for large scale teacher upgrading programmes leading to an Advanced Certificate in Education (ACE) in priority areas. Nine South African tertiary institutions formed the collaborative group for the development of Mathematics teacher education materials. Six of these institutions committed to using the pilot materials in their teacher education programmes in 2007. Methodologically, the research is a case study of cases (Adler & Reed, 2002), in which the varying uses of the materials in these six institutional sites constituted the individual cases. At each site data were gathered from session observations, questionnaires and interviews. Artefacts, such as examples of customised materials, were also collected. Cross case analysis revealed that institutions used the ACEMaths materials in both similar and different ways and in a range of programmes. Findings from this analysis and their implications for both initial inter-institutional designing and subsequent intra-institutional re-designing and re-use of OER are discussed.

A presente dissertação é relativa a uma investigação sobre as potencialidades e limitações do trabalho de um grupo colaborativo durante a formação inicial de professores que ensinam frações. Participaram da pesquisa alunos de um curso de Pedagogia. O objetivo principal da pesquisa foi identificar as concepções de frações que os estudantes apresentam e analisar de que modo a participação nas atividades de um grupo colaborativo podem contribuir para o processo de ressignificação de tais concepções. Para tanto, constituiu-se um grupo de oito alunas de um curso de Pedagogia, que interagiram durante um total de oito encontros, nos quais foram produzidos os dados para a análise. Como referencial teórico nos aproximamos da teoria sócio-histórica de Vygostky, da educação matemática crítica de Skovsmose e dos estudos sobre grupos colaborativos e das comunidades de prática, dentre outros que tomam por objeto a formação de professores que ensinam matemática, em especial nos cursos de Pedagogia. A abordagem metodológica adotada foi a qualitativa com a utilização de diferentes tipos de registros, permitindo a triangulação dos dados. Identificamos alguns limitadores durante o percurso: o período curto de realização do trabalho, a postura dos participantes internalizada e apropriada através do ambiente acadêmico que reproduz crenças e discursos sem uma adequada construção conceitual e, principalmente, significativas dificuldades com relação ao conteúdo matemático de frações. Em contrapartida, algumas características ou dimensões de um grupo colaborativo foram evidenciadas. Os participantes demonstraram diferentes identidades de participação, compartilharam um objetivo comum, um empreendimento mútuo e as tarefas foram compartilhadas. A pesquisadora, como sendo também uma integrante do grupo, foi provocada a desenvolver as diferentes dimensões de sua participação. Nesse sentido, a pesquisa mostrou ser viável o trabalho com grupos colaborativos na formação inicial considerando o contexto, particularidades dos participantes da pesquisa e as atividades desenvolvidas. / This thesis reports a research about the potentialities and restrictions of collaborative group work during initial training of teachers who teach fractions. Teaching academics took part in this research. The main objective was to identify the notion of fractions held by the students and to analyze the way in which participation in the activities of a collaborative group may contribute to the process of re-establishing the meaning in those conceptions. In order to do so, a total of eight students of the teaching course interacted in eight meetings through which data was produced for the analysis. As a theoretical basis we used Vykotsky’s Socio-historical Approach, Critical Mathematics Education by Skovsmose and studies about collaborative work, communities of practice, among others whose object is vocational training of Math teachers, especially in teaching courses. The methodological approach chosen was qualitative and interpretative with the use of different types of register, allowing triangulation of data. Some limitations were identified in the process: the short duration of the project, participants’ attitudes internalized and borrowed from the academic environment, which reproduces beliefs and discourses without an appropriate conceptual construction, and, mainly, important difficulties related to the mathematical subject: fractions. On the other hand, some characteristics or dimensions of a collaborative group were evidenced. The participants demonstrated different identities of participation, shared a common objective, a mutual undertaking and the tasks were shared. The researcher, as part of the group, was provoked to develop different dimensions of participation. The group knew how to determine priorities, drawing its paths and building its history of participation. This way, the research showed that working with collaborative groups in teachers’ education is practicable, taking into account the context and particularities of the participants and the activities developed.

For many preservice elementary and secondary teachers, the first time they encounter the notion that mathematics can be taught in ways other than what they experienced is in their teacher preparation program. Therefore, the potential impact of the mathematics teacher educator on the understanding and development of preservice teachers is immense, especially as that impact is considered in connection to the various reform efforts related to mathematics education that have spread across the country for the past three decades. Given the scarcity of systematic research focused on mathematics teacher educators, the author sought to understand defining characteristics of that role. He looked specifically for beliefs that mathematics teacher educators have in common as well as shared ways of enacting their craft by interviewing 16 university professors from around the United States who support the learning and development of preservice and inservice mathematics teachers. The beliefs that emerged from this study related to mathematics teaching, the learning of mathematics teaching, and the teaching of mathematics teaching. Potential communities of practice were also identified, through which the enactment of mathematics teacher educators' craft could be better understood. The specific beliefs and ways of interacting are discussed in terms of how they can support development and reflection among current and prospective mathematics teacher educators, as well as how they can support continued systematic research of mathematics teacher education.

This thesis concerns teaching in mathematics teacher education and is based on the implementation of a learning study at teacher training. The overall purpose was to investigate in what way teacher training could facilitate and improve student teachers’ Mathematical Knowledge for Teaching (MKT). In the learning study design, MKT was conceptualized as an object of learning with a meta-character, which meant that it was applicable to and transferable between different content areas of mathematics. This made it possible to vary the mathematical content between lessons but to keep the object of learning constant. Four critical features of the object of learning were found, giving insight in some of the problems related to teacher education. Student teachers had to be able to formulate proper aims for a lesson and to give detailed descriptions of elements of MKT for coherence in their MKT to occur. A focus on student teachers’ role as mathematics teachers had to be established and finally, sufficient mathematical knowledge was found to be a prerequisite for their MKT to develop. The study shows that enactment of these critical features improved the teaching by the teacher educators, which in its turn improved the student teachers’ learning with regard to MKT. The study also indicates that the prescribed design is worth considering for future collaborative efforts of improving teaching where other objects of learning with a similar meta-character are involved.

This thesis is about the process of becoming, or not becoming, a primary school mathematics teacher. The aim is to understand and describe the professional identity development of novice primary school mathematics teachers from the perspective of the novice teachers themselves. The study is a case study with an ethnographic direction where seven novice teachers have been followed from their graduation and two years onwards. The ethnographic direction has been used to make visible the whole process of identity development, both the individual and the social part. The empirical material in the study consists of self-recordings made by the respondents, observations and interviews. The empirical material is analysed in two different but co-operating ways. First a conceptual framework was developed and used as a lens. Second, methods inspired by grounded theory are used. The purpose of using them both is to retain the perspective of the respondents as far as possible. At the time of graduation the respondents are members in a community of reform mathematics teaching and they want to reform mathematics teaching in schools. In their visions they strive away from their own experiences of mathematics in school and practice periods. Four cases are presented closely in the thesis as they show four various routes into, and out of, the teaching profession. These four cases make visible that the respondents’ patterns of participation regarding teaching mathematics changes when they become members in new communities of practice with mathematics teaching as part of the shared repertoire. But, the four cases also make visible that the existence of such communities of practice seems to be rare and that the respondents’ different working conditions limit their possibilities of becoming members in those that exist. During the time span of this study, the respondents hardly receive any feedback for their performance as mathematics teachers. Even if they teach mathematics they don´t teach it as they would like to and they don´t think of themselves as mathematics teachers. Two years after graduation none of the respondents has developed a professional identity as primary school mathematics teacher. A primary school teacher in Sweden is a teacher of many subjects but they are the first teachers to teach our school children mathematics. For the respondents to develop a sense of themselves as a kind of primary school mathematics teacher, mathematics teaching has to become part of their teacher identities. For this to become possible, mathematics must become a part of their image of a primary school teacher as an image of a primary school mathematics teacher. Furthermore memberships in communities of practice with mathematics in the shared repertoire must be accessible, both during teacher education and after graduation. Then professional identity development as a primary school teacher would include becoming and being a teacher of mathematics.

It is no unknown fact that South African learners underachieve in mathematics. Due to the fact that the quality of mathematics teaching is one possible factor that has an influence on learners' mathematics achievement, there are valid reasons questioning the conceptual mathematical knowledge of mathematics teachers. In order to facilitate conceptual understanding teachers themselves must possess profound mathematical knowledge. Apart from the influence of a teacher's knowledge for teaching, teachers' attitudes and beliefs play a meaningful role in the way they teach mathematics. The deficient nature of prospective and practising teachers' knowledge of school mathematics, as well as their attitudes and beliefs towards mathematics has serious implications for the training of prospective mathematics teachers. Literature reveals that a technologically enhanced environment can improve the conceptual learning of prospective mathematics teachers. The purpose of this study was to determine the influence of a dynamic technologically enhanced environment on the attitudes and beliefs, as well as the conceptualisation of prospective mathematics teachers regarding the function concept. In this study, prospective teachers were exposed to Geometer's Sketchpad®, a dynamic software programme providing a powerful learning context that promotes the investigation of algebraic relationships. In order to answer the research question, an explanatory mixed method design was used. In the quantitative part of the study, the Study Orientation Questionnaire in Mathematics and a function test were administered to prospective teachers. In the latter, conceptualisation of the function concept was measured in terms of four competence components, namely interpretation, modelling, translation and reification. In the qualitative part of the investigation semi-structured and task-based interviews were held with a group of prospective teachers. Analysis of the results revealed that the dynamic technologically enhanced environment did not contribute to an improvement of the prospective teachers' attitudes and beliefs. In fact, these decreased visibly. Regarding their conceptualisation, only the reification component showed a practically significant improvement. It therefore appears as if prospective teachers are not being prepared to benefit from the dynamic technologically enhanced environment. A model is proposed for the effective use of such a learning environment. The model involves that diagnostic assessment be made of prospective teachers' basic knowledge of the function concept, their study habits, their attitudes and beliefs with respect to mathematics, as well as their mathematics anxiety. The second component comprises recommendations made to prospective teachers as a result of the diagnostic assessment, as well as continuous support being offered as an integrated part of the mathematics module. Support is offered with respect to cognitive and meta-cognitive skills, affective factors and the creation of an advantageous technologically enhanced learning environment. Despite the restricted value of generalisation of the findings from this study, I still recommend the expansion, refining and implementation of the model so that prospective mathematics teachers can effectively benefit from a technologically enhanced environment. Key words for indexing: mathematics education, mathematics teacher education, teacher knowledge, prospective mathematics teachers, function concept, conceptual learning, tertiary education. / Thesis (Ph.D. (Education))--North-West University, Potchefstroom Campus, 2009.