Vårt problem i detta arbete är att det i läroplanen för förskolan saknas en tydlig definition av vad begreppet kvalitet innebär. Syftet med vår studie är att undersöka hur pedagoger ser på kvalitet samt hur de arbetar kring kvalitet för att uppnå de strävandemål som finns i läroplanen för förskolan. För att få en förståelse för detta har vi valt att utgå från två frågor. Hur definierar pedagogerna ordet kvalitet i förskolorna? Hur arbetas det med kvalitet i förskolorna? Vi har valt att intervjua pedagoger för att få en så verklig skildring av verksamheten som möjligt.Det vi har kommit fram till i vår studie är att synen på kvalitet är väldigt personlig och därmed bedöms kvalitet på många olika sätt. Det har även framkommit att en personlig syn på kvalitet inte behöver vara någonting negativt eftersom alla pedagoger arbetar mot samma strävandemål i läroplanen. Pedagogerna anser att genom att uppnå strävandemålen så uppnår de också önskad kvalitetsnivå på förskolan. I slutändan står ordet kvalitet för en personlig syn som alltid ska gynna barngruppen. Slutsatsen är att kvalitet handlar om att planera sin verksamhet för att uppnå läroplanens strävandemål och att barnen med fördel ska vara inkluderade i dessa planeringsprocesser.

Submitted by Nathalya Silva (nathyjf033@gmail.com) on 2017-05-15T19:12:33Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese_AprendizagemModelagemMatematica.pdf: 3756683 bytes, checksum: 724f4033f449d33cbbe21ff6c959486b (MD5) / Approved for entry into archive by Edisangela Bastos (edisangela@ufpa.br) on 2017-05-29T12:00:58Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese_AprendizagemModelagemMatematica.pdf: 3756683 bytes, checksum: 724f4033f449d33cbbe21ff6c959486b (MD5) / Made available in DSpace on 2017-05-29T12:00:58Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese_AprendizagemModelagemMatematica.pdf: 3756683 bytes, checksum: 724f4033f449d33cbbe21ff6c959486b (MD5) Previous issue date: 2015-10-23 / A presente tese, intitulada “Aprendizagem em Modelagem Matemática pelas interações dos elementos de um sistema de atividade na perspectiva da Teoria da Atividade de Engeström” teve como objetivo compreender repercussões na aprendizagem pelas interações evidenciadas no ambiente de Modelagem Matemática, na perspectiva da Teoria da Atividade de Engeström. Para alcançar este objetivo desenvolvi, no âmbito do Laboratório Experimental de Modelagem Matemática (LEMM), do Campus Universitário de Castanhal (UFPA), atividades de Modelagem com grupos de alunos do curso de Matemática em formação, graduados ou pós-graduandos para obtenção dos dados via observação e entrevista. A partir dos princípios da Teoria da Atividade de Engeström, a Modelagem Matemática desenvolvida pelos alunos foi compreendida como um sistema de atividade que envolve os elementos (sujeito, objeto e comunidade, artefatos mediadores, regras e divisão do trabalho) que se relacionam para atingir um resultado, ou seja, são mediados por interações para alcançar um resultado. A pesquisa mostrou que o trabalho coletivo, a historicidade e a multivocalidade dos sujeitos atuando na superação de contradições para alcançar transformações expansivas repercutem em aprendizagem em Modelagem Matemática, configurada como um sistema de atividade, pelas interações dos elementos do próprio sistema. / This thesis entitled "Learning Mathematical Modelling the interactions of the elements of an activity system from the perspective of the Engeström activity theory" aimed at understanding effects on learning by interactions evidenced in Mathematical Modeling environment, from the perspective of Engeström activity theory. To accomplish this, I developed in the Mathematical Modeling Experimental Laboratory (LEMM), at the University Campus of Castanhal (UFPA), modeling activities with groups of Math Course students in graduating, graduate or post graduate students to obtain data through observation and interview. Based on the principles of the Engeström activity theory, Mathematical Modeling developed by the students were understood as an activity system that involves the elements (subject, object and community artifacts mediators, rules and division of labor) that relate to a result, that are mediated by interactions for achieving a result. Research has shown that the collective work, the historicity and multivocality of subjects acting in overcoming contradictions to reach expansive transformations have repercussions on learning in Mathematical Modeling, configured as an activity system, the interactions of the elements of the system itself.

We live in a high tech era of electronic media, which is changing our lives (Giddens, 1999). Apps are examples of technologies that affect our lives. An interesting question in this context is what apps will have for significance; on one hand for the development of technology, and on other hand for humans’ relation to technology. Since the development and change process are central issues in the science of education I will explore the development of applications. The purpose of this paper is to seek knowledge about applications (apps) development from a design and user perspective. This dissertation discusses activity theory as an academic framework for understanding of apps development from two different types of operating systems or practices, to be precise design practice and user practice. To clarify my point, I have defined the following questions: why user apps are designed, how user apps are designed, and what contradictions occur between the design and the use of apps? My research is based on a qualitative approach with an abductive approach. I used multiple case studies as research approach based on three data collection techniques: interviews, observiews (interviews and observations) and observations of social media and an archived document of wireframes about apps. The result shows that apps designed and published either for their function or for promotional purposes. The design process is fast and dynamic process where applications are published before they are ready and constantly updated later. The use of apps characterized by either an active or a passive use operations. In the passive activity apps are tested through trial and error, and when they do not meet the user's expectations they are thrown away. This activity contributes in relation to previous research on technology and social change to the consumer’s throwaway culture. While in the active using, activities becomes part of the development activities where development aspects are communicated through social media – interact active users and designers to develop the app, which is both an artifact and an object of their own development. Activity theory thus contributes to theories of design by considering design not only as production but also as a fully operational system itself with the production, consumption, exchange and distribution. / Vi lever i en högmodern tid som präglas av elektroniska medier som förändrar vårt liv enligt Giddens (1999). Appar är exempel på teknik som påverkar vårt liv. En intressant fråga i detta sammanhang är vad appar får för betydelse för – å ena sidan utveckling av teknik å andra sidan människans förhållande till teknik. Eftersom utveckling och förändringsprocesser är centrala i pedagogik vill jag studera utveckling av appar. Syftet med denna uppsats är att söka kunskap om apputveckling ur ett design- och användarperspektiv. I uppsatsen används verksamhetsteori som teoretiskt ramverk för att förstå apputveckling utifrån två olika typer av verksamhetssystem eller praktiker, nämligen designpraktiken och användarpraktiken. För att närmare precisera mitt syfte har jag definierat följande frågeställningar: varför designas respektive används appar, hur designas respektive används appar, och vilka motsättningar uppstår/finns mellan design och användning av appar? Min uppsats bygger på ett kvalitativt tillvägagångssätt med en abduktiv ansats som innebär en pendling mellan teori och empiri. Jag använder flerfallsstudien som forskningsansats, med tre datasamlingstekniker: intervjuer, observjuer och observationer av sociala medier och ett arkiverat dokument med skisser över appar. Resultatet visar att appar designas och publiceras antingen för sin funktion eller i marknadsföringssyfte. Designprocessen är en snabb, dynamisk process där appar publiceras innan de är klara och därefter ständigt uppdateras. Användning av appar kännetecknas av antingen en aktiv eller en passiv användning. I den passiva användningsverksamheten prövas appar genom trial-and-error och när de inte motsvarar användarens förväntningar kastas de bort. Denna verksamhet bidrar i relation till tidigare forskning om teknik och social förändring till konsumtionssamhällets slit och slängkultur. Den aktiva användningsverksamheten blir istället en del av utvecklings­verksamheten där utvecklingsaspekter kommuniceras via sociala medier där aktiva användare och designer samverkar i att utveckla appen som blir både en artefakt och ett objekt för sin egen utveckling. Verksamhetsteori bidrar således till teorier om design genom att betrakta design inte bara som produktion utan som ett helt verksamhetssystem i sig med produktion, konsumtion, utbyte och fördelning.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2017-10-10T12:23:17Z No. of bitstreams: 2 Dissertação - Adriane Sardinha Macedo - 2017.pdf: 3588869 bytes, checksum: 2257f2940deb22a656c769ea8d21b807 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-10-10T12:31:06Z (GMT) No. of bitstreams: 2 Dissertação - Adriane Sardinha Macedo - 2017.pdf: 3588869 bytes, checksum: 2257f2940deb22a656c769ea8d21b807 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-10-10T12:31:06Z (GMT). No. of bitstreams: 2 Dissertação - Adriane Sardinha Macedo - 2017.pdf: 3588869 bytes, checksum: 2257f2940deb22a656c769ea8d21b807 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-09-12 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this research we are looking for indications of the meanings attributed by the graduates of PETMAT / UFG, professor of mathematics, to the pedagogical activity. Vigotski, Leontiev, Moura, Cedro, Engeström and Asbahr were fundamental for the apprehension of the object searched. We focus on historical-cultural theory as a basis for the apprehension of the phenomenon investigated and, for this, the theory of activity was present throughout the work. Our research was based on a bibliographical research, a documentary analysis in which we evaluated the documents that underpin the organization of the Tutorial Education Program (PET) and, from there, we made a documentary comprehension movement of the Tutorial Education Program of the Education Teachers in Mathematics from the Federal University of Goiás (PETMAT / UFG). We analyze all the tasks and projects developed in the program over the years 2007 to 2014 and, in addition to this, we interviewed some alumni who were linked to the group during those years. The teacher-tutor of the group was also part of our work and is among the subjects participating in the research. The activity, the social meaning and the personal sense are presented in the work, based on the Leontievian proposal. For the analysis of the data, we proposed two categories: [1] the personal sense of the future teacher about the Pedagogical Activity of the mathematics teacher; and [2] the PETMAT / UFG and its contradictions as a source of change and development. In the first category we conclude that individuals, starting from the indigence of joining a university, from the influences of their teachers, and from the affinity they believe they had with the exact areas, hoped to graduate. There are those who were looking for the teaching or marketing of the pre-college preparatory teacher; and there were others who wanted a training in Mathematics that was not destined to be performed in the classroom. In the second category, we analyzed some projects carried out in PETMAT / UFG and supported them in Engeström (1999 and 2009) and, from there, we constructed some Activity Systems. By introducing such systems we intend to propose that, instead of the socially mediated individual being taken as the basic unit of analysis, the historically localized system of activity has become a fundamental unit for looking at egresses in the collective as well. The object of activity as a horizon of possibility is, in the Engeströmapproach, theorized as a collective project that is stabilized by shared tools, signals, and procedures. The results allowed us to perceive the necessity of a differentiated proposal for the formation of the mathematics teacher, in which the teaching learning organization allows the collective work as organization of a non-alienated work, making possible the construction of a knowledge production space. / Nesta pesquisa estamos em busca de indícios dos sentidos atribuídos, pelos egressos doPETMAT/UFG, professor de matemática, à atividade pedagógica. Vigotski, Leontiev, Moura, Cedro, Engeström e Asbahr foram fundamentais para a apreensão do objeto pesquisado. Pautamo-nos na teoria histórico-cultural como base para a apreensão do fenômeno investigado e, para tal, a teoria da atividade se fez presente ao longo do trabalho. Nossa busca perpassou por uma investigação bibliográfica, uma análise documental na qual avaliamos os documentos que fundamentam a organização do Programa de Educação Tutorial (PET) e, partindo daí, fizemos um movimento de compreensão, também documental, do Programa de Educação Tutorial da Licenciatura em Matemática da Universidade Federal de Goiás (PETMAT/UFG). Analisamos todas as tarefas e projetos desenvolvidos no programa ao longo dos anos de 2007 a 2014 e, agregado a isso, entrevistamos alguns egressos que estiveram vinculados ao grupo durante esses anos. O professor-tutor do grupo também fez parte do nosso trabalho e está entre os sujeitos participantes da pesquisa. A atividade, o significado social e o sentido pessoal apresentam-se no trabalho, firmados na proposta leontieviana. Para a análise dos dados, propusemos duas categorias: [1] o sentido pessoal do futuro professor acerca da Atividade Pedagógica do professor de matemática; e [2] o PETMAT/UFG e suas contradições como fonte de mudança e desenvolvimento. Na primeira categoria concluímos que os indivíduos, partindo da indigência de ingressar em uma universidade, das influências de seus professores e da afinidade que acredita ter com as áreas exatas, esperava graduar-se. Há aqueles que estavam em busca da docência ou do marketing do professor de cursinho; e existiam outros que almejam uma formação em Matemática que não fosse destinada à atuação em sala de aula. Já na segunda categoria, analisamos alguns projetos realizados no PETMAT/UFG e respaldando-nos em Engeström (1999 e 2009)e, partindo daí, construímos alguns Sistemas de Atividades. Apresentando tais sistemas tivemos a intenção de propor que, ao invés de o indivíduo socialmente mediado ser tomado como a unidade básica de análise, o sistema de atividade historicamente localizado tornou-se unidade fundamental para olharmos os egressos também no coletivo. O objeto da atividade como horizonte de possibilidade é, na abordagem de Engeström, teorizado como um projeto coletivo que é estabilizado por ferramentas, sinais e procedimentos compartilhados. Os resultados permitiram-nos perceber a necessidade de uma proposta diferenciada para a formação do professor de matemática, na qual a organização da aprendizagem da docência permita o trabalho coletivo como organização de um trabalho não alienado, possibilitando a construção de um espaço de produção do conhecimento.

Notre thèse étudie les conditions favorables à l’autonomisation scolaire des élèves. L’étude empirique est menée en grande section de maternelle. Dans la plupart des situations de formation, les temps « d'autonomie » sont structurellement inévitables puisque le formateur ne peut être présent pour tous à chaque instant. Nous nous intéressons aux temps de classe au cours desquels l’enseignant n’intervient pas directement, soit parce qu’il n’est pas disponible, soit parce qu’il se retire volontairement de la situation. Nous les appelons temps faibles en raison de cette faible présence de l’enseignant : l’élève doit agir en fonction de ses propres forces, sans l’intervention directe du maître pour réguler l’apprentissage et les comportements. Il appert que les élèves n’y sont pas naturellement autonomes : laissées au hasard de capacités acquises hors l’école, les activités dites « en autonomie » contribuent à creuser les écarts entre les élèves face aux savoirs qui leurs sont proposés. L’autonomie ferait partie de ces comportements implicitement attendus et « davantage supposés ou requis par les enseignants que construits dans, avec et par l’école ». Comment penser le processus d’autonomisation scolaire et comment l’opérationnaliser en contexte ordinaire de classe ? Nous cherchons les outils, les leviers, les interactions et les dispositifs qui permettraient aux élèves, – à tous les élèves – de profiter des temps faibles au bénéfice de leurs apprentissages. Les données sont recueillies dans 14 classes sur 117 demi-journées d’observation directe, puis traitées à l’aide de l’analyse par les catégories conceptualisantes (Paillé, 2012). Dans la perspective (socio)constructiviste de l’apprentissage, pour construire un savoir nouveau, l’élève doit rencontrer un obstacle dans la réalisation de la tâche, l’apprentissage résultant du dépassement de celui-ci. Nous relevons des comportements différenciés face à l’obstacle dans les ateliers en autonomie : certains élèves entrent dans des conduites d’évitement, refusant d’affronter cet obstacle, s’en trouvant détournés en amont ou bien le contournant. D’autres, au contraire, entrent dans des conduites de ressources pour le dépasser et construire de nouvelles connaissances. En cours d’étude apparaissent des dynamiques remarquables : certains élèves, d’habitude « évitants », rejoignent ou se maintiennent parfois dans des conduites de ressources. L’étude de ces « exceptions notables » fait émerger les conditions favorables ayant permis leur dynamique particulière en termes d’outils, d’activités, d’interactions et de dispositifs. Ce qui aura pu fonctionner au bénéfice des exceptions notables pourrait être exploité comme levier pédagogique durable au bénéfice de tous. Ces conditions deviennent alors supposées favorables et sont réinvesties dans des dispositifs expérimentaux afin d’observer si elles produisent les effets attendus, dans quelle mesure et selon quelles limites (analyse des dispositifs expérimentaux par une adaptation du modèle systémique d’Engeström, 1987). Il apparait clairement que le processus d’autonomisation, en contexte scolaire de classe hétérogène et nombreuse, s’observe et se construit de façon privilégiée dans les temps faibles de la structuration pédagogique et leur articulation avec les temps forts, notamment les retours collectifs sur ateliers. Une pédagogie des temps faibles supposerait que soit accordé à ceux-ci un véritable statut pédagogique, en tant qu’étape et instrument essentiels au processus d’autonomisation scolaire. Une telle pédagogie supposerait également d’organiser avec soin les interventions de l’enseignant en mode opératoire indirect, au travers d’un dispositif de classe qui le relaie et dont les différentes dispositions (outils, règles, activités, interactions) peuvent « être appropriées » par l’élève comme instruments psychologiques pour agir sur lui-même, en première personne. ..... / This dissertation studies favorable conditions to empowerment of pupils. The empirical study was carried out in the final year of kindergarten. In most learning/teaching situations, "autonomy moments" are structurally inevitable since the teacher cannot be systematically available to everyone all the time. Interest is focused on moments during which the teacher does not directly intervene, either because he/she is not available or because he/she voluntarily withdraws from the learning situation. We call these moments "low times" because of the teacher's low presence: during these specific moments, each student responds according to his own strengths without the teacher's direct intervention to regulate both learning and behavior. It appears that students are not naturally autonomous: when left unattended, the so-called "autonomous" learning activities contribute to widening the knowledge gap between students in learning situations. Autonomy would be part of this implicitly expected behavior and is "all the more expected and required from teachers rather than being constructed in, with and by school". How can student empowerment be perceived and operationalized in an ordinary class context? Our goal is to identify tools, levers, interactions and devices which enable students to benefit from "low times" for their own learning. The data are collected in 14 classes in 117 half-days of direct observation. Socio-constructivist approach to learning suggests that in order to construct new knowledge, the student must encounter an obstacle in the course of accomplishing his task. Learning results from overcoming this obstacle. We highlight differentiated behaviors of students when facing obstacles in autonomy classroom workshops: some resort to avoidance strategies and refuse to deal with this obstacle by bypassing or circumventing it. Conversely, others draw on (their own) resources in order to overcome it and construct new knowledge. During the study period, remarkable dynamics appear: some students, with usually an "avoidant" attitude, join or maintain a "drawing on resource conduct". The study of the "notable exceptions" leads to the emergence of the favorable conditions which fostered this particular dynamic in terms of tools, activities, interactions and devices. What would have worked to the benefit of the notable exceptions could be further used as a sustainable and pedagogical lever to the benefit of all students. These conditions become then supposedly favorable and are reinvested in experimental devices in order to see if they produce the expected effects, to which extent and within what limits? Il clearly appears that the empowerment process, in classroom context of a large and heterogeneous class, is developed in a special way in "low times" of pedagogical structuration and their articulation with "strong times", notably collective feedbacks on workshops. A pedagogy of "low times" entails providing the teacher with substantial pedagogical status, which would be a crucial step as well as an instrument in the school empowerment process. Such pedagogy would also entail carefully organizing teacher's intervention in an indirect mode, through a class device which would relay it through its various dispositions (tools, rules, activities, interactions). The student would then internalize these dispositions as psychological instruments in referring to oneself in the first person. This pedagogy would finally entail a redefinition of teacher's role: his/her apparent "absence" from the situation which would paradoxically become, a teaching-learning tool to the benefit of school empowerment.

Professional development (PD) of teachers is part of the Department of Basic Education‘s (DBE) initiative to encourage school communities to use of information and communication technology (ICT) to improve the quality of Mathematics teaching and learning. The South African Council of Educators stipulates that PD programmes should align with system-wide needs, strengthen learning area content and outcomes, and promote system transformation. Imbedded in this system-wide criterion is The White Paper on e-Education to employ a fully ICT integrated system at all levels of education: management, teaching and learning, and administration by 2013. Mathematics teachers require PD that develops their technological pedagogical and content knowledge (TPACK) and their social professional identity (SPI). The PD of Mathematics teachers for ICT integration can assist the DBE to achieve the aims of The White Paper on e-Education and bridge the technology gap between South Africa and international education systems. Open distance learning (ODL) could be a viable method to deliver PD to Mathematics teachers to address their zone of proximal development, develop their TPACK, and establish and maintain their SPI. This study made use of a fully mixed sequential equal status multi-mode research design and methodologies to develop guidelines for the PD of Mathematics teachers in the pedagogical use of ICT in ODL. The qualitative phase (Phase I) was rooted in the interpretivist paradigm. Through an adjustable exploration of a systematic literature review, the researcher identified 23 core documents, analysed them with Atlas.ti™, and conceptualised four themes according to Engeström‘s third generation activity theory (AT). Phase II (radical exploration phase) of the research design was rooted in the radical structuralist paradigm. In the context of transformation, it developed, validated, and standardised a research instrument for the measurement of Mathematics teachers‘ PD requirements. The instrument was distributed to 300 senior phase (grades 7-9) Mathematics teachers in eight education management district centres of the WCED. The analyses of the quantitative data conceptualised a fifth activity system. The five activity systems from the adjustable and radical exploration phases were symbiotic, and co-dependent. Expansive learning was used for boundary crossing and network building during six phases of this study. The findings from the six phases of the expansive learning cycle indicated that PD of Mathematics teachers in ODL for Phase III implementation of the e-Education policy should be a joint initiative. Fundamentally ICT integration and implementation should start with Department of Basic Education (DBE) initiatives. The DBE and Provincial Departments of Education (PDEs) should conduct a needs analysis of ICT implementation, evaluate previous ICT PD programmes, plan ICT PD strategies aligned with the ICT development plan, as well as with the requirements of the Mathematics teachers. The DBE and PDE should invest in the provision of ICT equipment, afford human capital, reinstate the laptop initiative for teachers, and supply schools with networked-computer facilities to explore online platforms for PD. Mathematics teachers should assess their professional knowledge to construct new philosophies, create a subject network group, and interact as participants and members within their social environments. The standardised instrument could be used to determine and compare the PD of Mathematics teachers in other provinces and contexts. / PhD (Training and development), North-West University, Potchefstroom Campus, 2014

Professional development (PD) of teachers is part of the Department of Basic Education‘s (DBE) initiative to encourage school communities to use of information and communication technology (ICT) to improve the quality of Mathematics teaching and learning. The South African Council of Educators stipulates that PD programmes should align with system-wide needs, strengthen learning area content and outcomes, and promote system transformation. Imbedded in this system-wide criterion is The White Paper on e-Education to employ a fully ICT integrated system at all levels of education: management, teaching and learning, and administration by 2013. Mathematics teachers require PD that develops their technological pedagogical and content knowledge (TPACK) and their social professional identity (SPI). The PD of Mathematics teachers for ICT integration can assist the DBE to achieve the aims of The White Paper on e-Education and bridge the technology gap between South Africa and international education systems. Open distance learning (ODL) could be a viable method to deliver PD to Mathematics teachers to address their zone of proximal development, develop their TPACK, and establish and maintain their SPI. This study made use of a fully mixed sequential equal status multi-mode research design and methodologies to develop guidelines for the PD of Mathematics teachers in the pedagogical use of ICT in ODL. The qualitative phase (Phase I) was rooted in the interpretivist paradigm. Through an adjustable exploration of a systematic literature review, the researcher identified 23 core documents, analysed them with Atlas.ti™, and conceptualised four themes according to Engeström‘s third generation activity theory (AT). Phase II (radical exploration phase) of the research design was rooted in the radical structuralist paradigm. In the context of transformation, it developed, validated, and standardised a research instrument for the measurement of Mathematics teachers‘ PD requirements. The instrument was distributed to 300 senior phase (grades 7-9) Mathematics teachers in eight education management district centres of the WCED. The analyses of the quantitative data conceptualised a fifth activity system. The five activity systems from the adjustable and radical exploration phases were symbiotic, and co-dependent. Expansive learning was used for boundary crossing and network building during six phases of this study. The findings from the six phases of the expansive learning cycle indicated that PD of Mathematics teachers in ODL for Phase III implementation of the e-Education policy should be a joint initiative. Fundamentally ICT integration and implementation should start with Department of Basic Education (DBE) initiatives. The DBE and Provincial Departments of Education (PDEs) should conduct a needs analysis of ICT implementation, evaluate previous ICT PD programmes, plan ICT PD strategies aligned with the ICT development plan, as well as with the requirements of the Mathematics teachers. The DBE and PDE should invest in the provision of ICT equipment, afford human capital, reinstate the laptop initiative for teachers, and supply schools with networked-computer facilities to explore online platforms for PD. Mathematics teachers should assess their professional knowledge to construct new philosophies, create a subject network group, and interact as participants and members within their social environments. The standardised instrument could be used to determine and compare the PD of Mathematics teachers in other provinces and contexts. / PhD (Training and development), North-West University, Potchefstroom Campus, 2014