Metaphor provides a potentially powerful rhetorical device to help me to tell informed and persuasive stories about mathematics education. In this ethnographic study I consider key episodes that serve to exemplify the complex experience of Initial Teacher Education (ITE) students of secondary mathematics education. I use a narrative analysis to shine a spotlight on the experiences of six beginning teachers so that the metaphors in their stories expose the impact that separately situated sites of teacher education have upon their beliefs and behaviour as teachers. Tensions between school and university contributors to teacher education have been well documented over many decades, but recent policy changes in the nature of post-graduate ITE in England bring these issues to the fore. In this study, I consider the influences of school-based and university-based teacher educators upon the beliefs of student secondary mathematics teachers and interpret the students’ perceptions of these influences on their actions as novice teachers. My analysis is framed by a model of experience and education articulated by Dewey as well as a framework of representations of knowledge in a culture of education articulated by theorists concerned with the relevance of constructivism and situated cognition as theories of learning. In this study, disturbances and discontinuities relating to the location and culture of ITE, together with the development of ITE students’ professional knowledge are uncovered, warranting further research.

The Swedish government has authorised the teaching of mathematics in English to Swedish speaking students. Much of that teaching is performed by foreign trained native English speaking teachers lacking training in second language learners. This systematic review summarises international studies from the last ten years that deal with the teaching of mathematics to second language learners. The review shows that second language students working in a bilingual environment achieve higher rates of content and language knowledge than learners in a monolingual environment. This study also summarises some of the teacher practices that are effective for teaching mathematics in English to second language learners.

This thesis is primarily concerned with the effects of education for future teachers in the context of the Swedish teacher training (Government Bill 1999/2000:135 2000). It belongs to a theoretical tradition in which the education system is viewed as a key factor in cultural production and reproduction in educational practices through symbolic control (Apple 2009; Ball 2006; Bernstein 2000, 2003). Symbolic control defines how forms of social interaction affect what is possible to think, say and do in different situations. The thesis is focused specifically on student mathematics teachers learning to become teachers of mathematics. It has a particular focus on the materials used in this, the meanings given to these materials and the identities produced through the possible embodiment of these meanings. The use of different educational technologies, including in particular ICT, has been of special interest. It aims therefore to understand both how mathematical discourses are produced and reproduced in teacher education and how this colours student teachers’ views on mathematics and their professional identity (Bernstein 2000, 2003; Valero 2007). The main outcomes of my thesis are that through the way that mathematics is taught and learned, mathematics teacher education in practice reproduces traditional ways of teaching and learning. This in that mathematics instruction is built around a ritualized practice based on the ability to solve exercises related to an examined-textbook-based content. ICT use in this context is not transformative. Rather it seems as if teaching and learning with digital technology operate as a relay in the reproduction of traditional forms of education practice. This is contrary to the intentions to renew and revitalise mathematics education and the thesis thus suggests that there is a need to scrutinize the way new technology is formulated in official discourses and appropriated in educational work. Two other things are also noteworthy in the thesis findings. The first is an increased emphasis on formal subject content through recent policy developments. This re-emphasis reaffirms the value of authoritative subject studies content as the central and most important component in the professional knowledge base. On the basis of the finding from the thesis the logic of the reform may be questioned. Also important is the ICT discourse that is constituted in wider society by selected agents. In this discourse digital technology often in many ways defines (post)modern society and the position it and education have as a driving force toward economic competitiveness. An alternative, more reflexive and critical approach where questions about technology uses in education are emphasized is suggested as necessary. / Disputationen äger rum fredagen den 4 maj 2012, kl. 13.15, Sal Gamma, Hus Svea, IT Fakulteten, Forskningsgången 4, Lindholmen

Η παρούσα εργασία έχει ως κύριο στόχο να αναδείξει την επιρροή των σχολικών βιβλίων στη διδασκαλία και τη μάθηση των μαθηματικών, μελετώντας ως κύριο θέμα την παρουσίαση της έννοιας του ορίου. Προς το σκοπό αυτό αξιοποιούνται τρία σχολικά βιβλία που διδάσκονται σήμερα (2012 – 2013) στα ημερήσια γενικά λύκεια και στα ημερήσια επαγγελματικά λύκεια (ΕΠΑ.Λ.) της Ελλάδας και ένα ακόμη που διδασκόταν μέχρι τα τέλη της δεκαετίας του 1990, στα γενικά λύκεια της Ελλάδας. Η εργασία χωρίζεται σε τρία κύρια μέρη. Στο Α΄ μέρος παρουσιάζεται ένα πείραμα μικρής κλίμακας, με σκοπό να αναδειχθεί η δύναμη επιρροής των σχολικών βιβλίων στη διαδικασία της μάθησης. Περιλαμβάνεται επίσης και μία σύντομη ιστορική αναφορά στην εξέλιξη των επ’ άπειρον διαδικασιών στα Μαθηματικά. Στο Β΄ μέρος παρουσιάζονται κάποια από τα ερευνητικά θεωρητικά σχήματα μέσω των οποίων μελετάται η κατανόηση μαθηματικών εννοιών, καθώς και η επίδραση του ανθρώπινου παράγοντα (πεποιθήσεις, κοινωνικό περιβάλλον της τάξης, «διδακτικό συμβόλαιο») κατά τη διδασκαλία και την πορεία προς την κατανόηση. Ακόμη αναφέρονται κάποιες ειδικές παρατηρήσεις επί της διδασκαλίας της έννοιας του ορίου. Το Γ΄ μέρος περιλαμβάνει την παρουσίαση της γενικής φιλοσοφίας που διαπνέει τα σχολικά βιβλία εστιάζοντας στην παρουσίαση της έννοιας του ορίου. Το τελευταίο τμήμα αυτού του μέρους περιλαμβάνει επίσης σχολιασμό της παρουσίασης των βιβλίων, αξιοποιώντας το θεωρητικό υπόβαθρο του Β΄ μέρους της εργασίας. / This dissertation’s main purpose is to point out the influence of school books in the teaching, and the learning of mathematics. It focuses on the presentation of the limit concept. For this purpose three school books that are in use today (2012 – 2013) in “general high schools” and in “professional high schools” of Greece are utilized. Also another one that was used until the late 90’s in “general high schools” in Greece. This dissertation is divided in three main parts. In part A΄ a small scale experiment is presented, in order to mark out the influence of school books in the teaching and learning of mathematics. In this part a brief historical reference is also included on the evolution of Calculus. In part B΄ research theoretical frameworks that analyze the conceptual understanding are presented, as well as the influence of social factors (beliefs, social classroom environment, “didactical contract”) in the reality of the mathematical classroom. In addition some specific observations related with the teaching of the limit concept are mentioned. Part C΄ refers to the general philosophy that governs the presentation in school books and the limit concept in particular. The last section presents the books through the lenses of the theoretical background in part B΄ of this dissertation.

Teacher educators continually strive to find ways to improve the preparation of preservice teacher candidates. In the area of mathematics education, methods courses that follow National Council of Teachers of Mathematics (NCTM) standards for professional development have been successful. This study supports the notion that a mathematics methods course can improve mathematics teaching efficacy in the constructs of personal mathematics teaching efficacy (PMTE) and mathematics teaching outcome expectancy (MTOE). Findings also suggest that mathematics teaching efficacy is developmental in its nature with PMTE developing before MTOE. Employing a quasiexperimental nonequivalent comparison groups pre- and posttest design, the present study examined the effects of guided imagery as an added component of a mathematics methods course and found no significant advantageous treatment effects on mathematics teaching efficacy. However, there were no detrimental effects on mathematics content knowledge and pedagogical skills either. Participation in a reform-based mathematics methods course did affect mathematics teaching efficacy for both groups in the study. Mathematics teaching efficacy beliefs were measured by the Mathematics Teaching Efficacy Beliefs Instrument (MTEBI), and data were analyzed by ANCOVA and paired-samples t-tests. Recommendations for further research on the developmental nature of general teacher efficacy and mathematics teaching efficacy are included.

Thesis (M.ED.) --University of Limpopo, 2008 / The Department of Education language policy states that all official languages may be used in the teaching and learning at South African schools. The department of Education has adopted an Additive Multilingualism as an approach to teaching. English is however, still being used as the language of learning and teaching, even to the learners who are not mother-tongue speakers of the language. This study explores the question of whether code-switching aids or impedes teaching and learning in Mathematics. The problem arises when learners encounter concepts in Mathematics which are written in English and need to be explained in English. Learners often struggled to understand these concepts with the results that educators resort to using their home language to try to explain what these concepts mean. To understand the nature of this problem and how it affects teaching and learning, a qualitative research was undertaken. Two secondary schools in the Sekgosese East Circuit were purposefully sampled for this study. The purpose of the study was to explore the role of code-switching in the teaching and learning of concepts in Mathematics and its effects on the acquisition of Mathematics. The findings revealed that the school were code-switching was applied performed better in Mathematics than the school where code-switching was not employed. The study recommended that educators should use the learners’ home language in instances where their knowledge of English impedes them to convey the meaning clearly.

Thesis (M.ED. (Mathematics Education)) -- University of Limpopo, 2012 / This study investigated Mathematics teachers’ beliefs about the nature of Mathematics and their impact on classroom practices. It was conducted in a public semi-urban school in the Capricorn District-Limpopo Province. It was a case study targeting two FET teachers with teaching experiences of 15 years or more. The central research questions addressed in this study are, namely: What are Mathematics teachers’ beliefs about the nature of Mathematics? And, what is the relationship between teachers’ beliefs and their classroom practices? Data were collected through pre-observation interviews, classroom observation and through post observation interviews. Pre-observation interviews were conducted once before the participants were observed. I was a complete observer during my colleagues’ lessons. Interviews and observations data were analysed using categorisation and interpretation of data in terms of common themes and synthesis into an overall portrait of the case. Each case study teacher’s data were analysed individually (that is within-case analysis) first and thereafter cross-case analysis was done in order to compare the two case studies.

The purpose of this research is to explore the aspects of abilities of mathematics communication of grade two students in the elementary school, including spoken understanding and as well as written and figural understanding. This researcher adopted action research, having the investigator implemented two months teaching. After referring to mathematics teaching materials grade two, the researcher designed four units. During the period of research, the teacher utilized a variety ways to collect data, such as; video recording, audio recording, questionnaires, reflective notes, observation records and student activities sheets. Eventually, the teacher made qualitative analyzes and explored methods of improvement on her ways of teaching. The results of this research illustrated seven aspects of spoken language expression of understanding. The students were weak in listening; dare to express their opinions; put forward queries regarding teacher's or schoolmates¡¦ questions; some were unable to raise conceptual related questions; when students made exchanges they needed help from the teacher, students spoke with low or vague voice; and, finally, students replied intermittently or silently. Besides the above seven findings on spoken language, there are four findings of phenomena in written and figural understanding. First, students were able to examine mistakes or others¡¦ mistakes according to the record on blackboard. Moreover, the students even can put forward the queries on others¡¦ problem solving records. Yet, they were capable of understanding others¡¦ mathematics records and explained others¡¦ ideas.

Ο στόχος της συγκεκριμένης έρευνας είναι να μελετηθεί η θέση των Λογιστικών Φύλλων στην ελληνική Δευτεροβάθμια Εκπαίδευση και συγκεκριμένα στο Γυμνάσιο, πάνω σε δύο άξονες. Αρχικά, θέλουμε να μελετήσουμε τη χρήση των Λογιστικών Φύλλων, και συγκεκριμένα του Excel, όσον αφορά τις βασικές λειτουργίες του και τα γνωστικά – διδακτικά προβλήματα που προκύπτουν από τις βασικές έννοιες των Λογιστικών Φύλλων. Σε δεύτερη φάση θέλουμε να δούμε πώς το Excel υποστηρίζει συγκεκριμένες μαθηματικές έννοιες και πιο συγκεκριμένα πως το Excel μπορεί να χρησιμοποιηθεί σαν υποστηρικτικό εργαλείο για διερεύνηση και μοντελοποίηση πραγματικών καταστάσεων στον άξονα μιας διαθεματικής προσέγγισης. Όσον αφορά τον πρώτο στόχο, στο θεωρητικό πλαίσιο ασχοληθήκαμε αρχικά με γενικές έννοιες διδακτικής και στη συνέχεια με τα δύο επιμέρους αντικείμενα που μας ενδιαφέρουν: την Πληροφορική και τα Μαθηματικά. Όσον αφορά την Πληροφορική, ασχοληθήκαμε με την ενότητα των Λογιστικών Φύλλων και συγκεκριμένα: • εντοπίσαμε τις βασικές έννοιες που έχει ως στόχο να αναδείξει η συμβατική διδασκαλία των Λογιστικών Φύλλων σύμφωνα με τα επίσημα κείμενα των προγραμμάτων σπουδών, • εντοπίσαμε τις έννοιες που πραγματεύεται το βιβλίο Πληροφορικής της Β΄ τάξης Γυμνασίου όσον αφορά την ενότητα των Λογιστικών Φύλλων και • πήραμε συνεντεύξεις από καθηγητές της Δευτεροβάθμιας Εκπαίδευσης που έχουν διδάξει το μάθημα της Πληροφορικής στην Β΄ τάξη Γυμνασίου, για να διαπιστώσουμε τις γνωστικές δυσκολίες των βασικών εννοιών και τις λανθασμένες ή ανεπαρκείς αναπαραστάσεις των μαθητών που αφορούν τα Λογιστικά Φύλλα.. Για να μπορέσουμε να επιτύχουμε τον δεύτερο στόχο, ασχοληθήκαμε σε θεωρητικό πλαίσιο και με τα Μαθηματικά. Ασχοληθήκαμε με βασικές έννοιες διδακτικής των Μαθηματικών αλλά και με συγκεκριμένες μαθηματικές έννοιες, (την έννοια της αναλογίας των Μαθηματικών - ανάλογα και αντιστρόφως ανάλογα ποσά), με το πού εντοπίζονται στο πρόγραμμα σπουδών και τη μέθοδο που προτείνεται για τη διδασκαλία τους. Όσον αφορά το μεθοδολογικό πλαίσιο, βασίστηκε κυρίως στην έρευνα που έγινε με μαθητές της Β΄ τάξης Γυμνασίου, στους οποίους ζητήθηκε αρχικά να αντιμετωπίσουν κάποια ερωτήματα, αποκλειστικά πάνω στις βασικές έννοιες των Λογιστικών Φύλλων, όπως αυτές προέκυψαν απ’ το θεωρητικό πλαίσιο. Στη συνέχεια τους ζητήθηκε να εμπλακούν σε δύο προβληματικές καταστάσεις μαθηματικής μοντελοποίησης, που είχαν στόχο να αναδείξουν την έννοια της αναλογίας στα Μαθηματικά. Η διαδικασία αυτή έγινε σε κατάλληλα διαμορφωμένο περιβάλλον όπου υπήρχε υπολογιστής για να χρησιμοποιήσουν οι μαθητές το πρόγραμμα των Λογιστικών Φύλλων, αλλά και έτοιμα φύλλα εργασίας, που δίνονταν τμηματικά από τους ερευνητές. Πρέπει να σημειωθεί ότι η σχολική διδακτέα ύλη στην ελληνική διδασκαλία βασίζεται σε μια προσέγγιση που υποστηρίζει τις παραγωγικές διδακτικές πρακτικές (δηλ. την εφαρμογή της θεωρίας και των γενικών κανόνων σε συγκεκριμένες περιπτώσεις στην επίλυση προβλημάτων) και όχι σε μια προσέγγιση που ενθαρρύνει τις επαγωγικές διδακτικές πρακτικές (δηλ. συγκεκριμένα παραδείγματα και συγκεκριμένες εφαρμογές για τη γενίκευση και κατανόηση). Πάνω σ’ αυτή την προσέγγιση βασίζεται και η παρούσα μελέτη. / -

Submitted by Silvio Marcelino da Silva (silviomarcelinosilva@yahoo.com.br) on 2018-08-04T13:28:58Z No. of bitstreams: 1 Dissertação - Silvio M. da Silva.pdf: 2606887 bytes, checksum: 9d7669e60abb6c7229274eff9e58f309 (MD5) / Rejected by Elza Mitiko Sato null (elzasato@ibilce.unesp.br), reason: Solicitamos que realize correções na submissão seguindo as orientações abaixo: 01)Solicito que corrija a descrição na natureza da pesquisa(folha de rosto e aprovação): Dissertação apresentada como parte dos requisitos para obtenção do título de Mestre, junto ao Programa de Pós-Graduação Mestrado Profissional em Matemática em Rede Nacional – PROFMAT, da Faculdade de Ciências da Universidade Estadual Paulista “Júlio de Mesquita Filho”, Campus de Bauru. Lembramos que o arquivo depositado no repositório deve ser igual ao impresso, o rigor com o padrão da Universidade se deve ao fato de que o seu trabalho passará a ser visível mundialmente. Agradecemos a compreensão. on 2018-08-06T11:58:50Z (GMT) / Submitted by Silvio Marcelino da Silva (silviomarcelinosilva@yahoo.com.br) on 2018-08-07T02:06:08Z No. of bitstreams: 1 Dissertação - Silvio M. da Silva.pdf: 2607702 bytes, checksum: 0a14a98c674f30483ae0c50601d8475b (MD5) / Approved for entry into archive by Elza Mitiko Sato null (elzasato@ibilce.unesp.br) on 2018-08-07T11:54:20Z (GMT) No. of bitstreams: 1 silva_sm_me_sjrp.pdf: 2607702 bytes, checksum: 0a14a98c674f30483ae0c50601d8475b (MD5) / Made available in DSpace on 2018-08-07T11:54:21Z (GMT). No. of bitstreams: 1 silva_sm_me_sjrp.pdf: 2607702 bytes, checksum: 0a14a98c674f30483ae0c50601d8475b (MD5) Previous issue date: 2018-06-29 / Este trabalho foi formulado, visando diminuir as dificuldades apresentadas na aprendizagem da geometria, e também, proporcionar aos professores da área mais um recurso didático para trabalhar este assunto que é de total relevância no ensino da Matemática. Vivemos em um mundo real e não abstrata. Além de demonstrações virtuais das figuras planas e espaciais, podemos muitas vezes, construí-las e torná-las reais manualmente, e assim, colaborar com o desenvolvimento das habilidades de construção dos educandos, além do que a aprendizagem se torna mais prazerosa e mais prática. Nosso objetivo geral é reafirmar que a geometria está presente em toda parte, que tudo o que nos cerca tem formas geométricas, tanto na natureza quanto nas coisas produzidas pelo homem no decorrer da evolução da espécie humana. E nosso objetivo específico tem como estrutura os seguintes pensamentos: facilitar uma maior compreensão da geometria plana e espacial para os alunos do Ensino Fundamental e Médio, através de construções geométricas; desenvolver um estudo mais aprofundado sobre esta temática, visando colaborar com o trabalho do professor que atua no ensino de geometria; oferecer um recurso didático adicional para facilitar a exposição do conteúdo de geometria. / This work was formulated aiming to reduce the difficulties presented in the learning of geometry, and also to provide to the teachers of this field an extra didactic resource to work on this subject which is of total relevance in the teaching of Mathematics. We live in a real world, not in a virtual one. In addition to virtual demonstrations of flat and spatial figures, we can often construct them and make them real by hand, and thus collaborate with the development of the students' construction skills, and the learning becomes more pleasurable and more practical. Our general objective is to reaffirm that geometry is present everywhere, and everything around us has geometric forms, both in nature and in things produced by man in the course of the evolution of the human species. And our specific objectives are structured as follows: facilitate a better understanding of flat and spatial geometry for elementary, middle and high school students through geometric constructions; develop a more detailed study on this subject, aiming to collaborate with teachers who work in the teaching of geometry, and offer an additional didactic resource to facilitate the exposure of the geometry contents