Conceptions of mathematics teacher education : thoughts among teacher educators in Tanzania

This study addresses the question of teacher educators’ conceptions of mathematics teacher education (MTE) in teacher colleges in Tanzania, and their thoughts on how to further develop it. The tension between exponents of content as opposed to pedagogy has continued to cause challenging conceptual differences, which also influences what teacher educators conceive as desirable in the development of this domain. This tension is connected to the dissatisfaction of parents and teachers with the failure of school mathematics. From this point of view, the overall aim was to identify and describe teacher educators’ various conceptions of MTE. Inspired by the debate among teacher educators about what the balance should be between subject matter and pedagogical knowledge, it was important to look at the theoretical faces of MTE. The theoretical background involved the review of what is visible in MTE, what is yet to be known and the challenges within the practice. This task revealed meanings, perspectives in MTE, professional development and assessment. To do this, two questions were asked, to which no clear solutions satisfactorily existed. The questions to guide the investigation were, firstly, what are teacher educators’ conceptions of MTE, and secondly, what are teacher educators’ thoughts on the development of MTE? The two questions led to the choice of phenomenography as the methodological approach. Against the guiding questions, 27 mathematics teacher educators were interviewed in relation to the first question, while 32 responded to an open-ended questionnaire regarding question two. The interview statements as well as the questionnaire responses were coded and analysed (classified). The process of classification generated patterns of qualitatively different ways of seeing MTE. The results indicate that MTE is conceived as a process of learning through investigation, fostering inspiration, an approach to learning with an emphasis on problem solving, and a focus on pedagogical knowledge and skills in the process of teaching and learning. In addition, the teaching and learning of mathematics is seen as subject didactics with a focus on subject matter and as an organized integration of subject matter, pedagogical knowledge and some school practice; and also as academic content knowledge in which assessment is inherent. The respondents also saw the need to build learner-educator relationships. Finally, they emphasized taking advantage of teacher educators’ neighbourhood learning groups, networking and collaboration as sustainable knowledge and skills sharing strategies in professional development. Regarding desirable development, teacher educators’ thoughts emphasised enhancing pedagogical knowledge and subject matter, and to be determined by them as opposed to conventional top-down seminars and workshops. This study has revealed various conceptions and thoughts about MTE based on teacher educators´ diverse history of professional development in mathematics. It has been reasonably substantiated that some teacher educators teach school mathematics in the name of MTE, hardly distinguishing between the role and purpose of the two in developing a mathematics teacher. What teacher educators conceive as MTE and what they do regarding the education of teachers of mathematics revealed variations in terms of seeing the phenomenon of interest. Within limits, desirable thoughts shed light on solutions to phobias, and in the same way low self-esteem and stigmatization call for the building of teacher educator-student teacher relationships.

Two Cultures of Arts Education, Finland and Canada? An integrated View

Taidekasvatuksen kaksi kulttuuria, Suomi ja Kanada? Integroitu näkemys Tutkimuksessa kuvataan kanadalaisen Learning Through The Arts –pedagogiikan mukainen suomalainen kokeiluhanke, jonka aikana taiteilija–opettaja-parit opettivat yhdessä eri oppiaineita koululuokille: esim. matematiikkaa tanssien, biologiaa maalaten tai yhdistäen eri taiteenlajeja projektimuotoiseen oppimiseen. Hanketta arvioitaessa nousee esille, ei niinkään yksittäisten taiteilijoiden ja opettajien toiminta, vaan pikemminkin Kanadan ja Suomen rakenteelliset sekä kulttuuriset eroavuudet. Tutkimus sivuaa myös Suomessa käytävää keskustelua taiteen hyödyllisyydestä ja pohtii samalla taito- ja taideaineiden asemaa koulussa. Työn teoreettisessa osassa integroidaan opetussuunnitelmateoriaa, kasvatuksen historiaa ja filosofiaa, tähdentäen taidekasvatuksen merkitystä osana koko ihmisen kasvatusta. Opetussuunnitelmateorian osalta tarkastellaan romanttista ja klassista opetussuunnitelmaa, jotka eroavat toisistaan menetelmiensä, sisältöjensä, tavoitteidensa sekä arvioinnin osalta. Ns. kovat ja pehmeät aineet tai matemaattis-luonnontieteelliset aineet vastakohtanaan humanismi, voidaan ymmärtää sekä historiallisia että epistemologisia taustojaan vasten. Pepperin maailmanhypoteesien mukaisesti on kasvatuksen ongelmien ratkaisemiseksi hahmotettavissa neljä selvästi toisistaan eroavaa lähestymistapaa: formismi; organisismi; mekanisismi; sekä kontekstualismi. Kantin filosofiaan viitaten tutkimus puolustaa käsitystä taiteesta rationaalisena ja propositionaalisena kokonaisuutena, joka ei ole vain kommunikaation väline, vaan yksi todellisuuden kohtaamisen lajeista, tiedon ja etiikan rinnalla. Näin ajateltuna taito- ja taidekasvatuksen tulisi olla luonteeltaan aina myös kulttuurikasvatusta. Tutkimuksen tulosten perusteella voidaan väittää, että moniammatillinen yhteistyö monipuolistaa koulun opetusta. Mikäli huolehditaan siitä, että taiteilijat saavat riittävästi koulutusta opettamiseen liittyvissä asioissa, on mahdollista käyttää taiteilijoita opettajien rinnalla koulutyössä.

Matemaattiset opetusympäristöt ja matemaattisen käyttöliittymän käytettävyys

Tämän diplomityön tarkoituksena on kuvata Lappeenrannan teknillisessä yliopistossa kehitetyn luentojen tueksi tarkoitetun Matematiikan virtuaalimateriaalin hallintaympäristön kehityskaari. Järjestelmä luotiin parantamaanopetuksen laatua siten, että sen avulla opiskelijat saavat helposti käyttöönsä suomenkielistä, laadukkaalla kirjoitusjäljellä olevaa opiskelumateriaalia 24 tuntia vuorokaudessa. Lisäksi järjestelmän tavoitteena oli helpottaa opettajien työtaakkaa siten, että he pystyvät luomaan viikoittaiset harjoitustehtäväpaketit sekä tentit suoraan tietokannasta. Järjestelmän kehitys alkoi vuonna 2001, jonka jälkeen sitä on jatkuvasti muokattu opettajien ja opiskelijoiden avustuksella yhäkäyttäjäystävällisempään suuntaan. Testausmenetelminä on käytetty asiantuntijatestausta, lomakkeita ja varsinaista loppukäyttäjätestausta. Kehityksen tuloksenaon saatu järjestelmä, joka voidaan ottaa käyttöön kaikessa matematiikan perusopetuksessa.

Matematiikan opetuksen virtuaaliympäristöjen pedagoginen käyttö

Tämän kandityön tarkoituksena on selvittää ja kehittää Lappeenrannan teknillisen yliopiston sovelletun matematiikan laitoksella luotua virtuaalimateriaalin käyttöä eri kohderyhmille sopivaksi sekä käyttäjäystävällisemmäksi. Matematiikan virtuaalimateriaali on luotu tukemaan lähiopetusta matematiikan perusopetuksessa. Matematiikan virtuaalimateriaalin hallintaympäristöä on kehitetty vuodesta 2001. Järjestelmää sekä sen opiskelumateriaalia on kehitetty opettajien ja opiskelijoiden avulla. Järjestelmä kattaa teknillisen yliopiston eri osastojen matematiikan peruskurssien materiaalit. Sen käytöllä opettajat voivat hankkia itselleen lisää aikaa opetuksen suunnitteluun materiaalin luomisen nopeutuessa, koska opetusmateriaali voidaan nopeasti kasata valmiista tehtävistä ja teoriaosioista. Opiskelijoiden kannalta hyvätasoinen oppimateriaali on jatkuvasti saatavilla ja sen avulla on myös helppo opiskella hyvien hakutoimintojen ansiosta.

Matematiikan perusopetuksen internet-aineiston tuottaminen

Tämän diplomityön tarkoituksena on kuvata Lappeenrannan teknillisessä yliopistossa matematiikan perusopetuksen virtuaaliympäristöä pedagogisesti toimivana oppimisympäristönä. Matematiikan virtuaalimateriaali on luotu tukemaan lähiopetusta matematiikan perusopetuksessa. Virtuaalimateriaalin kehittämisessä tähdätään pedagogiseen osaamiseen ja järjestelmän toimintalogiikan kehittämiseen sisällönhallintatyökalujen avulla. Opiskelun ja opetuksen kansainvälistymisen myötä on kehitetty perusmatematiikan virtuaaliympäristöä niin, että järjestelmä tarjoaa yliopiston opettajille ja suomalaisille sekä ulkomaalasille opiskelijoille yhteisen perusmatematiikan virtuaaliympäristön. Kehityksen tuloksena on saatu järjestelmä, joka hyödyntää tietoverkkoja kuten Wikipediaa verkko-opetuksen aputyökaluna.

The effects of ICT on school: teachers’ and students’ perspectives

The purpose of this study was to investigate the effects of information and communication technology (ICT) on school from teachers’ and students’ perspectives. The focus was on three main subject matters: on ICT use and competence, on teacher and school community, and on learning environment and teaching practices. The study is closely connected to the national educational policy which has aimed strongly at supporting the implementation of ICT in pedagogical practices at all institutional levels. The phenomena were investigated using a mixed methods approach. The qualitative data from three cases studies and the quantitative data from three statistical studies were combined. In this study, mixed methods were used to investigate the complex phenomena from various stakeholders’ points of view, and to support validation by combining different perspectives in order to give a fuller and more complete picture of the phenomena. The data were used in a complementary manner. The results indicate that the technical resources for using ICT both at school and at homes are very good. In general, students are capable and motivated users of new technology; these skills and attitudes are mainly based on home resources and leisuretime use. Students have the skills to use new kinds of applications and new forms of technology, and their ICT skills are wide, although not necessarily adequate; the working habits might be ineffective and even wrong. Some students have a special kind of ICT-related adaptive expertise which develops in a beneficial interaction between school guidance and challenges, and individual interest and activity. Teachers’ skills are more heterogeneous. The large majority of teachers have sufficient skills for everyday and routine working practices, but many of them still have difficulties in finding a meaningful pedagogical use for technology. The intensive case study indicated that for the majority of teachers the intensive ICT projects offer a possibility for learning new skills and competences intertwined in the work, often also supported by external experts and a collaborative teacher community; a possibility that “ordinary” teachers usually do not have. Further, teachers’ good ICT competence help them to adopt new pedagogical practices and integrate ICT in a meaningful way. The genders differ in their use of and skills in ICT: males show better skills especially in purely technical issues also in schools and classrooms, whereas female students and younger female teachers use ICT in their ordinary practices quite naturally. With time, the technology has become less technical and its communication and creation affordances have become stronger, easier to use, more popular and motivating, all of which has increased female interest in the technology. There is a generation gap in ICT use and competence between teachers and students. This is apparent especially in the ICT-related pedagogical practices in the majority of schools. The new digital affordances not only replace some previous practices; the new functionalities change many of our existing conceptions, values, attitudes and practices. The very different conceptions that generations have about technology leads, in the worst case, to a digital gap in education; the technology used in school is boring and ineffective compared to the ICT use outside school, and it does not provide the competence needed for using advanced technology in learning. The results indicate that in schools which have special ICT projects (“ICT pilot schools”) for improving pedagogy, these have led to true changes in teaching practices. Many teachers adopted student-centred and collaborative, inquiry-oriented teaching practices as well as practices that supported students' authentic activities, independent work, knowledge building, and students' responsibility. This is, indeed, strongly dependent on the ICT-related pedagogical competence of the teacher. However, the daily practices of some teachers still reflected a rather traditional teacher-centred approach. As a matter of fact, very few teachers ever represented solely, e.g. the knowledge building approach; teachers used various approaches or mixed them, based on the situation, teaching and learning goals, and on their pedagogical and technical competence. In general, changes towards pedagogical improvements even in wellorganised developmental projects are slow. As a result, there are two kinds of ICT stories: successful “ICT pilot schools” with pedagogical innovations related to ICT and with school community level agreement about the visions and aims, and “ordinary schools”, which have no particular interest in or external support for using ICT for improvement, and in which ICT is used in a more routine way, and as a tool for individual teachers, not for the school community.

Nuorten koherenssin tunne: mittaaminen, ennustavat tekijät, seuraukset

Sense of coherence in adolescence: measuring, predictive factors, consequences The aim of this study was to explore the stability of sense of coherence (SOC) in adolescence and the associations between childhood psychological symptoms and SOC in adolescence. Furthermore, the aim of this study was to explore whether the 13-item SOC scale for adults is applicable to adolescents 12 years of age and to determine which factors are associated with perceived health and SOC. Data relating to SOC and factors associated with perceived health and SOC were collected in class in a cross-sectional setting by self-administered questionnaires in all publicly funded elementary schools (N=35) of Turku. A total of 1 231 (83%) of 1 481 12-year-old schoolchildren participated in the study. The data was, with appropriated authority consent, anonymously completed with marks in mathematics, native and first foreign language at the end of sixth class. The examination of stability of SOC in adolescence and the associations between childhood psychological symptoms and SOC was based on data of a prospective population-based mail survey. The source population originated in 11 health authority areas of the Province of Turku and Pori. The study was carried out by using questionnaires at child’s ages of 3, 12, 15, and 18 years. Acceptably completed questionnaires were returned by 1 086 (84%) parents at the child’s age of 3, at the age of 12 by 70% adolescents and parents, at the age of 15, by 66% adolescents and 58% parents, and at the age of 18, by 61.5% adolescents and 61% parents. The results of the study showed that childhood behavioural problems from the age of 3 years predicted poor SOC at the age of 18 years. A poor SOC was associated with psychological symptoms and behavioural problems in adolescence. Contrary to assumptions in Antonovsky’s theory, there was no significant change in SOC between the ages of 15 to 18 years, and the stability of SOC did not depend on initial SOC. Slight fluctuation in SOC scores was seen at the individual level. When studied cross-sectionally, in 12-year-old schoolchildren, insufficient physical exercise, less than excellent marks in mathematics, weak SOC, insufficient social support from teachers, and perceived various problems in class climate associated with perception of poor health. Identification of behavioural problems in early childhood helps to identify the children at risk of ill-being and poor SOC in adolescence since problems seem to persist unchanged until adolescence. The 13-item SOC scale aimed at adults is applicable to adolescents of 12 years of age or older and the SOC scale is a useful tool in identifying adolescents in need of supportive interventions.

Teaching mathematics and programming : new approaches with empirical evaluation

Programming and mathematics are core areas of computer science (CS) and consequently also important parts of CS education. Introductory instruction in these two topics is, however, not without problems. Studies show that CS students find programming difficult to learn and that teaching mathematical topics to CS novices is challenging. One reason for the latter is the disconnection between mathematics and programming found in many CS curricula, which results in students not seeing the relevance of the subject for their studies. In addition, reports indicate that students' mathematical capability and maturity levels are dropping. The challenges faced when teaching mathematics and programming at CS departments can also be traced back to gaps in students' prior education. In Finland the high school curriculum does not include CS as a subject; instead, focus is on learning to use the computer and its applications as tools. Similarly, many of the mathematics courses emphasize application of formulas, while logic, formalisms and proofs, which are important in CS, are avoided. Consequently, high school graduates are not well prepared for studies in CS. Motivated by these challenges, the goal of the present work is to describe new approaches to teaching mathematics and programming aimed at addressing these issues: Structured derivations is a logic-based approach to teaching mathematics, where formalisms and justifications are made explicit. The aim is to help students become better at communicating their reasoning using mathematical language and logical notation at the same time as they become more confident with formalisms. The Python programming language was originally designed with education in mind, and has a simple syntax compared to many other popular languages. The aim of using it in instruction is to address algorithms and their implementation in a way that allows focus to be put on learning algorithmic thinking and programming instead of on learning a complex syntax. Invariant based programming is a diagrammatic approach to developing programs that are correct by construction. The approach is based on elementary propositional and predicate logic, and makes explicit the underlying mathematical foundations of programming. The aim is also to show how mathematics in general, and logic in particular, can be used to create better programs.

In pursuit of an intercultural dimension in EFL-teaching : exploring cognitions among Finland-Swedish comprehensive school teachers

This thesis is about the educational purpose of foreign language teaching (FLT) in an increasingly internationalised world.The past 20-30 years have witnessed a fundamental rethinking of the aims of FLT, entailing a shift in emphasis from linguistic competence over communicative competence to intercultural competence. The growing emphasis on cultural issues, called for by research and international curricular documents, places new demandson language teachers. The overall aim of this study is to deepen the knowledge about the attitudes of teachers at the upper level of the Finland-Swedish comprehensive school towards the treatment of culture in English foreign language (EFL) teaching. The questions in focus are: 1) How do teachers interpret the concept"culture" in EFL-teaching?, 2) How do they specify the cultural objectives of their teaching? and 3) What do they do to attain these objectives? The thesis strives to reveal whether or not language teaching today can be describedas intercultural, in the sense that culture is taught with the aim of promotingintercultural understanding, tolerance and empathy. This abductive and largely exploratory study is placed within a constructivist and sociocultural framework,and is inspired by both phenomenography and hermeneutics. It takes its starting-point in language didactics, and can also be regarded as a contribution to teacher cognition research. The empirical data consists of verbatim transcribed interviews with 13 Finland-Swedish teachers of English at grades 7-9. The findings are presented according to three orientations and reviewed with reference to the 2004 Finnish National Framework Curriculum. Within the cognitive orientation, "culture" is perceived as factual knowledge, and the teaching of cultureis defined in terms of the transmission of knowledge, especially about Britain and the USA (Pedagogy of Information). Within the action-related orientation, "culture" is seen as skills of a social and socio-linguistic nature, andthe teaching aims at preparing the students for contacts with people from the target language areas (Pedagogy of Preparation). Within the affective orientation, which takes a more holistic approach, "culture" is seen as a bi-directional perspective. Students are encouraged to look at their own familiar culture from another perspective, and learn to empathise with and show respect for otherness in general, not just concerning representatives of English-speaking countries (Pedagogy of Encounter). Very few of the interviewed teachers represent the third approach, which is the one that can be characterised as truly intercultural. The study indicates that many teachers feel unsure about how to teach culture in an appropriate and up-to-date manner. This is attributed to, among other things, lack of teacher insights as well as lack of time and adequate material. The thesis ends with a set of recommendations as to how EFL could be developed ina more intercultural direction.

Integrating environmental education in primary school education in Tanzania : teachers’ perceptions and teaching practices

The study focuses on primary school teachers’ perceptions of environmental education, its integration into primary school education and teachers’ teaching practices in Tanzania. The thesis is based on empirical research. The theoretical underpinnings of the study are based on Palmer’s (1998) model of environmental education. According to the model, meaningful environmental education should include education about, in or through and for the environment. The study is supported by national and international literature from research done on environmental education and education for sustainable development and policy statements. The study is qualitative in nature, adopting phenomenography and phenomenology as points of departure. The empirical data was collected from four primary schools in Morogoro region in Tanzania. The study sample consisted of 31 primary school teachers. Data was collected through interviews and lesson observations. According to the results of the study, primary school teachers expressed variations in their perceptions of environmental education and education for sustainable development. Most of the teachers focused on the aspect of knowledge acquisition. According to Tanzanian education and training policy, environmental education has to be integrated into all subjects. Although there is environmental education in the primary school curriculum, it is not integrated on an equal footing in all subjects. Some subjects like science, social studies and geography have more environmental content than other subjects. Teachers claim that the approach used to integrate environmental education into the school curriculum was not favoured because many claimed that what is to be taught as environmental education in the various subjects is not shown clearly. As a result, many teachers suggested that to ensure that it is taught properly it should be included in the curriculum as an independent subject or as specific topics. The study revealed that teachers’ teaching practices in integrating environmental education varied from one subject to another. Although most of the teachers said that they used participatory methods, lesson observations showed that they limited themselves to question and answer and group discussion. However, the teachers faced a number of barriers in the teaching of environmental education, some of which include lack of teaching and learning resources, time and large class size. The role of teachers in the implementation of environmental education in developing an environmentally literate citizenry is of great significance. The responsibility of the government in developing a curriculum with clear goals and content, developing teachers’ capacity in the teaching of environmental education and provision of teaching and learning materials needs to be taken seriously by the government in educational plans and programs.

Teachers' conceptions of literacies during and after a school library development project

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