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.

Evaluation of Teacher Education Programs by Students and Graduates

The purpose of this research was to do a repeated cross-sectional research on class teachers who study in the 4th year and also graduated at the Faculty of Education, University of Turku between the years of 2000 through 2004. Specifically, seven research questions were addressed to target the main purpose of the study: How do class teacher education masters’ degree senior students and graduates rate “importance; effectiveness; and quality” of training they have received at the Faculty of Education? Are there significant differences between overall ratings of importance; effectiveness and quality of training by year of graduation, sex, and age (for graduates) and sex and age (for senior students)? Is there significant relationship between respondents’ overall ratings of importance; effectiveness and their overall ratings of the quality of training and preparation they have received? Are there significant differences between graduates and senior students about importance, effectiveness, and quality of teacher education programs? And what do teachers’ [Graduates] believe about how increasing work experience has changed their opinions of their preservice training? Moreover the following concepts related to the instructional activities were studied: critical thinking skills, communication skills, attention to ethics, curriculum and instruction (planning), role of teacher and teaching knowledge, assessment skills, attention to continuous professional development, subject matters knowledge, knowledge of learning environment, and using educational technology. Researcher also tried to find influence of some moderator variables e.g. year of graduation, sex, and age on the dependent and independent variables. This study consisted of two questionnaires (a structured likert-scale and an open ended questionnaire). The population in study 1 was all senior students and 2000-2004 class teacher education masters’ degree from the departments of Teacher Education Faculty of Education at University of Turku. Of the 1020 students and graduates the researcher was able to find current addresses of 675 of the subjects and of the 675 graduates contacted, 439 or 66.2 percent responded to the survey. The population in study 2 was all class teachers who graduated from Turku University and now work in the few basic schools (59 Schools) in South- West Finland. 257 teachers answered to the open ended web-based questions. SPSS was used to produce standard deviations; Analysis of Variance; Pearson Product Moment Correlation (r); T-test; ANOVA, Bonferroni post-hoc test; and Polynomial Contrast tests meant to analyze linear trend. An alpha level of .05 was used to determine statistical significance. The results of the study showed that: A majority of the respondents (graduates and students) rated the overall importance, effectiveness and quality of the teacher education programs as important, effective and good. Generally speaking there were only a few significant differences between the cohorts and groups related to the background variables (gender, age). The different cohorts were rating the quality of the programs very similarly but some differences between the cohorts were found in the importance and effectiveness ratings. Graduates of 2001 and 2002 rated the importance of the program significantly higher than 2000 graduates. The effectiveness of the programs was rated significantly higher by 2001 and 2003 graduates than other groups. In spite of these individual differences between cohorts there were no linear trends among the year cohorts in any measure. In respondents’ ratings of the effectiveness of teacher education programs there was significant difference between males and females; females rated it higher than males. There were no significant differences between males’ and females’ ratings of the importance and quality of programs. In the ratings there was only one difference between age groups. Older graduates (35 years or older) rated the importance of the teacher training significantly higher that 25-35 years old graduates. In graduates’ ratings there were positive but relatively low correlations between all variables related to importance, effectiveness and quality of Teacher Education Programs. Generally speaking students’ ratings about importance, effectiveness and quality of teacher education program were very positive. There was only one significant difference related to the background variables. Females rated higher the effectiveness of the program. The comparison of students’ and graduates’ perception about importance, effectiveness, and quality of teacher education programs showed that there were no significant differences between graduates and students in the overall ratings. However there were differences in some individual variables. Students rated higher in importance of “Continuous Professional Development”, effectiveness of “Critical Thinking Skills” and “Using Educational Technology” and quality of “Advice received from the advisor”. Graduates rated higher in importance of “Knowledge of Learning Environment” and effectiveness of “Continuous Professional Development”. According to the qualitative data of study 2 some graduates expressed that their perceptions have not changed about the importance, effectiveness, and quality of training that they received during their study time. They pointed out that teacher education programs have provided them the basic theoretical/formal knowledge and some training of practical routines. However, a majority of the teachers seems to have somewhat critical opinions about the teacher education. These teachers were not satisfied with teacher education programs because they argued that the programs failed to meet their practical demands in different everyday situations of the classroom e.g. in coping with students’ learning difficulties, multiprofessional communication with parents and other professional groups (psychologists and social workers), and classroom management problems. Participants also emphasized more practice oriented knowledge of subject matter, evaluation methods and teachers’ rights and responsibilities. Therefore, they (54.1% of participants) suggested that teacher education departments should provide more practice-based courses and programs as well as closer collaboration between regular schools and teacher education departments in order to fill gap between theory and practice.

Towards Innovative Virtual Learning in Vocational Teacher Education: Narratives as a Form of Meaningful Learning

http://www.eurodl.org/.

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.

Curriculum innovation in teacher education : exploring conceptions among Tanzanian teacher educators

The focus of the study is to understand curriculum innovation from the perspective of Tanzanian teacher educators. It is argued that the deterioration of quality of education in schools is partly to be attributed to the way in which teachers are educated. Curriculum innovation is considered as an essential strategy for bringing about improvement in teacher education. Therefore, in 2000 a new curriculum was introduced; however, right from the inception the curriculum was criticised by teacher educators. The overall aim of the study is to investigate teacher educators’ conceptions of curriculum innovation. In the theoretical framework the main focus is on discussion about different curriculum approaches for teacher education and innovation. In order to achieve the aim of the study, a phenomenographic approach is employed. This approach is used in order to identify similarities and variation in educators’ conceptions of curriculum innovation. The empirical basis of the study consists of interviews with thirty teacher educators working in eight teachers’ colleges situated in various parts of Tanzania. The findings, in brief, reveal variation in teacher educators’ conceptions of the dominant domains of innovation. Two broad conceptions of teaching with six aspects are identified. Conceptions of educational studies are presented in four broad categories of description with four aspects. Similarly, in methodology subjects two conceptions are described with four aspects. On the integration of subject matter studies and subject methods, two broad conceptions are presented with six aspects. Conceptions of textbook prescription policy are characterised in two broad categories of description with four aspects. With the use of modules two broad conceptions are identified with six aspects. In addition, the study identifies four broad conceptions of future curriculum approaches with eight aspects. Looking across the categories of description, the results indicate that educators cope with innovation individually. Three character types of teacher educators are presented: loyal, creative and critical. Furthermore, four types of phenomena suggesting critical areas about teacher educators’ conceptions of innovation are described: educators’ prior educational background, technical factors, student teachers’ factors and shifting from teaching to learning. On the whole, educators express a number of frame factors in the process of change towards the aim of curriculum innovation. This indicates that the new curriculum (2000) is not implemented as intended by curriculum developers. Constraints to the implementation are presented and discussed in detail. From these findings, two models of educators’ stance towards curriculum innovation are presented and can be used as a framework for planning successful curriculum innovations and analysing practice in teachers’ colleges.

Conditions for EFL learning and professional development : Finland-Swedish learner and teacher perspectives

Engelskans dominerande roll som internationellt språk och andra globaliseringstrender påverkar också Svenskfinland. Dessa trender påverkar i sin tur förutsättningarna för lärande och undervisning i engelska som främmande språk, det vill säga undervisningsmålen, de förväntade elev- och lärarroller, materialens ändamålsenlighet, lärares och elevers initiala erfarenheter av engelska och engelskspråkiga länder. Denna studie undersöker förutsättningarna för lärande och professionell utveckling i det svenskspråkiga nybörjarklassrummet i engelska som främmande språk. Utgångsläget för 351 nybörjare i engelska som främmande språk och 19 av deras lärare beskrivs och analyseras. Resultaten tyder på att engelska håller på att bli ett andraspråk snarare än ett traditionellt främmande språk för många unga elever. Dessa elever har också goda förutsättningar att lära sig engelska utanför skolan. Sådan var dock inte situationen för alla elever, vilket tyder på att det finns en anmärkningsvärd heterogenitet och även regional variation i det finlandssvenska klassrummet i engelska som främmande språk. Lärarresultaten tyder på att vissa lärare har klarat av att på ett konstruktivt sätt att tackla de förutsättningar de möter. Andra lärare uttrycker frustration över sin arbetssituation, läroplanen, undervisningsmaterialen och andra aktörer som kommer är av betydelse för skolmiljön. Studien påvisar att förutsättningarna för lärande och undervisning i engelska som främmande språk varierar i Svenskfinland. För att stöda elevers och lärares utveckling föreslås att dialogen mellan aktörer på olika nivå i samhället bör förbättras och systematiseras.