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.

Structure learning of context-specific graphical models

Abstract The ultimate problem considered in this thesis is modeling a high-dimensional joint distribution over a set of discrete variables. For this purpose, we consider classes of context-specific graphical models and the main emphasis is on learning the structure of such models from data. Traditional graphical models compactly represent a joint distribution through a factorization justi ed by statements of conditional independence which are encoded by a graph structure. Context-speci c independence is a natural generalization of conditional independence that only holds in a certain context, speci ed by the conditioning variables. We introduce context-speci c generalizations of both Bayesian networks and Markov networks by including statements of context-specific independence which can be encoded as a part of the model structures. For the purpose of learning context-speci c model structures from data, we derive score functions, based on results from Bayesian statistics, by which the plausibility of a structure is assessed. To identify high-scoring structures, we construct stochastic and deterministic search algorithms designed to exploit the structural decomposition of our score functions. Numerical experiments on synthetic and real-world data show that the increased exibility of context-specific structures can more accurately emulate the dependence structure among the variables and thereby improve the predictive accuracy of the models.

Neural correlates of language learning in adults

The human language-learning ability persists throughout life, indicating considerable flexibility at the cognitive and neural level. This ability spans from expanding the vocabulary in the mother tongue to acquisition of a new language with its lexicon and grammar. The present thesis consists of five studies that tap both of these aspects of adult language learning by using magnetoencephalography (MEG) and functional magnetic resonance imaging (fMRI) during language processing and language learning tasks. The thesis shows that learning novel phonological word forms, either in the native tongue or when exposed to a foreign phonology, activates the brain in similar ways. The results also show that novel native words readily become integrated in the mental lexicon. Several studies in the thesis highlight the left temporal cortex as an important brain region in learning and accessing phonological forms. Incidental learning of foreign phonological word forms was reflected in functionally distinct temporal lobe areas that, respectively, reflected short-term memory processes and more stable learning that persisted to the next day. In a study where explicitly trained items were tracked for ten months, it was found that enhanced naming-related temporal and frontal activation one week after learning was predictive of good long-term memory. The results suggest that memory maintenance is an active process that depends on mechanisms of reconsolidation, and that these process vary considerably between individuals. The thesis put special emphasis on studying language learning in the context of language production. The neural foundation of language production has been studied considerably less than that of perceptive language, especially on the sentence level. A well-known paradigm in language production studies is picture naming, also used as a clinical tool in neuropsychology. This thesis shows that accessing the meaning and phonological form of a depicted object are subserved by different neural implementations. Moreover, a comparison between action and object naming from identical images indicated that the grammatical class of the retrieved word (verb, noun) is less important than the visual content of the image. In the present thesis, the picture naming was further modified into a novel paradigm in order to probe sentence-level speech production in a newly learned miniature language. Neural activity related to grammatical processing did not differ between the novel language and the mother tongue, but stronger neural activation for the novel language was observed during the planning of the upcoming output, likely related to more demanding lexical retrieval and short-term memory. In sum, the thesis aimed at examining language learning by combining different linguistic domains, such as phonology, semantics, and grammar, in a dynamic description of language processing in the human brain.

A multimethod examination of contributors to successful on-the-job learning for vocational students

Rapid changes in working life and competence requirements of different professions have increased interest in workplace learning. It is considered an effective way to learn and update professional skills by performing daily tasks in an authentic environment. Especially, ensuring a supply of skilled future workers is a crucial issue for firms facing tight competition and a shortage of competent employees due to the retirement of current professionals. In order to develop and make the most of workplace learning, it is important to focus on workplace learning environments and the individual characteristics of those participating in workplace learning. The literature has suggested various factors that influence adults' and professionals’ workplace learning of profession-related skills, but lacks empirical studies on contextual and individual-related factors that positively affect students' workplace learning. Workers with vocational education form a large group in modern firms. Therefore, elements of vocational students’ successful workplace learning during their studies, before starting their career paths, need to be examined. To fill this gap in the literature, this dissertation examines contributors to vocational students’ workplace learning in Finland, where students’ workplace learning is included in the vocational education and training system. The study is divided into two parts: the introduction, comprised of the overview of the relevant literature and the conclusion of the entire study, and five separate articles. Three of the articles utilize quantitative methods and two use qualitative methods to examine factors that contribute to vocational students’ workplace learning. The results show that, from the students’ perspective, attitudinal, motivational, and organizationrelated factors enhance the student’s development of professionalism during the on-the-job learning period. Specifically, the organization-related factors such as innovative climate, guidance, and interactions with seniors have a strong positive impact on the students’ perceived development of professional skills because, for example, the seniors’ guidance and provision of new viewpoints for the tasks helps the vocational students to gain autonomy at work performance. A multilevel analysis shows that of those factors enhancing workplace learning from the student perspective, innovative climate, knowledge transfer accuracy, and the students’ performance orientation were significantly related to the workplace instructors’ assessment regarding the students’ professional performance. Furthermore, support from senior colleagues and the students’ self-efficacy were both significantly associated with the formal grades measuring how well the students managed to learn necessary professional skills. In addition, the results suggest that the students’ on-the-job learning can be divided into three main phases, of which two require efforts from both the student and the on-the-job learning organization. The first phase includes the student’s application of basic professional skills, demonstration of potential in performing daily tasks, and orientation provided by the organization at the beginning of the on-the-job learning period. In the second phase, the student actively develops profession-related skills by performing daily tasks, thus learning a fluent working style while observing the seniors’ performance. The organization offers relevant tasks and follows the student’s development. The third level indicates a student who has reached the professional level described as a full occupation. The results suggest that constructing the vocational students’ successful on-the-job learning period requires feedback from seniors, opportunities to learn to manage entire work processes, self-efficacy on the part of the students, proactive behavior, and initiative in learning. The study contributes to research on workplace learning in three ways: firstly, it identifies the key individual- and organization-based factors that influence the vocational students’ successful on-the-job learning from their perspective and examines mutual relationships between these factors. Second, the study provides knowledge of how the factors related to the students’ view of successful workplace learning are associated with the workplace instructors’ perspective and the formal grades. Third, the present study finds elements needed to construct a successful on-the-job learning for the students.

To Succeed Is to Believe: Comparison of Self-Efficacy Beliefs in Language Learning between Learner Groups of English and Swedish in Finland

In this thesis, I studied self-efficacy in the learning of English and Swedish in Finland. The theory of self-efficacy, which was created by Albert Bandura, suggests that the beliefs a person has of his or her capabilities in a certain task affect the person’s performance in the task. My aim was to study whether there are differences in self-efficacy beliefs between the learners of English and Swedish, and whether these beliefs correlate with the performance in the language in question. My hypotheses were that the learners of English have higher self-efficacy beliefs than the learners of Swedish and that self-efficacy beliefs correlate with language performance. The study was quantitative, and it consisted of a self-efficacy questionnaire and a language test which were distributed to students of English and Swedish in an upper secondary school in Rovaniemi. The study was answered by 137 students, of whom 93 were learners of English and 44 were learners of Swedish. The results indicated that the learners of English had a higher sense of efficacy than the learners of Swedish. The analysis proved that there was a significant correlation between English students’ self-efficacy and their performance in the language measured by the test and the grades. In addition, a significant correlation existed between Swedish students’ self-efficacy and their grades. However, there was no correlation between the Swedish students’ self-efficacy and their test results. The difference in the self-efficacy beliefs of the two language groups indicates that people in Finland are more confident in using English than Swedish, which also implies that English is more valued in Finnish society than Swedish. It is important to acknowledge the lower self-efficacy beliefs in Swedish because various studies have proven that self-efficacy affects academic achievement. As a suggestion for further research, the self-efficacy beliefs of different language groups could be compared in a qualitative study in order to understand the development of self-efficacy more profoundly.

Learning English is Fun! Incidental vocabulary acquisition of music and traditional class ninth graders via listening to pop songs

Finnish youth are constantly exposed to music and lyrics in English in their free time. It is likely that this has a positive effect on vocabulary learning. Learning vocabulary while simultaneously accompanied with melodies is likely to result in better learning outcomes. The present thesis covers a study on the vocabulary learning of traditional and music class ninth graders in a south-western upper comprehensive school in Finland, mainly concentrating on vocabulary learning as a by-product of listening to pop music and learning vocabulary through semantic priming. The theoretical background presents viable linguistic arguments and theories, which provide clarity for why it would be possible to learn English vocabulary via listening to pop songs. There is conflicting evidence on the benefits of music on vocabulary learning, and this thesis sets out to shed light on the situation. Additionally, incorporating pop music in English classes could assist in decreasing the gap between real world English and school English. The thesis is a mixed method research study consisting of both quantitative and qualitative research materials. The methodology comprises vocabulary tests both before and after pop music samples and a background questionnaire filled by students. According to the results, all students reported liking listening to music and they clearly listened to English pop music the most. A statistically significant difference was found when analysing the results of the differences in pre- and post-vocabulary tests. However, the traditional class appeared to listen to mainstream pop music more than the students in the music class, and thus it seems likely that the traditional class benefited more from vocabulary learning occurring via listening to pop songs. In conclusion, it can be established that it is possible to learn English vocabulary via listening to pop songs and that students wish their English lectures would involve more music-related vocabulary exercises in the future. Thus, when it comes to school learning, pop songs should be utilised in vocabulary learning, which could also in turn result in more diverse learning and the students could, more easily than before, relate to the themes and topics of the lectures. Furthermore, with the help of pop songs it would be possible to decrease the gap between school English and real-world English.

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.

Profiles of Second Language Learners in Bilingual Education: A Comparative Study of the Characteristics of Finnish and American Students

The purpose of this comparative study is to profile second language learners by exploring the factors which have an impact on their learning. The subjects come from two different countries: one group comes from Milwaukee, US, and the other from Turku, Finland. The subjects have attended bilingual classes from elementary school to senior high school in their respective countries. In the United States, the subjects (N = 57) started in one elementary school from where they moved on to two high schools in the district. The Finnish subjects (N = 39) attended the same school from elementary to high school. The longitudinal study was conducted during 1994-2004 and combines both qualitative and quantitative research methods. A Pilot Study carried out in 1990-1991 preceded the two subsequent studies that form the core material of this research. The theoretical part of the study focuses first on language policies in the United States and Finland: special emphasis is given to the history, development and current state of bilingual education, and the factors that have affected policy-making in the provision of language instruction. Current language learning theories and models form the theoretical foundation of the research, and underpin the empirical studies. Cognitively-labeled theories are at the forefront, but sociocultural theory and the ecological approach are also accounted for. The research methods consist of questionnaires, compositions and interviews. A combination of statistical methods as well as content analysis were used in the analysis. The attitude of the bilingual learners toward L1 and L2 was generally positive: the subjects enjoyed learning through two languages and were motivated to learn both. The knowledge of L1 and parental support, along with early literacy in L1, facilitated the learning of L2. This was particularly evident in the American subject group. The American subjects’ L2 learning was affected by the attitudes of the learners to the L1 culture and its speakers. Furthermore, the negative attitudes taken by L1 speakers toward L2 speakers and the lack of opportunities to engage in activities in the L1 culture affected the American subjects’ learning of L2, English. The research showed that many American L2 learners were isolated from the L1 culture and were even afraid to use English in everyday communication situations. In light of the research results, a politically neutral linguistic environment, which the Finnish subjects inhabited, was seen to be more favorable for learning. The Finnish subjects were learning L2, English, in a neutral zone where their own attitudes and motivation dictated their learning. The role of L2 as a means of international communication in Finland, as opposed to a means of exercising linguistic power, provided a neutral atmosphere for learning English. In both the American and Finnish groups, the learning of other languages was facilitated when the learner had a good foundation in their L1, and the learning of L1 and L2 were in balance. Learning was also fostered when the learners drew positive experiences from their surroundings and were provided with opportunities to engage in activities where L2 was used.

Learning Preferences with Kernel-Based Methods

Learning of preference relations has recently received significant attention in machine learning community. It is closely related to the classification and regression analysis and can be reduced to these tasks. However, preference learning involves prediction of ordering of the data points rather than prediction of a single numerical value as in case of regression or a class label as in case of classification. Therefore, studying preference relations within a separate framework facilitates not only better theoretical understanding of the problem, but also motivates development of the efficient algorithms for the task. Preference learning has many applications in domains such as information retrieval, bioinformatics, natural language processing, etc. For example, algorithms that learn to rank are frequently used in search engines for ordering documents retrieved by the query. Preference learning methods have been also applied to collaborative filtering problems for predicting individual customer choices from the vast amount of user generated feedback. In this thesis we propose several algorithms for learning preference relations. These algorithms stem from well founded and robust class of regularized least-squares methods and have many attractive computational properties. In order to improve the performance of our methods, we introduce several non-linear kernel functions. Thus, contribution of this thesis is twofold: kernel functions for structured data that are used to take advantage of various non-vectorial data representations and the preference learning algorithms that are suitable for different tasks, namely efficient learning of preference relations, learning with large amount of training data, and semi-supervised preference learning. Proposed kernel-based algorithms and kernels are applied to the parse ranking task in natural language processing, document ranking in information retrieval, and remote homology detection in bioinformatics domain. Training of kernel-based ranking algorithms can be infeasible when the size of the training set is large. This problem is addressed by proposing a preference learning algorithm whose computation complexity scales linearly with the number of training data points. We also introduce sparse approximation of the algorithm that can be efficiently trained with large amount of data. For situations when small amount of labeled data but a large amount of unlabeled data is available, we propose a co-regularized preference learning algorithm. To conclude, the methods presented in this thesis address not only the problem of the efficient training of the algorithms but also fast regularization parameter selection, multiple output prediction, and cross-validation. Furthermore, proposed algorithms lead to notably better performance in many preference learning tasks considered.

Fuzzy subgroups, algebraic and topological points of view and complex analysis

Fuzzy subsets and fuzzy subgroups are basic concepts in fuzzy mathematics. We shall concentrate on fuzzy subgroups dealing with some of their algebraic, topological and complex analytical properties. Explorations are theoretical belonging to pure mathematics. One of our ideas is to show how widely fuzzy subgroups can be used in mathematics, which brings out the wealth of this concept. In complex analysis we focus on Möbius transformations, combining them with fuzzy subgroups in the algebraic and topological sense. We also survey MV spaces with or without a link to fuzzy subgroups. Spectral space is known in MV algebra. We are interested in its topological properties in MV-semilinear space. Later on, we shall study MV algebras in connection with Riemann surfaces. In fact, the Riemann surface as a concept belongs to complex analysis. On the other hand, Möbius transformations form a part of the theory of Riemann surfaces. In general, this work gives a good understanding how it is possible to fit together different fields of mathematics.

Hållpunkter för lärande : småbarns möten

Developed from human activities, mathematical knowledge is bound to the world and cultures that men and women experience. One can say that mathematics is rooted in humans’ everyday life, an environment where people reach agreement regarding certain “laws” and principles in mathematics. Through interaction with worldly phenomena and people, children will always gain experience that they can then in turn use to understand future situations. Consequently, the environment in which a child grows up plays an important role in what that child experiences and what possibilities for learning that child has. Variation theory, a branch of phenomenographical research, defines human learning as changes in understanding and acting towards a specific phenomenon. Variation theory implies a focus on that which it is possible to learn in a specific learning situation, since only a limited number of critical aspects of a phenomenon can be simultaneously discerned and focused on. The aim of this study is to discern how toddlers experience and learn mathematics in a daycare environment. The study focuses on what toddlers experience, how their learning experience is formed, and how toddlers use their understanding to master their environment. Twenty-three children were observed videographically during everyday activities. The videographic methodology aims to describe and interpret human actions in natural settings. The children are aged from 1 year, 1 month to 3 years, 9 months. Descriptions of the toddlers’ actions and communication with other children and adults are analyzed phenomenographically in order to discover how the children come to understand the different aspects of mathematics they encounter. The study’s analysis reveals that toddlers encounter various mathematical concepts, similarities and differences, and the relationship between parts and whole. Children form their understanding of such aspects in interaction with other children and adults in their everyday life. The results also show that for a certain type of learning to occur, some critical conditions must exist. Variation, simultaneity, reasonableness and fixed points are critical conditions of learning that appear to be important for toddlers’ learning. These four critical conditions are integral parts of the learning process. How children understand mathematics influences how they use mathematics as a tool to master their surrounding world. The results of the study’s analysis of how children use their understanding of mathematics shows that children use mathematics to uphold societal rules, to describe their surrounding world, and as a tool for problem solving. Accordingly, mathematics can be considered a very important phenomenon that children should come into contact with in different ways and which needs to be recognized as a necessary part of children’s everyday life. Adults working with young children play an important role in setting perimeters for children’s experiences and possibilities to explore mathematical concepts and phenomena. Therefore, this study is significant as regards understanding how children learn mathematics through everyday activities.

The cultural dimension in focus : promoting awareness of diversity and respect for difference in a Finland-Swedish EFL classroom

This study addresses the role of EFL education, its potential and shortcomings, and the challenges the future of EFL education will bring. It is argued that new societal demands and the limited time we have at our disposal in the classroom make it necessary to rethink goals and content and move away from the transmissionof limited sets of facts and information to helping students develop awareness and competences that can be applied in many different situations, also in a perspective of lifelong learning. The overall aim of the current study is to problematize and increase understanding of the implementation of cultural aspects in the language classroom by addressing the interrelated what, why and how of the cultural dimension within EFL education. This has been conducted by means of theoretical explorations into the area, alongside an attempt at promoting intercultural competence (IC) in a more systematic and insightful manner within my own educational praxis. The focus of the intercultural work in the classroom was on the promotion of awareness of difference and diversity, as well as respect for such difference through the ability to decenter from cultural norms and behavior that previously have been taken for granted. These are two elements that have been suggested as fundamental for other work with IC in the classroom and for the realization of important aspects of the underlying values of basic education. In the context of this study, IC comprises several interconnected components supportingeach other in a variety of ways, with the further aim being interaction with and respect for difference in general, not only concerning e.g. representatives ofcertain English-speaking communities. The methodology was informed by action research, with myself in the role of the teacher-researcher or the reflective practitioner. For the purpose of the project I was authorized to take on the EFL education for the three years of upper comprehensive school of one random class of students originally assigned to one of the language teachers of the selected Finland-Swedish school. Thus, the class of 17 students was not specifically chosen for the project, and the aims and contents chosen for the development project were placed within the framework of the ordinary curriculum. By exploring the students¿ insights concerning different English-speaking cultural groups, mainly through a set of questionnaires, it was possible to outline the work with the cultural dimension in the classroom for the following three years. Work progress was evaluated at specific stages, and the final project evaluations were conducted through individual student interviews in grade 9. The interviews were focused on possible development of students¿ insights concerning different aspects of the cultural dimension. In particular this concerned awareness of difference and diversity, including modification of stereotypes, as well as the ability to decenterin order to be better able to respect such difference. I also explored students¿ awareness and views of the activities and approaches used in class, as well asaffordances both inside and outside the EFL classroom in relation to these intended insights. A further focus area was the perceived relevance to students of different aspects of the cultural dimension. The frameworks and approaches adopted for the work in the classroom all have in common that they are based on a constructivist framework, where knowledge is constructed and reconstructed through interaction with one¿s social and cultural environment, including interaction with others. Reflective processes precede or are simultaneous with the learning of basic factual knowledge. This entails a view of learning as a progression from simple to more complex models rather than as a progression from facts to understanding and analysis. Here, the development of intercultural competence is seen asa cyclical process, or along a spiral curriculum, from simple to more complex levels through a combination of cognitive, affective and behavioral elements within a framework of experiential learning. This project has shown one possible wayforward concerning the development of intercultural competence within EFL education through a more systematic and comprehensive approach regarding linguistic and cultural aspects. The evaluation of the educational process explored in the study suggests the possibilities for work with the promotion of awareness of difference and diversity concerning some specific context that, based on students¿ prior knowledge and preconceptions, would benefit from further work. In this case, the specific context primarily concerned different aspects of both cultural and linguistic conditions in the UK. It is also suggested that many students developed the ability to decenter, described in the study as integral to being able to respect otherness. What still remains to be explored are more individualized approaches considering students¿ different levels of departure. Further work alsoneeds to be put into how to apply insights gained in these specific situations to more general contexts. It is also necessary to explore the use of the suggested approaches in a wider range of different contexts.