The cultural construction of school mathematics and student achievement. Trends in Science Education Research from a German Perspective

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1 The cultural construction of school mathematics and student achievement Paul Andrews Stockholm University, Sweden In this talk I will consider the extent to which school mathematics is a cultural construction. Curricula may be similar, at least as far as their content is concerned, but the underlying expectations and the extent to which systems mandate particular didactics vary considerably. Schools are located in cultural contexts that determine the ways in which they are structured and participants behave. Teachers themselves are, typically, products of the system in which they teach. Consequently their actions tend to be governed by hidden assumptions and beliefs about what constitutes good practice. Students also are conditioned to behave in ways that identify them with their cultural backgrounds. Drawing on a range of sources, but mostly my own research and video-recordings of European mathematics lessons, I will show how mathematics teaching is conceptualised in different cultural contexts and ask the question; can analyses of classroom practice explain students performance on international tests of achievement like TIMSS and PISA? Trends in Science Education Research from a German Perspective Elke Sumfleth University of Duisburg-Essen, Germany In Germany, Science Education became a university discipline in the early 1970s caused by a growing interest in science education following the so-called sputnik-shock. Professorships were established mainly with a perspective on the education of future science teachers. Yet, in order to develop into an equal university discipline fully integrated into the academic system, Science Education learned to sharply focus on fundamental research, instead of a predominantly pragmatic focus on, e.g., the development of instructional material. The first big challenge in Science Education research lay in the field of students preconceptions. Starting from this and relying on psychological learning theories a lot of still current research topics in science education have developed: e.g., improving learning strategies focusing on multimedia learning; designing learning environments integrating experiments; investigating context-based instruction and scientific modeling; employing large scale assessments like TIMSS and PISA, or the evaluation of national standards and the assessment of competencies in science for informing educational policy; teaching the Nature of Science as well as science-related communication skills; and last but not least, advancing professional knowledge of science teachers. In the presentation, I will delineate some of these trends that now span over 40 years of devoted research in Science Education. Focusing on recent results in Chemistry Education research these trends relevance for science learners of yesterday, today and tomorrow will thus be emphasized.

2 Students with mathematical learning difficulties Who are they? How to support their mathematics learning? Pirjo Aunio University of Helsinki, Finland The purpose of this talk is to discuss about the learning difficulties in mathematics (e.g., learning difficulties in mathematics, mathematical learning disability, dyscalculia, low performers in mathematics). The focus will be in comprehensive school students (grades K- 9). My aim is to describe the reasons for low performance and the variance in performance in this group of students. Moreover, I will discuss the evidence-based-practice to identify and follow-up the learning of students with mathematical learning difficulties (i.e., assessment) and the educational solutions to support them (i.e., intervention).

3 Leading the change in science and math education in Palestine Jeanne Albert and Khansaa Diab Al-Quds-Bard University, Israel Moving experienced teachers from the comfort of traditional teacher-centred rote learning practices to a student-centred problem solving classroom learning culture is a key difficulty of school change. During the past 4 years, the Al-Quds Bard MAT Program, working exclusively with in-service teachers, has helped teachers make large scale transformations in their teaching. Our presentation will show how two key factors program design and student motivation have contributed to these changes. Though the sequence and structure of course requirements has provided the meaningful contexts for learning, we believe that the motivation to earn their degree and a commitment to doing what is necessary to complete coursework has helped these teachers step beyond their past experiences to try something new and recognize its value for classroom learning. Data was collected by: pre-survey, free writing, photos, students self- reflections and final action research projects and analyzed by qualitative and descriptive methods. The impact of a comprehensive teacher professional development program in formative assessment on teachers practice and students achievement Catarina Andersson Umeå University, Sweden A vast amount of research has shown that the use of formative assessment is one of the most effective ways of increasing student achievement. However, a strong research base for how to help teachers to implement such a practice is lacking. This motivates the overall aim of a larger research project, conducted at Umeå Mathematics Education Research Centre (UMERC) in collaboration with a Swedish municipality. Catarina Andersson (PhD student) presents results about the impact of a professional development program on teachers classroom practice and students performance in mathematics. In these studies 22 randomly selected grade 4 teachers were observed and interviewed before the PDP and in the school year after. Questionnaires were administered to the teachers both directly after the PDP and one year after. Their students took mathematics pre and post-test.

4 Using tutorials in physics teaching at university Mervi Asikainen, Mikko Kesonen, Risto Leinonen and Pekka E. Hirvonen University of Eastern Finland Tutorials in Introductory Physics is a teaching material designed to supplement traditional lecture-based physics teaching at university level. The material has been developed at University of Washington during 20 years. We have tested the use of tutorials during two Basics Physics courses in Department of Physics, Joensuu. Our results showed that the tutorials enhance students learning and students attitudes to the use of tutorials are various but mainly positive. Our experiences encouraged us to widen the use of the tutorials to cover all four introductory physics courses starting from the autumn 2013 with a more detailed monitoring of students reactions to find out reasons for their attitudes. In this presentation, we describe the challenges of using the tutorials and observed students reactions for this non-traditional university physics teaching. The impact of a teacher professional development program in formative assessment on mathematics teachers classroom practice Erika Boström Umeå university, Sweden This study is a substudy in a project about a comprehensive professional development program (PDP) for mathematics teachers in formative assessment (FA). My aim is to investigate in which ways the participating teachers classroom practice change, due to the delivered PDP, and what some of the reasons may be for the variation in the teachers' implementation of a FA practice. Fourteen randomly chosen mathematics teachers in secondary school participated in the PDP. The teachers were interviewed and their classroom practice observed before and after the PDP. They have also answered two questionnaires. Preliminary results show that all teachers were motivated to change and did change their practice, but to varying degrees. Factors that were important for the change to take place have been identified.

5 Teacher-guided problem sequences Lars Burman Åbo Akademi University A general trend in teaching of mathematics at Finnish lower-secondary school may be the use of tasks, in which pupils are supposed to imitate already solved tasks in a textbook. The tasks inviting to higher-order thinking are few and they are often placed at the end of chapters, which means that many pupils very rarely work with these tasks. In order to address this problem, I have started a work with the aim to design tasks that should give more pupils the possibility to work more often in a desired way. More precisely, these tasks should be a part of instruction and not just tasks for practice and homework. Moreover, the exercises should also develop the pupils competences to solve problems and work with projects in courses to come in mathematics. I will present some results of this ongoing work so far, concerning both the theoretical progress and experiences from the use in classes. At this moment, for instance, I should label the exercises teacher-guided problem sequences. The work, in which pupils work (often in groups) with a problem, then discuss the results with the teacher, then get new information and guide-lines and then go on working and so on, seems very promising. Voidaanko luokanopettajaopiskelijoiden käsityksiin matematiikasta ja sen opettamisesta vaikuttaa? Pasi Eskelinen ja Lenni Haapasalo Itä-Suomen yliopisto, Finland On näyttöä siitä, että suomalainen matematiikan opetus on oppikirjasidonnaista ja siinä hyödynnetään melko vaatimattomalla tavalla tieto- ja viestintäteknologian tarjoamia mahdollisuuksia. Matematiikan pedagogiikka 1 & 2 kursseilla toteutetulla seurantatutkimuksella selvitettiin, missä määrin luokanopettajaopiskelijoiden käsitykset vahvistavat näitä löydöksiä ja miten näihin käsityksiin voidaan vaikuttaa näillä kahdella peruskurssilla.

6 Teaching Cultural Knowledge of Physics through a summative lecture example from optics Igal Galili Science Teaching Center, The Hebrew University of Jerusalem, Israel Cultural Content Knowledge (CCK) was suggested as a framework of knowledge studied at schools at the introductory level (1). Its counterpart is disciplinary knowledge which is usually framed within one fundamental theory of mechanics, electromagnetism, etc. Cultural knowledge structures any theory to its nucleus-body-periphery and displays the content knowledge in its affiliation to a few basic theories. We suggested providing this knowledge to the students in the form of a summative lecture after a regular course of physics in high school. Optics was chosen for an experiment for this domain includes three theories already in introductory instruction (2). A natural narrative of presentation is historical excurse. I will briefly describe the experiment held in two Italian high schools and some of its findings (3). Among them, we may mention students' interest to the theory-model relationship, hierarchical structure of the scientific knowledge, appreciation of the historical perspective of conceptual nature as a bridge to humanities and revealing the nature of physics knowledge. Discovering and handling mistakes during problem solving Carina Granberg Department of Applied educational Science, Umeå University, Sweden The present study will give some insights into how students discover and, without teacher support; deal with mistakes when they are solving complex mathematical problems in pairs, supported by GeoGebra. Their activities will be recorded and observed. Critical situations regarding discovered and handled mistakes will be identified. After their problem solving they are invited to clarify the identified situations by recounting their ideas, thoughts, strategies etc. (stimulated recall). Data will analyzed using the research framework: Creative and imitative reasoning (Lithner, 2008). Concepts like creativity, argumentation, anchoring will be used to scrutinize how students choose to handle their mistakes in order to move on in their problem solving process.

7 Luokanopettajaopiskelijoiden tietoisuus NCTM:n standardeista ja kestävistä aktiviteeteista Lenni Haapasalo ja Pasi Eskelinen Itä-Suomen yliopisto, Finland Curriculum and Evaluation Standards käynnisti matematiikan opetuksen laatua koskevan vilkkaan keskustelun tiedeyhteisössä jo 25 vuotta sitten. Kuitenkaan ei löydy empiiristä dataa siitä, ovatko opettajat edelleenkään tietoisia näistä standardeista, toteutuvatko ne käytännön opetuksessa, ja miten ne otetaan huomioon opettajankoulutuksessa. Sama koskee niitä kahdeksaa kestävää heuristista aktiviteettia, jotka ovat olleet matematiikan historiassa kestäviä jo yli 5000 vuoden ajan. Seurantatyyppisillä survey-tutkimuksilla ja opintotehtävien analyysillä selvitettiin, miten luokanopettajaopiskelijoiden tietoisuus näistä opetuksen laadun indikaattoreista kehittyy matematiikan pedagogisten opintojen aikana. How teaching variables and grade six learning outcomes predict learning outcomes on grade nine Markku S. Hannula and Susanna Oksanen University of Helsinki, Finland The Finnish national board of education collected longitudinal assessment data for mathematics learning from grades 3 to 9. We have analysed those students' (N = 3082) progress from grade 6 to grade 9 whose 9 th grade teachers completed a teacher survey (N = 566). We used a multivariate GLM analysis to predict cognitive and affective learning outcomes of students on grade 9 using their cognitive and affective learning outcomes on grade 6 and teacher survey responses as predictive variables. From this analysis, we identified teaching variables which predicted student learning gains and changes in their affect. In this presentation we focus on a comparison between students of different achievement levels on grade 6. We observed, for example, that emphasis on student thinking improved the affect of below average students, while emphasis on peer teaching improved the attainment of above average students.

8 Change and stability in the mathematical performing groups in grade one Heidi Hellstrand a *, Karin Linnanmäki a and Pirjo Aunio b a Åbo Akademi University, Faculty of Education, Finland b University of Helsinki, Faculty of Behavioral Sciences, Finland The aim of this study was to analyze what kinds of different performing groups can be identified among children in first grade. The study group consisted of grade one children (N = 334, boys = 171) from 19 schools in the Swedish-speaking areas of Finland. Children s mathematical performance was measured at three time points during the grade one (autumn, winter and spring). A person centered approach was used to find students with similar patterns of performance. Four distinct performing groups were found through latent profile analysis: well performing across all math subskills (51%), low performing in number sense and basic arithmetic skills (11%), low performing in mathematical relational skills (25%), and low performing across all math subskills (13%). There was a significant association between gender and group-belonging in autumn (p<.05) and in spring (p<.05). Mostly, the group-belonging was stable during the school year, markedly in the all low-group. Development of mathematical problem solving at the university level Peter Hästö University of Oulu, Finland In this presentation I will discuss ongoing work with Henry Leppäaho (Jyväskylä) and Raimo Kaasila (Oulu) on the analysis of the development of prospective secondary school teachers views on mathematical problem solving. Our main data source is a collection of reflective essays written by the students during a one-semester MPS-course. Using a qualitative, datadriven analysis we identify changes in students conceptions and stated actions, as well as students views on the reasons for the changes. Peruskoulun 6. luokkalaisen matemaattisen ajattelun jäljillä Jorma Joutsenlahti a, Henry Leppäaho ja Harry Silfverberg a University of Tampere, Finland Esityksessämme kuvaamme, minkälaisia sanallisia merkityksiä peruskoulun kuudesluokkalaiset oppilaat löytävät peruslaskutoimituksia sisältäville lausekkeille ja minkälaisiin konteksteihin oppilaat laatimansa tehtävät liittävät. Esitämme esimerkkejä oppilaiden laskulausekkeisiin liittämistä tulkinnoista ja käytännön tilanteista. Tutkimme myös osin käänteisten prosessien eli matemaattisesta lausekkeesta muodostettavan sanallisen tehtävän ja sanallisesta tehtävästä muodostetun lausekkeen keskinäistä yhteyttä oppilaiden suorituksissa. Tutkimusaineistomme perustuu Opetushallituksen vuonna 2008 keräämään matematiikan oppimistuloksia mittaavaan 5560 oppilaan aineistoon, josta olemme saaneet käyttöömme edustavan, noin 900 vastauspaperin osa-aineiston. Olemme analysoineet pääosin kvalitatiivisin menetelmin oppilaiden vastauksia ja näin pyrkineet syventämään jo olemassa olevaa tilastollista tietoa mainitusta aineistosta.

9 Semi-automatic Derivation of Conceptual Graphs from Student Interviews Using Natural Language Processing Henri Kauhanen 1,2, Tommi Kokkonen 1, Otto Lappi 2, Terhi Mäntylä 1 & Ismo T. Koponen 1 1 Department of Physics, University of Helsinki, Finland 2 Institute of Behavioural Sciences, University of Helsinki, Finland In higher education, students must often undergo a process of conceptual change, where new concepts are acquired and old conceptual structures are revised. Previous studies have suggested that empirical research into conceptual change can stand to benefit from a networktheoretic approach in which students conceptual structures are modelled as conceptual graphs. In previous applications of such network-theoretic methods, the conceptual graphs have been manually determined from empirical data. In this talk, we describe a method for producing conceptual graphs in a semi-automatic manner. Using tools from natural language processing, we show how conceptual graphs may be computationally derived from student interview transcripts. We compare the results of this method with results from previous research based on manual content analysis. We discuss advantages and limitations of the method, arguing that it may complement manual content analysis in important ways. Finally, we discuss possibilities of refining and further automatizing the method. Changes in university students explanation models in DC-circuit tasks Tommi Kokkonen and Terhi Mäntylä Department of Physics, University of Helsinki, Finland Broadly speaking, there are two different perspectives in research on conceptual change: so called knowledge-as-theory views and knowledge-as-elements views. According to the former, the learner s knowledge is best described as coherent and theory-like whereas the latter describes the knowledge as a collection of loosely related pieces. The question is: Can these views be combined? In order to examine this question, a study was carried out where university students conceptions of voltage and current were analysed. In the study, the students first predicted and, after experimenting, explained the behaviour of different DCcircuits in small groups. These small group sessions were transcribed and analysed in order to identify the students explanation models. The models are presented as graphs, which allow a fine-grained analysis of changes in the models. The results show how larger conceptual structures are formed from smaller pieces thus making it possible to combine different views at some level.

10 Pre-service teachers understanding of relatedness physics concepts: A network approach Ismo Koponen University of Helsinki, Finland Scientific conceptual knowledge is a complex and interlinked set of concepts, principles, laws and models. Such a structure of conceptual knowledge is at the same time coherent, in a sense that it is interlinked and its parts mutually support each other, and contingent, in the sense that there are always many ways to support the parts of the structure. Maintaining the coherence and contingency in learning is difficult for a learner and requires effort. In this study we examine the pre-service teachers understanding of the relatedness of physics concepts and use concept networks as representations of the conceptual knowledge. The coherency and contingency of the representations is analysed through three centrality measures for a given concept s structural and epistemic centrality in the network. It is shown, that the centrality measures provide a comprehensive picture of students ability to conceive the complex relations between physics concepts. Työssä olevien matematiikanopettajien ja opettajankouluttajien näkemyksiä opettajankoulutuksen opetusmenetelmistä Mika Koponen, Mervi Asikainen, Antti Viholainen ja Pekka E. Hirvonen Itä-Suomen yliopisto, Finland Osana laajempaa matematiikan opettajankoulutuksen kehittämishanketta selvitimme kyselytutkimuksen avulla Itä-Suomen yliopistosta valmistuneiden matematiikanopettajien (N=101) ja Itä-Suomen yliopiston opettajankouluttajien (N=19) näkemyksiä matematiikan opettajankoulutuksen nykytilasta ja sen kehittämisestä. Tässä artikkelissa tarkastelemme valmistuneiden opettajien ja opettajankouluttajien näkemyksiä matematiikan opettajankoulutuksen opetusmenetelmistä. Näkemysten tarkastelu jaetaan tutkintorakenteen mukaisesti koskemaan ainelaitoksen matematiikan opintoja sekä pedagogisten opintojen ja opetusharjoittelun kokonaisuutta. Enemmistö valmistuneista opettajista suhtautui negatiivisesti ainelaitoksen opetusmenetelmiin ja positiivisesti pedagogisten opintojen ja opetusharjoittelun opetusmenetelmiin. Erityisesti luento-opetusta kritisoitiin liian yksipuolisena ja opettajakeskeisenä menetelmänä, oppijakeskeisiä ja keskustelevia menetelmiä puolestaan arvostettiin. Tulokset viittaavat siihen, että valmistuneet opettajat ovat koulutuksen aikana omaksuneet modernin oppimiskäsityksen, minkä vuoksi he kritisoivat opettajakeskeisiä opetusmenetelmiä ja vastaavasti näkevät oppijakeskeiset ja yhteistoiminnallisuutta lisäävät opetuksen lähestymistavat opettajan työtä tukevina. Opettajankouluttajista noin puolet suhtautui käyttämiinsä opetusmenetelmiin myönteisesti. Opettajankouluttajien kertomat esimerkit opetusmenetelmistä edustivat kuitenkin usein demonstroivaa tai havainnollistavaa opetusta, joka voi opettajaopiskelijan näkökulmasta näyttäytyä yksisuuntaisena, opettajajohtoisena ja siten nykyaikaiseen kouluopetukseen soveltumattomana toimintana.

11 Learning difficulties and academic well-being as predictors of educational aspirations and choice of secondary education Johan Korhonen 1, Karin Linnanmäki 1 and Pirjo Aunio 2 1 Åbo Akademi University, Finland 2 University of Helsinki, Finland The aim of this study is to examine how lower secondary students (N=1,152) achievement (reading and mathematics) and academic well-being (academic self-concept and school burnout) predict educational aspirations and choice of secondary education. Previous research has identified learning difficulties as the most important predictor for educational dropout (Battin-Pearson et al., 2000; Korhonen et al., under review). We will extend the research base by investigating the predictive power of learning difficulties and academic well-being on educational aspirations and choices. The analyses will start with establishing measurement invariance across gender by conducting multiple group factor analyses. We will then pursue the aim of the study by conducting multiple-groups SEM path analyses with a) educational aspirations and b) a dichotomous secondary education choice as the dependent variable. Preliminary analyses indicate measurement invariance across gender. Furthermore, mathematics and reading skills seem to predict educational aspirations differently for boys and girls.

12 Ympäristökasvatus ja kestävä kehitys fysiikassa Pirkko Kärnä Tämä tutkimus käsittelee oppilaiden ympäristöasenteita ja ympäristökasvatusta fysiikan kontekstissa. Tutkimusaineistona on vuoden 2011 luonnontieteiden oppimistulosten kansallisen arvioinnin (N= 2 949) ja siihen liittyvän esikokeen (N= n. 300) data, josta analysoitiin fysiikan ja kemian ympäristöasenneväittämien vastauksia tilastollisten menetelmien avulla (SPSS). Selvitettiin sitä, miten oppilaan ympäristöasenteet liittyvät hänen arvioinnissa osaamiseensa ja oppiainekohtaisiin asenteisiin. Tulosten mukaan ympäristökysymyksiin liittyvät asenneväittämät korreloivat kohtalaisesti sekä arvioinnissa menestymiseen että oppiainekohtaisten asenneväittämien kanssa. Eniten yhteyttä oli oppilaan kulutusvalintojen ja kemian opetuksen hyödylliseksi kokemisen välillä. Tytöillä oli myönteisemmän ympäristöasenteet kuin pojilla, jotka ilmaisivat tyttöjä useammin osaamista ja aiheen hyödyllisyyttä koskevia asenteita. Ympäristöaiheet eivät kuitenkaan kiinnostaneet oppilaita kovin paljon. Lisäksi tehtiin kirjallisuusanalyysejä siitä, mitä kestävän kehityksen mukainen fysiikan opetus tarkoittaa ja miten tämän tulisi näkyä oppilaan arvioinnissa. Ajankohtaisia aiheita sekä ekologisia, ekonomisia, kulttuurisia ja sosiaalisia näkökulmia esiintuova opetus voisi edistää fysiikan kiinnostavuutta ja sitä, että oppilaat saavat selityksiä maailmasta myös fysiikan tunneilla. Tavoitteiden, opetuksen ja arvioinnin tulee olla linjassa. Bringing authentic science to science education Nano-researchers views Antti Laherto 1, Frederike Tirre 2 and Ilka Parchmann 2, 1 Department of Teacher Education, University of Helsinki, Finland 2 IPN, University of Kiel, Germany Increasing the authenticity of science education is one of the suggested responses to the declining attitudes to school science. Here we describe work carried out within a research and development project that aims to contribute to authentic science learning by presenting contemporary cutting-edge research in out-of-school learning environments. In the first phase of the project, 8 professors (6 in Kiel and 2 in Helsinki) working in various fields of nanoresearch were interviewed on the educational and communicational aspects of nanoscale science and technology. The interview results and their use in the development of a science exhibition and a student lab are discussed in the presentation.

13 Millaisia havaintoja lukion oppilaat tekevät kidevedellisen kuparisulfaatin reaktioista? Jarkko Lampiselkä University of Helsinki, Finland Reversiibelin reaktion toimintaperiaatetta havainnollistetaan opetuksessa tyypillisesti kidevedellisen kuparisulfaatin reaktioilla. Se, millaisia havaintoja oppilas tästä työstä tekee, tai se, miten kokeen näyttäminen oppilaan ymmärrystä ilmiöstä lisää, on jossain määrin epäselvää. Tässä tutkimuksessa 39 lukion oppilaalle demonstroitiin reversiibelin reaktion toimintaperiaatetta kyseisellä reaktiolla ja kurssikokeen yhteydessä heidän käsitystään mitattiin puolistrukturoidulla lomakkeella. Induktiivinen sisällönanalyysi osoitti, että opiskelijoiden tekemät havainnot keskittyivät yleensä vain johonkin tiettyyn muutokseen ja muut muutokset jäivät vähemmälle huomiolle. On siten mahdollista, ettei opiskelijoille muodostu sellaista ehyttä, kokonaisvaltaista käsitystä ilmiöstä ja sen teoreettisista perusteluista, joita opettaja olettaa tällä kokeella muodostuvan. On siten tärkeää keskustella kriittisesti siitä, miten kyseistä koetta pitäisi käyttää kouluopetuksessa, jotta opettajan ja opiskelijan näkemykset kohtaisivat. Does practice make perfect? A study of the Granger-causal relationship between attempting to solve exercises and mathematical proficiency Krista Linnoinen Department of mathematics and systems analysis, Aalto University, Finland Computer-aided mathematics teaching has been an active field of research and development at Aalto University. This study is motivated by a desire to increase the number of students that pass compulsory basic mathematics courses. The courses aim to provide engineering students with the mathematical skills needed in their degree programmes. Here the first two basic courses are examined. On the courses a web-based automated assessment system called STACK was used for supplementary exercises and later to quantify mathematical proficiency. The Granger causality tests show that there exists a Granger-causal relationship such that mathematical proficiency affects the desire to attempt to solve exercises. The test, its results and implications will be presented. This presentation is based on a joint research project with Antti Rasila (Aalto University) and is a part of the EU-project S3M2.

14 Developing educational practice: experiments on mathematics students' construction of knowledge Johan Lithner Umeå University, Sweden The purpose of the research project Learning by Imitative or Creative Reasoning is to contribute to the solution of the persistent problem that inefficient rote learning by imitation dominates in mathematics classrooms. A design research methodology is used in collaboration between researchers from cognitive neuroscience, cognitive psychology and mathematics education to construct, implement, evaluate and form theoretical design principles with respect to practice tasks that give students opportunity and responsibility to construct new knowledge through creative reasoning. The results so far indicate that algorithmic support (in common school format, i.e. of templates to mimic) is more efficient for practice success but less efficient for learning than student s own construction of target knowledge. Contrary to common beliefs, the relative positive learning effect from creative reasoning is stronger for less able students. Conceptual development of electric field and pre-service physics teachers understanding of it Terhi Mäntylä and Maija Nousiainen Department of Physics, University of Helsinki, Finland Electric field is an abstract and complex scientific concept, which is important to understand in the university physics. The foundation of the electric field concept is laid at upper secondary school and it is continued at introductory university physics courses. However, research has shown that the field concept is problematic and difficult to learn. It has been noted that pre-service physics teachers knowledge of electric field after introductory studies is unorganized and fragmented. In this study, we first introduce a conceptual trajectory of electric field concept for purposes of physics teacher education. Second, the learning results of pre-service physics teachers understanding of the conceptual development of electric field concept are discussed. The results are based on the qualitative graphical and content analysis of the pre-service teachers concept networks presenting the development of electric field concept.

15 Learning from the DaNa-project: finding best practices for deployment of data logging equipment in secondary schools Markus Norrby, T. Jacobson and S. Svenlin Åbo Akademi University, Finland In 2011 twelve Swedish speaking upper secondary schools in Western Finland were awarded financing from the Board of Education for a joint project to buy and start using data logging equipment in physics, chemistry and biology (DaNa). The two year project is now coming to an end and will be evaluated through a long term research project at Åbo Akademi University in cooperation with the teacher training school. Since deployment of this kind of equipment is growing rapidly in popularity in Finland and elsewhere it is relevant to learn from weaknesses and strengths found in this specific project. In the first phase the attitudes of the teachers involved and their students are investigated, and an attempt is made to develop a method for evaluation of individual demonstrations in the relevant context. In the future quantitative comparisons of the results in e.g. matriculation exams are planned. Coherence and contingency of pre-service physics teachers views of the relatedness of physics concepts Maija Nousiainen Department of Physics, University of Helsinki, Finland The understanding of the relatedness of physics concepts is very important for physics teachers in order to introduce the physic concepts in ordered and logical way in their teaching, so that there is kind of continuity and contingency of teaching. In physics teacher education the use of graphical knowledge representation tools like concept maps are abundantly used because they are known to support the formation of coherent and contingent knowledge. It is widely assumed that certain structural characteristics of concept maps (interconnectedness identified as a feature for coherence and hierarchy for contingency) can be connected to the usefulness of content. In order to study this relationship, the concept maps made by pre-service physics teachers are examined. The design principles of the concept maps are based on quantitative experiments and modelling as the basic procedures in physics concept formation. The epistemic acceptability of justifications written in links is evaluated by using a four-level classification. The new method to evaluate links by their level of epistemic justification is suitable to visualise the degree of organisation and knowledge. The results show that the epistemic analysis of links affects remarkably to the acceptability of knowledge which can be interpreted as an affect to the degree of coherence and contingency. However, the relation between acceptability and coherence is not linear, and even with a substantial number of low acceptability links, coherence may remain high. This shows the robustness of coherently connected conceptual systems.

16 The role of cognitive-affective factors in underachievement Mikaela Nyroos a, Johan Korhonen b, Bert Jonsson a and Hanna Eklöf a a Umeå University, Sweden b Åbo Akademi University, Finland There is converging evidence on the strong relationship between working memory capacity and mathematical performance. Test anxiety is a potential moderating factor involved in the relationship between working memory and academic performance. Based on Eysenck and Calvo s (1992) Processing Efficiency Theory the present study investigated whether associations between working memory and educational achievement in mathematics were moderated by test anxiety. 624 children aged 9-10 years completed verbal, spatial, and complex working memory tasks. Test anxiety was measured using the Children s Test Anxiety Scale (Wren & Benson, 2004). Mathematical performance was assessed using the Swedish national test in mathematics. Opettajien kysymykset heidän ohjatessaan 3-5-luokkalaisten avoimia ongelmanratkaisutehtäviä Liisa Näveri, Anu Laine, Maija Ahtee, Päivi Portaankorva-Koivisto, Erkki Pehkonen ja Markku S. Hannula Helsingin yliopisto, Finland Matematiikan oppimisen tavoitteena on kaikissa ikäryhmissä matematiikan rakenteiden ymmärtäminen ja matemaattisen ajattelun kehittyminen (Opetushallitus 2004). Keskustelu ja perusteleminen ovat keinoja kehittää ajattelua ja tehdä sitä näkyväksi (Joutsenlahti 2003). Opetussuunnitelman perusteissa tämä on asetettu tavoitteeksi jo ensimmäisiltä alakoululuokilta lähtien (OPH 2004). Tässä artikkelissa seurataan luokissa tarkemmin käytävän keskustelun kehittymistä tarkastelemalla opettajien ja oppilaiden kysymyksiä. Tutkimuksessa analysoitiin opettajien ja heidän oppilaidensa alakoulun kolmannelta luokalta lähtien, kolmen vuoden ajan, olleilla ongelmanratkaisutunneilla esittämiä kysymyksiä. Tunneilla käytetyt tehtävät olivat avoimia ongelmanratkaisutehtäviä. Opettajien kysymykset luokiteltiin kuuteen kategoriaan käyttämällä induktiivista sisällönanalyysiä, myös oppilaiden kysymysluokkia oli kuusi. Opettajat erosivat toisistaan selvästi sekä kysymysten määrän että yleisimmän kategorian suhteen. Opettaja- ja oppilaskohtaisissa kysymyksien kokonaismäärissä esiintyy selkeää vaihtelua, ja oppitunnit poikkesivatkin toisistaan opettajan ja oppilaiden välisen keskustelun määrän suhteen.

17 Creative reasoning and computer based feedback Jan Olsson Umeå University, Sweden The study will investigate how dynamic software, GeoGebra, will guide and structure students reasoning during mathematical problem solving. In a previous study (Granberg & Olsson, on review), students were found to take advantages of GeoGebras providing of a shared working space, visualization, and as a generator of creative feedback. It was also apparent student did not justify their solutions explicitly, therefore, in the planned study; their argumentation is out of particular interest. About 20 students between the ages of 16 and 17 will in dyads solve a task designed to engage in creative reasoning. Their computer-activity, conversation, and gestures will be recorded and analyzed using Lithner s (2008) framework of imitative and creative mathematical reasoning together with definitions and descriptions of collaborative learning and formative feedback. The results are expected to consist of examples of predictive and verificative argumentation and characterization of feedback. Distribution of lesson time in introductory algebra classes from four countries Anna-Maija Partanen a and Cecilia Kilhamn b a University of Lapland and Åbo Akademi University, Finland b University of Gothenburg, Sweden In the VIDEOMAT project, introductory algebra lessons from Sweden, Norway, California (USA) and the Swedish speaking part of Finland were video recorded. The initial organization of data included dividing lessons into phases using coverage coding developed for the project. The mutually exclusive codes show, for example, whether class time is spent on whole-class activities: introduction of a new topic or follow up, or on student work: individual or group work. The distribution of lesson time during four successive lessons in five classes from Sweden and four classes from all the other countries is illustrated graphically for comparison. Initial descriptive analyses show that there was much variation in spending lesson time inside each country. However, an example of the differences is the emphasis on individual student work in Finland when compared to the other countries.

18 Oppikirja matematiikan opetuksessa: instrumentin kehittelyä Leila Pehkonen 1, Heidi Krzywacki 2 & Anu Laine 1 1 Helsingin yliopisto, Finland 2 Mälardalen University, Sweden Tutkimushankkeemme tavoitteena on tutkia oppikirjan roolia matematiikan opetuksessa erityisesti opettajien näkökulmasta. Tämänhetkisen tutkimuksen valossa opettaja-oppikirja - yhteydestä tiedetään kaikkiaan varsin vähän. Esittelemme hankkeessamme käytettävän instrumentin kehittämistä ja validiointia. Lähtökohtana kehittämisessä on ollut aiempi tutkimus, jossa tarkasteltiin opettajien puhetta muutoksesta ja pysyvyydestä matematiikan opetuksessa (Pehkonen 2007). Siinä keskeiseksi teemaksi nousi oppikirja, vaikkei siitä varsinaisesti tutkittavilta kysytty mitään. Haastatteluaineistosta oli jäsennettävissä kolme laadullisesti erilaista tapaa puhua oppikirjasta, jotka nimettiin oikeuttamiseksi, kritiikiksi ja syyllisyyden tunteeksi (Pehkonen 2004). Näiden teemojen pohjalta laadimme 60 väitettä, jotka muotoiltiin suoraan opettajien puheesta. Väitteistä ja muutamista taustamuuttujista rakensimme e-lomakkeen. Vastaajia haimme sekä MAOLin kerhokirjeen että LUMAkeskuksen luokanopettajien tiedotuslistan kautta huhtikuussa Toukokuun loppuun mennessä saimme yhteensä 222 vastausta. Faktorianalyysin avulla näin saadusta aineistosta jäsentyy, ekstrakointitavasta riippumatta, neljä ulottuvuutta, jotka selittävät noin 49 % muuttujien varianssista. Alkuperäisistä 60 osioista karsiutuu pois kolmannes jo tässä vaiheessa. Esityksessä tarkastelemme mittarin kehittämisen nykyvaihetta ja siihen liittyviä haasteita sekä jatkosuunnitelmiamme. Adults and mathematics learning do they need concreteness to learn mathematics Päivi Perkkilä Kokkola University Consortium Chydenius, Finland All adult learners have a learning history that is intimately connected with their experience of learning at school. The school experience has a great influence on learning as adults. Mathematics learning in adulthood often requires the reconstruction of the elementary school mathematics basic concepts. This is true in adult teacher education. These adults have very different backgrounds and some of them are afraid of mathematics. They might have had learning disabilities in mathematics or they have forgotten some of the basic concepts or they have learnt to memorize mathematics but not to understand it. In this article I try to open adult pre-service students mathematics learning situations with concrete materials during basic mathematics studies in class teacher education. The solid basis for mathematics learning is created during primary school. The basic concepts are learnt then and future teachers should understand these concepts. The most important issue is to learn and understand primary school mathematics, first!, said Nea, an adult woman who realized that she had to rebuilt the basic mathematical concepts if she wants to learn mathematics.

19 Analyzing prospective mathematics teachers dreams and nightmares Päivi Portaankorva-Koivisto and Lasse Eronen University of Helsinki, Finland Teachers beliefs do not lend themselves easily to empirical investigation (Swan, 2006). In this paper we analyzed prospective mathematics teachers student-centered vs teachercentered beliefs by using short writings. At the end of their pedagogical studies teacher students (N = 66) read an article about pupils dreams and nightmares concerning mathematics lessons. Afterwards they wrote about their own dreamful and nightmarish mathematics lessons as teachers. In the analysis, based on grounded theory approach, we found three teacher categories: student-centered (24 %), teacher-centered (32 %) and teachers balancing in between (44 %). In student-centered texts the dreams come true, when students are doing well. In teacher-centered texts the dreams come true, when the teacher is doing well. Swan, M. (2006).Designing and using research instruments to describe the beliefs and practices of mathematics teachers. Research in Education, 75(1), Lukiolaisten näkemyksiä fysiikasta ja fysiikan oppimisesta Jenni Saarela Tutkimuksessa selvitettiin lukiolaisten näkemyksiä fysiikasta ja fysiikan oppimisesta kvantitatiivisen kyselytutkimuksen, Colorado Learning Attitudes about Science Surveyn (CLASS) avulla. Tutkimus toteutettiin kahdessa lukiossa alkuvuonna 2012 niin, että tutkimusjoukon muodostivat lukion ensimmäisen vuosikurssin opiskelijat (N=88). Opiskelijoiden vastauksia 42 väittämään verrattiin eksperttien vastauksiin, joita pidettiin suotuisina näkemyksinä. Tutkimustuloksia käsiteltäessä kiinnitettiin erityistä huomiota siihen, onko tyttöjen ja poikien näkemysten tasossa eroa sekä eroaako näkemysten taso sen mukaan aikooko opiskelija jatkaa fysiikan opiskelua lukiossa syventävillä kursseilla vai ei. Tulosten perusteella voidaan todeta, että lukion ensimmäisen vuosikurssin opiskelijalla on hyvin noviisimaiset käsitykset fysiikasta ja sen oppimisesta. Erityisesti opiskelijat, jotka eivät aikoneet jatkaa fysiikan opiskelua, saavuttivat hyvin alhaisen näkemysten tason verrattuna heihin, jotka aikoivat jatkaa fysiikan opiskelua tai edes harkitsivat sitä. Lisäksi poikien näkemykset fysiikasta olivat tyttöjen näkemyksiä hieman suotuisampia. Yksittäisiä väittämiä tarkasteltaessa havaittiin myös, että opiskelijoille ei ole selvää mikä merkitys matemaattisilla kaavoilla on fysiikassa.

20 A study of concept image of function and view of mathematics in a Finnish middle years programme school Jessica Salminen University of Helsinki, Finland This study was inspired by earlier studies of view of mathematics and the need to create learning material in English for teaching functions for ninth graders. The goal of the research was to find out the following: 1) how the students had understood functions, 2) the connection between the view of mathematics and a student s concept image of function, and 3) the connection between view of mathematics and overall success in mathematics. The underlying theoretical foundation of this paper was based on a study of concept image of function conducted by Vinner and Dreyfus (1989) and a study of view of mathematics conducted by Pietilä (2002). The participants of the study were all ninth graders of one school who were present on the day of the study (N = 49). Concept image results from these students were compared with the data from an upper secondary school collected by Hannula and Tuomi (2012). Both qualitative and quantitative methods were used in analyzing the data. Building the base for early addition: A computerized intervention Jonna B. Salminen 1, Tuire K. Koponen 2, and Mikko T. Aro 1 1 University of Jyväskylä, Finland 2 Niilo Mäki Institute, Jyväskylä, Finland In this study, a hierarchically oriented mathematical content, starting from the numerical base and proceeding towards addition, was implemented into a computer format. Short and intensive training with such a program was hypothesized to deepen understanding of basic addition in kindergarteners (n = 13) with poor addition skills (-1.5 SD). The results indicated both immediate and delayed intervention effects in basic addition, counting skills, and in Number Sets Test. After analysing the log data and contrasting the results to a performance level control group (n = 8), individual differences in terms of responsiveness to intervention are discussed. Suggesting, that a well-planned computer program holds promise in supporting, but also in identifying kindergarteners individual gaps in early number skills.

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