Integrative phenomena in visual arts and mathematics

The aim of our article is to find suitable integrative phenomena for both visual arts and mathematics, with a focus on preserving the nature of each of these subjects and their specific methods of acquiring and processing information. This article builds a picture of how to design and conduct an integrative learning continuum which genuinely preserves the nature of mathematics. To draw conclusions, we combined datasets from mathematics teacher education and the lower secondary school context. We found out that suitable integrative phenomena can relate to concepts shared by each of the integrating disciplines, such as ratio; or they can be typical processes of knowledge acquisition and construction, such as sorting. The teaching experiments revealed that the integrative phenomena appropriate for use in school must enable a joint investigative learning experience. The third finding was that the pupils needed teacher support to view the subjects more broadly. [GRAPHICS] .Peer reviewe

Adult learners’ career paths – from IT profession to education within two-year study programme in Finnish university context

Higher education and lifelong learning projects aimed at adults have become more widespread and have sparked a debate on how to restructure higher education policies and support lifelong learning. In Finland, a recent initiative in higher education policy is based on the theme of continuous learning. Different supporting structures and practices at the governmental level are being sought. During the academic year 2017–2018, the Ministry of Education and Culture in Finland funded a project that provided pedagogical studies in teaching for 16 IT professionals. The aim was to enable the participants to focus on the educational field and find new options for their careers. We utilized a narrative research approach to explore the types of adult learners’ storylines and positions that were constructed during these studies, of which we identified three: the storyline of different alternatives, in which participants positioned themselves as a career path builders, the storyline of becoming a teacher, in which participants positioned themselves as a teacherhood reflectors and becoming a teacher was an enriching alternative, and the storyline of looking forward, in which participants positioned themselves as a developers and mainly saw their studies as expanding their ongoing career opportunities.Higher education and lifelong learning projects aimed at adults have become more widespread and have sparked a debate on how to restructure higher education policies and support lifelong learning. In Finland, a recent initiative in higher education policy is based on the theme of continuous learning. Different supporting structures and practices at the governmental level are being sought. During the academic year 2017-2018, the Ministry of Education and Culture in Finland funded a project that provided pedagogical studies in teaching for 16 IT professionals. The aim was to enable the participants to focus on the educational field and find new options for their careers. We utilised a narrative research approach to explore the types of adult learners' storylines and positions that were constructed during these studies, of which we identified three: the storyline of different alternatives, in which participants positioned themselves as a career path builders, the storyline of becoming a teacher, in which participants positioned themselves as a teacherhood reflectors and becoming a teacher was an enriching alternative, and the storyline of looking forward, in which participants positioned themselves as a developers and mainly saw their studies as expanding their ongoing career opportunities.Peer reviewe

Prospective mathematics teachers’ self-referential metaphors as indicators of the emerging professional identity

Ideals play a key role in a student teachers’ identity work. They form targets to strive for and a mirror for reflection. In this paper, we examine Finnish mathematics student teachers’ metaphors for the teacher’s role (N= 188). We classified the metaphors according to a model that identified teachers as subject matter experts, didactical experts, and pedagogical experts, with the addition of another two categories, self-referential and contextual. For the exploration of emerging professional identities, we studied the self-referential metaphors, which formed the most common category in the data. We observed that every third metaphor described either student teachers’ personalities or their incompleteness as teachers, or new beginnings or eras. Although these aspects were expected, they also inform us as teacher educators of the values and ideals that student teachers have in terms of teaching and being a teacher. The metaphors that mathematics student teachers produced illustrated their identity processes and their emerging identity as a mathematics teacher.Peer reviewe

From Life to Autofiction : Retracing the Genre Tradition in Pirkko Saisio's Novel Series Pienin yhteinen jaettava, Vastavalo and Punainen erokirja

Pirkko Saisio's trilogy Pienin yhteinen jaettava (The Smallest Shared Dividend, 1998), Vastavalo (Against the Light, 2000), and Punainen erokirja (The Red Book of Separation, 2003), depicts the development of a masculine girl who at the end of the trilogy comes out as a homosexual women, a mother, and a writer. The main character is named Pirkko Saisio, and many of the events are picked from Saisio's real life. Nevertheless, the author wants the trilogy to be read as a novel, not a memoir. The present study analyses the generic elements of Saisio s trilogy and contextualizes the narrative identity that Saisio is creating in her fiction. Following Alastair Fowler s theory of genres as types without strict borders and a tendency to hybridity, the trilogy is linked to several genres. Serge Doubrovsky s genre concept of autofiction is the basis for the analysis: it explains the trilogy s borderline identity between autobiography and novel, and designates the main elements that render Saisio s autobiographical narrative into fiction. Both Doubrovsky and Saisio emphasize the role of the unconscious in writing, and at the same time stress the importance of a skilled composition. As well as autofiction, the trilogy is analyzed as a Bildungsroman, a confession and conversion narrative, a coming-out -narrative and a portrait-of-the-artist novel. Each genre is illuminated by its paradigmatic work: Wilhelm Meister s Apprenticeship by Goethe, The Confessions by St. Augustine, and The Well of Loneliness by Radclyffe Hall. The parallelisms between Saisio s trilogy and the typical plots of the genres and thematics of the classics show how the tradition works in Saisio s text. The thematic parallelisms highlight Saisio s concern for the conflicts that occur between an individual and the surrounding society, while the similarities in plots question the autobiographicality of Saisio s narrative but also clarify how Saisio refines the traditional genres. Read in the light of Saisio s trilogy, the classics are shown to have their gender-transgressive elements that the non-normative reader can identify with. Saisio s text also challenges universalizing claims about genre and gender. As a narrative of identity it follows the example of 1970s essentialistic coming-out stories, but at the same time depicts the notion of identity in a manner that manifests postmodern ideas about identity as multiple and ever-transforming. Keywords: autobiographicality, autofiction, identity narrative, genre research, Bildungsroman, conversion narrative, confession, coming-out story, a portrait-of-an-artist novelPirkko Saision romaanitrilogia Pienin yhteinen jaettava (1998), Vastavalo (2000) ja Punainen erokirja (2003), ilmentää 1990-luvulla Suomessa vallinnutta omaelämäkerrallisuuden uudelleen arviointia. Väitöskirja Elämästä autofiktioksi osoittaa Saision trilogian rakentuvan romaaniksi erityisesti sen kautta, että se nojaa vahvasti minuuden kertomisen konventioihin, etenkin tiettyihin lajimalleihin. Tutkimuksessa analysoidaan trilogian suhdetta omaelämäkerrallisuuteen ja muihin yksilöllisyyden esittämisen lajeihin, trilogian tematiikkaa ja sen esittämää identiteettikäsitystä. Tutkimuksessa lähdetään liikkeelle trilogiasta autofiktiona siten kuin tutkija-kirjailija Serge Doubrovsky on lajin määritellyt. Trilogiassa kommentoidaan autofiktiolle tyypilliseen tapaan omaelämäkerrallisuuden konventioita, teoksissa vaikuttaa psykoanalyyttinen ihmiskuva ja Saision teksti rakentuu konventionaalisten kertomusrakenteiden, tiettyjen lajien ja traditionaalisten kertomusten, mm. satujen, varaan. Saision tematiikka kirkastuu, kun sitä luetaan kehitysromaanin, tunnustuksen ja kääntymyskertomuksen lajirepertuaarien valossa ja verrataan näiden lajien paradigmaattisiin teoksiin. Tutkimuksessa keskitytään Goethen Wilhelm Meisterin oppivuosiin, Augustinuksen Tunnustuksiin ja Radclyffe Hallin The Well of Loneliness -romaaniin, joka on klassinen esimerkki tunnustus- ja kääntymyskertomuksen maallisesta versiosta, ulostulokertomuksesta. Lisäksi trilogia rinnastetaan Matti Hyvärisen Viimeiset taistot -tutkimuksen poliittisiin elämäkertoihin, jotka vahvistavat trilogian poliittisen kääntymyksen uskonnonkaltaisuutta ja joista trilogiaa vasten luettuna paljastuu tosikertomuksina esitettyjen elämäkertojen konventionaalisuus. Vastaavuudet klassikkoteoksiin leikkaavat trilogian merkitystä yksityisenä identiteettikertomuksena ja selventävät Saision tapaa jalostaa traditiota omaan suuntaansa. Saision trilogiaa vasten luettuna klassikoista paljastuu hegemonisen sukupuoli- ja seksuaalisuusmallin rikkomuksia, ja trilogia haastaa teoreettisia yleistyksiä lajien ja lajiteorioiden sukupuolittuneisuudesta. Trilogia on esimerkki tavasta, jolla seksuaalinen identiteetti on kerrottavissa 2000-luvun vaihteessa: se pohjaa 1970-lukulaiseen ulostulokertomukseen mutta sisällyttää itseensä postmodernin identiteetin moninaisuuden ja liikkuvuuden. Asiasanat: omaelämäkerrallisuus, autofiktio, identiteetin kerronta, lajitutkimus, kehitysromaani, kääntymyskertomus, ulostulokertomus, taiteilijaromaan

Elämyksellisyyttä tavoittelemassa - narratiivinen tutkimus matematiikan opettajaksi kasvusta

Päivi Portaankorva-Koiviston (FM) väitöstutkimuksen tavoitteena oli tarkastella elämyksellisyyden merkityksiä matematiikan opetuksessa ja matematiikan opettajaksi kasvamisessa. Tutkimuksessa seurattiin kolmen lukuvuoden ajan kuutta opettajaopiskelijaa ja heidän yksilöllisiä kasvuprosessejaan haastattelujen ja kirjoitelmien avulla. Elämyksellistä matematiikan opetusta etsimässä Elämykset ovat välittömästi itse koettuja, kestäviä ja merkittäviä kokemuksia, joita matematiikan tunneilla voidaan tavoitella joko sisältöjen tai työskentelytapojen kautta. Portaankorva-Koiviston tutkimuksessa keskeisiksi matematiikan opetuksen elämyksellisyyden piirteiksi nousivat vuorovaikutuksellisuus, kokemuksellisuus, havainnollisuus, tutkimuksellisuus, yhteistoiminnallisuus ja matematiikan kielenomaisuus. Tutkittavat kokivat näistä kolme ensimmäistä itselleen läheisimpinä. Oppimiskokemus vahvistuu, kun oppilaat innostetaan väittelemään, selittämään ja perustelemaan matemaattisia oivalluksiaan. Tutkittavat kokivat tärkeäksi myös toimintamateriaalien ja -välineiden sekä eleiden ja liikkeiden käytön oppimistilanteiden apuna. Tutkimuksellisuus, yhteistoiminnallisuus ja matematiikan kielinäkökulma vaativat opettajalta hyvää aineenhallintaa ja uskallusta heittäytyä tutkivaan työskentelyyn. Näissä aloitteleva opettaja kokee epävarmuutta. Elämyksellisen opetuksen tavoitteena on saada oppilaat sisäistämään oppiaineelle ominaista ajattelua ja toimintaa, kuten loogista tapaa esittää asioita ja perustella niiden paikkansapitävyyttä. Opettajaksi kasvamassa Portaankorva-Koiviston kolmen lukuvuoden seurantatutkimuksessa tutkittavien kokemuksistaan kertomat ja kirjoittamat tarinat kuvasivat matematiikan opettajan kasvamisen vaiheita. Opintojen alussa tuleva opettaja katsoo kaikkea oppimiseen ja opetukseen liittyvää tietoa oppilaan näkökulmasta. Hän esimerkiksi valitsee esitellyistä oppimateriaaleista, työtavoista ja arviointimenetelmistä ne, joista hän on itse oppilaana pitänyt tai joista hän ajattelee oppilaiden pitävän. Opetusharjoitteluvuoden aikana syntyy opettajaharjoittelijanäkökulma. Harjoittelija pyrkii selviämään oppitunneista turvallisesti, ohjaavien opettajien menetelmiin ja mielipiteisiin tukeutuen. Kun varsinaista vastuuta oppitunneista ei ole, itse oppimiseen kiinnitetään vähemmän huomiota. Harjoittelun aikana nuori opettaja kuitenkin pääsee selvyyteen siitä, haluaako hän opettajaksi ja soveltuuko hän tähän työhön. Tavallisimmin varsinainen opettajankoulutus päättyy tähän. Tekemällä opettajan sijaisuuksia nuori opettaja saa käytännön koulutusta työhönsä. Sijaisena hankittu oppilaantuntemus, kokemukset erilaisista oppijaryhmistä, oppimistyyleistä ja työyhteisöistä muuttivatkin tutkittavien mukaan näkemystä opetustyöstä. Opettajankoulutuksessa Suomalainen opettajakoulutus on kunnianhimoista ja arvokasta. Nuoria opettajia tuetaan monipuolisesti sekä aineenhallinnassa että opetuksen ja oppimisen kysymyksissäkin. Kokemukseen tai elämykseen kytkemätön teoria ei kuitenkaan löydä tartuntapintaa opettajaksi kasvamisessa tai matematiikan opetuksessa. Työelämä ei aina tue koulutuksen tavoitteita ja nuori opettaja sosiaalistuu nopeasti työyhteisöönsä tavoitellessaan sen hyväksyntää ja jäsenyyttä. Tutkittavien tarinat kertoivat myös opettajaksi kasvun keskeneräisyydestä. Nuori opettaja ei näe itseään tekemässä yhteistyötä oppilaittensa vanhempien kanssa, kehittämässä työyhteisöään sen jäsenenä, muuttamassa luokan toimintakulttuuria ja ilmapiiriä tai ratkaisemassa ongelmatilanteisiin liittyviä haasteita. Opettajana kasvaminen jatkuu siis matematiikan sisältöjen ulkopuolellakin.My research aims at examining and reflecting on lived experiences provided in mathematics education in Finnish comprehensive school along with issues related to growing to be a teacher of mathematics. In the research, a framework has been created and developed to describe lived-experience-oriented mathematics education by means of the following six aspects: interaction, experientiality, illustrativeness, research-orientation, collaborativeness and orientation to mathematics as a language. These aspects have been in the process of being worked on throughout the whole research, partly in cooperation with those examined. The growth into teachership has been examined as changes in and enrichment of the existing notions and conceptions. In the growth process the following areas play a central role: the notions of mathematics, how to teach it and how to learn it, the notions of a good teacher and good teaching, the informants´ notions of themselves as teachers and of the grade in which they believe they will work in the future. Those examined in this research were the students who had started their studies in the Master´s programme in the Unit of Subject Teacher Education of the Department of Teacher Education at the University of Tampere in 2005. The whole group of these students has been involved, i.e. 5 women and 1 man. This is a narrative-type longitudinal research in which the research material consists of written essays ( 3 essays / an informant ) as well as interviews ( 4 interviews / an informant ). The material has been collected during three academic years from 2005 to 2008. The material proper comprises 516 pages. Materials of lectures held to those examined along with notes of the researcher have been included as additional research material in the report. The material proper has been examined by means of an analysis of the narratives and a narrative analysis. The additional material has been used as a contribution to the report. The following questions have been the objectives of this research: 1. What do the individual narratives of growth tell us about the growth of the prospective teachers to become teachers of mathematics ? 2. In what ways have the prospective teachers? notions of lived-experience-oriented mathematics education developed during the years of teacher education ? 3. What kind of light does the research material as a whole shed on the growth process of becoming a mathematics teacher ? As a conclusion of this research we can state that three perspectives emerge in the professional growth process of the prospective teachers throughout the three academic years. The first is the perspective of the pupil, with the informants reflecting on issues of teachership on the basis of their own experiences at school, i.e. from the position of the pupil. The second is the perspective of the prospective teacher in the process of being educated, with the teaching practice and the relevant feedback forming the basis of assessing the teachership. The third is the perspective of the novice teachers who distance themselves from the earlier stages to assess their personal teachership, first, as an on-going process and, second, as part of a particular working community. In the reflections on lived-experience orientation, the informants´ notions of mathematics, and teaching and learning mathematics, are strongly interlinked. Changes in these notions are obviously required for lived-experience-oriented mathematics education to be realised. Illustrativeness, experientiality and interaction provide the most practicable starting points for planning the actual teaching, and the informants´ attitudes to these aspects remained positive. Research orientation, collaborativeness and orientation to mathematics as a language require of a prospective teacher a very good mastery of the subject along with an ability to envision and create joint research-type activities for the lessons in the classroom. The informants felt that they were not very familiar with these aspects

Learning to learn in mathematics: Two Fulbright distinguished awards in teaching fellows’ narratives

Two middle school educators earned a Fulbright Distinguished Award in Teaching fellowship. A Fulbright Finland Foundation inter-country travel grant provided the grantees with a unique opportunity to connect and collaborate at the University of Helsinki. Within this research, they described their inquiry experiences. The research included examining authentic student-centered learning continuums and phenomenon-based learning in Finland and teachers’ adaptability in relation to meeting the needs of linguistically and culturally diverse math classrooms in the Netherlands. This paper summarizes how cross-cultural dialogues, classroom observations, and informal interviews with educators, students, and thought leaders informed each grantee’s discovery of how student-centered learning is structured, delivered, and valued in Finland and the Netherlands. This article (1) describes how communication empowers middle school mathematics students, (2) analyzes the learning-to-learn framework, and (3) provides insights into how to utilize language diversity in a mathematics classroom.Peer reviewe