Teaching mathematics and programming : new approaches with empirical evaluation

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

Infective Endocarditis in a Finnish Teaching Hospital. 25 Years of Experience of Adult Patients

Infektiivinen endokardiitti yliopistollisessa keskussairaalassa vuosina 1980-2004 hoidetuilla aikuispotilailla Tausta: Infektiivinen endokardiitti on edelleen vakava sairaus. Huolimatta siitä, että taudin diagnostiikka ja hoito ovat kehittyneet, siihen liittyy edelleen merkittävää sairastuvuutta ja kuolleisuutta. Endokardiitin taudinkuvassa on viime vuosina tapahtunut muutoksia monissa maissa. Tavoitteet: Tutkia endokardiitin kliinista kuvaa ja ennustetta suomalaisessa yliopistosairaalassa vuosina 1980-2004 endokardiitin vuoksi hoidetuilla aikuispotilailla. Aineisto: Osatyössä I endokardiitin todennäköisyyttä analysoitiin 222:lla vuosina 1980-1995 endokardiittiepäilyn vuoksi hoidetulla potilaalla käyttäen apuna sekä Duken että von Reyn diagnostisia kriteereitä. Osatyössä II tutkittiin endokardiittiin liittyviä neurologisia komplikaatioita 218 varmassa tai mahdollisessa endokardiittiepisodissa. Osatyössä III tutkittiin seerumin C-reaktiivisen proteiinin (CRP) käyttökelpoisuutta hoitovasteen arvioinnissa 134:ssä varmaksi luokitellussa endokardiittiepisodissa. Osatyössä IV tutkittiin yleisbakteeri-PCRmenetelmän käyttökelpoisuutta etiologisessa diagnostiikassa 56:lla endokardiittiepäilyn vuoksi leikatulla potilaalla. Osatöissä V ja VI analysoitiin kaikki vuosina 1980-2004 hoidetut 303 endokardiittipotilasta lyhytaikais- ja 1-vuotisennusteen suhteen sekä tutkittiin endokardiitin taudinkuvassa tapahtuneita muutoksia sairaalassamme. Tulokset: Duken kriteerit osoittautuivat von Reyn kriteereitä herkemmiksi endokardiitin diagnostiikassa: 243 tutkitusta episodista 114 luokiteltiin varmoiksi endokardiiteiksi Duken kriteereillä, kun vastaavasti ainoastaan 64 luoteltiin varmoiksi von Reyn kriteereillä (p<0.001). Lisäksi peräti 115 episodissa endokardiitin diagnoosi hylättiin von Reyn kriteereillä, kun diagnoosi hylättiin Duken kriteereillä ainoastaan 37 episodissa (p<0.001). Neurologinen komplikaatio ilmeni ennen mikrobilääkehoidon aloittamista 76 %:ssa episodeja ollen ensimmäinen oire 47 %:ssa. Kuolema oli merkitsevästi yhteydessä neurologisiin komplikaatioihin. Hoitovastetta seurattaessa seerumin CRP:n lasku oli merkitsevästi nopeampaa komplikaatioitta toipuvilla potilailla kuin niillä, joille kehittyi komplikaatioita tai jotka menehtyivät tautiinsa. PCR-tutkimus poistetusta läpästä antoi ainoana menetelmänä etiologisen diagnoosin neljässä tapauksessa (2 stafylokokkilajia, 1 Streptococcus bovis,1 Bartonella quintana), joissa kaikissa mikrobilääkehoito oli ollut käytössä ennen näytteiden ottamista. Koko aineistossa kahden läpän infektio tai neurologisten komplikaatioiden, perifeeristen embolioiden tai sydämen vajaatoiminnan kehittyminen ennustivat sekä sairaalakuolleisuutta että 1-vuotiskuolleisuutta, kun taas ≥65 vuoden ikä ja sydämen ultraäänitutkimuksessa todettu vegetaatio tai Duken luokittelun mukainen pääkriteeri ennustivat kuolemaa vuoden sisällä. Korkea CRP-taso sairaalaan tullessa ennusti sekä sairaalakuolleisuutta että 1-vuotiskuolleisuutta. Huumeiden käyttäjien endokardiitit lisääntyivät tutkimusaikana merkitsevästi (p<0.001). Päätelmät: Tässä työssä vahvistetaan Duken kriteerien käyttökelpoisuus endokardiitin diagnostiikassa. Lisäksi vahvistui käsitys, että nopea diagnoosi ja mikrobilääkehoidon aloittaminen ovat parhaat keinot ehkäistä neurologisia komplikaatioita ja parantaa endokardiittipotilaiden ennustetta. CRP:n normalisoituminen on endokardiittipotilailla hyvän ennusteen merkki. Suoraan läppäkudoksesta tehty PCR-tutkimus on hyödyllinen, kun taudin aiheuttaja on kasvuominaisuuksiltaan vaativa tai potilas on saanut mikrobilääkehoitoa ennen viljelynäytteiden ottamista. Muutamat aiemmissa tutkimuksissa todetut huonon ennusteen merkit ennustavat huonoa ennustetta myös tämän tutkimuksen potilailla. Uutena löydöksenä ilmeni, että korkea CRP-arvo sairaalaan tullessa merkitsee sekä huonoa lyhyt- että pitkäaikaisennustetta. Huumeiden käyttäjien endokardiittien ilmaantuminen on tärkein epidemiologinen muutos 25 vuoden tutkimusaikana.

Stand dynamics modelling approaches for multicohort management of eastern Canadian boreal forests

Abstract

Maahanmuuttajaoppilaat erityiskouluissa

Immigrant Pupils in Special Education Schools The study focused on the opinions of immigrant pupils in the 1st–9th grades of basic education in four special education schools of the City of Turku and in need of special support about the following: 1. Their difficulties in going to school in general education before the transfer to a special education school. 2. Their opinions about the transfer process to special education and the changes in their school practice after being transferred to a special education school. 3. Their experiences about their school and coping in special education school. The study strengthened the idea that immigrant pupils need positive special treatment, linguistic support, individual guidance, small teaching groups and operating models that promote well-being on their integration and education path. The central educational idea of inclusive education is based on deconstructing the power structures concerning gender, ethnicity and “race” and approval of differences in the pupils. Shifting the emphasis from the pupil to working on the learning environment has resulted in special education no longer being primarily separate special education tied to a certain place, but directing the teaching more towards individuality. The central dimension of intercultural competence of a teacher working in a multicultural class seems to be the attitudes and approaches to a different pupil; the teacher must be interculturally sensitive when facing children and young people from a foreign culture. Education and teaching affect every sector of the pupil’s well-being. Learning and learning results have a connection with teaching, education and well-being. Every sector is important for the going to school and integration of an immigrant pupil in need of special support. The basis of the study is the equality of opportunities and the humanistic idea of the human being in the Finnish education policy. The immigrant pupils selected for the study represented the following language groups: Arabian, Albanian, Somali, Russian and Vietnamese. In the four special education schools, the number of immigrant pupils belonging to these language groups (2004) totalled 104. A total of 89 pupils i.e. 86% answered the questionnaire, which is sufficient considering the generalisation of the study. Although this is basically a quantitative study, the interviewing method was used in part of the study, because the questionnaires were in Finnish and consequently, it was difficult for some immigrant pupils to understand them. Understanding the questions was also affected by the fact that the age distribution in the study was very wide (7–18). According to the results of the study, the immigrants felt that the biggest drawbacks in general education were their inability to speak Finnish and lack of concentration. The actual process of being transferred to a special education class remained unclear for immigrant pupils, and they could do very little about the transfer themselves. The results show that immigrant pupils coped well in special education school; they felt that their learning ability and concentration improved in the small groups of the special education school. They considered the individual support given in the special education schools to be useful. The lower-grade immigrant pupils had a more positive attitude towards special education school than the upper-grade immigrant pupils. In all the special education schools the immigrant pupils experienced that they were in a good position in the class; girls felt this even a little more strongly than boys. The teacher-pupil-relationship was felt to be good. School bullying being so common was a negative feature experienced by immigrant pupils, who were often targets or bullies themselves. Immigrant pupils believed in their success at school and in the opportunities offered by special education schools. Generally they were of the opinion that pupils are not labelled by special school; however, upper-grade immigrant pupils were more hesitant than lower-grade immigrant pupils. This study aimed at bringing out the immigrant pupils’ own opinions. Teaching immigrant pupils in special education schools has not been very much studied in Finland, which made the topic new and even more challenging.

Siirtyminen C-kielestä Pythoniin ohjelmoinnin perusopetuksessa

Ohjelmointitaito on asia, jonka oppimisesta ja opettamisesta voidaan olla montaa mieltä, eikä yhtä oikeaa tapaa toteuttaa ohjelmoinnin opetusta tunnu olevan olemassa. Se on kuitenkin selvää, että jotkin menetelmät ja työkalut tuntuvat olevan parempia kuin toiset. Lukuvuoden 2005-2006 päätteeksi Lappeenrannan teknillinen yliopisto päätti päivittää ohjelmoinnin perusopetusta, ja kokeili siirtymistä Python-ohjelmointikieleen ohjelmoinnin alkeiskursseilla. Koska kurssin varsinaiset muutokset keskittyivät tekniseen infrastruktuuriin, tutustuttiin alustavassa kirjallisuustutkimuksessa ensin erilaisiin lähestymistapoihin,aiempiin tapauksiin sekä mielekkäiden työkalujen löytämiseen. Tässä diplomityössä perehdytään ohjelmoinnin opetuksen työkaluihin sekä erityisesti Python-ohjelmointikielen hyödyntämiseen ohjelmoinnin perusopetuksessa. Diplomityö esittelee useita lähestymistapoja sekä keskittyy tutkimaan Pythonin soveltuvuutta alkeisopetuksen käyttötarkoituksiin. Diplomityö tutustuu myös Lappeenrannassa järjestetyn ohjelmoinnin perusteiden kurssin tuloksiin, ja analysoi sitä, pystyikö Python-pohjainen kurssi toteuttamaan teknisen yliopiston sille asettamat vaatimukset. Lopuksi aineistosta analysoidaan jatkotutkimuksen tarpeita sekä pyritään löytämään ne osa-alueet, joita näissä jatkotutkimuksissa tulisi vielä kehittää.

Colligation and Cross Moment-Based Approaches for Independent Component Analysis

Diplomityössä on käsitelty uudenlaisia menetelmiä riippumattomien komponenttien analyysiin(ICA): Menetelmät perustuvat colligaatioon ja cross-momenttiin. Colligaatio menetelmä perustuu painojen colligaatioon. Menetelmässä on käytetty kahden tyyppisiä todennäköisyysjakaumia yhden sijasta joka perustuu yleiseen itsenäisyyden kriteeriin. Työssä on käytetty colligaatio lähestymistapaa kahdella asymptoottisella esityksellä. Gram-Charlie ja Edgeworth laajennuksia käytetty arvioimaan todennäköisyyksiä näissä menetelmissä. Työssä on myös käytetty cross-momentti menetelmää joka perustuu neljännen asteen cross-momenttiin. Menetelmä on hyvin samankaltainen FastICA algoritmin kanssa. Molempia menetelmiä on tarkasteltu lineaarisella kahden itsenäisen muuttajan sekoituksella. Lähtö signaalit ja sekoitetut matriisit ovattuntemattomia signaali lähteiden määrää lukuunottamatta. Työssä on vertailtu colligaatio menetelmään ja sen modifikaatioita FastICA:an ja JADE:en. Työssä on myös tehty vertailu analyysi suorituskyvyn ja keskusprosessori ajan suhteen cross-momenttiin perustuvien menetelmien, FastICA:n ja JADE:n useiden sekoitettujen parien kanssa.

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

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