A mathematical study of fuzzy logic; an algebraic approach

Fuzzy set theory and Fuzzy logic is studied from a mathematical point of view. The main goal is to investigatecommon mathematical structures in various fuzzy logical inference systems and to establish a general mathematical basis for fuzzy logic when considered as multi-valued logic. The study is composed of six distinct publications. The first paper deals with Mattila'sLPC+Ch Calculus. THis fuzzy inference system is an attempt to introduce linguistic objects to mathematical logic without defining these objects mathematically.LPC+Ch Calculus is analyzed from algebraic point of view and it is demonstratedthat suitable factorization of the set of well formed formulae (in fact, Lindenbaum algebra) leads to a structure called ET-algebra and introduced in the beginning of the paper. On its basis, all the theorems presented by Mattila and many others can be proved in a simple way which is demonstrated in the Lemmas 1 and 2and Propositions 1-3. The conclusion critically discusses some other issues of LPC+Ch Calculus, specially that no formal semantics for it is given.In the second paper the characterization of solvability of the relational equation RoX=T, where R, X, T are fuzzy relations, X the unknown one, and o the minimum-induced composition by Sanchez, is extended to compositions induced by more general products in the general value lattice. Moreover, the procedure also applies to systemsof equations. In the third publication common features in various fuzzy logicalsystems are investigated. It turns out that adjoint couples and residuated lattices are very often present, though not always explicitly expressed. Some minor new results are also proved.The fourth study concerns Novak's paper, in which Novak introduced first-order fuzzy logic and proved, among other things, the semantico-syntactical completeness of this logic. He also demonstrated that the algebra of his logic is a generalized residuated lattice. In proving that the examination of Novak's logic can be reduced to the examination of locally finite MV-algebras.In the fifth paper a multi-valued sentential logic with values of truth in an injective MV-algebra is introduced and the axiomatizability of this logic is proved. The paper developes some ideas of Goguen and generalizes the results of Pavelka on the unit interval. Our proof for the completeness is purely algebraic. A corollary of the Completeness Theorem is that fuzzy logic on the unit interval is semantically complete if, and only if the algebra of the valuesof truth is a complete MV-algebra. The Compactness Theorem holds in our well-defined fuzzy sentential logic, while the Deduction Theorem and the Finiteness Theorem do not. Because of its generality and good-behaviour, MV-valued logic can be regarded as a mathematical basis of fuzzy reasoning. The last paper is a continuation of the fifth study. The semantics and syntax of fuzzy predicate logic with values of truth in ana injective MV-algerba are introduced, and a list of universally valid sentences is established. The system is proved to be semanticallycomplete. This proof is based on an idea utilizing some elementary properties of injective MV-algebras and MV-homomorphisms, and is purely algebraic.

Integrating environmental education in primary school education in Tanzania : teachers’ perceptions and teaching practices

The study focuses on primary school teachers’ perceptions of environmental education, its integration into primary school education and teachers’ teaching practices in Tanzania. The thesis is based on empirical research. The theoretical underpinnings of the study are based on Palmer’s (1998) model of environmental education. According to the model, meaningful environmental education should include education about, in or through and for the environment. The study is supported by national and international literature from research done on environmental education and education for sustainable development and policy statements. The study is qualitative in nature, adopting phenomenography and phenomenology as points of departure. The empirical data was collected from four primary schools in Morogoro region in Tanzania. The study sample consisted of 31 primary school teachers. Data was collected through interviews and lesson observations. According to the results of the study, primary school teachers expressed variations in their perceptions of environmental education and education for sustainable development. Most of the teachers focused on the aspect of knowledge acquisition. According to Tanzanian education and training policy, environmental education has to be integrated into all subjects. Although there is environmental education in the primary school curriculum, it is not integrated on an equal footing in all subjects. Some subjects like science, social studies and geography have more environmental content than other subjects. Teachers claim that the approach used to integrate environmental education into the school curriculum was not favoured because many claimed that what is to be taught as environmental education in the various subjects is not shown clearly. As a result, many teachers suggested that to ensure that it is taught properly it should be included in the curriculum as an independent subject or as specific topics. The study revealed that teachers’ teaching practices in integrating environmental education varied from one subject to another. Although most of the teachers said that they used participatory methods, lesson observations showed that they limited themselves to question and answer and group discussion. However, the teachers faced a number of barriers in the teaching of environmental education, some of which include lack of teaching and learning resources, time and large class size. The role of teachers in the implementation of environmental education in developing an environmentally literate citizenry is of great significance. The responsibility of the government in developing a curriculum with clear goals and content, developing teachers’ capacity in the teaching of environmental education and provision of teaching and learning materials needs to be taken seriously by the government in educational plans and programs.

Towards the Best A++ Rating Productivity of Research and Teaching in Finnish Universities

Tämän tutkimusraportin suomenkielinen versio on osoitteessa: http://urn.fi/URN:ISBN:978-951-29-4509-2

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.

Spontaneous Focusing on Quantitative Relations and the Development of Rational Number Conceptual Knowledge

The aim of the present set of studies was to explore primary school children’s Spontaneous Focusing On quantitative Relations (SFOR) and its role in the development of rational number conceptual knowledge. The specific goals were to determine if it was possible to identify a spontaneous quantitative focusing tendency that indexes children’s tendency to recognize and utilize quantitative relations in non-explicitly mathematical situations and to determine if this tendency has an impact on the development of rational number conceptual knowledge in late primary school. To this end, we report on six original empirical studies that measure SFOR in children ages five to thirteen years and the development of rational number conceptual knowledge in ten- to thirteen-year-olds. SFOR measures were developed to determine if there are substantial differences in SFOR that are not explained by the ability to use quantitative relations. A measure of children’s conceptual knowledge of the magnitude representations of rational numbers and the density of rational numbers is utilized to capture the process of conceptual change with rational numbers in late primary school students. Finally, SFOR tendency was examined in relation to the development of rational number conceptual knowledge in these students. Study I concerned the first attempts to measure individual differences in children’s spontaneous recognition and use of quantitative relations in 86 Finnish children from the ages of five to seven years. Results revealed that there were substantial inter-individual differences in the spontaneous recognition and use of quantitative relations in these tasks. This was particularly true for the oldest group of participants, who were in grade one (roughly seven years old). However, the study did not control for ability to solve the tasks using quantitative relations, so it was not clear if these differences were due to ability or SFOR. Study II more deeply investigated the nature of the two tasks reported in Study I, through the use of a stimulated-recall procedure examining children’s verbalizations of how they interpreted the tasks. Results reveal that participants were able to verbalize reasoning about their quantitative relational responses, but not their responses based on exact number. Furthermore, participants’ non-mathematical responses revealed a variety of other aspects, beyond quantitative relations and exact number, which participants focused on in completing the tasks. These results suggest that exact number may be more easily perceived than quantitative relations. As well, these tasks were revealed to contain both mathematical and non-mathematical aspects which were interpreted by the participants as relevant. Study III investigated individual differences in SFOR 84 children, ages five to nine, from the US and is the first to report on the connection between SFOR and other mathematical abilities. The cross-sectional data revealed that there were individual differences in SFOR. Importantly, these differences were not entirely explained by the ability to solve the tasks using quantitative relations, suggesting that SFOR is partially independent from the ability to use quantitative relations. In other words, the lack of use of quantitative relations on the SFOR tasks was not solely due to participants being unable to solve the tasks using quantitative relations, but due to a lack of the spontaneous attention to the quantitative relations in the tasks. Furthermore, SFOR tendency was found to be related to arithmetic fluency among these participants. This is the first evidence to suggest that SFOR may be a partially distinct aspect of children’s existing mathematical competences. Study IV presented a follow-up study of the first graders who participated in Studies I and II, examining SFOR tendency as a predictor of their conceptual knowledge of fraction magnitudes in fourth grade. Results revealed that first graders’ SFOR tendency was a unique predictor of fraction conceptual knowledge in fourth grade, even after controlling for general mathematical skills. These results are the first to suggest that SFOR tendency may play a role in the development of rational number conceptual knowledge. Study V presents a longitudinal study of the development of 263 Finnish students’ rational number conceptual knowledge over a one year period. During this time participants completed a measure of conceptual knowledge of the magnitude representations and the density of rational numbers at three time points. First, a Latent Profile Analysis indicated that a four-class model, differentiating between those participants with high magnitude comparison and density knowledge, was the most appropriate. A Latent Transition Analysis reveal that few students display sustained conceptual change with density concepts, though conceptual change with magnitude representations is present in this group. Overall, this study indicated that there were severe deficiencies in conceptual knowledge of rational numbers, especially concepts of density. The longitudinal Study VI presented a synthesis of the previous studies in order to specifically detail the role of SFOR tendency in the development of rational number conceptual knowledge. Thus, the same participants from Study V completed a measure of SFOR, along with the rational number test, including a fourth time point. Results reveal that SFOR tendency was a predictor of rational number conceptual knowledge after two school years, even after taking into consideration prior rational number knowledge (through the use of residualized SFOR scores), arithmetic fluency, and non-verbal intelligence. Furthermore, those participants with higher-than-expected SFOR scores improved significantly more on magnitude representation and density concepts over the four time points. These results indicate that SFOR tendency is a strong predictor of rational number conceptual development in late primary school children. The results of the six studies reveal that within children’s existing mathematical competences there can be identified a spontaneous quantitative focusing tendency named spontaneous focusing on quantitative relations. Furthermore, this tendency is found to play a role in the development of rational number conceptual knowledge in primary school children. Results suggest that conceptual change with the magnitude representations and density of rational numbers is rare among this group of students. However, those children who are more likely to notice and use quantitative relations in situations that are not explicitly mathematical seem to have an advantage in the development of rational number conceptual knowledge. It may be that these students gain quantitative more and qualitatively better self-initiated deliberate practice with quantitative relations in everyday situations due to an increased SFOR tendency. This suggests that it may be important to promote this type of mathematical activity in teaching rational numbers. Furthermore, these results suggest that there may be a series of spontaneous quantitative focusing tendencies that have an impact on mathematical development throughout the learning trajectory.

Exploring Relationship between Pakistani Teachers’ Pedagogical Beliefs and ICT Use for Teaching and Learning

Background: The aim of present study is to investigate relationship between Pakistani teachers’ pedagogical beliefs and ICT use for teaching and learning. Previous studies found close relationship between pedagogical beliefs and teaching practices including use of ICT. However, variation in results is also reported and attributed to cultural and contextual differences. Methodology: Quantitative approach was used to study a sample of 231 Pakistani basic education teachers from middle and upper-middle range private schools, mostly from large urban centres. Results: This study confirmed previously study results that constructivist-compatible pedagogical beliefs are significantly related to both traditional and constructivist use of ICT. However, it is also found that traditional-transmission pedagogical beliefs are significantly related to traditional use of ICT – a finding not reported in previous studies. Some amounts of ICT training for pedagogical purpose exhibit significant impact on ICT use, in particular constructivist use of ICT. Similarly age also play a role as younger teachers are more likely to use ICT, however, no significant difference of pedagogical beliefs and ICT use was found between male and female teachers. Recommendation for practice and further investigation are made in chapter 5.

The role of culture in international students' image formation: the emergence of expected and perceived university image

Tämän tutkimuksen tavoitteena oli selvittää, vaikuttaako kansainvälisen opiskelijan kulttuuritausta opiskelijan odotetun ja koetun yliopistoimagon muodostumiseen. Jotta kulttuurin vaikutuksia yliopistoimagoon voitiin tutkia, tutkimuksessa tunnistettiin yliopistoimagon muodostumiseen oleellisesti vaikuttavat tekijät. Kulttuurin roolia organisaation imagon muodostumisessa ei ole tutkittu aiemmissa tieteellisissä julkaisuissa. Näin ollen tämän tutkimuksen voidaan katsoa edistäneen nykyistä imagotutkimusta. Tutkimuksen kohdeyliopistona oli Lappeenrannan teknillinen yliopisto (LTY). Tutkimuksen empiirinen osa toteutettiin kvantitatiivisena Internet - pohjaisena kyselytutkimuksena tilastollisen analyysin menetelmin. Otos (N=179) koostui kaikista Lappeenrannan teknillisessä yliopistossa lukuvuonna 2005-2006 opiskelleista kansainvälisistä opiskelijoista. Kyselyyn vastasi 68,7 % opiskelijoista. Johtopäätöksenä voidaan todeta, että kulttuurilla ei ole merkittävää vaikutusta yliopistoimagon muodostumiseen. Tutkimuksessa saatiin selville, että yliopiston Internet-sivujen laatu vaikuttaa positiivisesti odotetun yliopistoimagon muodostumiseen, kun taas koettuun yliopistoimagoon vaikuttavat positiivisesti odotettu yliopistoimago, pedagoginen laatu sekä opetusympäristö. Markkinoinnin näkökulmasta tulokset voidaan vetää yhteen toteamalla, että yliopistojen ei tarvitsisi räätälöidä tutkimuksessa tunnistettuja imagoon vaikuttavia tekijöitä eri kulttuureistatulevia opiskelijoita varten.

Evaluation of Teacher Education Programs by Students and Graduates

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

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.

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

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

Revenue Logic inSoftware Business Context

Tutkimuksen tavoitteena oli selvittää ohjelmistotoimialan avaintekijöitä, jotka vaikuttavat yrityksen ansaintalogiikkaan sekä lisätä tietoisuutta ansaintalogiikan muodostumisesta pienissä ja keskisuurissa ohjelmistoyrityksissä. Tutkimuksen teoreettisessa osassa keskityttiin tarkastelemaan ansaintalogiikan, strategian ja liiketoimintamallin käsitteiden suhteita sekä arvioitiin toimialan osatekijöiden, hinnoitteluperiaatteiden ja ansaintamallien vaikutusta ansainnan muodostumiseen ohjelmistotoimialalla. Ohjelmistotuote ja - palveluliiketoimintaa koskien oli merkityksellistä tutkia tuotteistamisasteen ja arvoketjujen vaikutusta ansaintalogiikan muodostumisessa sekä esitellä erilaisia, tyypillisiä ohjelmistotoimialalla käytettäviä hinnoittelumenetelmiä. Työn empiirisessä osassa tarkasteltiin 23 suomalaisen ohjelmistoalan yrityksen ansaintalogiikkaa. Tiedot kerättiin haastatteluin ja analysoitiin laadullisen tutkimuksen keinoin. Tutkimustulokset korostivat ansaintalogiikan 'epämääräisyyttä' terminä mutta osoittivat, että ydinliiketoimintaan keskittyminen, tuote-, palvelu-, tai projektiliiketoiminnan osaaminen, tuotteistusaste ja kanavavalinnat ovat avaintekijöitä ansaintalogiikanmuodostumisessa. Ansaintalogiikan muodostamiseen liittyy paljon yrityksen sisäisiä ja ulkoisia haasteita sekä muutospaineita, eikä ohjelmistotoimialalla ole todennettavissa yhtä yleismaailmallista, menestyksen takaavaa ansaintalogiikkaa.

Matematiskt gestaltande i förskolan

The purpose of the thesis is to study how mathematics is experienced and used in preschool children’s activities and how preschool teachers frame their teaching of mathematical content. The studies include analyses of children’s actions in different activities from a mathematical perspective and preschool teachers’ intentions with and their teaching of mathematics. Preschool teachers’ understanding of the knowledge required in this area is also scrutinised. The theoretical points of departure are variation theory and sociocultural theory. With variation theory the focus is directed towards how mathematical content is dealt with in teaching situations where preschool teachers have chosen the learning objects. The sociocultural perspective has been chosen because children’s mathematical learning in play often takes place in interactions with others and in the encounter with culturally mediated concepts. The theoretical framework also includes didactical points of departure. The study is qualitative, with videography and phenomenography as metholological research approaches. In the study, video observations and interviews with preschool teachers have been used as data collection methods. The results show that in children’s play mathematics consists of volume, geometrical shapes, gravity, quantity and positioning. The situations also include size, patterns, proportions, counting and the creation of pairs. The preschool teachers’ intentions, planning and staging of their goal-oriented work are that all children should be given the opportunity to discern a mathematical content. This also includes making learning objects visible in here-and-now-situations. Variation and a clear focus on the mathematical content are important in this context. One of the study’s knowledge contributions concerns the didactics of mathematics in the preschool. This relates to the teaching of mathematics and includes the knowledge that preschool teachers regard as essential for their teaching. This includes theoretical and practical knowledge about children and children’s learning and didactical issues and strategies. The conclusion is that preschool teachers need to have a basic knowledge of mathematics and the didactics of mathematics.