Mathematics inspired by Darwin. Adaptive dynamics of dispersal and cooperation

In 1859, Charles Darwin published his theory of evolution by natural selection, the process occurring based on fitness benefits and fitness costs at the individual level. Traditionally, evolution has been investigated by biologists, but it has induced mathematical approaches, too. For example, adaptive dynamics has proven to be a very applicable framework to the purpose. Its core concept is the invasion fitness, the sign of which tells whether a mutant phenotype can invade the prevalent phenotype. In this thesis, four real-world applications on evolutionary questions are provided. Inspiration for the first two studies arose from a cold-adapted species, American pika. First, it is studied how the global climate change may affect the evolution of dispersal and viability of pika metapopulations. Based on the results gained here, it is shown that the evolution of dispersal can result in extinction and indeed, evolution of dispersalshould be incorporated into the viability analysis of species living in fragmented habitats. The second study is focused on the evolution of densitydependent dispersal in metapopulations with small habitat patches. It resulted a very surprising unintuitive evolutionary phenomenon, how a non-monotone density-dependent dispersal may evolve. Cooperation is surprisingly common in many levels of life, despite of its obvious vulnerability to selfish cheating. This motivated two applications. First, it is shown that density-dependent cooperative investment can evolve to have a qualitatively different, monotone or non-monotone, form depending on modelling details. The last study investigates the evolution of investing into two public-goods resources. The results suggest one general path by which labour division can arise via evolutionary branching. In addition to applications, two novel methodological derivations of fitness measures in structured metapopulations are given.

Building the ‘Digital’ Library: Routes to Managing our Institutional Digital Learning, Teaching and Research Assets Together

Presentation at Open Repositories 2014, Helsinki, Finland, June 9-13, 2014

Learning information technology business in a changing industry landscape. Introducing Team Entrepreneurship in Renewing Bachelor Education in Renewing Bachelor Education in Information

Speed, uncertainty and complexity are increasing in the business world all the time. When knowledge and skills become quickly irrelevant, new challenges are set for information technology (IT) education. Meta-learning skills – learning how to learn rapidly - and innovation skills have become more essential than single technologies or other specific issues. The drastic changes in the information and communications technology (ICT) sector have caused a need to reconsider how IT Bachelor education in Universities of Applied Sciences should be organized and employed to cope with the change. The objective of the study was to evaluate how a new approach to IT Bachelor education, the ICT entrepreneurship study path (ICT-ESP) fits IT Bachelor education in a Finnish University of Applied Sciences. This kind of educational arrangement has not been employed elsewhere in the context of IT Bachelor education. The study presents the results of a four-year period during which IT Bachelor education was renewed in a Finnish University of Applied Sciences. The learning environment was organized into an ICT-ESP based on Nonaka’s knowledge theory and Kolb’s experiental learning. The IT students who studied in the ICT-ESP established a cooperative and learned ICT by running their cooperative at the University of Applied Sciences. The students (called team entrepreneurs) studied by reading theory in books and other sources of explicit information, doing projects for their customers, and reflecting in training sessions on what was learnt by doing and by studying the literature. Action research was used as the research strategy in this study. Empirical data was collected via theme-based interviews, direct observation, and participative observation. Grounded theory method was utilized in the data analysis and the theoretical sampling was used to guide the data collection. The context of the University of Applied Sciences provided a good basis for fostering team entrepreneurship. However, the results showed that the employment of the ICT-ESP did not fit into the IT Bachelor education well enough. The ICT-ESP was cognitively too tough for the team entrepreneurs because they had two different set of rules to follow in their studies. The conventional courses engaged lot of energy which should have been spent for professional development in the ICT-ESP. The amount of competencies needed in the ICT-ESP for professional development was greater than those needed for any other ways of studying. The team entrepreneurs needed to develop skills in ICT, leadership and self-leadership, team development and entrepreneurship skills. The entrepreneurship skills included skills on marketing and sales, brand development, productization, and business administration. Considering the three-year time the team entrepreneurs spent in the ICT-ESP, the challenges were remarkable. Changes to the organization of IT Bachelor education are also suggested in the study. At first, it should be admitted that the ICT-ESP produces IT Bachelors with a different set of competencies compared to the conventional way of educating IT Bachelors. Secondly, the number of courses on general topics in mathematics, physics, and languages for team entrepreneurs studying in the ICTESP should be reconsidered and the conventional course-based teaching of the topics should be reorganized to support the team coaching process of the team entrepreneurs with their practiceoriented projects. Third, the upcoming team entrepreneurs should be equipped with relevant information about the ICT-ESP and what it would require in practice to study as a team entrepreneur. Finally, the upcoming team entrepreneurs should be carefully selected before they start in the ICT-ESP to have a possibility to eliminate solo players and those who have a too romantic view of being a team entrepreneur. The results gained in the study provided answers to the original research questions and the objectives of the study were met. Even though the IT degree programme was terminated during the research process, the amount of qualitative data gathered made it possible to justify the interpretations done.

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.

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.

Ohjelmoinnin opetus peruskoulussa: toiminnallisuutta ja graafista ohjelmointikieltä hyödyntävien opetusmenetelmien vertailu

Ohjelmoinnin opettaminen yleissivistävänä oppiaineena on viime aikoina herättänyt kiinnostusta Suomessa ja muualla maailmassa. Esimerkiksi Suomen opetushallituksen määrittämien, vuonna 2016 käyttöön otettavien peruskoulun opintosuunnitelman perusteiden mukaan, ohjelmointitaitoja aletaan opettaa suomalaisissa peruskouluissa ensimmäiseltä luokalta alkaen. Ohjelmointia ei olla lisäämässä omaksi oppiaineekseen, vaan sen opetuksen on tarkoitus tapahtua muiden oppiaineiden, kuten matematiikan yhteydessä. Tämä tutkimus käsittelee yleissivistävää ohjelmoinnin opetusta yleisesti, käy läpi yleisimpiä haasteita ohjelmoinnin oppimisessa ja tarkastelee erilaisten opetusmenetelmien soveltuvuutta erityisesti nuorten oppilaiden opettamiseen. Tutkimusta varten toteutettiin verkkoympäristössä toimiva, noin 9–12-vuotiaille oppilaille suunnattu graafista ohjelmointikieltä ja visuaalisuutta tehokkaasti hyödyntävä oppimissovellus. Oppimissovelluksen avulla toteutettiin alakoulun neljänsien luokkien kanssa vertailututkimus, jossa graafisella ohjelmointikielellä tapahtuvan opetuksen toimivuutta vertailtiin toiseen opetusmenetelmään, jossa oppilaat tutustuivat ohjelmoinnin perusteisiin toiminnallisten leikkien avulla. Vertailututkimuksessa kahden neljännen luokan oppilaat suorittivat samankaltaisia, ohjelmoinnin peruskäsitteisiin liittyviä ohjelmointitehtäviä molemmilla opetus-menetelmillä. Tutkimuksen tavoitteena oli selvittää alakouluoppilaiden nykyistä ohjelmointiosaamista, sitä minkälaisen vastaanoton ohjelmoinnin opetus alakouluoppilailta saa, onko erilaisilla opetusmenetelmillä merkitystä opetuksen toteutuksen kannalta ja näkyykö eri opetusmenetelmillä opetettujen luokkien oppimistuloksissa eroja. Oppilaat suhtautuivat kumpaankin opetusmenetelmään myönteisesti, ja osoittivat kiinnostusta ohjelmoinnin opiskeluun. Sisällöllisesti oppitunneille oli varattu turhan paljon materiaalia, mutta esimerkiksi yhden keskeisimmän aiheen, eli toiston käsitteen oppimisessa aktiivisilla leikeillä harjoitellut luokka osoitti huomattavasti graafisella ohjelmointikielellä harjoitellutta luokkaa parempaa osaamista oppitunnin jälkeen. Ohjelmakoodin peräkkäisyyteen liittyvä osaaminen oli neljäsluokkalaisilla hyvin hallussa jo ennen ohjelmointiharjoituksia. Aiheeseen liittyvän taustatutkimuksen ja luokkien opettajien haastatteluiden perusteella havaittiin koulujen valmiuksien opetussuunnitelmauudistuksen mukaiseen ohjelmoinnin opettamiseen olevan vielä heikolla tasolla.