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.

Two Cultures of Arts Education, Finland and Canada? An integrated View

Taidekasvatuksen kaksi kulttuuria, Suomi ja Kanada? Integroitu näkemys Tutkimuksessa kuvataan kanadalaisen Learning Through The Arts –pedagogiikan mukainen suomalainen kokeiluhanke, jonka aikana taiteilija–opettaja-parit opettivat yhdessä eri oppiaineita koululuokille: esim. matematiikkaa tanssien, biologiaa maalaten tai yhdistäen eri taiteenlajeja projektimuotoiseen oppimiseen. Hanketta arvioitaessa nousee esille, ei niinkään yksittäisten taiteilijoiden ja opettajien toiminta, vaan pikemminkin Kanadan ja Suomen rakenteelliset sekä kulttuuriset eroavuudet. Tutkimus sivuaa myös Suomessa käytävää keskustelua taiteen hyödyllisyydestä ja pohtii samalla taito- ja taideaineiden asemaa koulussa. Työn teoreettisessa osassa integroidaan opetussuunnitelmateoriaa, kasvatuksen historiaa ja filosofiaa, tähdentäen taidekasvatuksen merkitystä osana koko ihmisen kasvatusta. Opetussuunnitelmateorian osalta tarkastellaan romanttista ja klassista opetussuunnitelmaa, jotka eroavat toisistaan menetelmiensä, sisältöjensä, tavoitteidensa sekä arvioinnin osalta. Ns. kovat ja pehmeät aineet tai matemaattis-luonnontieteelliset aineet vastakohtanaan humanismi, voidaan ymmärtää sekä historiallisia että epistemologisia taustojaan vasten. Pepperin maailmanhypoteesien mukaisesti on kasvatuksen ongelmien ratkaisemiseksi hahmotettavissa neljä selvästi toisistaan eroavaa lähestymistapaa: formismi; organisismi; mekanisismi; sekä kontekstualismi. Kantin filosofiaan viitaten tutkimus puolustaa käsitystä taiteesta rationaalisena ja propositionaalisena kokonaisuutena, joka ei ole vain kommunikaation väline, vaan yksi todellisuuden kohtaamisen lajeista, tiedon ja etiikan rinnalla. Näin ajateltuna taito- ja taidekasvatuksen tulisi olla luonteeltaan aina myös kulttuurikasvatusta. Tutkimuksen tulosten perusteella voidaan väittää, että moniammatillinen yhteistyö monipuolistaa koulun opetusta. Mikäli huolehditaan siitä, että taiteilijat saavat riittävästi koulutusta opettamiseen liittyvissä asioissa, on mahdollista käyttää taiteilijoita opettajien rinnalla koulutyössä.

The effectiveness of short-term literacy skills intervention on children at risk of reading and writing difficulties in Tanzania : a study of grade one children with dynamic assessment approach

The aim of the study was to create and evaluate an intervention programme for Tanzanian children from a low-income area who are at risk of reading and writing difficulties. The learning difficulties, including reading and writing difficulties, are likely to be behind many of the common school problems in Tanzania, but they are not well understood, and research is needed. The design of the study included an identification and intervention phase with follow-up. A group based dynamic assessment approach was used in identifying children at risk of difficulties in reading and writing. The same approach was used in the intervention. The study was a randomized experiment with one experimental and two control groups. For the experimental and the control groups, a total of 96 (46 girls and 50 boys) children from grade one were screened out of 301 children from two schools in a low income urban area of Dar-es-Salaam. One third of the children, the experimental group, participated in an intensive training programme in literacy skills for five weeks, six hours per week, aimed at promoting reading and writing ability, while the children in the control groups had a mathematics and art programme. Follow-up was performed five months after the intervention. The intervention programme and the tests were based on the Zambian BASAT (Basic Skill Assessment Tool, Ketonen & Mulenga, 2003), but the content was drawn from the Kiswahili school curriculum in Tanzania. The main components of the training and testing programme were the same, only differing in content. The training process was different from traditional training in Tanzanian schools in that principles of teaching and training in dynamic assessment were followed. Feedback was the cornerstone of the training and the focus was on supporting the children in exploring knowledge and strategies in performing the tasks. The experimental group improved significantly more (p = .000) than the control groups during the intervention from pre-test to follow-up (repeated measures ANOVA). No differences between the control groups were noticed. The effect was significant on all the measures: phonological awareness, reading skills, writing skills and overall literacy skills. A transfer effect on school marks in Kiswahili and English was found. Following a discussion of the results, suggestions for further research and adaptation of the programme are presented.

Communicative and Anticipatory Decision-Making Supported by Bayesian Networks

The purpose of this research is to draw up a clear construction of an anticipatory communicative decision-making process and a successful implementation of a Bayesian application that can be used as an anticipatory communicative decision-making support system. This study is a decision-oriented and constructive research project, and it includes examples of simulated situations. As a basis for further methodological discussion about different approaches to management research, in this research, a decision-oriented approach is used, which is based on mathematics and logic, and it is intended to develop problem solving methods. The approach is theoretical and characteristic of normative management science research. Also, the approach of this study is constructive. An essential part of the constructive approach is to tie the problem to its solution with theoretical knowledge. Firstly, the basic definitions and behaviours of an anticipatory management and managerial communication are provided. These descriptions include discussions of the research environment and formed management processes. These issues define and explain the background to further research. Secondly, it is processed to managerial communication and anticipatory decision-making based on preparation, problem solution, and solution search, which are also related to risk management analysis. After that, a solution to the decision-making support application is formed, using four different Bayesian methods, as follows: the Bayesian network, the influence diagram, the qualitative probabilistic network, and the time critical dynamic network. The purpose of the discussion is not to discuss different theories but to explain the theories which are being implemented. Finally, an application of Bayesian networks to the research problem is presented. The usefulness of the prepared model in examining a problem and the represented results of research is shown. The theoretical contribution includes definitions and a model of anticipatory decision-making. The main theoretical contribution of this study has been to develop a process for anticipatory decision-making that includes management with communication, problem-solving, and the improvement of knowledge. The practical contribution includes a Bayesian Decision Support Model, which is based on Bayesian influenced diagrams. The main contributions of this research are two developed processes, one for anticipatory decision-making, and the other to produce a model of a Bayesian network for anticipatory decision-making. In summary, this research contributes to decision-making support by being one of the few publicly available academic descriptions of the anticipatory decision support system, by representing a Bayesian model that is grounded on firm theoretical discussion, by publishing algorithms suitable for decision-making support, and by defining the idea of anticipatory decision-making for a parallel version. Finally, according to the results of research, an analysis of anticipatory management for planned decision-making is presented, which is based on observation of environment, analysis of weak signals, and alternatives to creative problem solving and communication.

Foodstuffs and medicines as legal categories in the EU and China. Functional foods as a borderline case

The thesis discusses the regulation of foodstuffs and medicines, and particularly the regulation of functional foods. Legal systems investigated are the EU and China. Both are members of the WTO and Codex Alimentarius, which binds European and Chinese rules together. The study uses three Chinese berries as case examples of how product development faces regulation in practice. The berries have traditional uses as herbal medicines. Europe and China have similar nutrition problems to be resolved, such as obesity, cardiovascular disease, and diabetes. The three berries might be suitable raw materials for functional foods. Consumer products with health-enhancing functions, such as lowering blood pressure, might legally be classifi ed either as foodstuffs or medicines. The classifi cation will depend on functions and presentation of the product. In our opinion, food and medicine regulation should come closer together so the classifi cation issue would no longer be an issue. Safety of both foodstuffs and medicines is strictly regulated. With medicines, safety is a more relative concept, where benefi ts of the product are compared to side-effects in thorough scientifi c tests and trials. Foods, on the other hand, are not allowed to have side-effects. Hygiene rules and rules on the use of chemicals apply. In China, food safety is currently at focus as China has had several severe food scandals. Newly developed foods are called novel foods, and are specifi cally regulated. The current European novel food regulation from 1997 treats traditional third country products as novel. The Chinese regulation of 2007 also defi nes novel foods as something unfamiliar to a Chinese consumer. The concepts of novel food thus serve a protectionist purpose. As regards marketing, foods are allowed to bear health claims, whereas medicines bear medicinal claims. The separation is legally strict: foods are not to be presented as having medicinal functions. European nutrition and health claim regulation exists since 2006. China also has its regulation on health foods, listing the permitted claims and how to substantiate them. Health claims are allowed only on health foods. The European rules on medicines include separate categories for herbal medicines, traditional herbal medicines, and homeopathic medicines, where there are differing requirements for scientifi c substantiation. The scientifi c and political grounds for the separate categories provoke criticism. At surface, the Chinese legal system seems similar to the European one. To facilitate trade, China has enacted modern laws. Laws are needed as the country moves from planned economy to market economy: ‘rule of law’ needs to replace ‘rule of man’. Instead of being citizens, Chinese people long were subordinates to the Emperor. Confucius himself advised to avoid confl ict. Still, Chinese people do not and cannot always trust the legal system, as laws are enforced in an inconsistent manner, and courts are weak. In China, there have been problems with confl icting national and local laws. In Europe, the competence of the EU vs. the competence of the Member States is still not resolved, even though the European Commission often states that free trade requires harmonisation. Food and medicine regulation is created by international organisations, food and medicine control agencies, standards agencies, companies and their organisations. Regulation can be divided in ‘hard law’ and ‘soft law’. One might claim that hard law is in crisis, as soft law is gaining importance. If law is out of fashion, regulation certainly isn’t. In the future, ‘law’ might mean a process where rules and incentives are created by states, NGOs, companies, consumers, and other stakeholders. ‘Law’ might thus refer to a constant negotiation between public and private actors. Legal principles such as transparency, equal treatment, and the right to be heard would still be important.

Data analysis tools and methods for DNA microarray and high-throughput sequencing data

The recent rapid development of biotechnological approaches has enabled the production of large whole genome level biological data sets. In order to handle thesedata sets, reliable and efficient automated tools and methods for data processingand result interpretation are required. Bioinformatics, as the field of studying andprocessing biological data, tries to answer this need by combining methods and approaches across computer science, statistics, mathematics and engineering to studyand process biological data. The need is also increasing for tools that can be used by the biological researchers themselves who may not have a strong statistical or computational background, which requires creating tools and pipelines with intuitive user interfaces, robust analysis workflows and strong emphasis on result reportingand visualization. Within this thesis, several data analysis tools and methods have been developed for analyzing high-throughput biological data sets. These approaches, coveringseveral aspects of high-throughput data analysis, are specifically aimed for gene expression and genotyping data although in principle they are suitable for analyzing other data types as well. Coherent handling of the data across the various data analysis steps is highly important in order to ensure robust and reliable results. Thus,robust data analysis workflows are also described, putting the developed tools andmethods into a wider context. The choice of the correct analysis method may also depend on the properties of the specific data setandthereforeguidelinesforchoosing an optimal method are given. The data analysis tools, methods and workflows developed within this thesis have been applied to several research studies, of which two representative examplesare included in the thesis. The first study focuses on spermatogenesis in murinetestis and the second one examines cell lineage specification in mouse embryonicstem cells.

Globaalikasvatus avaa ikkunoita maailmaan

Kirjallisuusarvostelu

Matematiikan opetuksen virtuaaliympäristöjen pedagoginen käyttö

Tämän kandityön tarkoituksena on selvittää ja kehittää Lappeenrannan teknillisen yliopiston sovelletun matematiikan laitoksella luotua virtuaalimateriaalin käyttöä eri kohderyhmille sopivaksi sekä käyttäjäystävällisemmäksi. Matematiikan virtuaalimateriaali on luotu tukemaan lähiopetusta matematiikan perusopetuksessa. Matematiikan virtuaalimateriaalin hallintaympäristöä on kehitetty vuodesta 2001. Järjestelmää sekä sen opiskelumateriaalia on kehitetty opettajien ja opiskelijoiden avulla. Järjestelmä kattaa teknillisen yliopiston eri osastojen matematiikan peruskurssien materiaalit. Sen käytöllä opettajat voivat hankkia itselleen lisää aikaa opetuksen suunnitteluun materiaalin luomisen nopeutuessa, koska opetusmateriaali voidaan nopeasti kasata valmiista tehtävistä ja teoriaosioista. Opiskelijoiden kannalta hyvätasoinen oppimateriaali on jatkuvasti saatavilla ja sen avulla on myös helppo opiskella hyvien hakutoimintojen ansiosta.

Agendi Modus; Yrittäjyyskasvatusta Etelä-Karjalassa. Yrittäjyys, koulut ja yrittäjyyskasvatuksenhanketoiminta

Julkaisu on kuvaus Agendi Modus - yrittäjyyskasvatushankkeesta, joka toteutettiin Etelä- Karjalassa vuosina 2004-2007. Samalla se on hankkeeseen osallistuneiden kokemuksista tehty vaikuttavuuden arviointiraportti. Agendi Modus-hanke oli Lappeenrannan teknillisen yliopiston Koulutus ja kehittämiskeskuksen kouluille ja yrityksille suunnattu projekti. Hankkeen tavoitteet olivat 1. pedagogisen muutoksen tuottaminen, 2. oppimisympäristöjen kehittäminen ja 3. yrittäjämäistä koulutyötä tukevan koulun kulttuurin ja johtamisen muutoksen tuottaminen. Julkaisusta käy ilmi, että hankevoi oppia yhdessä asiakkaidensa eli hankkeen yhteistyötahojen kanssa. Raportin toisessa osassa tuodaan esille muutamia yrittäjyyskasvatuksen näkökulmia. Lukija voi myös pohtia, tulisiko yrittäjyyskasvatuksen koulutuskokonaisuus rakentua kuten Agendi Moduksessa, eli esitellen aihealuetta sekäyleisesti että perehtyen sen eri olemuspuoliin. Julkaisun keskeisimmät huomiot ovat että A) hanke, joka kuuntelee asiakastaan, tuottaa sen tarvitsemia tuotteita, B) pitkäkestoinen koulutusprosessi tarjoaa mahdollisuuden ymmärtää yrittäjyyskasvatuksen metodologiaa ja pedagogiaa ja tukee aihealueen didaktiikan kokeilemista, C) on tärkeää kouluttaa sekä työyhteisöjä että näiden yksittäisiä toimijoita, D) eri osallistujilla on omanlaistaan osaamista yrittäjyyskasvatuksessa, koska kukin on valinnut erityyppistä koulutuksista itselleen soveltuvimpia, E) näyttää siltä, että noin puolet koulutuksiin osallistuneista käyttää yrittäjyyskasvatusta opetuksensa käyttöteoriana, F) oppimisympäristöjen kehittäminen on vähäisempää kuin yrittäjyyskasvatuksen käyttö oman opetuksen osana, G) hankkeen jälkeen osallistujilla on laaja ymmärrys yrittäjyyskasvatusta suosivasta oppimiskulttuurista, mutta vain harvat kokevat luovansa yrittäjämäistä koulukulttuuria. Jos uutta aihealueen hanketta suunnitellaan, se voisi keskittyä tätä hanketta tarkemmin koulukulttuurin muuttamiseen, jonka lisäksi toiminta-ajatuksissa kannattaisi huomioida oppimisen, teknologian ja yrittäjyyden strategiat.

Wavelets in real-time paper web analysis

Online paper web analysis relies on traversing scanners that criss-cross on top of a rapidly moving paper web. The sensors embedded in the scanners measure many important quality variables of paper, such as basis weight, caliper and porosity. Most of these quantities are varying a lot and the measurements are noisy at many different scales. The zigzagging nature of scanning makes it difficult to separate machine direction (MD) and cross direction (CD) variability from one another. For improving the 2D resolution of the quality variables above, the paper quality control team at the Department of Mathematics and Physics at LUT has implemented efficient Kalman filtering based methods that currently use 2D Fourier series. Fourier series are global and therefore resolve local spatial detail on the paper web rather poorly. The target of the current thesis is to study alternative wavelet based representations as candidates to replace the Fourier basis for a higher resolution spatial reconstruction of these quality variables. The accuracy of wavelet compressed 2D web fields will be compared with corresponding truncated Fourier series based fields.

Linguistic models for decision support

Linguistic modelling is a rather new branch of mathematics that is still undergoing rapid development. It is closely related to fuzzy set theory and fuzzy logic, but knowledge and experience from other fields of mathematics, as well as other fields of science including linguistics and behavioral sciences, is also necessary to build appropriate mathematical models. This topic has received considerable attention as it provides tools for mathematical representation of the most common means of human communication - natural language. Adding a natural language level to mathematical models can provide an interface between the mathematical representation of the modelled system and the user of the model - one that is sufficiently easy to use and understand, but yet conveys all the information necessary to avoid misinterpretations. It is, however, not a trivial task and the link between the linguistic and computational level of such models has to be established and maintained properly during the whole modelling process. In this thesis, we focus on the relationship between the linguistic and the mathematical level of decision support models. We discuss several important issues concerning the mathematical representation of meaning of linguistic expressions, their transformation into the language of mathematics and the retranslation of mathematical outputs back into natural language. In the first part of the thesis, our view of the linguistic modelling for decision support is presented and the main guidelines for building linguistic models for real-life decision support that are the basis of our modeling methodology are outlined. From the theoretical point of view, the issues of representation of meaning of linguistic terms, computations with these representations and the retranslation process back into the linguistic level (linguistic approximation) are studied in this part of the thesis. We focus on the reasonability of operations with the meanings of linguistic terms, the correspondence of the linguistic and mathematical level of the models and on proper presentation of appropriate outputs. We also discuss several issues concerning the ethical aspects of decision support - particularly the loss of meaning due to the transformation of mathematical outputs into natural language and the issue or responsibility for the final decisions. In the second part several case studies of real-life problems are presented. These provide background and necessary context and motivation for the mathematical results and models presented in this part. A linguistic decision support model for disaster management is presented here – formulated as a fuzzy linear programming problem and a heuristic solution to it is proposed. Uncertainty of outputs, expert knowledge concerning disaster response practice and the necessity of obtaining outputs that are easy to interpret (and available in very short time) are reflected in the design of the model. Saaty’s analytic hierarchy process (AHP) is considered in two case studies - first in the context of the evaluation of works of art, where a weak consistency condition is introduced and an adaptation of AHP for large matrices of preference intensities is presented. The second AHP case-study deals with the fuzzified version of AHP and its use for evaluation purposes – particularly the integration of peer-review into the evaluation of R&D outputs is considered. In the context of HR management, we present a fuzzy rule based evaluation model (academic faculty evaluation is considered) constructed to provide outputs that do not require linguistic approximation and are easily transformed into graphical information. This is achieved by designing a specific form of fuzzy inference. Finally the last case study is from the area of humanities - psychological diagnostics is considered and a linguistic fuzzy model for the interpretation of outputs of multidimensional questionnaires is suggested. The issue of the quality of data in mathematical classification models is also studied here. A modification of the receiver operating characteristics (ROC) method is presented to reflect variable quality of data instances in the validation set during classifier performance assessment. Twelve publications on which the author participated are appended as a third part of this thesis. These summarize the mathematical results and provide a closer insight into the issues of the practicalapplications that are considered in the second part of the thesis.

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.

Johtajan jäljillä – Johtaminen varhaiskasvatuksen hajautetuissa organisaatioissa laadun ja pedagogisen tuen näkökulmasta

Tutkimus sijoittuu varhaiskasvatuksen hajautetun organisaation kontekstiin, mutta tulokset ovat siirrettävissä muihinkin suomalaisiin kasvatus- ja opetustoimen organisaatioihin. Hajautettujen organisaatioiden tutkimus on ollut varhaiskasvatuksen kentällä vielä vähäistä, vaikka organisaatiomallin vaikutukset johtajuuden toteuttamiselle ovat merkittävät. Hajautetulla organisaatiolla varhaiskasvatuksessa tarkoitetaan sitä, että yhden johtajan alaisuudessa on monta eri päiväkotia tai erilaisia päivähoitomuotoja. Tämä organisaatiomalli on yhä enenevässä määrin kasvava suomalaisessa varhaiskasvatuksessa. Varhaiskasvatuksen hajautettujen organisaatioiden tutkimuksessa on aiemmin tarkasteltu johtajan ja työntekijöiden ja työntekijöiden keskinäisiä ammatillisia suhteita. Tässä tutkimuksessa näkökulma painottuu johtamiseen ja työskentelyyn hajautetuissa organisaatiossa sinänsä sekä myös laadunarviointiin sekä pedagogiikkaan. Viitekehyksenä tutkimuksessa on LMX-teoria (leader-member-exchange, johtajuuden vaihtoteoria), jossa tarkastellaan esimies-alaissuhdetta ja siihen kiinteästi liittyvää luottamuksen käsitettä. Luottamuksen merkitys hajautetuissa organisaatioissa korostuu, koska esimies ei ole fyysisesti päivittäin läsnä työntekijöiden arjessa. Tutkimuksessa tarkastellaan hajautetuissa varhaiskasvatuksen organisaatioissa työskentelyä seuraavien tutkimuskysymysten avulla: 1) Mitkä ovat varhaiskasvatuksen hajautettujen organisaatioiden johtamisen erityispiirteet? 2) Miten eri työntekijäryhmät kokevat hajautetussa organisaatiossa työskentelyn? 3) Millaisia kokemuksia esimiehillä ja työntekijöillä on heidän yksiköissään toteutetusta laadunarvioinnista? 4) Millaiseksi työntekijät ja esimiehet kokevat esimieheltään saadun tuen? Tutkimuksessa oli kolme eri aineistoa. Ensimmäinen aineisto koostui 11 hajautetun organisaation johtajan haastattelusta. Toinen aineisto (n = 223) sisälsi haastateltujen esimiesten lomakevastausten lisäksi heidän alaisuudessaan toimivien työntekijöiden, 10 esimieskoulutukseen osallistuneen johtajan sekä kolmen erillisyksikön työntekijöiden vastaukset. Kolmas aineisto oli kerätty pääkaupunkiseudulta varhaiskasvatuksen johtajilta lomakekyselynä (n = 112). Aineistoa on analysoitu teorialähtöisen ja aineistolähtöisen sisällönanalyysin ja tilastollisten analyysien avulla Tulokset osoittavat, että johtajat kokivat hallinnollisten töiden vievän paljon aikaa. Esimiehen kanssa eri työpaikassa työskentelevät työntekijät hahmottivat koko organisaation selkeämmin kuin esimiehen kanssa fyysisesti samassa paikassa työskentelevät. Esimiesten käsitysten mukaan laadunarviointia suoritettiin enemmän kuin mitä työntekijöiden mukaan. Työntekijät kaipasivat esimiehiltään tukea yhteistyöhön ja vuorovaikutukseen, pedagogiseen ohjaukseen, kehittämiseen ja toiminnan resursseihin liittyen. Erillisyksikössä työskentelevät kokivat saavansa enemmän tukea kuin esimiehen kanssa fyysisesti samassa yksikössä työskentelevät työntekijät. Sekä esimieheltä saadun pedagogisen tuen että luottamuksen kokemukset kiinnittävät tämän tutkimuksen tulosten mukaan huomion rakenteiden merkitykseen hajautetuissa organisaatioissa. Arviointiin, pedagogiseen tukeen ja tiedonkulkuun liittyvien rakenteiden huomioiminen helpottaa hajautetussa organisaatiossa johtamista. Edellisten lisäksi johtajan selkeä visio omasta johtamistyöstään ja jaetun johtajuuden hyödyntäminen edesauttavat työn hallinnan kokemuksia.