Este trabalho objetivou determinar a disponibilidade do aqüífero Serra Grande e estabelecer as diretrizes para o seu gerenciamento sustentável no município de Picos, localizado no sudeste do Estado do Piauí. Principal sistema de água subterrânea da região, este aqüífero é o único com capacidade para atender as demandas futuras da população. Porém, a falta de regras básicas na exploração dos seus recursos poderá comprometer sua sustentabilidade. O desenvolvimento deste estudo teve início com a elaboração do modelo conceitual da área e a análise das condições de uso dos recursos hídricos. Nesta etapa, verificando-se que os conceitos hidrogeológicos vigentes consideravam apenas o limite físico do sistema para definir sua disponibilidade, foi estabelecido um novo princípio para determinação do volume de recursos que pode ser explorado de um aqüífero, denominado de princípio sustentável, tendo como base os fatores econômicos envolvidos na sua exploração. Para determinação da disponibilidade física e econômica do aqüífero Serra Grande, primeiramente, foi estimado o déficit hídrico acumulado desde o início da exploração do sistema, estabelecida sua relação com a posição do nível potenciométrico e calculado o custo atual de produção da água. Em seguida, foram traçados dois cenários futuros para a exploração dos recursos hídricos no município, representando os modelos de gestão da oferta e gestão da demanda, para o período de 15 e 50 anos. Posteriormente, foi construído um modelo matemático para representar o sistema de subsuperfície, no qual foi simulada a evolução futura do nível d’água. Com base nos valores obtidos, foi estimado o volume de água a ser produzido do armazenamento, a quantidade de recursos que deverão ser incorporados ao sistema e o custo futuro de produção. Os resultados mostraram que o aqüífero precisará incorporar um volume significativo de recursos, que talvez não esteja disponível na região estudada, e que a elevação real do custo da água poderá comprometer a capacidade de pagamento da população para dispor destes recursos. Verificada esta situação, foram definidas as medidas que precisam ser implementadas para o gerenciamento sustentável do aqüífero estudado, de modo a garantir o abastecimento futuro do município e da região. Com a elaboração deste trabalho, concluiu-se que o aqüífero Serra Grande não é “intensamente explorado” em Picos, porém é mal explorado atualmente, o que deverá provocar prejuízos na exploração futura dos seus recursos. / This work’s goals were to determinate the availability of the Serra Grande aquifer and to establish the governess for its sustainable management in the municipality of Picos, located on the southeast of Piauí State. This aquifer, the region’s most important groundwater system, has an unique capacity of fulfilling the population’s future demand. However, the absence of basic rules for the exploitation of its resources would compromise its sustainability. The study began with the development of the conceptual model of the area and the analyses of the water resources use. During this step, after verify that the hydrological actual concepts only observe the physical limit of the system to define its availability, it was established a new principle to determinate the volume of resources that can be exploited from an aquifer, named sustainable principle, based on the economical factors involved in its exploitation. In order to determine the physical and economical availability of the Serra Grande aquifer, first, it was estimated the water deficit accumulated since the begging exploitation of the system, established its relationship with the potenciometric level and was calculated the present cost of water production. Later on, two hypothetical scenarios concerning future exploration of water resources were drawn, representing the models of supply and demand management, for a period of 15 and 50 years. Furthermore, a mathematic model was built to represent the subsurface system, which was simulated the evolution of the water level. Based on the values found, it was estimated the amount of water that should be produced from storage, the quantity of resources that have to be incorporated to the system and the future production cost. Moreover, the results showed that the aquifer will need to incorporate a meaningful quantity of resources, that may be not available in the studied region, and that the real increase of the cost of the water would compromise the payment capacity of the population to dispose those resources. After verify this situation, it was defined the actions that must be taken for the sustainable management of the studied aquifer, to guarantee the future water supply of the municipality and the region. In conclusion, this work confirmed that the Serra Grande aquifer is not “overexploited” in Picos, instead, it is not being correctly exploited, which will negatively affect the future exploitation of its resources.

[pt] A produção e o uso de DRI (Direct Reduction Iron) são cada vez maiores hoje em dia nos países desenvolvidos, essencialmente pela redução do preço do gás natural e do sucesso da tecnologia de extração de gás de xisto. Além disso, o menor teor de elementos contaminantes em DRI do que nas sucatas de aço, levou-o a ser considerado uma boa alternativa como carga metálica para o Forno Elétrico a Arco (FEA) e o processo no conversor LD /BOF. Os custos operacionais e os problemas ambientais, são atualmente dois fatores tecnológicos importantes a serem considerados na otimização da produção de DRI, afetando à produtividade, sustentabilidade e competitividade do processo industrial. O teor de carbono do DRI, por exemplo, tem se tornado cada vez mais importante, devido à sua capacidade de gerar energia química nas aciarias, complementando o uso de energia elétrica nos FEA e os inputs energéticos no LD. Este trabalho foi uma das partes do programa de cooperação entre a Companhia de Mineração Samarco e o Grupo de Siderurgia da Pontifícia Universidade Católica do Rio de Janeiro / PUC-Rio, que tratou especificamente do modelo cinético para a metalização e carburização simultâneas em fornos RD tipo cuba. No âmbito deste objetivo o reator foi dividido em três zonas: Redução, Transição e Resfriamento. Foram também consideradas mais três camadas concêntricas: periférica, media e central. Com base nos resultados obtidos em experiências que abrangeram diferentes tipos de pelotas, empregando misturas gasosas semelhantes às presentes nos processos industriais e obedecendo às suas correspondentes semelhanças fluidodinâmicas, foi desenvolvido um software, denominado METCARB, que incluiu na sua elaboração todas as equações e modelos cinéticos desenvolvidos experimentalmente nas três zonas do reator RD. A parte experimental foi, portanto, uma das partes principais do presente trabalho, conjuntamente com a concepção do modelo computacional e suas validações industriais. Com o METCARB, as previsões acerca da metalização e carburização simultâneas, em qualquer região interna do forno, se tornou possível, utilizando como entradas as dimensões do forno, medidas de temperaturas, composições dos gases, etc. Os resultados de metalização e carburização, também em formato gráfico, são gerados pelo sistema computacional, bem como as curvas cronométricas e tabelas de resultados. Estudos sobre dois casos reais foram realizados, a fim de validarem a ferramenta computacional desenvolvida. Constatou-se que a carburização do ferro metálico sempre ocorre simultaneamente com a redução dos óxidos de ferro e que, dependendo da temperatura e composição dos gases, pode ocorrer precipitação de finos de carbono. As simulações realizadas com o modelo METCARB mostraram que na periferia da ZR é gerado um DRI mais metalizado que na região do centro. Fenômeno contrário foi, entretanto, verificado com a carburização; Nas condições experimentais empregadas neste trabalho, os valores médios obtidos para a carburização e a metalização, no final da ZR, variam entre 0,4 - 0,7 por cento C, e 92 por cento - 97 por cento, respectivamente; Constatou-se não ocorrer progresso do grau de redução nas zonas de Transição (ZT) e de Arrefecimento (ZA), ou seja, mantiveram-se ao longo dessas zonas os valores de metalização obtidos no fundo da ZR; A influência do vapor de água no processo da carburização no caso estudado (0 - 4.25 por cento H2O) leva menor porcentagem de carburização (2,7 por cento C – 2,35). / [en] The production and the use of DRI (Direct Reduction Iron) are increasing today in developed countries, mainly by reducing the price of natural gas and the success of shale gas extraction technology. In addition, the lower level of contaminants in DRI than in metal scraps, led it to be considered a good alternative as metallic charge for the Electric Arc Furnace (EAF) and the process in LD / BOF converter. This work was one part of the cooperation program between Samarco Mining Company and Steel Group of the Pontifical Catholic University of Rio de Janeiro / PUC-Rio, which specifically dealt with the kinetic model for the metallization and carburization simultaneous in RD shaft furnaces. Under this purpose the reactor was divided into three zones: Reduction, Transition and Cooling. There were also three concentric regions considered: peripheral, media and center. Based on the results from experiments covering different types of pellets, using gas mixtures similar to those present in the industrial processes and obeying their corresponding fluid dynamic similarities, it developed a software called METCARB, which included in its preparation all kinetic equations and models developed experimentally in the three reactor zones of RD. The experimental part was therefore a major part of this work, together with the design of computational model and its industrial validations. With METCARB predictions about the simultaneous metallization and carburization in any internal region of the furnaces, it became possible, using as inputs the dimensions of the furnace, temperature measurements, compositions of gases, etc. The results of metallization and carburization also in graphic format are generated by the computer system, and the chronometric curves and results tables. Studies on two real cases were performed in order to validate the developed computational tool. It was found that the carburization always occurs simultaneously with the reduction of iron oxides and, depending on the temperature and composition of the gases; precipitation of fine carbon may occur. The simulations with METCARB model showed that the periphery of the ZR generated more DRI metallized than the center area. A contrary phenomenon has been verified with the carburization; With the experimental conditions used in this study, averages values obtained for the metallization and carburization in the final ZR vary between 0.4 - 0.7 percent C and 92 percent - 97 percent, respectively; It was not found that the progress of reduction degree occurred in the transition (ZT) and cooling (ZA) regions, in other words, it remained along these zones of the metallization values obtained at the bottom of ZR; The influence of water vapor in the carburization process in the case studies (0 - 4.25 percent H 2 O) takes a smaller percentage of carburization (2.7 percent C - 2.35).

L’avènement du concept d’Open Innovation a été perçu par les industriels comme une formidable opportunité pour améliorer leur processus d’innovation et augmenter leur marge. En effet, ce concept prônant la large distribution des connaissances, suggère que les entreprises doivent solliciter leur environnement pour acquérir de nouvelles technologies par le biais de collaborations et que la valorisation des technologies internes à l’entreprise peut se faire de divers manières, comme le licensing. Alors les frontières de l’entreprise deviennent poreuses pour permettre une forte interaction avec des partenaires externes. Malgré toutes les promesses de ce concept, celui-ci a apporté un certain nombre de problématiques allant de la propriété intellectuelle à la culture d’entreprise en passant par les freins cognitifs. En accord avec le partenaire industriel de cette thèse, notre observation terrain et les constats bibliographiques, nous nous sommes concentrés sur les aspects organisationnels à mettre en œuvre pour mener une politique d’Open Innovation. Ainsi, cette thèse propose un premier modèle conceptuel pour ancrer une organisation dans son environnement et prendre pleinement en compte le paradigme d’Open Innovation. Ce modèle se base sur l’hypothèse que l’environnement est composé de facteurs d’influence qui ont un impact sur les projets de l’entreprise et que ceux-ci doivent posséder un capital compétence adéquate pour maitriser ces facteurs et atteindre les objectifs. Fort de ce cadre conceptuel, nous avons modélisé mathématiquement une organisation avec une approche coût/bénéfice pour comprendre le fonctionnement d’une organisation en mode « open ». Cela nous a permis de mettre en évidence le rôle de la structure organisationnelle et de la stratégie pour une politique d’Open Innovation. Enfin, en accord avec notre posture épistémologique d’action-recherche, nous avons développé un outil d’aide à l’orientation de l’action, RO²I (Relevant Organization for Open Innovation). L’objectif de cet outil est de proposé aux porteurs de projets, à t=0 du projet, une aide pour prendre en compte les aspects collaboratifs afin de mener leurs projets à bien et de choisir le bon modèle organisationnel pour inclure les compétences des partenaires. Nous avons pu tester la pertinence de notre proposition sur plusieurs projets passés d’une équipe d’innovation de rupture. Une fois validé, nous avons souhaité vérifier que notre outil était utilisable par les porteurs de projet, eux-mêmes, donc nous avons effectué une expérimentation sur deux projets en phase de démarrage dans les services supports de Solvay. Ce travail conclue sur la nécessité de posséder une organisation adaptée aux activités de collaboration et sur la nécessité d’un outil permettant de prendre en compte l’Open Innovation. Nous proposons, en perspective, d’utiliser cet outil pour mesurer la capacité à Open Innover d’une entreprise / Companies showed the arising of the Open Innovation concept as an amazing opportunity to improve their innovation process and increase profitability. Indeed, Open Innovation proposes to solicit external environment to acquire new technologies thanks to collaborations and, also, to add value to internal technologies by different path, like licensing-out, for instance. Then, firm boundaries become porous to allow strong interactions with external stakeholders. Despite to promises of this concept, it brings a lot of specific issues as intellectual property, firm culture or cognitive brakes. According to our industrial partner, our field observation and our state of art, we focused this work on organizational issues to perform an Open Innovation policy. To solve these issues, first, this these proposes a conceptual model to anchor an organization into it environment and to fully encompass the Open Innovation paradigm. We base our model on the next assumption: environment is composed by influence factors which impact projects of organization and these projects have to own an appropriate capital competence to master the factors and reach the purposes. Thanks to this conceptual framework, we modeled an organization with a mathematic cost/benefits approach to understand the functioning of an organization with « open » policy. Then, we highlighted the role of organizational structure and strategy to perform Open Innovation. Finally, we developed a decision-making tool, RO²I (Relevant Organization for Open Innovation). The objective of this tool is to help project manager to take into account the collaborations to lead his project at t=0 and to choose a suitable organization to anchor his project and acquire external competences. We tested our proposal on past project in an innovation team. After the validation, we verified the usability of our tool in industrial context. We experiment our tool on two projects into shared services of Solvay. We conclude this work on the necessity to anchor a project into a suitable organization for collaboration and on the necessity of a decision-making tool to take into account Open Innovation. For further researches based of our work, we propose to use RO²I to measure the capacity to Open Innovate of a firm

Covid-19 pandemin ledde till att stora delar av världens utbildningsväsen tvingades ställa om till distansundervisning. Denna studie undersöker möjligheter som digitala verktyg bidrar med för att lösa utmaningar med elevers lärande, då matematikundervisning övergår till distansundervisning. Sex semistrukturerade videointervjuer genomfördes med matematiklärare från gymnasieskolor runtom i Sverige. Kategorierna som identifierades utifrån intervjuerna var Elevers motivation och matematikprestationer, Bedömning samt Kommunikation. Flera elevers motivation missgynnades av den fysiska distansen, men vissa gynnades av situationen. En rättvis bedömning ansågs omöjlig att genomföra och den synkrona kommunikationen minskade då elever drog sig för att be om hjälp. Digitala verktyg möjliggjorde dock högre närvaro, formativ bedömning samt ökad asynkron kommunikation på distans. I diskussionen framställs de möjligheter med digitala verktyg som denna studie bidrar med samt bekräftar lärares upplevelser av eleverna mot tidigare forskning om elevers upplevelser i distansundervisning. / The covid-19 pandemic led to large parts of the world's education system being forced to switch to distance education. This study examines opportunities that digital tools contribute  to solving challenges with students learning, as mathematics education is transitioned to distance learning. Six semi-structured video interviews were conducted with mathematics teachers from upper secondary schools around Sweden. The categories identified on the basis of the interviews were Student motivation and mathematics performance, Assessment and Communication. Several students' motivation was disadvantaged by the physical distance, but some were favored by the situation. A fair assessment was considered impossible to carry out and synchronous communication decreased as students withdrew to ask for help. However, digital tools allow for higher attendance, formative assessment and increased asynchronous distance communication. The discussion highlights the opportunities with digital tools that this study contributes to and that teachers 'experiences of students are confirmed by previous research on students' experiences in distance education.

Digitaliseringen sprids i samhället, inte minst inom skolan. Allt fler klassrum använder digitala läromedel och inom matematik finns det många förlag som marknadsför sig med återkoppling. Formativ återkoppling syftar till att svara på tre återkopplingsfrågor vilka är ”vart är jag på väg?”, ”hur ska jag komma dit?” samt ”vad är nästa steg?”. I denna studie har vi analyserat fyra digitala läromedel inom matematik som alla marknadsför sig med återkoppling. Vi har med hjälp av en innehållsanalys försökt synliggöra hur digitala läromedel arbetar med formativ återkoppling. Resultatet visar att endast ett av dessa fyra läromedel använder alla fyra återkopplingsstrukturer. Vi har även försökt identifiera vilka möjligheter elever får för att se sitt eget lärande när de får återkoppling från digitala läromedel. / Digitalization is spreading in society, not least in schools. More and more classrooms use digital teaching materials and in mathematics there are many publishers who market their tools as providing feedback. Formative feedback aims to answer three feedback questions which are “where am I going?”, “how do I get there?” and “what’s the next step?”. In this study, we have analyzed four digital teaching resources in mathematics, all which market themselves as providing feedback. With the help of a content analysis, we have tried to show how digital teaching materials work with formative feedback. We found that only one of these four digital teaching materials uses all four feedback structures. We have also tried to identify the opportunities provided to students to help them see their own learning when they receive feedback from digital teaching resources.

Syftet med studien är att få en inblick i hur matematiska läroböcker, riktade till förskoleklass, kan bidra till utvecklingen av en problemlösningskompetens. Detta gjordes genom att undersöka omfattningen och placeringen av problemlösningsuppgifter i läroböcker riktade till förskoleklass. Med hjälp av ett tidigare beprövat ramverk kunde vi kategorisera uppgifter från sex olika läroböcker genom en kvantitativ innehållsanalys. Resultatet visade att problemlösningsuppgifter var underrepresenterade i alla läroböckerna och att högst procent problemlösningsuppgifter var placerade som en första deluppgift och minst procent som avslutande uppgifter. Vid de tillfällen där läroböckerna explicit markerat att det handlade om problemlösning var majoriteten av uppgifterna problemlösningsuppgifter. Samtliga läroböcker ansågs innehålla för låg andel problemlösningsuppgifter för att i tillräcklig mån kunna bidra till utvecklandet av en problemlösningskompetens. Placeringen av problemlösningsuppgifterna i läroböckerna var generellt positiv för att kunna bidra till ökat problemlösningskompetens. Att problemlösningsuppgifter dominerar där det beskrivs handla om problemlösning anses vara positivt, dock återfanns ändå 29,5% andra uppgifter, vilket kan skapa en skev bild av vad problemlösning är. / The purpose of the study is to gain an insight into how mathematical textbooks, aimed for preschool class, can contribute to development of a problem-solving competence. This was done by examining the extent and location of problem-solving tasks in textbooks aimed for preschool class. Using a previously proven framework, we were able to categorize data from six different textbooks through a quantitative content analysis. The results showed that problem-solving tasks were underrepresented in all textbooks and that the highest percentage of problem-solving tasks was placed as a first sub-task and the lowest percentage as concluding tasks. At the times when the textbooks explicitly stated that it was a problem-solving task, the majority of the tasks were problem-solving tasks. All textbooks were considered to include too low a share of problem-solving tasks, for it to be able to contribute to the development of a problem-solving competence. The placement of the problem-solving tasks in the textbooks was generally positive, in the meaning that it enabled them to contribute to increased problem-solving competence. Problem-solving dominates where it is described to be a problem-solving task which is considered positive, however, 29.5% other tasks were still found, and that can create a skew picture of what problem-solving is.

Sverige har under flera år fått svaga resultat i matematik i flera olika internationella undersökningar. Under min VFU-erfarenhet på ett gymnasium var matematik 2b en stor utmaning där cirka 83% av alla elever som skrev nationella provet år 2019 fick betyget F. Extra anpassningar i form av ett anpassat läromedel för dessa elever ansågs vara nödvändig och ett nytt utbildningsmaterial togs fram av mig. Syftet med arbetet är att skapa ett utbildningsmaterial för matematik 2b för att eleverna ska klara nationella provet. För att uppnå syftet har gamla nationella prov analyserats och ett utbildningsmaterial har tagits fram som grundar sig på områden som kommit flest gånger på dessa nationella prov. Vidare syftar rapporten till att följa upp eleverna som använt utbildningsmaterialet. Uppföljningen sker genom att utvärdera dessa elevers motivation och självförtroende med hjälp av intervjuer samt att deras resultat på nationella prov bedöms. Motivation är en viktig faktor i matematikundervisning och kan delas in i inre och yttre motivation. Inre motivation handlar om egen drivkraft medan yttre motivation handlar om att bli belönad av en annan person och motiveras genom detta. En studie gjord i USA visar att motivation är viktigare än intelligens för att lyckas inom matematik. Det finns även starka samband mellan självförtroende och betyg inom matematik. Det utvecklade utbildningsmaterialet prövades på 15 elever som tidigare fått ett F i kursen under en 2 veckorsperiod på en sommarlovsskola. Sedan utvärderades den genom att eleverna fick uppskatta hur materialet påverkat deras motivation och självförtroende. Denna uppskattning gjordes genom kvalitativa intervjuer via google meet. Eleverna skrev även ett nationellt prov som rättades. Åtta av de femton elever som deltog i sommarlovsskolan fick ett godkänt betyg på nationella provet. Eleverna tyckte även att utbildningsmaterialet hade en positiv påverkan på deras självförtroende och motivation. Det är inte säkert hur stor del av denna positiva påverkan utbildningsmaterialet haft. Andra saker som kan ha påverkat elevernas motivation och resultat är att sommarlovsskolan bestod av en mindre elevgrupp och att det var en ny lärare som undervisade dem. / Sweden has during many years received weak results in mathematics in different international surveys. During my placement experience at a high school, I noticed that mathematics 2b was a major challenge for the high school, where approximately 83% of all students who wrote the national exam received an F in 2019. The high school considered that extra adjustments in the form of adapted teaching materials were necessary for the students with an F. Therefore I created a teaching material for those students. The purpose was to create a teaching material for mathematics 2b to enable the students to pass the national exam. The teaching material was based on previous national exams and the types of questions that had occurred most often. Motivation is an important factor in mathematics teaching. Motivation can be divided into intrinsic and external motivation. Intrinsic motivation is about self-motivation, while external motivation is about being rewarded by another person and getting motivated by this. A study conducted in the United States shows that motivation is more important than intelligence to succeed in mathematics. There is also a strong connection between self-confidence and grades in mathematics. The educational material was tested on 15 students who had received an F in the course during two weeks in the form of a summer school. The educational material was evaluated by feedback from the students based on qualitative interviews via Google meet focusing on how the material affected their motivation and self-confidence. The students also wrote a national test that was corrected. Eight of the fifteen students who attended the summer school and used the teaching material received a passing grade on the national exam. In addition to this, the students also made it clear that the teaching material had a positive impact on their self-confidence and motivation.

Forskning och internationella analyser har visat att elevers kompetenser inom algebra är bristfälliga. Syftet med denna studie är därför att undersöka vilka kompetenser eleverna på låg och mellanstadiet behöver befästa för att uppnå kunskapskraven och för att kunna ta sig an framtida studier. Syftet kommer att besvaras genom tre framtagna forskningsfrågor: I vilken utsträckning följer läromedlen på lågstadiet forskningen kring early algebra? Hur ser progressionen ut från lågstadiet till mellanstadiet i lärobokserier beträffande matematiska kompetenser inom algebraområdet? och I vilken utsträckning behandlar mellanstadiets läromedel de kompetenser som forskning menar är bristande kunskaper på högstadiet? En läromedelsanalys genomfördes för att få syn på i vilken utsträckning de olika kompetenserna finns representerade i läromedlen. Genom tidigare forskning har studien identifierat vilka kompetenser som eleverna behöver befästa på låg och mellanstadiet för att kunskapskraven ska uppnås.Resultatet från analysen visar på att de kompetenser som efterfrågas finns med till viss del i de analyserade läromedlen men att det finns utvecklings möjligheter. / Research and international analyses have shown that students' skills in algebra are deficient. The purpose of this study is therefore to investigate whichcompetencies students in primary and middle school need to consolidate to achieve the knowledge requirements and to be able to take on future studies.The purpose will be answered through three developed research questions: To what extent do the teaching materials in primary school follow the research about early algebra? What is the progression from primary to middleschool in textbook series regarding mathematical skills in the field of algebra? To what extent do middle school teaching materials deal with the skillsthat research believes are lack of knowledge in high school? A teaching material analysis was implemented to see to what extent the different competencies are represented in the teaching materials. Through previus reasearch, the study has identified which competencies the students needto consolidate at the primary and intermediate leves for the knowledge requirements to be achieved. The results from the analysis show that the competencies that are in demandare included to some extent in the analysed teaching materials, but that thereare development opportunities

Syftet med denna studie är att få inblick på hur lärare i årskurs 1–3 ser på användandet av digitala verktyg för att främja elevers lärande inom programmering i matematikundervisningen. Studien har genomförts med semistrukturerade intervjuer av kvalitativ karaktär. Deltagande lärare som har medverkat kommer från olika skolor i mellersta Sverige och är utbildade inom matematikämnet i årskurs 1–3. Den insamlade data har analyserats genom både SAMR (Substitution, Augmentation, Modification, Redefinition) -  modellen som handlar om hur lärarna använder sig av digitala verktyg i undervisningen och Finger och Houguets konceptuella ramverk för utmaningar vid införande av teknologi i undervisning. Resultatet av denna studie visar att de berörda lärarna tycker att digitala verktyg är en viktig komponent till programmering och att de kan underlätta i programmeringsundervisningen på grund av de möjligheter som det digitala kan erbjuda. / The purpose of this study is to gain insight into how teachers throughout grades 1 – 3 view the use of digital tools to encourage student learning about programming within the subject of mathematics in addition to possibilities and challenges. The study has been accomplished using semi-structured interviews of a qualitative nature. The contributing teachers derive from multiple schools throughout central Sweden and are trained in mathematics through grades 1–3. The collected data has been analyzed using both the SAMR (Substitution, Augmentation, Modification, Redefinition)- a model which deals with how teachers utilize digital tools to educate, and Vinnervik's translated framework for challenges when implementing technology education. The results show that affected teachers believe that using digital tools is an essential factor when learning programming due to the possibilities they provide.

Syftet med studien är att undersöka förskollärares uppfattningar om digitala verktyg som stöd i matematikundervisningen i förskolan. Studien är en kvalitativ ansats där empirin har samlats in genom semistrukturerade intervjuer. Vi har intervjuat sju förskollärare. Resultatet visar att förskollärarna är enade om att matematiken ständigt finns bland oss, men de väljer att fokusera på det på olika sätt. Resultatet visar att förskollärarna har delade uppfattningar kring hur de ser på de digitala verktygen som stöd i matematikundervisningen och detta visar att det påverkar de digitala verktygens möjligheter i matematikundervisningen. I diskussionen och analysen utgår studien från begreppen scaffolding, proximal utvecklingszon och artefakter. / The purpose of this study is to study preschool teacher´s perceptions when it comes to digital resources to support mathematics in preschool. The empirical data has been collected through semi-structured interviews with a qualitative approach. We have interviewed seven qualified preschool teachers. The result shows that the preschool teachers agree that mathematics is always among as, but they choose to focus on it in different ways. The result shows that these teachers have varying perceptions on how they view the digital resources that are currently available to support teaching mathematics. Which means that currently, they are effecting the digital ways and opportunities to teach mathematics. In the discussion and analysis, the study is based off the concepts of scaffolding, proximal development zone and artifacts.