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Denna uppsats är en undersökning och en jämförelse av redigeringsprogrammen Avid Media Composer och Final Cut Pro X. Utgångspunkten i analysen är användbarhet och användaren. Saker som tas upp och diskuteras är teknikutvecklingen och konkurrensen mellan redigeringsprogrammen. Den historiska aspekten presenteras och förklaras för att lägga en grund till hur det ser ut i dagsläget. Några av de sakerna som jag kommer fram till är att teknikutvecklingen ofta sker på användbarhetens bekostnad och att användaren ofta måste anpassa sig efter tekniken. Konkurrensen mellan programmen påverkas av den växande marknaden för hobbyredigering och det leder till annorlunda utveckling.

The thesis consists of four articles and this summarizing part. All parts have focused on bringing some insights into how to design a didactical situation including dynamic software (GeoGebra) to support students’ mathematical problem solving and creative reasoning as means for learning. The four included articles are: I. Granberg, C., & Olsson, J. (2015). ICT-supported problem solving and collaborative creative reasoning: Exploring linear functions using dynamic mathematics software. The Journal of Mathematical Behavior, 37, 48-62. II. Olsson, J. (2017). The Contribution of Reasoning to the Utilization of Feedback from Software When Solving Mathematical Problems. International Journal of Science and Mathematics Education, 1-21. III. Olsson, J. Relations between task design and students’ utilization of GeoGebra. Mathematical Thinking and Learning. (Under review) IV. Olsson, J., & Granberg, C. Dynamic software, problem solving with or without guidelines, and learning outcome. Technology, Knowledge and Learning. (Under review) Background A common way of teaching mathematics is to provide students with solution methods, for example strategies and algorithms that, if followed correctly, will solve specific tasks. However, questions have been raised whether these teaching methods will support students to develop general mathematical competencies, such as problem solving skills, ability to reason and acquire mathematical knowledge. To merely follow provided methods students might develop strategies of memorizing procedures usable to solve specific tasks rather than drawing general conclusions. If students instead of being provided with algorithms, are given the responsibility to construct solution methods, they may produce arguments for why the method will solve the task. There is research suggesting that if those arguments are based on mathematics they are more likely to develop problem solving and reasoning-skill, and learn the included mathematics better. In such didactic situations, where students construct solutions, it is important that students have instructions and tasks that frame the activity and clarify goals without revealing solution methods. Furthermore, the environment must be responsive. That is, students need to receive responses on their actions. If students have an idea on how to solve (parts of) the given problem they need to test their method and receive feedback to verify or falsify ideas and/or hypotheses. Such activities could be supported by dynamic software. Dynamic software such as GeoGebra provides features that support students to quickly and easily create mathematical objects that GeoGebra will display as visual representations like algebraic expressions and corresponding graphs. These representations are dynamically linked, if anything is changed in one representation the other representations will be altered accordingly, circumstances that could be used to explore and investigate different aspects and relations of these objects. The first three studies included in the thesis investigate in what way GeoGebra supports creative reasoning and collaboration. These studies focus questions about how students apply feedback from GeoGebra to support their reasoning and how students utilize the potentials of GeoGebra to construct solutions during problem solving. The fourth study examine students’ learning outcome from solving tasks by constructing their methods. Methods A didactical situation was designed to engage students in problem solving and reasoning supported by GeoGebra. That is, the given problems were not accompanied with any guidelines how to solve the task and the students were supposed to construct their own methods supported by GeoGebra. The students were working in pairs and their activities and dialogues were recorded and used as data to analyse their engagement in reasoning and problem solving together with their use of GeoGebra. This design was used in all four studies. A second didactical situation, differing only with respect of providing students with guidelines how to solve the task was designed. These didactical situations were used to compare students’ use of GeoGebra, their engagement in problem solving and reasoning (study III) and students’ learning outcome (study IV) whether the students solved the task with or without guidelines. In the fourth study a quantitative method was applied. The data from study IV consisted of students’ results during training (whether they managed to solve the task or not), their results on the post-test, and their grades. Statistical analysis where applied. Results The results of the first three studies show qualitative aspects of students solving of task with assistance of GeoGebra. GeoGebra was shown to support collaboration, creative mathematical reasoning, and problem solving by providing students with a shared working space and feedback on their actions. Students used GeoGebra to test their ideas by formulating and submitting input according to their questions and hypotheses. GeoGebra’ s output was then used as feedback to answer questions and verify/falsify hypotheses. These interactions with GeoGebra were used to move the constructing of solutions forward. However, the way students engage in problem solving and reasoning, and using GeoGebra to do so, is dependent on whether they were provided with guidelines or not. Study III and IV showed that merely the students who solved unguided tasks utilized the potential of GeoGebra to explore and investigate the given task. Furthermore, the unguided students engaged to a larger extent in problem solving and creative reasoning and they expressed a greater understanding of their solutions. Finally study IV showed that the students who managed to solve the unguided task outperformed, on posttest the students who successfully solved the guided task. Conclusions The aim of this thesis was to bring some insights into how to design a didactical situation, including dynamic software (GeoGebra), to support students' mathematical problem solving and creative reasoning as means for learning. Taking the results of the four studies included in this thesis as a starting point, one conclusion is that a didactical design that engage students to construct solutions by creative reasoning supported by GeoGebra may enhance their learning of mathematics. Furthermore, the mere presence of GeoGebra will not ensure that students will utilize its potential for exploration and analysis of mathematical concepts and relations during problem solving. The design of the given tasks will affect if this will happen or not. The instructions of the task should include clear goals and frames for the activity, but no guidelines for how to construct the solution. It was also found that when students reasoning included predictive argumentation for the outcomes of operations carried out by the software, they could better utilize the potential of GeoGebra than if they just, for example, submitted an algebraic representation of a linear function and then focused on interpreting the graphical output. / Det övergripande syftet med avhandlingen har varit att nå insikter i hur man kan designa en didaktisk situation inklusive en dynamisk programvara (GeoGebra) för att stödja elevernas lärande genom matematisk problemlösning och kreativt resonemang. En bärande idé har varit att elever som själva konstruerar lösningsmetoder till problembaserade uppgifter lär sig matematik bättre än elever som får en metod att följa. Resultaten visar att GeoGebra är ett stöd vid konstruerandet av lösningsmetoder och att elever då också resonerar kreativt. Det vill säga, de skapar en för dem en ny resonemangssekvens som innehåller en lösningsmetod som stöds av argument förankrade i matematik. Idén med att elever på egen hand konstruerar lösningen på uppgifter har även belysts genom att jämföra med elever som löser uppgifter där de får vägledning till lösningsmetoden. Resultaten visar att elever som får en lösningsmetod inte resonerar kreativt, de utnyttjar inte GeoGebras potential att stödja ett undersökande arbetssätt, och de lär sig mindre av den matematik som ingår i uppgifterna. Denna avhandling består av 4 artiklar och en kappa. De fyra artiklarna är: I. Granberg, C., & Olsson, J. (2015). ICT-supported problem solving and collaborative creative reasoning: Exploring linear functions using dynamic mathematics software. The Journal of Mathematical Behavior, 37, 48-62. II. Olsson, J. (2017). The Contribution of Reasoning to the Utilization of Feedback from Software When Solving Mathematical Problems. International Journal of Science and Mathematics Education, 1-21. III. Olsson, J. Relations between task design and students’ utilization of GeoGebra. Mathematical Thinking and Learning. (Under review) IV. Olsson, J., & Granberg, C. Dynamic software, problem solving with or without guidelines, and learning outcome. Technology, Knowledge and Learning. (Under review) Artikel 2 och 3 är jag ensam författare till. Det innebär att jag designat studien, planerat och genomfört datainsamling, analyserat data och formulerat slutsatser, samt skrivit texten och korresponderat med tidskrifter. Artikel 1 och 4 har jag skrivit i samarbete med Carina Granberg. Vi bedömer att arbetet med artikel 1 fördelats lika. Allt skrivarbete har fortgått genom åtskilliga granskningar av varandras utkast och diskussioner om slutgiltiga formuleringar. I arbetet med artikel 4 har jag haft huvudansvaret för designen av studien och planering för datainsamlingen. Skrivarbetet har genomförts på samma sätt som i arbetet med artikel 1.

Denna studie syftar till att utifrån aktuell forskning få kunskap om hur digitala verktyg och framförallt surfplattor/iPads används i matematikundervisning för årskurs f-3, med avseendet att stimulera och motivera elevers lärande i matematik och möjlighet till interaktion. För att besvara studiens frågeställning har en systematisk litteraturstudie genomförts för att finna relevant forskning inom studiens område, fynden har sedan granskats genom en innehållsanalys. Resultatet av denna litteraturstudie visar att det visuella uttrycket som digitala verktyg erbjuder lockar och engagerar elever. Samtidigt framkommer att det matematiska innehållet ibland får stå tillbaka för den visuella upplevelsen. Det tydliggörs att utmanande spel eller spel med inbyggt matematiskt innehåll är de spel som motiverar och engagerar elever och som får elever att använda svårare matematiska strategier. I litteraturstudiens resultat synliggörs dock att de flesta appar eller programvaror saknar samarbete mellan elever. / <p>Matematik</p>

The thesis consists of four articles and this summarizing part. All parts have focused on bringing some insights into how to design a didactical situation including dynamic software (GeoGebra) to support students’ mathematical problem solving and creative reasoning as means for learning. The four included articles are: I. Granberg, C., &amp; Olsson, J. (2015). ICT-supported problem solving and collaborative creative reasoning: Exploring linear functions using dynamic mathematics software. The Journal of Mathematical Behavior, 37, 48-62. II. Olsson, J. (2017). The Contribution of Reasoning to the Utilization of Feedback from Software When Solving Mathematical Problems. International Journal of Science and Mathematics Education, 1-21. III. Olsson, J. Relations between task design and students’ utilization of GeoGebra. Mathematical Thinking and Learning. (Under review) IV. Olsson, J., &amp; Granberg, C. Dynamic software, problem solving with or without guidelines, and learning outcome. Technology, Knowledge and Learning. (Under review) Background A common way of teaching mathematics is to provide students with solution methods, for example strategies and algorithms that, if followed correctly, will solve specific tasks. However, questions have been raised whether these teaching methods will support students to develop general mathematical competencies, such as problem solving skills, ability to reason and acquire mathematical knowledge. To merely follow provided methods students might develop strategies of memorizing procedures usable to solve specific tasks rather than drawing general conclusions. If students instead of being provided with algorithms, are given the responsibility to construct solution methods, they may produce arguments for why the method will solve the task. There is research suggesting that if those arguments are based on mathematics they are more likely to develop problem solving and reasoning-skill, and learn the included mathematics better. In such didactic situations, where students construct solutions, it is important that students have instructions and tasks that frame the activity and clarify goals without revealing solution methods. Furthermore, the environment must be responsive. That is, students need to receive responses on their actions. If students have an idea on how to solve (parts of) the given problem they need to test their method and receive feedback to verify or falsify ideas and/or hypotheses. Such activities could be supported by dynamic software. Dynamic software such as GeoGebra provides features that support students to quickly and easily create mathematical objects that GeoGebra will display as visual representations like algebraic expressions and corresponding graphs. These representations are dynamically linked, if anything is changed in one representation the other representations will be altered accordingly, circumstances that could be used to explore and investigate different aspects and relations of these objects. The first three studies included in the thesis investigate in what way GeoGebra supports creative reasoning and collaboration. These studies focus questions about how students apply feedback from GeoGebra to support their reasoning and how students utilize the potentials of GeoGebra to construct solutions during problem solving. The fourth study examine students’ learning outcome from solving tasks by constructing their methods. Methods A didactical situation was designed to engage students in problem solving and reasoning supported by GeoGebra. That is, the given problems were not accompanied with any guidelines how to solve the task and the students were supposed to construct their own methods supported by GeoGebra. The students were working in pairs and their activities and dialogues were recorded and used as data to analyse their engagement in reasoning and problem solving together with their use of GeoGebra. This design was used in all four studies. A second didactical situation, differing only with respect of providing students with guidelines how to solve the task was designed. These didactical situations were used to compare students’ use of GeoGebra, their engagement in problem solving and reasoning (study III) and students’ learning outcome (study IV) whether the students solved the task with or without guidelines. In the fourth study a quantitative method was applied. The data from study IV consisted of students’ results during training (whether they managed to solve the task or not), their results on the post-test, and their grades. Statistical analysis where applied. Results The results of the first three studies show qualitative aspects of students solving of task with assistance of GeoGebra. GeoGebra was shown to support collaboration, creative mathematical reasoning, and problem solving by providing students with a shared working space and feedback on their actions. Students used GeoGebra to test their ideas by formulating and submitting input according to their questions and hypotheses. GeoGebra’ s output was then used as feedback to answer questions and verify/falsify hypotheses. These interactions with GeoGebra were used to move the constructing of solutions forward. However, the way students engage in problem solving and reasoning, and using GeoGebra to do so, is dependent on whether they were provided with guidelines or not. Study III and IV showed that merely the students who solved unguided tasks utilized the potential of GeoGebra to explore and investigate the given task. Furthermore, the unguided students engaged to a larger extent in problem solving and creative reasoning and they expressed a greater understanding of their solutions. Finally study IV showed that the students who managed to solve the unguided task outperformed, on posttest the students who successfully solved the guided task. Conclusions The aim of this thesis was to bring some insights into how to design a didactical situation, including dynamic software (GeoGebra), to support students' mathematical problem solving and creative reasoning as means for learning. Taking the results of the four studies included in this thesis as a starting point, one conclusion is that a didactical design that engage students to construct solutions by creative reasoning supported by GeoGebra may enhance their learning of mathematics. Furthermore, the mere presence of GeoGebra will not ensure that students will utilize its potential for exploration and analysis of mathematical concepts and relations during problem solving. The design of the given tasks will affect if this will happen or not. The instructions of the task should include clear goals and frames for the activity, but no guidelines for how to construct the solution. It was also found that when students reasoning included predictive argumentation for the outcomes of operations carried out by the software, they could better utilize the potential of GeoGebra than if they just, for example, submitted an algebraic representation of a linear function and then focused on interpreting the graphical output. / Det övergripande syftet med avhandlingen har varit att nå insikter i hur man kan designa en didaktisk situation inklusive en dynamisk programvara (GeoGebra) för att stödja elevernas lärande genom matematisk problemlösning och kreativt resonemang. En bärande idé har varit att elever som själva konstruerar lösningsmetoder till problembaserade uppgifter lär sig matematik bättre än elever som får en metod att följa. Resultaten visar att GeoGebra är ett stöd vid konstruerandet av lösningsmetoder och att elever då också resonerar kreativt. Det vill säga, de skapar en för dem en ny resonemangssekvens som innehåller en lösningsmetod som stöds av argument förankrade i matematik. Idén med att elever på egen hand konstruerar lösningen på uppgifter har även belysts genom att jämföra med elever som löser uppgifter där de får vägledning till lösningsmetoden. Resultaten visar att elever som får en lösningsmetod inte resonerar kreativt, de utnyttjar inte GeoGebras potential att stödja ett undersökande arbetssätt, och de lär sig mindre av den matematik som ingår i uppgifterna. Denna avhandling består av 4 artiklar och en kappa. De fyra artiklarna är: I. Granberg, C., &amp; Olsson, J. (2015). ICT-supported problem solving and collaborative creative reasoning: Exploring linear functions using dynamic mathematics software. The Journal of Mathematical Behavior, 37, 48-62. II. Olsson, J. (2017). The Contribution of Reasoning to the Utilization of Feedback from Software When Solving Mathematical Problems. International Journal of Science and Mathematics Education, 1-21. III. Olsson, J. Relations between task design and students’ utilization of GeoGebra. Mathematical Thinking and Learning. (Under review) IV. Olsson, J., &amp; Granberg, C. Dynamic software, problem solving with or without guidelines, and learning outcome. Technology, Knowledge and Learning. (Under review) Artikel 2 och 3 är jag ensam författare till. Det innebär att jag designat studien, planerat och genomfört datainsamling, analyserat data och formulerat slutsatser, samt skrivit texten och korresponderat med tidskrifter. Artikel 1 och 4 har jag skrivit i samarbete med Carina Granberg. Vi bedömer att arbetet med artikel 1 fördelats lika. Allt skrivarbete har fortgått genom åtskilliga granskningar av varandras utkast och diskussioner om slutgiltiga formuleringar. I arbetet med artikel 4 har jag haft huvudansvaret för designen av studien och planering för datainsamlingen. Skrivarbetet har genomförts på samma sätt som i arbetet med artikel 1.

<p>I denna rapport jämförs ett antal fria statistiska programvaror som gick att finna på och ladda ned från internet under våren 2007. Programmen som valts ut att ingå i denna studie ska ha uppfyllt följande krav:- heltäckande statistiskt program- helt kostnadsfritt- ingen prova-på-variant- kompatibelt med Windows XP (32-bitar) eller Windows Vista (64-bitar). De program som efter utsortering kom med i jämförelsen visade sig vara av ytterst skiftande inriktning och innehåll. Detta stämde inte alla gånger överens med den beskrivning som hemsidor eller tidigare jämförelser gett. Samtliga programvaror har jämförts, dels genom att studera om några förbestämda analyser går att genomföra och dels genom ett allmänt intryck om hur programmen är att arbeta med. Utskrifter finns som bilaga för att läsaren ska kunna få se hur dessa ser ut och själv kunna förstå hur vitt skilda de olika programmen är. I avsnitt 6 gås samtliga program igenom och där finns kommentarer om hur de är att an-vända samt om något specifikt har ställt till besvär. Där finns även en tabell över vilka funktioner som finns (och ska enligt beskrivning finnas) och vilka som fungerar. De flesta program som har gått att installera har fungerat bra och har varit relativt lätta att använda. I regel skulle många problem gått att undvika alternativ förminska genom en bättre och mer innehållsrik hjälpguide.</p> / <p>This report is a comparison of a number of free statistical software that could be found and downloaded from the internet during the spring 2007. Programs selected to participate in this study should fulfill the following requirements:- Comprehensive statistical programs,- Completely free of charge,- No test version,- Compatible with Windows XP (32 bit) or Windows Vista (64-bit).The programs in the comparison proved to be of very diverse nature and content. This did not always agree with the description pages or earlier comparisons.All software have been analyzed by how the user should do to conduct some analyses as well as by a general impression of how the programs are to work with. Printouts are pre-sented as an Appendix, so that the reader is able to see how they look and understand how diverse the various programs are.In Section 6 comments about how user-friendly the programs are, and if something spe-cifically caused troubles, are given. There is also a table showing which features are available (and will be described) and which ones work.Most programs have functioned well and have been relatively easy to use. Generally, many problems could have been avoided or reduced by a better and more comprehensive help guide.</p>

I denna rapport jämförs ett antal fria statistiska programvaror som gick att finna på och ladda ned från internet under våren 2007. Programmen som valts ut att ingå i denna studie ska ha uppfyllt följande krav:- heltäckande statistiskt program- helt kostnadsfritt- ingen prova-på-variant- kompatibelt med Windows XP (32-bitar) eller Windows Vista (64-bitar). De program som efter utsortering kom med i jämförelsen visade sig vara av ytterst skiftande inriktning och innehåll. Detta stämde inte alla gånger överens med den beskrivning som hemsidor eller tidigare jämförelser gett. Samtliga programvaror har jämförts, dels genom att studera om några förbestämda analyser går att genomföra och dels genom ett allmänt intryck om hur programmen är att arbeta med. Utskrifter finns som bilaga för att läsaren ska kunna få se hur dessa ser ut och själv kunna förstå hur vitt skilda de olika programmen är. I avsnitt 6 gås samtliga program igenom och där finns kommentarer om hur de är att an-vända samt om något specifikt har ställt till besvär. Där finns även en tabell över vilka funktioner som finns (och ska enligt beskrivning finnas) och vilka som fungerar. De flesta program som har gått att installera har fungerat bra och har varit relativt lätta att använda. I regel skulle många problem gått att undvika alternativ förminska genom en bättre och mer innehållsrik hjälpguide. / This report is a comparison of a number of free statistical software that could be found and downloaded from the internet during the spring 2007. Programs selected to participate in this study should fulfill the following requirements:- Comprehensive statistical programs,- Completely free of charge,- No test version,- Compatible with Windows XP (32 bit) or Windows Vista (64-bit).The programs in the comparison proved to be of very diverse nature and content. This did not always agree with the description pages or earlier comparisons.All software have been analyzed by how the user should do to conduct some analyses as well as by a general impression of how the programs are to work with. Printouts are pre-sented as an Appendix, so that the reader is able to see how they look and understand how diverse the various programs are.In Section 6 comments about how user-friendly the programs are, and if something spe-cifically caused troubles, are given. There is also a table showing which features are available (and will be described) and which ones work.Most programs have functioned well and have been relatively easy to use. Generally, many problems could have been avoided or reduced by a better and more comprehensive help guide.