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Syftet med denna litteraturstudie var att undersöka vad den matematikdidaktiska forskningen skriver om att använda GeoGebra för att grafiskt representera funktioner och ekvationer i R^2 och R^3. Litteraturstudien fokuserar på att visa hur grafiska representationer med GeoGebra möjligtvis kan utveckla matematikundervisningen för såväl lärare som elever. Litteraturstudien är således av utforskande karaktär och 17 källor har analyserats. Litteraturstudien visar att matematikdidaktisk forskning om dynamiska geometriprograms (DG) roll i undervisningen fokuserar på geometri, medan matematisk analys hamnar i bakgrunden. Verksamma och blivande gymnasielärare förefaller se GeoGebras potential sträcka sig utöver geometriområdet. Dock kan lärare som ser GeoGebra som enbart ett DG missa att utnyttja dess algebraiska funktioner. Vidare så kan grafiska representationer med DG utveckla matematikundervisningen till att avancerad och tillämpad matematik behandlas mer. Slutligen så lyfts fram att pekdon till datorer styrs på 2D underlag vilket begränsar den dynamiska kontrollen av tredimensionella matematiska objekt. / The purpose of this literature review was to examine what mathematics education research writes about using GeoGebra for making graphical representations of functions and equations in R^2 and R^3. The literature review focuses on how graphical representations with GeoGebra possibly could evolve mathematics education for both teachers and students. Therefore, the literature review is explorative and 17 sources has been analysed. The result of the review indicates that mathematics education research of dynamic geometry systems (DGS) role in education, focuses on the teaching of geometry, while other topics are left in the background. Active and prospective teachers seem to see a potential in using GeoGebra that goes beyond the teaching of geometry. However, teachers who see GeoGebra as simply a DGS might not take advantage of its algebraic functions. Furthermore, graphical representations with DGS could evolve mathematics education to involve advanced and applied mathematics to a higher degree. Finally, pointing devices for computers are controlled on a 2D surface and limits the dynamic control of 3D mathematical objects.

Ibland påstås snabba förändringar i omvärlden utmana storföretagens överlevnad mer än någonsin tidigare. I studien undersöks hur stora teknikbaserade företag förnyas genom utveckling av nya affärsområden. Sådana förnyelseprocesser har aktualiserats av informationsteknologiers snabba utveckling, en utveckling som fått till följd att etablerade handlingsmönster i affärsutveckling behöver omprövas. I snabbföränderliga miljöer utvecklas spänningar i organisationer, något som tongivande teori antar behöver ellimineras för att tillväxt ska uppstå. Antagandet är dock problematiskt. Utan spänningar i förnyelseprocesser begränsas tillväxten till ett nollsummespel. Teori som ska kunna förklara tillväxt i företag med förnyelseprocesser behöver adressera spänningarnas egenskaper, hur dessa kan hanteras och utnyttjas som drivkraft i skapandet av tillväxt. Hur upprätthålls förnyelseprocesser i teknikbaserade koncerner som möter snabbföränderliga miljöer? Utifrån tongivande strategiteori om dynamiska förmågor undersöks framväxten av nya affärsområden i tre företag, ABB, Ericsson, och Saab, och hur de förnyade sig i mötet med snabbföränderliga miljöer av teknikskiften, kriser och andra spänningsrelaterade förändringar under 2000-talets första decennium. Studien av företagen visar att det finns spänningar som i sig själva utgör drivkraft till att förnyelseprocesser upprätthålls över tid. Sådana spänningar benämns paradoxala eftersom dess sociala dimensioner framstår som oförenliga i kombination med teknologisk förändring för att skapa tillväxt.  När paradoxal spänning förbises i företagsledning fortplantar sig diffusa spänningar i förnyelseprocessen. Som en följd av detta förtvinar ekonomiska värden när omorganisationer används som motmedel för att återskapa tillväxt. I avhandlingen utvecklas en teori som förklarar hur aktörer i evolutionära system av dynamiska förmågor utnyttjar olika typer av paradoxal spänning i förnyelseprocesser. Teorin bidrar till vår kunskap om huruvida adekvat kapacitet i företagsledning finns för att generera tillväxt med nya affärer som kontinuerlig förnyelse av företaget. Studien visar att paradoxal spänning är en realitet som påverkar handlingsutrymmet för att skapa tillväxt med innovation i företag, något som strategiteoretiker och företagsledningar behöver förhålla sig till. / As information technologies evolve quickly, the convergence between the technology platform of the firm and changes in business ecosystems raises the need for continuous renewal. This study explores how technology-based corporations’ drives renewal with new business areas, coping with organizational tensions invited by rapid change. Prominent theories assume that renewal-associated tension obstructs the renewal process and should consequently be eliminated. This assumption, however, is problematic since tension is also a source of firm growth, and eliminating it reduces strategic renewal to a zero-sum game. Therefore, a theory of strategic renewal needs to stress the properties of tensions and how these can drive growth. The dissertation approaches the problem of theory development, asking how the renewal process is sustained in technology-based corporations exposed to rapidly changing environments. Using the extended case method, the study addresses prominent theorizing about dynamic capabilities and examines new business development in three firms, ABB, Ericsson, and Saab, considering how they sustained the renewal process in the face of technological change, crises, and other tension-laden events in the first decade of the 21st century. The empirical study reveals how properties of tension constitute an inherent, socially constructed force that becomes a latent impetus underlying the renewal process. This feature can be termed paradoxical tension because its social dimensions appear irrational and absurd when juxtaposed to technological change and growth creation in the firm. Because paradoxical tension may develop as imperceptibly latent it challenges those who manage renewal across changeable environment. However, too frequent reorganizations of the division of units between existing and new businesses can be devastating for innovation and growth throughout the renewal process. In sum, a theory is developed that explains how actors in evolutionary systems of dynamic capabilities handle various types of paradoxical tension that ensures a firms prosperity and continuous renewal. This theory improves our knowledge of whether the firm possesses adequate entrepreneurial management capacity to generate new business areas that continuously renew the firm. Paradoxical tension is a reality that affects firm growth, and strategy theorists as well as executives need to address this problem of learning.

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Syftet med studien är att tillföra kunskap om hur dynamiska matematikprogram kan användas av lärare i lågstadiet (årskurs 2) för att utveckla elevers förståelse för fyrhörningar. Vi ämnade också ta reda på vilka faktorer som är viktiga att ta hänsyn till vid utformningen av en undervisningsaktivitet likt denna. För att besvara studiens syfte har vi valt en kvalitativ designbaserad forskningsansats, med tre interventioner som planerats, analyserats och reviderats. 17 elever deltog i studien.Resultaten visar att GeoGebra i samband med undervisningen före aktiviteten har utvecklat elevernas förståelse för fyrhörningar. Eleverna fick möjlighet att manipulera de olika formerna på ett sätt de inte tidigare testat vilket i samband med diskussionerna ledde till att de utvecklade en förståelse för namn, begrepp samt egenskaper hos fyrhörningarna. Vad som kunde konstateras var att formernas inbördes relationer fortfarande efter aktiviteten var svåra att förstå. Viktiga faktorer vid utformningen visade sig vara hur frågorna är formulerade samt att undervisningen före aktiviteten uppmärksammar kritiska drag hos lärandeobjektet för att eleverna ska ges möjlighet att urskilja dessa. / The aim of this study is to add knowledge about how dynamic mathematics software can be used by teachers in primary school (grade 2) to develop students' understanding of quadrilaterals. We also intended to find out which factors are important to consider when designing a teaching activity like this. To answer the purpose of the study, we have chosen a qualitative design-based research approach, with three interventions that were planned, analyzed and revised. 17 students participated in the study.The results show that GeoGebra together with the teaching before the activity has developed the students' understanding of quadrilaterals. The students were given the opportunity to manipulate the different shapes in a way they had not previously tested, which in connection with the discussions led to them developing an understanding of the names, concepts and properties of the quadrilaterals. What could be ascertained was that the mutual relations of the forms were still difficult to understand after the activity. Important factors in the design turn out to be how the questions are formulated and that the teaching priorto the activity draws attention to critical features of the learning object so that the students are given the opportunity to distinguish these.

Digitala läromedel används idag alltmer frekvent på skolor, samtidigt som det inte förekommer någon nationellt sammanhållen kvalitetsgranskning av dem. Det är därför av vikt att få insikt i vilka förmågor som bearbetas i digitala läromedel. Studiens syfte är att undersöka två digitala läromedel för årskurs 4 gällande vilka matematiska förmågor som tränas i vilken omfattning, samt att undersöka vilka interaktionsmöjligheter de digitala läromedlen erbjuder eleverna och hur representationen av de matematiska förmågorna hänger ihop med läromedlens dynamiska funktioner. Studiens frågeställningar lyder: Vilka matematiska förmågor representeras i de utvalda läromedlen och i vilken omfattning? Vilka interaktionsmöjligheter erbjuds eleverna i de utvalda läromedlen? Och i vilken utsträckning tränas respektive förmåga i läromedlens dynamiska element? De teoretiska utgångspunkterna som analysen tar avstamp i är Lithner et al. (2010) Mathematical Competency Research Framework och Bergvall och Dyrvold (2021) A Model for Analysing Digital Mathematics Teaching Material from a Social Semiotic Perspective. I studien undersöks kapitel berörande de fyra räknesätten i två digitala läromedel för årskurs fyra. Dessa är Gleerups läromedel Matematik 4 och Nationalencyklopedins läromedel Matematik åk 4. Metoden som används är innehållsanalys. Resultatet visar på en samstämmighet med tidigare forskning vad gäller att samtliga förmågor representeras samt att problemlösningsförmågan ges få träningstillfällen. När det gäller resonemangsförmågan bekräftar analys av Nationalencyklopedins läromedel tidigare forskning, medan Gleerups motsäger det då läromedlet erbjuder relativt många tillfällen att träna resonemang. Studiens viktigaste slutsatser är att Nationalencyklopedins läromedel utnyttjar ett digitalt läromedels specifika förutsättningar i högre grad än Gleerups läromedel, som i många fall är väldigt likt ett tryckt läromedel till funktionerna. Vidare visar även analysen att Gleerups läromedel tränar förmågorna mer jämnt fördelat än Nationalencyklopedins, som främst fokuserar på metod- och begreppsförmågorna.

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.

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.

No description available.