Este estudo, na perspectiva variacionista, visou a verificar se informantes cursando a oitava série do Ensino Fundamental, o terceiro ano do Ensino Médio e o quarto semestre da Licenciatura em Letras usam o clítico acusativo como uma variante de objeto direto pressuposto, em seus textos dissertativos e narrativos. Além disto, pretendeu determinar quais outras formas de objeto direto aparecem nesses textos, com quais delas o clítico acusativo rivaliza e que fatores condicionam a ocorrência dessas variantes. Os resultados indicam que, em relação às variáveis extra lingüísticas, o clítico é mais freqüente no texto narrativo e menos freqüente nas produções dos alunos do Ensino Superior. Indicam também que o clítico é favorecido quando seu antecedente é sujeito de oração anterior e que o verbo triargumental e o co-referente com traço semântico [+animado] condicionam o aparecimento do clítico na redação escolar. / This study aimed at verifying, under the Variation Theory perspective, whether eight grade elementary school students, high school third grade students and undergraduate Language fourth semester students use the accusative clitic as a variant for the presumed direct object on their compositions. It was also intended to determine which other kinds of direct object appear on their texts, which of them compete against the accusative clitic, and which features constrain such variants. The results indicate a decrease in the use of the accusative clitic as schooling increases. Therefore, its use is less frequent in the texts written by undergraduate students than in the ones written by elementary school students. As to linguistic variables, it was observed that the clitic is favored when it follows the subject of a preceding sentence. Triargumental verbs and [+animate] semantic feature also contribute to the appearance of clitics in school compositions.

Este estudo, na perspectiva variacionista, visou a verificar se informantes cursando a oitava série do Ensino Fundamental, o terceiro ano do Ensino Médio e o quarto semestre da Licenciatura em Letras usam o clítico acusativo como uma variante de objeto direto pressuposto, em seus textos dissertativos e narrativos. Além disto, pretendeu determinar quais outras formas de objeto direto aparecem nesses textos, com quais delas o clítico acusativo rivaliza e que fatores condicionam a ocorrência dessas variantes. Os resultados indicam que, em relação às variáveis extra lingüísticas, o clítico é mais freqüente no texto narrativo e menos freqüente nas produções dos alunos do Ensino Superior. Indicam também que o clítico é favorecido quando seu antecedente é sujeito de oração anterior e que o verbo triargumental e o co-referente com traço semântico [+animado] condicionam o aparecimento do clítico na redação escolar. / This study aimed at verifying, under the Variation Theory perspective, whether eight grade elementary school students, high school third grade students and undergraduate Language fourth semester students use the accusative clitic as a variant for the presumed direct object on their compositions. It was also intended to determine which other kinds of direct object appear on their texts, which of them compete against the accusative clitic, and which features constrain such variants. The results indicate a decrease in the use of the accusative clitic as schooling increases. Therefore, its use is less frequent in the texts written by undergraduate students than in the ones written by elementary school students. As to linguistic variables, it was observed that the clitic is favored when it follows the subject of a preceding sentence. Triargumental verbs and [+animate] semantic feature also contribute to the appearance of clitics in school compositions.

The aim of the thesis is to gain knowledge concerning what pupils aged 8 and 9 need to learn to become familiar with negative numbers. The framework used in this research, variation theory, impliesthat students' problems in learning what was intended may have to do with the fact that some critical aspects of the studied object have not yet been discerned by the student. To get the pupils to understand the idea behind each critical aspect, carefully constructed examples were used. According to variation theory it is necessary to experience differences before you experience similarities. To answer the research question data was collected by using the learning study model. It is characterized by an iterative design where I as a researcher collaborate with teachers to try to find and orchestrate the critical aspects. The method is interventionist, which means that interventions are done in teaching. In the learning study I have cooperated with two primary school teachers and 64 pupils in four different classes. The data consists of video-recordings of lessons, pre- and posttests, interviews with pupils and notes from the meetings of the learning study group. When planning lessons as well as analyzing data, concepts relating to the theory of variation have been used as analytical tools. This thesis contributes to research by investigating in detail what aspects students need to differentiate in order to become familiar with negative numbers. The results show that the pupils needed not only to discern, but also to differentiate three different critical aspects: To differentiate the values of two negative numbers. To differentiate the function of the minuend versus the function of the subtrahend in a subtraction. To differentiate the minus sign for negative numbers versus the minus sign for subtraction.

Internet är en plats där alla kan lära sig. Vem som helst kan publicera vilket digitalt läromaterial som helst. För att säkerställa att ett publicerat material är lämpligt är det viktigt att materialet är utformat på ett pedagogiskt sätt. Det är dessutom viktigt att nyttja de fördelar ett digitalt läromedel har som en konventionell bok inte har. Detta arbete undersöker hur Matteboken presenterar tröskelbegrepp i kursen Matematik 1. I arbetet har tröskelbegreppen på Matteboken analyserats med hjälp utav två didaktiska teorier. Den ena är variationsteorin, vilken handlar om att variera aspekter av ett innehåll för att göra uppenbart vad lärandeobjektet är. Den andra är att använda sig av olika representationer, vilket handlar om att representera ett material på olika sätt för att öka förståelsen av lärandeobjektet. Innehållet har även analyserats utifrån det faktum att det är konstruerat för att läsas på en skärm. Arbetets resultat är att det existerar två tröskelbegrepp inom kursen Matematik 1. Dessa två är funktionsbegreppet och bråkbegreppet. Ett centralt resultat i arbetet är att presentationen av dessa tröskelbegrepp på Matteboken kan förbättras med hjälp utav interaktiva moment, variation och olika representationer. / The Internet is a place where everyone can learn and anyone can publish any digital educational material. To make sure that the published material is adequate, it is important that the material is written with pedagogical support. It is also important to utilize the advantages a digital educational material has over conventional educational material. This paper examines and analyses how Matteboken is presenting threshold concepts in the course Matematik 1. This work is done by conducting literature studies and by analyzing Matteboken's presentation of threshold concepts. The analysis is done using two pedagogical theories. One of them is the theory of variation, explaining how varying certain critical features of a critical aspect is a good way to learn. The other one has to do with representations, utilizing different representations of a learning object to increase the understanding of the object of learning. The material at Matteboken has also been analyzed from the fact that the material is supposed to be read on a screen. The result of the paper is that there exists two threshold concepts in Matematik 1. The concept of a function and the concept of a fraction. The result of the paper indicates that Mattebokens’ presentation of the threshold concepts may be improved using interactive tools, variation and different representations.

This thesis consists of two studies, described in two papers, and a re-analysis of data from these studies. The aim is to broaden the knowledge about what contributions a learning theory, variation theory (Marton, 2015), can give to teachers’ teaching practice. The studies have an action research approach (Elliot, 1991). Data was generated in the two studies with two different “teacher groups” having different learning goals for their students. Each group consisted of a researcher and five mathematic teachers. Variation theory was used as a theoretical tool to plan, teach and assess teaching in the context of a Professional Learning Community (PLC) called Subject Didactic Groups. The empirical data consists of audio recordings and documentations from meetings with one of the teacher groups as well as video recordings from student interviews and one of the teachers teaching, in the other group. The thematic analysis (Braun & Clarke, 2006) resulted in the following themes: With variation theory as a theoretical tool the teachers could a) specify what the students needed to learn, b) design and teach tasks that afforded possibilities for the students to learn what was identified as necessary to learn and c) focus on and assess qualities in the students answers. This study suggests that variation theory is a learning theory that has bearing on teachers’ teaching practice.

The aim of the study is to generate knowledge about what students in years 4 and 5 (9-12 years old) need to discern in order to draw conclusions about a protagonist’s character traits in a fictional text, and how this ability can be developed. The method chosen to answer the research questions is Learning Study, an iterative classroom-based approach. Two primary school teachers in Swedish and the teacher researcher worked together. They collaborated to design, teach, evaluate, refine, and analyse a series of six lessons in a cyclic process with the Variation Theory as theoretical framework. The empirical data consists of pre- and post-lesson assessments, and video recordings of the lessons. The analyses resulted in five qualitatively different categories and four critical aspects. It is suggested that in order for the student to develop the ability to draw conclusions about a protagonist’s character traits, it is critical: (a) to discern that the protagonist’s character traits, both reproduced (explicit) and implied (implicit), are based in the text, (b) to discern, in the text, descriptions of how a protagonist for example acts, reacts, feels, thinks, and interacts with other characters in the story, as this could facilitate drawing conclusions about the protagonist’s (implicit) character traits, (c) to experience that when conclusions about the protagonist’s (implicit) character traits are related to how a protagonist acts, it is possible to discern what in the text the conclusion is based on, and (d) to experience that conclusions about aprotagonist’s (implicit) character traits can be discerned when they are linked to a character/person who is outside the story (eg in another story, film, or in real life).

I denna ämnesdidaktiska studie undersöker jag om elevers förståelse av dels begreppet hållbar utveckling, dels begreppen miljömässig, social och ekonomisk hållbarhet, förändras, hur de förändras och varför, genom undervisning i företagsekonomi, undervisning som i sin tur baseras på variationsteori. Syftet med studien är att bidra med ökad kunskap om vad som påverkar att förståelsen för begreppen förändras när de studeras i ämnet företagsekonomi. Metoden är en kvalitativ textanalys där 41 gymnasieelevers skriftliga svar i ett förtest respektive ett eftertest har kartlagts och analyserats. Resultatet visar att efter undervisningen har förståelsen för begreppen förändrats, för vissa elever från vardaglig till hybridförståelse, för andra från hybridförståelse till disciplinär ämnesförståelse och för ytterligare andra från vardagsförståelse till disciplinär ämnesförståelse. I diskussionen beskriver jag förändringen som assimilation eller ackommodation samt utifrån begreppsbildningsteori där elevers intresse och attityd inför begreppen, bakgrundskunskap och motivationsfaktorer samt egna mål att lära i ämnet lyfts fram som förklaringar till förändrad förståelse. Slutsatsen är att både förförståelse, det vill säga i vilken förståelsekategori eleverna befinner sig innan undervisningen, och deras inställning till begreppen, påverkar om och hur förståelse förändras och fördjupas.

The purpose of the study is to contribute knowledge about children's understanding of the physical phenomenon of friction by conducting a planned learning activity together with the children. In the activity, the children had the opportunity to investigate high and low friction with varied materials in a slide. A total of seven five-year-old children participated on two separate occasions. The observations were carried out at the respective preschool's slide, where the children had to ride with the different materials and investigate the friction that arose. The observations were recorded with audio and video recording, which were then analysed using a content analysis and based on the theory of variation. The results of the study indicate that most children had a certain understanding of the phenomenon of friction even before the activity, but not of the scientific concepts or knowledge enough to explain their thoughts about the phenomenon. The results also showed that the design of the learning activity contributed to an increased understanding of the phenomenon of friction. They developed their thoughts and explanations about the phenomenon in relation to the different materials that were investigated and several of the children also adopted the concept of friction towards the end of the activity. Key words: friction, research method, variation theory, preschool / Studiens syfte är att bidra med kunskap kring barns förståelse för det fysika-liska fenomenet friktion genom att genomföra en planerad lärandeaktivitet till-sammans med barnen. I aktiviteten fick barnen möjlighet att undersöka hög och låg friktion med olika material i en rutschkana. Det deltog totalt sju femå-riga barn vid två olika tillfällen. Observationerna genomfördes vid respektive förskolas rutschkana där barnen fick åka med de olika materialen och under-söka friktionen som uppstod. Observationerna spelades in med ljud och vide-oinspelning som sedan analyserades med hjälp av en innehållsanalys och uti-från variationsteorin. Resultatet av studien tyder på att de flesta barn hade en viss förståelse för fenomenet friktion redan innan aktiviteten, men dock inte för de vetenskapliga begreppen eller kunskaper tillräckligt för att förklara sina tankar kring fenomenet. I resultatet framkom även att utformningen av läran-deaktiviteten bidrog till en ökad förståelse för fenomenet friktion. De utveck-lade sina tankar och förklaringar om fenomenet i relation till de olika materi-alen som undersöktes och flera av barnen anammade även begreppet friktion mot slutet av aktiviteten.

Tidigare forskning har identifierat svårigheter och missuppfattningar kopplade till bokstavssymboler inom algebra. Vi väljer att avgränsa oss till obekanta tal eftersom många elever kan möta svårigheter när bokstäver introduceras i matematikundervisningen. Syftet med denna studie är att bidra med kunskap om hur undervisning om bokstavssymboler i tidigare skolår kan planeras och genomföras utifrån variationsteorin. Syftet besvaras med hjälp av följande frågeställningar: Vilka kritiska aspekter behöver elever i årkurs 1 urskilja för att utveckla förståelse för obekanta tal? Hur förändras elevernas kunskaper om obekanta tal mellan för- och eftertest? Hur kan undervisning planeras och iscensättas utifrån identifierade kritiska aspekter? Studiens teoretiska ramverk är variationsteorin, där centrala begrepp omfattar lärandeobjekt, kritiska aspekter och variationsmönster. Variationsmönster används för att hjälpa eleverna att urskilja kritiska aspekter av ett lärandeobjekt, vilket i denna studie är obekanta tal, genom att synliggöra dessa med olika variationer. Studiens metod inspirerades av Learning Study. Lektionerna genomfördes med två olika undervisningsdesigner som grundades på variationsteoretiska principer. Studiens data består av för- och eftertester och observationsanteckningar från två lektionstillfällen. Resultatet visar att fyra kritiska aspekter har identifierats till det specifika lärandeobjektet, vilka är urskilja att: en ekvation är en likhet som innehåller obekanta tal, det obekanta talet står för ett tal (värde), tidigare kunskaper inom aritmetiken kan användas vid ekvationslösning, till exempel talfakta eller inversa operationer och samma bokstavssymbol kan stå för olika värden beroende på ekvation. Resultatet visar även att elevernas kunskaper utvecklas mellan för- och eftertest, när undervisningarna planeras och iscensätts utifrån variationsteoretiska principer. Slutsatser som kan dras är att variationsteorin kan vara användbar för lärare när de ska identifiera kritiska aspekter och planera lektioner. Efter att ha genomfört två lektioner med årkurs 1 har vi kommit fram till att det är möjligt och fördelaktigt att introducera obekanta tal redan i tidig ålder. / Previous research has identified difficulties and misconceptions associated with letter symbols in algebra. A common difficulty can be interpreting and using unknown numbers. A misconception identified in a few studies is that letter symbols can be perceived to represent positions in the alphabet. We choose to focus on unknown numbers because many students may encounter difficulties when letter symbols are introduced in mathematics. The aim of this study is to investigate the teaching of letter symbols in grade 1. The aim is addressed through the following research questions: What critical aspects do students in grade 1 need to dicern in order to develop an understanding of unknown numbers? How do students' knowledge of unknown numbers change between pre- and post tests? How can teaching be planned and staged based on identified critical aspects?  The theoretical framework of the study is the variation theory of learning, where central concepts include learning object, critical aspects and patterns of variations. Patterns of variation are ursed to help students discern critical aspects of a learning object, which in this study are unknown numbers, by highlighting these through different variations. This method of study was inspired by Learning Study. Lessons was carried out with two different teaching designs, based on principles of variation theory. The study´s data include pre- and posttest and observation protocols from two conducted teaching sessions.  The results indicate that four critical aspects have been identified for the specific learning object, which are discerning that: an equation is an equality containing unknown quantities, the unknown quantity represents a number (value), prior knowledge in arithmetics can be used in equation solving, such as number facts or inverse operations, and the same letter symbol can represent different values depending on the equation. The results also show that students' knowledge evolve between pre- and post tests when teaching is planned and staged based on variation theoretical principles. It is shown that variation theory can be useful for teachers in identifying critical aspects and planning lessons. After conducting two lessons with grade 1, we have concluded that it is possible and beneficial to introduce unknown quantities at an early age.

This thesis reports results from a study that focuses on teachers’ professional development during an in-service training period.   The aim is to analyse and describe how the teachers talk about and handle lesson content. The first question concerns changes in relation to a specific object of learning. The second question concerns how they relate to a theoretical framework and the third question concerns differences in the students’ learning outcome and if it can be understood in relation to the teachers’ development.   The variation theory is the theoretical framework that is used for lesson planning as well as when analysing results. The basis of the study is that learning always is the learning of something and that the teachers’ activity as well as the students’ activity constitutes the space of variation that decides what is possible to learn concerning a delimited object of learning, i.e. the enacted object of learning. The object of learning is seen as a capability and it can be defined by its critical features. The constitution of the meaning aimed for the critical features of the object must be discerned. The intentional object of learning describes the teachers’ intention with the lesson, and the lived object of learning is what the students really discerned. The theoretical assumption is that learning always assumes an experienced variation where learning is seen as a change in the learners’ possibility to experience the world in a certain way. You have to have experienced a phenomenon’s variation to understand its meaning, i.e. what we experience is how something differs from something else.   The method is Learning study and it can be described as a hybrid of the Japanese Lesson study and Design experiment. A Learning study is theoretically grounded and the primary focus is on an object of learning. The learning study group consisted of three teachers and most often two researchers. Each member had equal status in the group. The object of learning seen from the teachers’ perspective was the variation theory that was gradually introduced by the researchers. The empirical material was generated from audio-taped discussions and from videotaped lessons.   The findings should be seen as a contribution to the discussion about teachers’ professional development. The teachers participated in a collective construction of professional knowledge and it can be stated that the teachers had no problem changing their discussions to focus on a specific object of learning when the theoretical framework was used in relation to their own practices. Another finding is that the change in how the teachers handled the object of learning influenced the students’ learning in a positive way although the results were subtle.