Syftet med denna empiriska studie är att undersöka hur lärare kan erbjuda möjligheter för 6-åringar att vidga sin förståelse av likhetstecknets innebörd. Undersökningen är inspirerad av Learning Study metoden vilket är en metod som har sin utgångspunkt i variationsteorin. Barnens initiala förmågor analyseras före planeringen av undervisningen och det ger en uppfattning om barnens kunskaper. Utifrån det planeras lektionerna och de aspekter som är de mest kritiska för barnen lyfts och på så sätt utvecklas deras kunskap. Vår slutsats är att det är viktigt att arbeta utifrån ett variationsinriktat lärandeperspektiv. Barnen lyckas bra i de uppgifter där de får laborera med konkret material. / The purpose of this empirical study is to examine how teachers can provide opportunities for children aged 6 to extend their understanding of the equal sign. This study is inspired by the Learning Study method which is a method that has its origins in variation theory.  By analyzing the children's initial abilities before planning our lessons, it gives us an idea of the children's knowledge. From there the lessons are planned and the aspects that are the most critical for the children are lifted and thereby develop their knowledge. Our conclusion is that it is important to work with variety oriented learning. The children are successful in tasks in which they are allowed to experiment with concrete materials.

A recurring question in science and engineering education is why the students do not link knowledge from theoretical classes to the real world met in laboratory courses. Mathematical models and visualisations are widely used in engineering and engineering education. Very often it is assumed that the students are familiar with the mathematical concepts used. These may be concepts taught in high school or at university level. One problem, though, is that many students have never or seldom applied their mathematical skills in other subjects, and it may be difficult for them to use their skills in a new context. Some concepts also seem to be "too difficult" to understand. One of these mathematical tools is to use Laplace Transforms to solve differential equations, and to use the derived functions to visualise transient responses in electric circuits, or control engineering. In many engineering programs at college level the application of the Laplace Transform is considered too difficult for the students to understand, but is it really, or does it depend on the teaching methods used? When applying mathematical concepts during lab work, and not teaching the mathematics and practical work in different sessions, and also using examples varied in a very systematic way, our research shows that the students approach the problem in a very different way. It shows that by developing tasks consequently according to the Theory of Variation, it is not impossible to apply the Laplace Transform already in the first year of an engineering program. The original aim of this thesis was to show: how students work with lab-tasks, especially concerning the goal to link theory to the real world how it is possible to change the ways students approach the task and thus their learning, by systematic changes in the lab-instructions During the spring 2002 students were video-recorded while working with labs in Electric Circuits. Their activity was analysed. Special focus was on what questions the students raised, and in what ways these questions were answered, and in what ways the answers were used in the further activities. This work informed the model ”learning of a complex concept”, which was used as well to analyse what students do during lab-work, and what teachers intend their students to learn. The model made it possible to see what changes in the lab-instructions that would facilitate students learning of the whole, to link theoretical models to the real world, through the labactivities. The aim of the thesis has thus become to develop a model: The learning of a complex concept show how this model can be used as well for analysis of the intended object of learning as students activities during lab-work, and thus the lived object of learning use the model in analysis of what changes in instruction that are critical for student learning. The model was used to change the instructions. The teacher interventions were included into the instructions in a systematic way, according to as well what questions that were raised by the students, as what questions that were not noticed, but expected by the teachers, as a means to form relations between theoretical aspects and measurement results. Also, problem solving sessions have been integrated into the lab sessions. Video recordings were also conducted during the spring 2003, when the new instructions were used. The students' activities were again analysed. A special focus of the thesis concerns the differences between the results from 2002 and 2003. The results are presented in four sections: Analysis of the students' questions and the teachers' answers during the lab-course 2002 Analysis of the links students need to make, the critical links for learning Analysis of the task structure before and after changes Analysis of the students' activities during the new course The thesis ends with a discussion of the conclusions which may be drawn about the possibilities to model and develop teaching sequences through research, especially concerning the aim to link theoretical models to the real world. / En stående fråga som lärare i naturvetenskapliga och tekniska utbildningar ställer är varför elever och studenter inte kopplar samman kunskaper från teoretiska kursmoment med den verklighet som möts vid laborationerna. Ett vanligt syfte med laborationer är att åstadkomma länkar mellan teori och verklighet, men dessa uteblir ofta. Många gånger används avancerade matematiska modeller och grafiska representationer, vilka studenterna lärt sig i tidigare kurser, men de har sällan eller aldrig tillämpat dessa kunskaper i andra ämnen. En av dessa matematiska hjälpmedel är Laplacetransformen, som främst används för att lösa differentialekvationer, och åskådliggöra transienta förlopp i ellära eller reglerteknik. På många universitet anses Laplacetransformen numera för svår för studenterna på kortare ingenjörsutbildningar, och kurser eller kursmoment som kräver denna har strukits ut utbildningsplanerna. Men, är det för svårt, eller beror det bara på hur man presenterar Laplacetransformen? Genom att låta studenterna arbeta parallellt med matematiken och de laborativa momenten, under kombinerade lab-lektionspass, och inte vid separata lektioner och laborationer, samt genom att variera övningsexemplen på ett mycket systematiskt sätt, enligt variationsteorin, visar vår forskning att studenterna arbetar med uppgifterna på ett helt annat sätt än tidigare. Det visar sig inte längre vara omöjligt att tillämpa Laplacetransformen redan under första året på civilingenjörsutbildning inom elektroteknik. Ursprungliga syftet med avhandlingen var att visa hur studenter arbetar med laborationsuppgifter, speciellt i relation till målet att länka samman teori och verklighet hur man kan förändra studenternas aktivitet, och därmed studenternas lärande, genom att förändra laborationsinstruktionen på ett systematiskt sätt. Under våren 2002 videofilmades studenter som utförde laborationer i en kurs i elkretsteori. Deras aktivitet analyserades. Speciellt studerades vilka frågor studenterna ställde till lärarna, på vilket sätt dessa frågor besvarades, och på vilket sätt svaren användes i den fortsatta aktiviteten. Detta ledde fram till en modell för lärande av sammansatta begrepp, som kunde användas både för att analysera vad studenterna gör och vad lärarna förväntar sig att studenterna ska lära sig. Med hjälp av modellen blev det då möjligt att se vad som behövde ändra i instruktionerna för att studenterna lättare skulle kunna utföra de aktiviteter som krävs för att länka teori och verklighet. Syftet med avhandlingen är därmed att ta fram en modell för lärande av ett sammansatt begrepp visa hur denna modell kan användas för såväl analys av önskat lärandeobjekt, som av studenternas aktivitet under laborationer, och därmed det upplevda lärandeobjektet använda modellen för att analysera vilka förändringar som är kritiska för  studenters lärande. Modellen användes för att förändra laborationsinstruktionerna. Lärarinterventionerna inkluderades i instruktionerna på ett systematiskt sätt utifrån dels vilka frågor som ställdes av studenterna, dels vilka frågor studenterna inte noterade, men som lärarna velat att studenterna skulle använda för att skapa relationer framför allt mellan teoretiska aspekter och mätresultat. Dessutom integrerades räkneövningar och laborationer. Videoinspelningar utfördes även våren 2003, då de nya instruktionerna användes. Även dessa analyserades med avseende på studenternas aktiviteter. Skillnader mellan resultaten från 2002 och 2003 står i fokus. Avhandlingens resultatdel består av: Analys av studenternas frågor och lärarnas svar under labkursen 2002 Analys av de länkar studenterna behöver skapa för att lära Analys av laborationsinstruktionerna före och efter förändringarna Analys av den laborationsaktivitet som blev resultatet av de nya instruktionerna, och vilket lärande som då blev möjligt Avhandlingen avlutas med en diskussion om de slutsatser som kan dras angående möjligheter att via forskning utveckla modeller av undervisningssekvenser för lärande där målet är att länka samman teori och verklighet

The aim of this study has been to investigate students’ understanding of fractions when they occur in the practical subject home economics. In order to investigate this, the learning study method was used. Learning study can be understood as a method to gain deeper understanding of what is learnt by students during a lesson to increase learning outcome. The variation theory framework has been utilized to analyze the results of this study. The object of learning was chosen to be addition of fractions bigger than one half when they appear in home economics. The results indicate that in order for the learners to experience the object of learning it requires that they discern some critical aspects; to distinguish between quarters and four parts, the relationship between the part and the whole in fractions, varied presentations of the same fraction along with an understanding of the meaning of the concept to double.   Moreover the students have carried out a math test which tested the students’ theoretical understanding of fractions to see whether they can transfer the knowledge from one learning context to another. The result evinces that most of the learners show a good understanding of fractions in a theoretical context as well as a practical. The learning study has increased the students learning according to the object of learning

The way in which music teachers choose and use the subject content in ensemble and music theory in the upper secondary school is focused in this study. The point of interest is the everyday classroom teaching of music teachers. The intentions that music teachers have with their teaching is also studied. This thesis is a study of music teaching and is a subject-didactic investigation, inspired by variation theory. The overarching aim of the thesis is to study how music teachers in upper secondary school choose teaching content when teaching ensemble and music theory. The teachers’ use of the teaching content implies that they choose to focus and teach certain parts in their teaching. This choice of con- tent and how it is used is in focus in this study. The research questions are: How do music teachers choose teaching content when teaching ensemble and music theory in upper secondary school? How do music teachers use the teaching con- tent in their teaching? The data collection includes video-documented lessons and qualitative inter- views with five music teachers in upper secondary school in 2004. The analysis reveals two different choices of content. When the teachers have music and theory as the content of their teaching, it is the content that guides the teaching methods, where the teacher uses a fixed content, which is then presented in different ways; this was mainly in music theory. When the content is music activities, the music teachers adjust the activity-based content in accordance with the level of the pupils’ skills in ensemble. The differences that occur in the varia- tion theory results are closely related to the teaching content. The foundations of the two different choices of content that are made by the music teachers, as well as the significance of the learning objects, are finally discussed.

This thesis examines meaning-making in three different areas of undergraduate physics: the refraction of light; electric circuits; and, electric potential and electric potential energy. In order to do this, a social semiotic perspective was constituted for the thesis to facilitate the analysis of meaning-making in terms of the semiotic resources that are typically used in the teaching and learning of physics. These semiotic resources include, for example, spoken and written language, diagrams, graphs, mathematical equations, gestures, simulations, laboratory equipment and working practices. The empirical context of the thesis is introductory undergraduate physics where interactive engagement was part of the educational setting. This setting presents a rich data source, which is made up of video- and audio recordings and field notes for examining how semiotic resources affect physics teaching and learning. Theory building is an integral part of the analysis in the thesis, which led to the constitution of a new analytical tool – patterns of disciplinary-relevant aspects. Part of this process then resulted in the development of a new construct, disciplinary affordance, which for a discipline such as physics, refers to the inherent potential of a semiotic resource to provide access to disciplinary knowledge. These two aspects, in turn, led to an exploration of new empirical and theoretical links to the Variation Theory of Learning. The implications of this work for the teaching and learning of physics means that new focus is brought to the physics content (object of learning), the semiotic resources that are used to deal with that content, and how the semiotic resources are used to create patterns of variation within and across the disciplinary-relevant aspects. As such, the thesis provides physics teachers with new and powerful ways to analyze the semiotic resources that get used in efforts to optimize the teaching and learning of physics.

Computer programming is a core area in computer science education that involves practical as well as conceptual learning goals. The literature in programming education reports however that novice students have great problems in their learning. These problems apply to concepts as well as to practise. The empirically based research presented in this thesis contributes to the body of knowledge on students' learning by investigating the relationship between conceptual and practical learning in novice student learning of programming. Previous research in programming education has focused either on students' practical or conceptual learning. The present research indicates however that students' problems with learning to program partly depend on a complex relationship and mutual dependence between the two. The most significant finding is that practise, in terms of activities at different levels of proficiency, and qualitatively different conceptual understandings, have dimensions of variation in common. An analytical model is suggested where the dimensions of variation relate both to concepts and activities. The implications of the model are several. With the dimensions of variation at the center of learning this implies that when students discern a dimension of variation, related conceptual understandings and the meaning embedded in related practises can be discerned. Activities as well as concepts can relate to more than one dimension. Activities at a higher level of proficiency, as well as qualitatively richer understandings of concepts, relate to more dimensions of variation. Concrete examples are given on how variation theory and patterns of variation can be applied in teaching programming. The results can be used by educators to help students discern dimensions of variation, and thus facilitate practical as well as conceptual learning.

Made available in DSpace on 2015-05-14T12:43:28Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 2125510 bytes, checksum: aa04eddf6c4ebfdab57270cd91d4cd05 (MD5) Previous issue date: 2010-06-21 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This paper describes the behavior of variable medial post-stressed vowel in nouns, in the dialect of the town of Sapé, located in the state of Paraiba. In this context, there were done two analyses. The first one is a variationist, in order to verify the effects of deletion of the medial post-stressed vowel, and compare the results with other studies of similar nature. To do so, we adopted the theoretical basis in Labov (1972) and Weinreich; Labov; Herzog (1968). The second analysis, phonological character, focused on analyzing the processes triggered either by resistance to syncope - the raising and rounding of the medial post-stressed vowels, based on Câmara Jr. (2002 [1970]) and Battisti; Vieira (2005) the former one is an occurrence of syncope: assimilation, resyllabification and restructuring of the feet, from two theoretical models Metrical Phonology: The Selkirk (1982) on the syllable, and Hayes (1995) on the accent. Under the Sociolinguistics Variation point of view, one analyzed statistically, linguistic and social variables that favor the deletion of the medial post-stressed vowel. The results were compared to those of other studies that aimed to investigate the same phenomenon, but with speech data from other regions of Brazil. It was found that the fact of year of schooling is the most important one in the medial poststressed vowels deletion in three out of four works under study, as well as the following phonological context, which was considered the most conducive to the process focused on this study. But Amaral (1999) and Lima (2008) state that the liquid vibrant is the most vibrant favoring the process of deletion, while Silva (2006) and Ramos (2009), state that the liquid side is the one. Thus, after the erasure process it occurs medial post-stressed vowel, the consonantal segment remaining after the deletion is incorporated herein to the stressed syllable, either to attack the unstressed final syllable, through resyllabification, causing a restructuring of syllabic feet, transforming them into penultimate stressed words as, respectively: música ~ musca and xícara ~ xicra. whenever this deletion does not occur, the medial post-stressed vowels [e] and [o] face prosecution for opening, for example, in a.bó.b[o].ra ~ a.bó.b[o].ra, and revolt in ár.v[o].re ~ ár.v[o]re. It is through this process of assimilation that a segment assimilates characteristics of the previous segment, as in física ~ [fizga], and/or segment, as in música ~ [musca]. / O presente trabalho descreve o comportamento variável das vogais postônicas mediais, em nomes, no dialeto da cidade de Sapé, localizada no interior do estado da Paraíba. Nesse contexto, objetivaram-se duas análises: uma variacionista, a fim de verificar os efeitos do apagamento da vogal postônica medial e comparar os resultados com outros estudos de mesma natureza. Para tanto, foram adotadas as propostas teóricas de Labov (1972) e de Weinreich, Labov e Herzog (1968). A segunda análise, de caráter fonológico, visou analisar os processos desencadeados ora pela resistência à síncope o alçamento e o arredondamento das vogais postônicas mediais, a partir da discussão de Câmara (2002 [1970]) e de Battisti e Vieira (2005) ora pela ocorrência da síncope: assimilação, ressilabação e reestruturação dos pés, a partir de dois modelos teóricos da Fonologia Métrica: o de Selkirk (1982), sobre sílaba, e o de Hayes (1995), sobre o acento. Sob a égide da Sociolinguística Variacionista, analisaram-se, estatisticamente, as variáveis linguísticas e sociais que favorecem o apagamento da vogal postônica medial. Os resultados foram comparados com os de outros trabalhos que tiveram por objetivo investigar o mesmo fenômeno, porém com dados de fala de outras regiões do Brasil. Constatou-se que o fator ano de escolarização é o mais relevante no processo de apagamento da vogal postônica medial em três dos quatro trabalhos em estudo, assim como o contexto fonológico seguinte, que foi tido por todos como sendo o mais propício ao processo aqui em estudo. Porém Amaral (1999) e Lima (2008) apontam a líquida vibrante como a mais favorecedora do processo de apagamento, ao passo que Silva (2006) e Ramos (2009), a líquida lateral. Assim sendo, depois de ocorrer o processo de apagamento da postônica medial, o segmento consonantal restante após o apagamento é incorporado ora à sílaba tônica, ora ao ataque da sílaba átona final, por meio da ressilabação, o que provoca uma reestruturação dos pés silábicos, transformando-as em palavras paroxítonas, como, respectivamente, em: música ~ musca e xícara ~ xicra. Quando não ocorre esse apagamento, as vogais [e] e [o] postônicas mediais sofrem processos de abertura, como por exemplo, em a.bó.b[o].ra ~ a.bó.b[o].ra, e de alçamento, em ár.v[o].re ~ ár.v[o].re. É por esse processo de assimilação que um segmento assimila características do segmento precedente, como em fizica ~ fizga, e/ou do segmento seguinte, como em música ~ musca.

The aim of the study at hand is to generate knowledge about what pupils aged nine to ten years old need to discern in order to develop the ability to write stories with a well-developed, exciting and coherent plot, and how teaching can make it possible for the pupils to develop this ability. The theoretical framework has been Variation Theory. It is a theory of learning that focuses on how discernment of aspects affects the way we perceive our world and how variation can be used to promote learning. A basic assumption is that we learn by seeing differences, not by seeing sameness. Learning Study was used to answer the research questions. It is an interventionist approach, where the focus is on an object of learning, in this case the ability to write stories with a well-developed, exciting and coherent plot. In the research process the aim was to find out which aspects were critical for the pupils to discern in order to develop the ability, and how these could be made visible in the teaching. Together with a group of teachers, lessons were planned, implemented, evaluated and refined in an iterative process. Interview data, pupils’ texts written before and after the lessons and video recordings from the lessons were the basis of the analysis. It was found that in order for these learners to handle the object of learning, they needed to discern eight critical aspects that can be related to two different areas: (a) discerning the perspective of a reader and (b) seeing that a plot consists of several problems and solutions. The aspects were made discernible by using contrast as a pedagogical tool. The result of the study contributes to previous research by identifying and specifying what the pupils need to discern, what it means in a classroom setting and how it can be taught in a powerful way.

The goal of this work is the study of the alternation between two verb tenses Futuro do Pretérito ( Future of Past Tense) and Pretérito Imperfeito of the Indicativo (Imperfect Tense) in main clauses of hypothetical contexts in the speech of alagoanos (people who live in Alagoas, in the northeast of Brazil). We adopt as the theoretical and methodological framework the theory of Linguistic Variation (LABOV, 1972). The alternation between these two verb tenses becomes possible because of the fact that these tenses share the property to refer to unfinished/unbounded events/actions. What puzzles us is the reason(s) that makes a speaker choose one or another verb tense. We start from the hypothesis that the Imperfect Tense supersedes the Future of Past Tense in main clauses of hypothetical contexts of spoken language. In this dissertation we intend to verify what linguistic and non-linguistic variables are statistically significant in terms of VARBRUL for the dependent variable. For this purpose, we selected as external factors age, gender and educational level; and as internal factors we selected the formal parallelism and the order of the clause. / Conselho Nacional de Desenvolvimento Científico e Tecnológico / O presente trabalho tem como objeto de estudo a variação entre o futuro do pretérito (FP) e o pretérito imperfeito do indicativo (PII) na oração principal em contextos hipotéticos na fala de alagoanos. Seguimos como pressuposto teórico/metodológico o da Teoria da Variação Linguística, representado por William Labov (1972), uma vez que a variação é algo inerente à língua, já que ela é indissociável da comunidade que a fala e não existe comunidade linguística homogênea (BELINE, 2003). A alternância entre os tempos verbais (FP) e (PII) se torna possível pelo fato de esses verbos compartilharem a possibilidade de manifestar traços de aspecto inconcluso. O que nos intriga é (são) o (s) motivo (s) que leva (m) o falante a optar por uma forma ou outra. Partimos da hipótese de que o (PII) suplanta o (FP) na oração principal em contextos hipotéticos, na língua falada. Nesta dissertação buscamos, portanto, verificar quais variáveis linguísticas e não linguísticas são estatisticamente significativas na rodagem do VARBRUL para a variável dependente. Para tanto, selecionamos como fatores externos: a idade, o sexo e a escolaridade; e como fatores internos: o paralelismo formal e a ordem da sentença.

Lärare som undervisar i matematik förväntas kunna mer avancerad matematik än vad de undervisar om. Men formell matematikkunskap anses inte vara tillräckligt för att lärare ska kunna undervisa så att ämnesinnehållet blir begripligt för eleverna, de behöver även pedagogical content knowledge (PCK). Begreppet belyser en speciell form av ämneskunskap för undervisning och skiljer sig från den matematikkunskap som används av andra välutbildade vuxna. Det har föreslagits att olika arrangemang av kollegialt och praktikbaserat lärande kan utveckla lärares PCK. Ett exempel på ett sådant arrangemang är learning study. Den här avhandlingen handlar om den kunskap om lärande och undervisning i matematik som studiens lärare utvecklar då de deltar i learning studies och utforskar sin praktik utifrån ett variationsteoretiskt perspektiv. Det yttersta syftet med en learning study är att utveckla elevernas lärande om specifika lärandeobjekt, genom att undersöka vad som kan vara kritiskt för elevernas lärande. I ett samarbetsprojekt med fyra högstadielärare genomfördes två learning studies i matematik, under ett år. Lärargruppen undersökte vad eleverna behöver lära för att de ska förstå i) varför en kvot kan vara större än talet i täljaren och ii) olika representationer av konstanterna k och m i räta linjens ekvation. Under learning study-arrangemangets olika steg samlades studiens empiri in och denna består av filmade lektioner, inspelade möten där lärargruppen planerade och analyserade undervisning och elevers lärande, skriftliga elevtest samt elevintervjuer. Studien har en variationsteoretisk utgångspunkt, vilket innebär att lärande förklaras ske när en person ser något på ett nytt och mer kvalitativt sätt, genom att personen urskiljer aspekter som han/hon inte tidigare har urskilt. Studien visar de två lärandeobjektens kritiska aspekter samt hur de kritiska aspekterna gradvis förändrades och specificerades. Förändringen var ett resultat av att lärargruppen fick syn på avgörande detaljer om på vilket sätt eleverna förstod ämnesinnehållet samt hur skilda sätt att förstå kunde användas i undervisningen för att utveckla elevernas lärande. Där av titeln att få syn på avgörande skillnader. Denna form av utvecklad kunskap om lärandeobjektet kan ses som ett bidrag om PCK och vad det kan vara. / It is a common view that teachers need more than formal content knowledge to teach and to make the content comprehensible to others. They also need pedagogical content knowledge, or PCK (Shulman, 1986). It has been suggested that different teacher collaboration approaches may support teachers’ development of PCK (Chapman, 2013, Davis & Renert, 2014; Steele & Rogers, 2012). This thesis aims to provide insights into the kind of knowledge about teaching and learning mathematics that teachers develop through their participation in a specific collaboration approach called learning study. Four teachers of mathematics and their 74 students (aged 15−16 years) participated in two learning studies over the course of one year. The foremost aim of a learning study is to enhance student learning about specific objects of learning and to identify what is critical for the students’ learning (Marton & Tsui, 2004). The objects of learningin the two learning studies were to understand that dividing with a denominator between 0 and 1 gives a quotient larger than the numerator and to understand different representations of the constants b and m in the equation of the straight line. During the two learning studies data were collected from 8 video-recorded lessons, 2 written student tests, student interviews, and 14 audio-recorded sessions in which the teachers and I (PhD student) planned, analysed and revised teaching and student learning. The analysis was based on variation theory (Marton & Tsui, 2004) and focused on what participants considered to be critical aspects of the objects of learning and on the components embedded in that knowledge. The result shows the identified critical aspects of the two objects of learning and, furthermore, how the teachers’ knowledge about those critical aspects gradually changed and became more refined and specified in relation to their students’ understanding. The thesis provides an insight into the value of the teachers’ enhanced knowledge of the object of learning, in relation to how PCK can be understood.