The aim of this thesis is to look for signs of students’ understanding of algebra by studying how they make the transition from arithmetic to algebra. Students in an Upper Secondary class on the Natural Science program and Science and Technology program were given a questionnaire with a number of algebraic problems of different levels of difficulty. Especially important for the study was that students leave comments and explanations of how they solved the problems. According to earlier research, transitions are the most critical steps in problem solving. The Algebraic Cycle is a theoretical tool that can be used to make different phases in problem solving visible. To formulate and communicate how the solution was made may lead to students becoming more aware of their thought processes. This may contribute to students gaining more understanding of the different phases involved in mathematical problem solving, and to students becoming more successful in mathematics in general.The study showed that the students could solve mathematical problems correctly, but that they in just over 50% of the cases, did not give any explanations to their solutions. / Uppsatsens syfte är att söka indikationer på elevers förståelse i algebra genom att studera hur de gör övergången från aritmetik till algebra. Elever i en gymnasieklass, på naturvetenskapliga och tekniska programmen, fick en enkät med ett antal algebraiska uppgifter av skiftande karaktär och svårighetsgrad. Speciellt viktigt för studien var elevernas kommentarer och förklaringar till hur de löst dessa uppgifter. Enligt tidigare forskning är övergångarna mellan olika faser i problemlösning de mest kritiska stegen. Den algebraiska cykeln är ett teoretiskt verktyg som kan användas för att synliggöra de olika faserna vid lösandet av algebraiska problem. Att formulera och kommunicera hur lösningen går till, kan leda till att eleven blir medveten om sina egna tankegångar. Detta kan bidra till att elever får mer förståelse för olika moment som ingår i lösandet av matematiska uppgifter och bidra till att de blir mer framgångsrika i ämnet matematik. Studien visade att eleverna kunde lösa matematiska uppgifter korrekt, men att eleverna i drygt 50% av fallen inte lämnade någon förklarande text till sina lösningar.

What do history teachers teach about? How do they represent it? Why do they choose to teach the way they do? The main purpose of this study is to analyse what teaching patterns and strategies history teachers in lower secondary schools use in their history teaching for pupils aged 13-16. An additional aim is to get hold of how teachers transform their knowledge and experiences into history teaching. The results are then compared to previous research concerning teaching strategies for history teachers in upper secondary schools. The language the teachers use when they talk about their teaching is also compared to the language found in the field of history didactic research.   Through interviews with five experienced history teachers in two different school contexts their own speech about what they regard as the aim of the teaching of history, what they choose to teach about and what methods they use in history teaching make the foundation for this empirical study. It is the teachers’ words about their own practice, i.e. the thought processes of experienced teachers that are in focus.   Although the study is based on the method of semi-structured qualitative interviews and in some aspects can be regarded as a Grounded Theory study, one theoretical point of view is developed from the thoughts around transformation of the subject history. It concerns how the teachers approach history teaching and what factors the teachers talk about as the main factors of influence.   The study shows both similarities and differences between the teachers’ teaching patterns and strategies as well as between the teachers at lower secondary schools compared to those who teach at upper secondary schools. There seem to be individual patterns for each teacher where their subject matter competence alongside with their personal experiences and interest for the subject history are factors that seem to influence the way the teachers teach. The pupils are one main factor that seems to be important for the teachers in lower secondary schools, as is the use of the national curriculum when planning their teaching. Concerning transformation the question about what methods to use is observed to be the most central. The didactic why, what and how-questions in history teaching are found to be intertwined, and together they build what can be viewed as a teacher’s subject didactic teaching pattern. There are only hints that some of the teachers have developed more sustainable and consequent strategies for their history teaching. One result is that teachers, although they in some sense talk about historical didactic concepts, lack a historical didactic vocabulary to talk about their teaching. / Baksidestext Vad väljer historielärare att undervisa om, vilka metoder används och varför gör lärarna de val de gör? I denna studie intervjuas fem erfarna högstadielärare i två olika skolkontexter. Lärarnas tal om vilka mål, vilket innehåll och vilka metoder som har varit mest centrala under deras senast genomförda historieundervisning ligger till grund för en beskrivning och tolkning av den didaktiska processen där lärare omformar sina ämneskunskaper och erfarenheter till konkret undervisning. De termer och begrepp lärarna använder när de talar om sin historieundervisning är liksom de omformningsfaktorer som påverkar lärarna i den didaktiska processen också av intresse. Resultatet visar att lärarna har funnit särskilda sätt att hantera skolämnet historia vilka kan betraktas som en lärares undervisningsmönster eller, i de fall där mönstret är mer varaktigt och sammanhållet, kan benämnas undervisningsstrategi. Studiens resultat visar både likheter och skillnader mellan lärarna, samt i jämförelse med tidigare studier av gymnasielärares undervisningsstrategier. Det språk lärarna använder liknar snarare den vokabulär som syns i läroplaner och läroböcker än det språk som används i historiedidaktisk forskning.