The purpose of this research is to investigate teaching strategies and teaching reflections of an experienced elementary teacher in the mathematical classroom. This study explored the changing process of students¡¦ learning attitudes toward mathematics. This research adopted qualitative research methods as a main means of inquiry and used quantitative questionnaires as a supplement means of inquiry. Researcher had inquired by observations, in-depth interviews, video recordings, document data collections and the pre-post questionnaire survey during one semester. This research used triangulation methods, including methodological triangulation, data triangulation, and investigator triangulation. The research concludes as follows: 1.The experienced teacher delivered the class mainly by lectures and questions, and added other multi-teaching strategies in accordance to the contents of the courses. 2.The experienced teacher has specific steps in mathematical classes: help students calm down

In recent years many teachers and students have begun having good access to digital technology in their classrooms, and in the context of Sweden the majority of secondary schools are known as one-to-one schools, with students having their own computer or tablet. However, the mere presence of technology in the classroom is not a guarantee for improved teaching and learning. In fact, there is a challenge involved with integrating technology in the classroom and many teachers need support. Therefore, the aim of this thesis is to contribute to the knowledge about support for teachers integrating digital technology, especially a classroom response system (CRS), in the mathematics classroom. This is done by focusing on frameworks for CRS task design and technology integration. The thesis consists of two papers and a kappa. Both papers use data from a design research project including interventions in two cases. Paper I focuses on the development of design principles and task types for CRS tasks in a multiple-choice format aiming to engineer mathematical classroom discussions. The study generated three design principles, six task types, and 31 empirically evaluated tasks. The empirical evaluation shows that teachers consider the evaluated CRS tasks useful for engineering mathematical classroom discussions. Paper II focuses on exploring the potential of Ruthven’s (2009) SFCP framework as tool for analyzing empirical data in order to conceptualize and analyze teachers’ reasoning about critical aspects of technology integration in the mathematics classroom. The results show that the SFCP framework can be useful for capturing teachers’ reasoning about critical aspects of technology integration, but also that the framework does not capture teachers’ reasoning about students’ attitudes and behaviors. Therefore, the framework would benefit from taking into consideration students’ attitudes and behaviors, as these features are a challenge teachers need to deal with when integrating technology in the classroom. This thesis kappa, building on earlier research as well as the results and methods of its own papers, ends with an elaborated discussion on the challenges and support for teachers wanting to integrate CRS in their mathematics classroom. / Lärare och elever har idag god tillgång till digital teknik i klassrummen. I Sverige är numera majoriteten av högstadie- och gymnasieskolorna en-till-en skolor där alla elever har en egen dator eller surfplatta. Blotta närvaron av digital teknik i klassrummen är inte en garanti för förbättrad undervisning och ökat lärande. I själva verket så är det en utmaning att integrera digital teknik i klassrummet och många lärare behöver stöd för att lyckas med detta. Syftet med den här uppsatsen är att bidra till kunskap om stöd för lärare som integrerar digitala verktyg i matematikklassrummet. Detta görs dels genom att fokusera på ramverk för att konstruera matematikuppgifter till digitala responssystem och dels genom att undersöka ett ramverk för teknikintegrering i undervisningen. Uppsatsen består av två artiklar och en kappa. Båda artiklarna använder data från ett designforskningsprojekt bestående av interventioner i två separat fall. Artikel I fokuserar på utvecklingen av designprinciper och uppgiftstyper för flervalsuppgifter till digitala responssystem. Uppgifterna syftar till att initiera och fördjupa matematiska diskussioner i klassrummet. Studien genererade tre designprinciper, sex uppgiftstyper och 31 empiriskt utvärderade flervalsuppgifter som kan användas för att välja, värdera och konstruera uppgifter till responssystem. Den empiriska utvärderingen visar att lärarna anser att de testade uppgifterna och uppgiftstyperna är användbara för att initiera matematiska klassrumsdiskussioner. Artikel II fokuserar på att undersöka potentialen av Ruthvens (2009) ramverk ”Structuring Features of Classroom Practice” (SFCP), som ett analytiskt verktyg för att begreppsliggöra och analysera lärares resonemang om kritiska aspekter vid teknikintegrering i matematikklassrummet. Resultatet visar att ramverket är användbart för att fånga lärares resonemang om kritiska aspekter vid teknikintegrering i undervisningen, men också att ramverket inte fångade lärares resonemang om elevers attityder och uppförande. Studien föreslår att ramverket kan utvecklas och förbättras genom att även ta hänsyn till elevernas attityder och uppförande, eftersom detta är kritiska aspekter som lärare behöver hantera när de integrerar teknik i klassrummet. Med utgångspunkt från tidigare forskning och resultaten i artiklarna avslutas uppsatsens kappa med en utvecklad diskussion om utmaningar och stöd för lärare som integrerar digitala responssystem i matematikklassrummet.

I varje klassrum och elevgrupp förekommer normer och förväntningar (Skott, Jess, Hansen & Lundin, 2010). Normer skapas i interaktion mellan lärare och elever, vilket leder till att normer byggs upp i klassrummet (Cobb & Yackel, 1996). Om det saknas förståelse och samsyn om normer finns det risk för att elevernas matematiklärande hämmas. Studiens syfte är att beskriva vilka sociomatematiska normer som visar sig i ett klassrum, i årskurs 5. Den teoretiska utgångspunkten för studien är socialkonstruktivism. 40 elever från en skola i Sverige observerades och åtta av dem samt en lärare intervjuades för att synliggöra vilka sociomatematiska normer som förekom under de observerande lektionerna. Därefter fick läraren och åtta elever beskriva normerna. Resultatet visade att det inte råder en samsyn mellan läraren och eleverna kring de tre normerna: 1) diskussion som arbetssätt för att förstå det matematiska innehållet 2) ett godtagbart matematiskt svar och slutligen 3) det matematiska språket och dess betydelse i undervisningen.  Det fanns en viss samsyn kring de sociomatematiska normerna dock beskrevs skillnader, vilket påverkar lärarens och elevernas syn på vad matematikundervisningen innebär. Slutsatsen av studien är att det i vissa fall finns ett glapp mellan lärarens och elevernas förståelse kring normer. Normen kan därmed ha skapats omedvetet, vilket i sin tur påverkar lärarens och elevernas agerande och var de lägger fokus på i matematikundervisningen. / In every classroom and group of students it occurs norms and expectations (Skott, Jess, Hansen & Lundin, 2010). Norms creates in interaction between the teacher and students, which conduce to that norms establish in the classroom (Cobb & Yackel, 1996). If the knowledge and consensus about norms is missing there is a risk that the students mathematical learning will be inhibit. The aim of the study is to describe which sociomathematical norms that shows in one classroom, in 5th grade. The theoretical basis of the study is social constructionism. 40 students from a school in Sweden was observed and eight of them and one of the teacher was interviewed in order to emphasize which sociomathematical norms that occurs during the observed lesson. Subsequently the teacher and eight students got to express the norms. The result showed that it’s not prevail a consensus between the teacher and students about the three norms: 1) discussion as a way to work 2) an acceptable mathematic answer and at last 3) the mathematic language and its meaning in the education. There was a consensus between some of the sociomathematical norms differences were founded though, which influences the teacher and the student view of what the mathematical education implicates. The conclusion of the study is that in some cases there is a gap between the teacher and the students’ knowledge about norms. The norm has accordingly been created unknowingly, which in turn can influence the teacher and the students acting and where they put their focus in their mathematical education.

The purpose of this study was to analyze and interpret specific aspects and characteristics of classroom discourse of an elementary mathematics classroom. To examine the classroom discourse, a fifth grade mathematics classroom was observed during sixteen weeks, and twenty lessons in total. The analysis was based on two main categories: (1) Student Learning and (2) Teacher Moves. Student Learning further divided into two sub-categories as content and learning. Additionally, Teacher Moves also divided into content knowledge and pedagogy and creating learning environment sub-categories. Results of this study showed that despite the many efforts in mathematics education in Turkey and the accepted importance of student-centered classrooms / still in some elementary classrooms teacher-centered instruction continue to be dominating. Moreover, the teacher questions generally seemed to have short answer and low-level characteristics that require students to recall mathematical rules and procedures rather than high-level questions that require students to recall mathematics rules and procedures rather than high-level questions that require students think deeper and draw inferences on mathematical content. Although, the results did not meet the assumptions of discursive classroom at all / based on the results, it could be said that in classroom practices, mathematics teachers try to make connections between mathematical content and other disciplines where they tried to give examples from real-world situations and also encourage students in that way / as pointed out in new mathematics curriculum.

Diese Arbeit untersucht das Verhalten und die Einstellungen von Mathematiklehrkräften im Implementationsprozess der nationalen Bildungsstandards. Als top-down eingeführte Bildungsinnovation wird eine Umstellung des Unterrichts intendiert, der auf die in den Standards formulierten Kompetenzen fokussiert. Es wird herausgearbeitet, was unter einem kompetenzorientierten Mathematikunterricht zu verstehen ist und anschließend aufgezeigt, wie eine solche Intention durch ein vom Institut zur Qualitätsentwicklung im Bildungswesen (IQB) entwickeltes Implementationskonzept in die Praxis überführt werden kann. Anhand von zwei Studien wurden jeweils zehn Merkmale eines kompetenzorientierten Unterrichts an Lehrkräften und Schülern im Längsschnitt analysiert und einzeln ausgewertet. Zusätzlich erhielten die Schülerinnen und Schüler einen kompetenzorientierten Leistungstest. Angelegt in einem Experimentaldesign erhielten die Projektschulen über die Projektlaufzeit eine externe Unterstützung durch eine Setkoordinatorin, die regelmäßig einen Input und beratende Hilfestellung bei der Entwicklung und Erprobung von kompetenzorientierten Lehr-Lernarrangements anbot. Angelehnt an das SINUS-Programm wurden weitere zentrale Fortbildungsveranstaltungen angeboten. Die Drop-Out-Analysen zeigen, dass Lehrkräfte, die den Bildungsstandards gegenüber positiv eingestellt sind und in einem höheren Grad miteinander kooperieren, Engagement im Projekt zeigen. Der Unterricht in den Projektschulen erfuhr eine stärkere Orientierung hin zum mathematischen Argumentieren, Modellieren und Probleme lösen. In den Projektschulen der Studie 1 nehmen die Schülerinnen und Schüler eine verstärkte Kompetenzorientierung im Bereich der Verwendung von mathematischen Darstellungen wahr. In einer zweiten Studie konnte das IQB-Implementationskonzept mit dem SINUS-Folgeprojekt „Kompetenzorientiert unterrichten in Mathematik und Naturwissenschaften (KOU)“ erfolgreich evaluiert werden. / This doctoral thesis focuses on teachers’ development during the implementation process of the national educational standards in Germany. Consider the standards, which were introduced by resolution, classroom activities are focused to improve student learning. To reach the standards, a change in teaching culture is necessary or at least an addition of teachers’ classroom activities. Therefore, the concept of competence-orientation especially for mathematics is described and discussed. Further implementation theories and implementation strategies are suggested and discussed. When educational standards became active, implementation concepts were missing so far. So, the Institute for Educational Quality Improvement (IQB) developed an implementation concept and got support by nine schools to test it. The professional learning communities in mathematics of the schools got external support by a supervisor and input by researchers during their intended change process. Study 1 focuses on analyzing teachers’ engagements and concerns as well as their classroom activities in a longitudinal design. Furthermore, students of ninth grade were tested in mathematics and asked about their classroom activities. Eight schools worked as a control group. Study 2 added another ten schools with a slightly different implementation concept. So, the IQB-concept could be evaluated. Even in study 2, the ten factors are analysed and differentiated by concept. Drop-out analyses show, teachers with a positive attitude towards the standards and a higher degree in cooperation, support the project and continued as participants in the longitudinal study. Furthermore, their classes changed in aspects of arguing, modeling and problems solving mathematically. Students of study 1 observe more activities in working with mathematical figures and diagrams. In study 2, the IQB implementation concept could be evaluated successfully by comparing teachers’ changes with the development in other schools.