This is a study of assessment in mathematics classrooms and assessment is here regarded as a concept with broad boundaries including e.g. diagnostic tests, portfolios, and acts in teacher-student communication. The study’s purpose is to analyse and understand assessment acts in discursive practices in mathematics classroom communication in terms of affordances for students’ active agency and learning. Five mathematics classrooms are visited and the main data consists of video-recordings and written classroom material. In the study, I examine assessment acts, focuses of assessment acts, and roles of semiotic resources (symbols, gestures, speech etc.). With these findings as a basis, four discourses of assessment in mathematics classrooms are construed. A main conclusion is how the construed discourses hold different affordances for students’ active agency and learning. One discourse, “Do it quick and do it right” has similarities to a traditional discourse of assessment described in previous research. In a second discourse, “Anything goes”, students’ performances that can be regarded as mathematically inappropriate are left unchallenged. In both these discourses the affordances for students’ active agency and learning of mathematics are considered low. In a third discourse, “Anything can be up for a discussion”, the focuses of assessment acts are mainly on mathematics processes and available semiotic resources are connected to these focuses. The fourth discourse, “Reasoning takes time”, takes it one step further with a lower pace and an emphasis on mathematics processes such as reasoning and problem-solving. In these two latter discourses the affordances for students’ active agency and learning of mathematics are high. I contend that there is positive power in an increased awareness of discourses like these. The four discourses of this study can be powerful in discussions about, understandings of, and positive changes in assessment practices in mathematics classrooms.

Syftet med avhandlingen är att beskriva, analysera och förstå matematikundervisning på lågstadiet. Mer precist är syftet att undersöka vad denna undervisning ger elever i några klassrum möjlighet att lära då undervisningsinnehållet är skriftliga räknemetoder för addition och  ubtraktion. Centrala frågor är vad lärare och elever gör i matematikklassrummet och vad eleverna, som en följd av undervisningen har möjlighet att lära. En fältstudie har genomförts i fem klasser med början på våren i år 2 och fortsättning under hösten i år 3. Sammanlagt 24 lektioner har videofilmats. Materialet har analyserats i två etapper, med början i en empiri nära, tematisk analys. Verksamhetsteorin är teoretisk utgångspunkt och analysverktyget som inspirerats av Engeströms modell för verksamhetssystem har varit vägledande i den andra etappen av analysen. Resultatet visar fyra typer av undervisningsverksamheter i matematik, vilka resulterar i möjligt lärande som varierar i förhållande till de förmågemål som anges i Lgr11. Det framgår också att de utmärkande metoder som lärare och elever använder kan ordnas i fem grupper, i huvudsak beroende på vilka kunskapsaspekter metoderna riktas mot. Det gäller metoder där procedurer, begrepp och samband, matematisk kommunikation och resonemang samt intresse och tilltro är i centrum, tillsammans med metoder som bidrar till stötestenar, vilka innebär utmaningar för både lärare och elever. Resultatet diskuteras mot bakgrund av forskning om undervisning och lärande i matematik med inriktning mot språklig kommunikation, användning av laborativt material, klassrumskultur och klassrumsorganisation. / The aim of this study is to describe, analyse and understand teaching of mathematics in lower primary school. More precisely, the aim is to investigate what this teaching offers pupils in some classrooms in terms of learning, when the content of teaching is written calculation methods for addition and subtraction. Teachers’ and pupils’ activities are in focus, as well as what it is possible for the pupils to learn as a consequence of these activities. Collection of data has been carried out in five classes, starting in spring when the pupils were in second grade and finished by the end of the autumn, when the pupils were in third grade. The video-recorded material comprises a total of 24 lessons. The collected research material has been analysed in two steps, where the first step can be described as empirically oriented and thematical. The theoretical perspective is Activity theory (CHAT) and an analysing tool, inspired by Engeström’s model has guided the second step of the analysis. The result demonstrates four types of teaching activities in mathematics, which leads to possible learning that varies in relation to the educational goals set in the curriculum (Lgr11). It is also shown that teachers and pupils make use of a variety of characteristic methods, which can be sorted into five groups, primarily based on ability aspects that are actualised by different methods. These are methods, where (1) procedures, (2) concepts and connections, (3) mathematical communication and reasoning, and (4) interest and confidence are in focus. There is also a fifth group, but it deviates from the others, as it consists of methods that contribute to (5) stumbling blocks, which in turn means that they become challenges for teachers as well as pupils. The results are discussed in relation to other research about teaching and learning mathematics.