This study is about how we build patterns of meaning in the world around us. Our learning and knowledge about the surrounding world begins in what we may call the life world. The dissonance between the environment in and outside school is very distinct in mathematics as a school subject. Students’ interpretations of real life problems may become an obstacle for their learning in mathematics. The focus of the study is how the language in the communicative situation or activity could be understood as a means of construction of meaning. The importance of context and communication in the teaching of mathematics is visualized through analyses of 5 and 6 grade students’ work with a real life task, which involves decimals. Through participation and interaction, in the dialogue, the students develop new patterns of meaning that may facilitate their learning of mathematics.
The present study shows how students, eleven years old, solve problems in mathematics when they work together in groups. The main question raised is about the difficulties students experience in finding the relationship between mathematics and everyday discourse and vice versa.
Two empirical studies about students' problemsolving in mathematics divided into three different articles are presented in this study. One is about how students discuss, while they are trying to solve what the area of the triangle is. The other study is about how different solutions in problemsolving have various meanings.
The main finding ofthis work concems communication. Depending on the social contexts, different kinds oflanguages are developed in. When children are in their everyday contexts, they use one kind oflanguage, that is they use everyday concepts. In school, children have to leam the language ofmathematics. Leaming mathematics is about getting students to use the language of mathematics to mediate events and phenomens in the world around. One can describe learning as assimilating communicative and technical tools. Which are used as mediating tools in social practices.
Another main finding of this study is to show how a teacher can get students attentive to how to change between different types of discourse and how to use special conc~pts for a special context. The most important aspect is that a teacher has pedagogical conversations with students on how to move between different communicative contexts. Often, students have difficulties in understanding in which communicative context they are involved.
The aim of this dissertation is to describe and analyze how discourse as a theoretical and didactical concept can help in advancing knowledge about the teaching of mathematics in school. The dissertation has been written within a socio-cultural perspective where active participation and support from artefacts and mediation are viewed as important contributions to the development of understanding. Discourse analysis was used as a theoretical point of departure to grasp language use, knowledge construction and mathematical content in the teaching practises. The collection of empirical data was made up of video and audio tape recordings of the interaction of teachers and pupils in mathematics classrooms when they deal with problem-solving tasks, as well as discussions between student teachers as they engage in planning a teaching situation in mathematics. Discourse analysis was used as a tool to shed light upon how pupils learn and develop understanding of mathematics.
The results of my studies demonstrate that discussions very often are located in either a mathematical or in an every-day discourse. Furthermore, the results demonstrate how change between every-day and mathematical language often takes place unknowingly. Also the results underline that a specific and precise dialogue can contribute towards teachers’ and pupils’ conscious participation in the learning process. Translated into common vocabulary such as speak, think, write, listen and read teachers and pupils would be able to interact over concepts, signs, words, symbols, situations and phenomena in every-day discourse and its mathematical counterpart. When teachers and pupils become aware of discursive boundary crossing in mathematics an understanding of mathematical phenomena can start to develop. Teachers and pupils can construct a meta-language leading to new knowledge and new learning in mathematics.
En av de största utmaningarna inom utbildningsområdet är att hitta en lagom balans mellan individ och grupp, mellan en individualiserande undervisning och läroformer inriktade på samverkan. Skolan har fortfarande potential att vara både kulturbärare och skapare av en kultur som tolererar och värdesätter olikhet. Det innebär att skolan måste ge plats för individuella läroerfarenheter och samtidigt odla samverkansprocesserna. Hur detta ska göras i praktiken har med både lärosyn och didaktisk kompetens att göra. Dessa frågor tas upp i boken och exempel ges på en rad konkreta inlärningssituationer.I fokus står lärande i samspel med andra. Att få detta att fungera bra, det vill säga att resultatet faktiskt blir lärande, är en stor utmaning. En av de kritiska punkterna är vad som binder samman den enskildes erfarenheter med de andras. Den viktigaste länken mellan kollektiva och individuella erfarenheter är olika slags kommunikation, vilket gör språket till ett centralt tema. Samtidigt är det ofrånkomligt att använda ämnesövergripande metoder. Därför omfattar boken bidrag av författare från olika fackområden pedagogik, psykologi och ämnesdidaktik.Boken är angelägen för alla som ägnar sig åt lärande, kulturförmedling och kunskapsutveckling och som vill skaffa sig en bättre insikt i kommunikations- och samspelsprocesserna samt i hur kvaliteten på dessa skulle kunna förbättras. Boken riktar sig i synnerhet till dem som ska bli lärare och handledare på alla nivåer i utbildningssystemet liksom andra som behöver pedagogisk kompetens i sitt arbete.