The present study is one part of a larger research project dealing with the teaching and learning of mathematics in the latter part of the Swedish compulsory education and the first year of upper secondary school. The focus of the project as such is upon classroom communication with respect to teacher-student interaction on the one hand and students’ interpretation and understanding of the learning content on the other. The mathematical domain that is studied is algebra, and both mathematical concepts, which are new to the students, and concepts, which students are already familiar with, are of interest. It is frequently argued that algebra is an abstract and problematic area (e.g., Olteanu, 2007; Kieran, 1992; The Swedish National Agency for Education, 1999), which most students have not encountered in primary education in any formal sense, and which contains a body of new mathematical concepts. Thus, the teaching and learning of this particular area is an urgent domain for research on mathematics education.

The aim of the present part study is to investigate students’ problem solving strategies when dealing with an algebraic learning content.

Research questions: 

• What kind of understanding of algebraic concepts can be found in students’ solutions? 

• How can classroom interaction and teachers’ scaffolding strategies be traced in students’ solving of algebraic problems?

To answer these questions an overall sociocultural perspective is adopted. Consequently, language is a prerequisite for the individual’s thinking and communication with others, and thus also has a crucial and fundamental role in all learning (Dysthe, 2003). Advocates of sociocultural perspectives tend to build upon, in one way or another, a Vygotskian mode of reasoning about teaching, learning and cognitive development. Vygotsky (1978, 1986) took a historical and cultural perspective on learning as well as on how learning can be scaffolded by artifacts such as sign and sign systems. We humans are tool producing and tool using beings. Tools (both physical and mental) are artifacts that we use to mediate knowledge. Vygotsky (1978) argued that the use of tools directly develops higher mental functions such as thinking and meaning making. In addition, Vygotsky (1978) argued that learning takes place twice. First we learn on the inter-personal level in interaction with others in social contexts, then on the intrapersonal level when what is learnt is transformed to internal psychological functions.

The present study deals with learning related to classroom situations involving both the use of artifacts and interpersonal interactions.

Even though the research presented here is conducted in Swedish schools only, the questions raised certainly have a broader scope, since they deal with issues related to research carried out in many other countries (Niss, & Jensen, 2002). Problems with algebra are not an issue for Sweden or the Nordic countries only. Thus, our research should certainly be of interest not only elsewhere in Europe but also in at least the rest of the western world, where countries have quite similar school cultures.

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