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    Toril Eskeland Rangnes

    Bergen University College

    The case study to which this paper refers focuses on 8th grade pupils' conversation in a mathematics learning situation related to a building company. The paper illustrates how school and company, having different goals for the use of mathematics, create a field of tension where the pupils meet differing languages and modes of thought. Taking mathematics conversations in and out of school as a starting point, the polyphony of this field of tension is analysed and discussed on the basis of Bakhtin’s ideas of dialogicity and how the encounter with different voices influences the pupils’ positioning and strengthens their participation in making decisions.


    In the Norwegian curriculum, the development of pupils’ literacy is, inter alia, manifested through principles of education, where cooperation outside of school (e.g. with local companies) is encouraged, in order to learn and be motivated. In addition, oral skills e.g. in mathematics are emphasized, as well as being able to apply problem solving and investigation on the basis of practical, everyday situations (LK06, Norwegian National Curriculum for Knowledge Promotion in Primary and Secondary Education and Training). Mathematics skills are seen as a tool for everyone in their life, and as a necessity for participating in democratic society (Ibid). This mirrors OECD´s (2006) definition of mathematical literacy as something good and necessary for succeeding in society and participating as a democratic citizen. In Norway we also have National tests (written), which aim to measure numeracy with results published on the web. Applying mathematics in practical settings and reflections on applications of mathematics described in the concept of mathemacy (Skovsmose, 2005, p. 46), appear to be difficult to give priority and is not common in Norwegian secondary classrooms.

    The intention of this paper is to shed light on conversations where pupils in lower secondary school (8th graders) meet different mathematics practices and how this influences the pupils positioning and language usage. This also entails exploring how dialogues can close or open up possibilities for further discussion and options and give potential for reflection about school mathematics vs. mathematics in company. Johnsen-Høines (2010) describes the pupils´ movement between school and company as a learning loop. This movement is not confined to location – rather, it is about how the moving between is present in conversations both in school and in the building company.

    The pupils meet two kinds of practices, the building company, guided by production, efficiency and profitability, and the school, governed by learning goals in mathematics as defined in the curriculum and effectuated by the teacher. This creates

  • a field of tension where participants are confronted with different goals, practices and language and where they have to cope with the challenges this entails.

    There are earlier studies of conversations where everyday discourse and school mathematics discourse meet (e.g. Rønning, 2009). There have also been studies of adults attending courses to develop numeracy associated with work and everyday life (e.g. Wedege, 2010). Essential in this paper is that the conversations are taken from a project where the aim is that secondary school pupils will learn mathematics through meeting with a company they initially know little about. It is not the pupils’ everyday life, and it is different from the school mathematics practice they know. The teacher and the pupils are developing a new practice together.

    The pupils (aged 13-14) were told beforehand what mathematical and social goals they were to work towards. The assignment given to them by the teacher and the building company was to construct 3D models of a rorbu, a combined boathouse and seaside cottage, popular as holiday resorts in this island district. Initially, the building company sent the pupils several construction drawings of rorbu of different sizes. These were to be taken as a basis for the pupils’ own construction drawings and suggestions for possible room plans. The group would take their construction drawing to the company, and discuss their drawing with a carpenter. Back in the classroom, the pupils would realize their construction drawing in a 3D model in scale 1:25.


    Wedege (2006) describes differences between working with mathematics at work and mathematics in school on the basis of the experience of her adult students. For instance, she notes that in professional life, one has to find the relevant information oneself, whereas in school, one is given problems cleansed of unnecessary information. Even “reality” has a different function, Wedege claims. In professional life, reality gives opportunities to use mathematical ideas and techniques, and solutions have practical consequences, whereas in school, it serves as pretence for using mathematics, and the results usually have no practical consequences. Furthermore, the tasks in professional life are governed and structured by technology, whereas in school, the mathematical problems structure the teaching (Wedege, 2006, p. 217).

    At a workplace one can expect to meet many activities which can be linked to mathematics. What should be counted as mathematical knowledge is a political question, associated with the power of definition. Mathematical activities in a company fall into what Mellin-Olsen calls ”folk mathematic”, and he makes it clear that it is a political choice whether to include it as part of "school mathematics" (Mellin-Olsen, 1987).

    The benefit that a meeting between school and company with so different cultures and different aims can produce, is a moot point. To understand and to question one’s

  • own culture, outsideness can be a most powerful factor, according to Bakhtin (1986, p. 7). The dialogue between cultures, does not result in merging and mixing, he says, “each retains to its own unity and open totality, but they are mutually enriched” (Ibid, p.7.). In Bakhtinian dialogism, the utterance is the unit of analysis. An utterance, which can be a word, a sentence, a drama or a dissertation, can never be studied in isolation, it must be seen in relation to the preceding utterance and its continuation in the utterance that follow. Utterances must, according to Bakhtin, be seen in light of time; present, past and future. They must be seen in relation to context: social, cultural and historical (Bakhtin, 1986).

    Bakhtin never explicitly define polyphony, he just provided a great deal about it (Morson & Emerson, 1990). Bakhtin (1981; 1986) describes polyphony where different opinions, understandings and linguistic settings are given room. The voices can be identified through choice of theme, expressivity and purpose. One utterance can contain several voices. For creating understanding it has to be more than different voices, there is also a need of tension and struggle between them (Dysthe, 1999, p. 76). A dialog which opens up for polyphony can be contrasted by monologic talk where one person or a group has the power to decide what to talk about and how to talk. Polyphony opens up for different possible positions where critique and negotiation of power are included. It fits with understanding “power as a relational capacity of social actors to position themselves in different situations and through the use of various resources of power” (Valero, 2004, p. 15). Bakhtinian theory about dialogue, polyphony and positioning is an approach to describing pupils’ movement between different argumentations which can be positioned in a school mathematics discourse or in a company discourse.

    The form of the conversation has a link to how power is divided between the participants. An inquiry dialog is seen as a conversation where there are symmetrical relationships between the participants and where the participants investigate each other’s perceptions (Alrø & Skovsmose, 2002). Lindfors (1999) stresses that the object of an inquiring utterance must be an authentic wish to seek others' help to investigate what lies beyond that which one understands. Through an inquiring attitude one also shows what one knows. To ask in order to invite others to investigate is a risky act. One demonstrates one’s need for the other’s good will to listen and interact (Ibid). Dialogue is not only about question/answer; it is about construction of meaning and is included in a social practice (Bakhtin, 1981, p. 121). With Lindfors’ (1999) inquiry dialog and Alrø & Skovsmose’s (2002) inquiry co- operation model (IC-model) as a background, I will in this paper describe dialogues where the participants show an intension to listen and contribute, as an “inquiry dialog”. In such a dialog, awarenesses meet, and the participants’ awarenesses have a potential for change (Lindfors, 1999, p. 150). In this respect, dialogical conversations stand in contrast to monologic ones where an authority holds the truth and tries to persuade or guide other people’s choices.

  • These perspectives give me a background for studying what are the characteristics of the pupils’ conversations when they encounter in school and workplace. What different positioning do the pupils take in the conversations in movement between different and to some degree contradictory voices? Implicitly, this enlightens how the relational power moves between the participants in conversations.


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