Contribution
Description: The main interest of this paper is the question " how we speak about mathematics at school ". However, this question has already been treated by a large number of researchers from both a linguistic and an educational viewpoint. But most of these researchers focussed on normal math lessons in an ordinary classroom situation. Conversations on math in a more informal, private setting have hardly been investigated, so far.
In contrast to this, my research project aims to describe and explain the way we speak about math in an informal learning situation. The aspects of interests are for example the vocabulary used by the speakers, the way they refer to mathematical terms, the way they organise their conversation etc..
In a first step, I analysed five private coaching lessons on college level (year 11), when one teacher and one student worked together in a face-to-face situation. The lesson's aim was to support the student to follow the regular math lessons and to reinforce what were taught at school. They were organised on a private basis.
The conversation between the teacher and the student was recorded und written down in a word by word transcript. Then I made a very detailed analysis of the transcript using the concepts of the linguistic conversational analysis. This methodology was originally introduced by H. Sacks, E. Schegloff and G. Jefferson in the 1970s and has been enhanced since by several researchers. For my work, I used the HIAT-system (Halb interpretative Arbeitstrankription) by K. Ehlich / J. Rehbein.
This research resulted in some very interesting results: They show, for example, that the conversation between the teacher and the student has very little in common with a normal classroom conversation. None of the two speakers seems to direct the conversation, and there is only a small number of explicit questions. In contrast to what one might expect, the use of technical terms is very poor. There are less sequences in which the teacher gives explications than expected. Instead, the teacher and the student seem to "think aloud together". Furthermore, they constantly refer with words and gestures to what they have written down, so that both the written and the spoken form of communication interact intensively. Over all, one can say that this type of conversation is a complete new form which has rarely been noticed by both the linguistic and the educational research so far.
In a second step, I will observe normal math lessons in a class in which a few students take additional private coaching lessons. A number of regular and of additional lessons will be recorded, so that I can compare the linguistic structures in both situations. Since the private lessons take place in addition to the normal lessons, the subject discussed in both situations will be the same. So, the comparison I will make becomes more relevant, and I might be able to see how the regular lessons influence the coaching situations. The records of the lessons will take place in September 2006.
Over all, my detailed analysis of conversational structures in learning situations might show " how we do speak about mathematics at school " . Once we have better answers to this question, we might also find better answers to the question " how we should speak about mathematics at school " .
Methodology: Empirical study based on the conversational analysis as introduced by K. Ehlich / J. Rehbein (vgl. z. B. H. Henne / H. Rehbock (1979/2001): Einführung in die Gesprächsanalyse). The methodology used is mainly a linguistic one, but the results of my research might be the basis for an educational and application-oriented interpretation.
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